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Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs! #### Online Quiz (WorksheetABCD) Questions Per Quiz = 2 4 6 8 10 ### Grade 2 - Mathematics1.27 Twelve is a Dozen Explanation: One dozen = 12 One-half dozen = 6 One-fourth dozen =3 Two dozens = 24 Example: How many dozens is 36 things? 1 dozen = 12 2 dozens = 24 3 dozens = 36 Answer : 3 Directions: Answer the following questions. Also write atleast 5 examples of your own. Q 1: At a grocery store you buy 2 dozens of candies. How many candies did you buy?122246 Q 2: You have 12 pencils. How many dozens do you have?2 dozens1 dozen3 dozens Q 3: If you need one-half dozen eggs to bake a cake, how many eggs do you need?36112 Q 4: You have 24 crayons in a box. How many dozens do you have?3 dozens2 dozens4 dozens Q 5: When you have 12 of something you have _____.one-half dozenone dozentwo dozen Q 6: If I bought one-half dozen donuts, how many donuts did I buy?101236 Q 7: How many is one-half dozen?612143 Q 8: 6 things =one dozenone-half dozenone-fourth dozen Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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# FINC634 Commercial Credit Analysis: Risk Management Perspective \$20 Bonus + 25% OFF ### Questions: Q1 Suppose you short 21 contracts of E-Mini S&P 500 futures at 4,486.  The next day, their price goes to 4,512.  What would be the profit or loss if you closed your short position at that price? Q2 Suppose you bought 33 futures contracts of gold (contract size = 100 oz.)  The current futures price is \$1,791 per ounce. The initial margin is \$9,900 per contract, the maintenance margin is \$9,000/contract. At what price level would you receive a margin call? Q3 The spot exchange rate for Britain and US is currently at 1.3845 (\$ per pound). Britain’s continuously compounded risk-free rate is 1.50%.  The U.S. continuously compounded risk-free is 0.50%.  Calculate the 8-month forward exchange rate. Q4 The S&P 500 Index is currently trading at 4,500.  The continuously compounded risk-free rate is 0.25%. Dividend yield (continuous comp.) is 1.30%. Calculate the fair-value futures price expiring in 10 months. Q5 An investor holds 20,000 shares of a certain stock. The stock is currently trading at \$245.00 per share. He is interested in hedging against short-term movements in the market and decides to use E-Mini S&P 500  futures to hedge his exposure.  The Index is currently at 4,500.  Contract size = \$50 times index. The Beta of the Stock is 1.2.  Calculate how many E-Mini S&P 500 futures contracts are needed to hedge the investor’s holdings against downside price risk.  What position (long or short) is required? Q6 Oil futures show the closing prices for the day as seen in the table below. Describe the condition and explain how an oil producer would most likely manage their current inventory given the condition in the futures markets. Month Close Open High Low Volume Oct-21 69.58 67.97 69.96 67.68 301672 Nov-21 69.33 67.73 69.71 67.48 122191 Dec-21 68.98 67.47 69.35 67.16 72566 Jan-22 68.58 67.04 68.92 66.82 21362 Q7 Explain how margins in futures markets are both a blessing and a curse.  From a risk management perspective, what are the pros and cons of margin requirements in futures? Q8 Why are futures prices and forward prices often different when, in principle, they have the same fair value calculation in principle? I need an expert in Finance options. there are 4 questions to be answered. Please see the attachment. ### FINC 634 Commercial Credit Analysis Solved by qualified expert Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet. Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet. Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet. Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh. MyAssignmenthelp.com is the only platform in Australia that offers dissertation writing help at the cheapest rates. Part of our services also includes the provision of dissertation methodology help. Students who search the internet with phrases such as ## More FINC634 FINC 634 Commercial Credit Analysis: Questions & Answers ### Management Raise awareness on safe driving on the Monash Freeway at morning peak hours part 7-8-9. plus any highlighted parts. the budget ive used its quiet low. feel free to adjust the budget so we can apply it to the budget part. … ### Defined Benefit Plan or the Investment QuestionsA.    What are the important factors that should be considered by tertiary sector employees when they are deciding whether to place their superannuation contributions in the Defined Benefit Plan or the Investment Choice Plan? What issues relating to the concept of the time va … ### Management Questions: Prepare a (not more than) five-page formal written summary report to CPI management explaining whether CPI should go ahead with the launching of the new product – Ouvertin? In doing so, provide a numerical justification in the context of ‘real option analysis’. The use of … ### BSBSMB406 Manage Small Business Finances Questions: 1. Which of the following sources of finance does not constitute a form of debt finance? (a) Bank overdrafts. (b) Venture capital. (c) Term loans. (d) Commercial hire purchase.  2. Indicate whether each of the foll … ### Content Removal Request If you are the original writer of this content and no longer wish to have your work published on Myassignmenthelp.com then please raise the content removal request. ##### David Company I have done my LLM, with specialization in Criminal law from University of Oxford 250 – Completed Orders Hire Me ##### Jane Mac I am a professor of social science in the University of Southern California. 450 – Completed Orders Hire Me ##### Emma Zhong Ph.D in Project Management with Specialization in Project Communications Management 2109 – Completed Orders Hire Me ## Still in Two Minds? 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# 807826 ## 807,826 is an even composite number composed of three prime numbers multiplied together. What does the number 807826 look like? This visualization shows the relationship between its 3 prime factors (large circles) and 8 divisors. 807826 is an even composite number. It is composed of three distinct prime numbers multiplied together. It has a total of eight divisors. ## Prime factorization of 807826: ### 2 × 53 × 7621 See below for interesting mathematical facts about the number 807826 from the Numbermatics database. ### Names of 807826 • Cardinal: 807826 can be written as Eight hundred seven thousand, eight hundred twenty-six. ### Scientific notation • Scientific notation: 8.07826 × 105 ### Factors of 807826 • Number of distinct prime factors ω(n): 3 • Total number of prime factors Ω(n): 3 • Sum of prime factors: 7676 ### Divisors of 807826 • Number of divisors d(n): 8 • Complete list of divisors: • Sum of all divisors σ(n): 1234764 • Sum of proper divisors (its aliquot sum) s(n): 426938 • 807826 is a deficient number, because the sum of its proper divisors (426938) is less than itself. Its deficiency is 380888 ### Bases of 807826 • Binary: 110001010011100100102 • Hexadecimal: 0xC5392 • Base-36: HBBM ### Squares and roots of 807826 • 807826 squared (8078262) is 652582846276 • 807826 cubed (8078263) is 527173390375755976 • The square root of 807826 is 898.7914107289 • The cube root of 807826 is 93.1335038703 ### Scales and comparisons How big is 807826? • 807,826 seconds is equal to 1 week, 2 days, 8 hours, 23 minutes, 46 seconds. • To count from 1 to 807,826 would take you about two days! This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!) • A cube with a volume of 807826 cubic inches would be around 7.8 feet tall. ### Recreational maths with 807826 • 807826 backwards is 628708 • The number of decimal digits it has is: 6 • The sum of 807826's digits is 31 • More coming soon! ## Link to this page HTML: To link to this page, just copy and paste the link below into your blog, web page or email. BBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below: ## Cite this page MLA style: "Number 807826 - Facts about the integer". Numbermatics.com. 2024. Web. 20 July 2024. APA style: Numbermatics. (2024). Number 807826 - Facts about the integer. Retrieved 20 July 2024, from https://numbermatics.com/n/807826/ Chicago style: Numbermatics. 2024. "Number 807826 - Facts about the integer". https://numbermatics.com/n/807826/ The information we have on file for 807826 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun! Keywords: Divisors of 807826, math, Factors of 807826, curriculum, school, college, exams, university, Prime factorization of 807826, STEM, science, technology, engineering, physics, economics, calculator, eight hundred seven thousand, eight hundred twenty-six. Oh no. Javascript is switched off in your browser. Some bits of this website may not work unless you switch it on.

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Page 1 of 1 ### Korean Won Posted: Mon Dec 28, 2009 3:49 pm Just noticing that KOFEX where the USDKRW is traded says the contract size is 10,000 usd whereas CSI data has a contract size of 50,000 usd with an equal multiple on , therefore tick size - i.e they are both very different any ideas who is correct thanks in advance Chris Posted: Mon Dec 28, 2009 4:27 pm This is a situation where a human (rather than an Interactive, i.e., software) broker would be very useful: Call her on the phone and inquire. You could of course just trade a 1-lot, hold it for a few minutes, and exit. Then figure out the BPV by working backwards from your gross P&L, your entry price, and your exit price. Found an old post: viewtopic.php?p=20189&highlight=bpv+comission#20189 Over the years, I've learned that when I am about to add a new market I've never traded before, it is cheap insurance to call my broker and give the following pair of orders: Buy 1 contract of February Burmese Artichokes at market on the open AND 60 minutes after the open, sell 1 contract of Feb Burmese Artichokes at the market Yes, really. It's cheap insurance. Now I get to see how the new market appears on (A) my broker's statement, and compare that to (B) how it appears in CSI, and also compare it to (C) how it is set up in my testing and order generating software. This has saved my hindquarters several times. I've gotten the BPV and/or the quote format wrong at least a half dozen times, which the above procedure has caught and corrected. If you assume it's a 50-50 proposition whether Burmese Artichokes will rise or fall in the first hour of trading, the little order pair above only costs 2*(Bid-ask-spread) + 1*commission on average, which isn't a huge amount. Another resource I have used, is to call my broker on the telephone and ask for the closing price of Feb Burmese Artichokes, including the decimal point. Make her say five zero nine three decimal two four. Then compare this to the futures exchange's "Contract Specification" and to CSI's quotes and to the trading software's setup tables. Posted: Tue Dec 29, 2009 4:35 am sluggo wrote: ....Buy 1 contract of February Burmese Artichokes at market on the open ... Apparently, artichoke was domesticated in Roman times, possibly in Sicily, and spread by the Arabs during early Middle Ages.The first certain records of artichoke commerce refer to Filippo Strozzi trading artichokes from Sicily to Florence in the early 15th century (Bianco, 1990). Posted: Sun Sep 14, 2014 11:03 pm 10,000 USD is correct, and the contract is very liquid, rolls monthly.

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# Sales off If a sweater sells for \$ 19 after a 5% markdown, what was its original price? Result x =  20 USD #### Solution: (1-5/100)*x = 19 95x = 1900 x = 20 Calculated by our simple equation calculator. Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### To solve this example are needed these knowledge from mathematics: Our percentage calculator will help you quickly calculate various typical tasks with percentages. Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? ## Next similar examples: 1. Washing machine The price of washing machine was decreased by 21% and then by 55 € due small sales. After two price decreases cost € 343. How much was originally cost? 2. Sale off 2 A pair of of blues jeans went on sale. After a 30% reduction the pants cost \$35. How much did the jeans cost before the price reduction? 3. The game of blind man's buff Slovak levy system makes the gross wage deductions from your pay state employees. It has two components - part employee pays and part pays by the employer Suppose that the super gross wage paid 23% employer. After deducting these contributions we receive g I longer watch processors for Socket A on ebay, Athlon XP 1.86GHz with a PR rating of 2500+ costs \$7 and Athlon XP 2.16Ghz with a PR rating of 3000+ currently cost \$16. Calculate: About what percentage of the Athlon XP 2.16Ghz is powerful than Athlon X 5. Cat One-fifth of the monthly pocket money contributes Maros for food for his cat, half of the rest postpone for a new smartphone. The remaining € 8 spend. How much pocket money gets Maros a month? 6. Savings and retirement The older sibling has saved 44% more euros than the youngest, which represents 22 euros. How many euros older brother has saved ? 7. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have? 8. Assistant Assistant rewrote 15% of the entire manuscript in 12 hours. How many hours must still write to rewrite the rest of the manuscript? 9. Percentage reduction Reducing the unknown number by 19% get number 700.7 Determine unknown number. 10. Jane class When asked how many students are in class, Jane said, if we increase the number of students in our class by hundred % and then add half the number of students, we get 100. How many students are in Jane's class? 11. Seeds 2 How many seeds germinated from 1000 pcs, when 23% no emergence? 12. Base, percents, value Base is 344084 which is 100 %. How many percent is 384177? 13. Apples 2 James has 13 apples. He has 30 percent more apples than Sam. How many apples has Sam? 14. Iron Iron ore contains 57% iron. How much ore is needed to produce 20 tons of iron? 15. Real estate 2 A real estate agent sold a lot for Php.550,000. If his agency pays at 10% commission, how much commission will he or she receive? 16. Percents - easy How many percent is 432 out of 434? 17. Budget plan In the construction of the building, the planned budget exceeded 13%, which was 32,500 euros. How many euros cost built the building?

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Actuarial Outpost > CAS B and W constants Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions Registration FormBe Notified of New Actuarial Jobs D.W. Simpson & Company InternationalActuarialRecruiters www.dwsimpson.com Australia Jobs Casualty, Life,Superannuation, Health &Investment PensionActuarial JobsConsulting &Insurers --Students, Associates &Fellows #1 11-03-2005, 10:05 PM ed999 Member CAS AAA Join Date: May 2002 Location: NYC Posts: 1,034 B and W constants one question where they asked you to comment on the fact that B and W were constants. I didn't exactly reproduce the list from all 10 but simply said that if B and W were constants, the weight given to large insureds would be too high while the weight for smaller insureds to low... do you think this makes sense??? #2 11-03-2005, 10:10 PM berad Join Date: May 2005 Posts: 4 that's what I put down. I tried to compare the B & W's in the prior plan to the newer one. #3 11-03-2005, 10:17 PM Jack Divine Member Join Date: Nov 2003 Posts: 97 I agree - the loss variation in large insureds is greater than the law of large numbers indicates. Therefore, constant B&W values give too much weight to large insured experience, and not enough to small insureds. #4 11-03-2005, 10:58 PM Avi Wiki ContributorSite Supporter Site Supporter CAS AAA Join Date: Aug 2002 Location: NY Studying for the rest of my life. College: Alumnus - Queens College - CUNY Favorite beer: Stone Ruination IPA Posts: 12,501 Blog Entries: 3 Being that Z = (E+B)/(E+W), I said that holding B&W fixed and letting E get large brings Z close to 1, which gives too much experience to large insureds. __________________ All scientists defer only to physicists Physicists defer only to mathematicians Mathematicians defer only to G-d! --with apologies to Dr. Leon Lederman #5 11-03-2005, 11:04 PM lee Member Join Date: May 2004 Posts: 139 Quote: Originally Posted by Avi Being that Z = (E+B)/(E+W), I said that holding B&W fixed and letting E get large brings Z close to 1, which gives too much experience to large insureds. Zp = E/E+B, Ze =E/E+K approaches 1, when E approaches infinity... Large insured will be seft-insured. Please check whether it is correct. Thread Tools Display Modes Linear Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off All times are GMT -4. The time now is 05:33 PM. -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top

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Differential equation In mathematics, a differential equation or DE is an equation relating a function and its derivatives, the idea being that how a quantity will change is related in some way to its current value. Many of the fundamental laws of physics, chemistry, biology and economics can be formulated as differential equations. The question then becomes how to find the solutions of those equations. The mathematical theory of differential equations has developed in parallel with the sciences where the equations originate and where the results find application. Diverse scientific fields often give rise to identical problems in differential equations. In such cases, the mathematical theory can unify otherwise quite distinct scientific fields. A celebrated example is Fourier's theory of the conduction of heat in terms of sums of trigonometric functions, Fourier series, which finds application in the propagation of sound; the propagation of electric and magnetic fields (including radio waves, visible light, X-rays, and the entire electromagnetic spectrum), as well as spectral analysis of radiation; elasticity; quantum mechanics; and many other areas of scientific research. Examples A simple differential equation is $\frac{du(t)}{dt} = u(t).$ This equation is satisfied by any function which equals its derivative. One of the solutions of this equation is u(t) = et. Note that to say that a specific function (in this case et ) is a solution to a differential equation means that if you plug that function into the left-hand side of the DE and evaluate it, the result will be the right-hand side. In this case that happens since $\frac{du(t)}{dt} = \frac{d\left(e^t\right)}{dt} = e^t = u(t)\ .$ Nonlinear equations and systems of equations frequently occur in the study of physical systems. An important example of a nonlinear oscillator is the Lorenz system \begin{align} \dot{x} &= \sigma(y - x) \\ \dot{y} &= \rho x - y - x - xz \\ \dot{z} &= - \beta z + xy \end{align} where x, y, and z are functions of t, and a dot represents the derivative with respect to t, i.e. $\dot{x}=\frac{dx(t)}{dt}\ .$ This is a basic example of a system with chaotic behavior. The Schrödinger equation is a partial differential equation (or PDE) of fundamental importance in quantum mechanics. It governs the evolution of quantum systems and is given by $i\hbar \frac{\partial\psi(x,t)}{\partial t} = - \frac{\hbar^2}{2m} \frac{\partial^2 \psi(x,t)}{\partial x^2} + V(x,t)\psi(x,t)\ .$ Another example of a PDE is the heat equation or diffusion equation, $\frac{\partial u}{\partial t} = k \left(\frac{\partial^2 u}{\partial x^2} +\frac{\partial^2 u}{\partial y^2}\right)$ The reason that these two equations (the Schrödinger equation and the heat equation) are called partial differential equations is that the unknown (ψ in the Schrödinger equation, and u in the heat equation) depends on multiple variables, and the equation involves partial derivatives with respect to these variables. The order of a differential equation is that of the highest derivative that it contains. For instance, the equation $\frac{du(t)}{dt} = u(t)$ is a first-order differential equation, while the Schrödinger equation and heat equation are examples of second order equations. List of differential equations • Inhomogeneous Helmholtz equation: $\nabla^2 u + k^2 u = -f$ • Schrödinger equation: $i\hbar \psi_t = - \frac{\hbar^2}{2m} \psi_{xx}$ • The simple harmonic oscillator equation: $m\ddot{x}+kx=0$ • General harmonic oscillator: $m\ddot{x}+b\dot{x}+kx=A\cos(\omega t)$ • Lotka-Volterra predator-prey: $\frac{dx}{dt}=Ax-Bxy$, $\frac{dy}{dt}=-Cy-Dxy$ Some content on this page may previously have appeared on Citizendium.

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## Factorization of 9 consecutive 552-digit numbers Expand Messages • Let x = (1320*(10^20 + 13065906))^3 y = (x*(5*x + 9)/2 - 31)^2 N = (y - 23^2)*(y - 24^2)/55440 - 7 then p544 = N/(2^2*85580203) p552a = (N + 1)/3 p546 = (N Message 1 of 178 , Nov 11, 2009 Let x = (1320*(10^20 + 13065906))^3 y = (x*(5*x + 9)/2 - 31)^2 N = (y - 23^2)*(y - 24^2)/55440 - 7 then p544 = N/(2^2*85580203) p552a = (N + 1)/3 p546 = (N + 2)/(2*7^2*16127) p540 = (N + 5)/(223*9887*252181) p552b = (N + 6)/2 p533 = (N + 8)/(2^2*9479*90863*15503173813) are prime. Moreover N + 3, N + 4 and N + 7 are completely factorized, with no prime factor having more than 128 digits. These 9 consecutive factorizations at 552 digits are in Notes: I used OpenPFGW, GMP-ECM, Msieve, ggnfs, Pari-GP. All primality proofs were performed by Pari-GP. The primality proof for p552b is easy, since we know the factorization of p552b - 1 = (N + 4)/2. The composite numbers c542 = (N - 1)/(5*53*151*259499) c524 = (N + 9)/(5*7*31*37*288232349*593280102498871) are unlikely to have any prime divisor less than 10^30. This particular constellation was studied because p539 = (N + 10)/(2*3*60647*24846803) is prime. Thus a complete factorization of N + 9 would have yielded 11 consecutive factorizations. • ... Yes. Moreover the proof is rather easy. Let C be a Carmicahel number and let p be its largest prime factor. Then p-1|C-1. and hence p-1|(C/p)-1. Thus p Message 178 of 178 , Feb 25, 2010 --- In primeform@yahoogroups.com,

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Upcoming SlideShare Loading in...5 × Unit 4 Physics Summary Sheet itute 3,164 -1 Published on Published in: Technology, Business 0 Comments 0 Likes Statistics Notes • Full Name Comment goes here. Are you sure you want to Yes No Your message goes here • Be the first to comment • Be the first to like this No Downloads Views Total Views 3,164 On Slideshare 0 From Embeds 0 Number of Embeds 0 Actions Shares 0 Downloads 59 Comments 0 Likes 0 Embeds 0 No embeds No notes for slide Unit 4 Physics Summary Sheet itute 1. 1. Ways to induce emf or current: Since Φ = BAcosθ, An AC supply of Vrms = 240 V provides the same power as a emf can be induced (1) by changing A to change Φ DC supply of constant V = 240 V. × × × × when the area of the Vp V pp V Ip loop inside B increases, Ip = , I pp = , I rms = rms , I rms = R R R 2 Physics Unit 4 Summary Sheets (09–12) × × × × the induced current I is as 2 Free download and print from www.itute.com I shown. Vp 1 2 Vp I p ©Copyright 2009 itute.com P = Pav = = I pR = or – × × × × 2R 2 2 + Magnetic field B (Unit: tesla (T); or weber per square metre V2 2 (wbm-2) ): × × × × P = Pav = rms = I rms R = Vrms I rms . + when a conductor moves R S In a power station the generator always rotates at the same × × × × across the magnetic field rate. If the power consumption by homes and offices is lines from a to b (change higher (lower), more (less) energy is required to maintain N S × × I× × in area enclosed by dotted the same rotation rate, 50 Hz in Australia. – lines), induced emf is Transformer: An electrical device that is used to change the × a × × b × shown as + –. voltage of an AC power supply without changing the power Aust to be delivered. N (2) by changing B to change Φ Working of a transformer: Alternating current at the when magnet moves closer primary (input) coil produces an alternating B inside the soft to the loop, magnetic field iron core. The secondary (output) coil is linked to the increases and the induced primary through the core, a changing B in the core results in N current I is as shown. a changing Φ in the secondary coil. According to Faraday’s I Law an emf is induced in the secondary coil (output). I Step-up transformer N S > N P ; step-down N S < N P . (3) by changing θ (either by rotating the loop or the magnet) to For an ideal (100% efficiency) transformer, PS = PP , × × × • • • change Φ × × × • • • NS V I VS I S = VP I P , = S = P . × × × I • • • N P VP IS I S N S N Power loss Ploss and voltage drop Vdrop occur when I I electricity is transmitted over a long distance by Use right-hand grip rule to find direction of B. transmission lines. Magnetic force on current-carrying wire: Direction of induced current and polarity of output terminals of F a generator are determined by Lenz’s Law: an induced current VA Transmission lines current I, resistance R VB < VA I in a conducting loop flows in a direction such that the magnetic × × × field of the induced current opposes the change in magnetic flux Vdrop = V A − VB = IR ; that produces it. The terminal that the induced current flows to × × × F = BIL is +, the other –. 2 Vdrop × × × ∆Φ Ploss = I 2 R = Vdrop I = . B Faraday’s Law: ξ av = n where n is the number of R ∆t Direction of F L (Right-hand slap rule) loops in the coil through which the flux passes. Ploss ∝ I 2 , power loss is greatly reduced by lowering I in 1 the lines; this can be achieved by increasing the voltage for ξ av ∝ n , ξ av ∝ ∆Φ , ξ av ∝ . ∆t transmission in order to deliver the same power, ∴step-up Magnetic force on current-carrying coil of n loops: AC generator (alternators): Alternating emf induced by a transformer is used at the power station end. At the Zero force rotating conducting coil (loop area A) in a magnetic field B is consumer end, step-down transformer is used to reduce made accessible with slip-rings connected to the terminals of voltage to 240 V. × × × × Load curve is a graph showing the demand of electric the coil, and the external circuit is connected to the rings via conducting brushes. power over a time period. Area under the curve represents L × × × × ξ the total consumption of electrical energy during the period. E = P∆t . θ Kilowatt-hour (kwh) is a unit of electrical energy. × × × × 1 kwh = 3.6 MJ r T = 360o Force into page Zero net torque If the slip-rings are replaced by a split-ring commutator, the Force out of page on coil device is a DC generator. Thermal oscillations of electrons in atoms give off Net clockwise torque electromagnetic radiation (visible light). In an incandescent on coil (view from above) ξ light bulb, the atoms in the filament are excited by heating, Refer to above diagrams, the two forces (each F = nBIL in T = 180o θ and they give off their excess energy as wave trains (with wide spectrum of wavelengths) of light, each lasts about and out of the page) exert a turning effect called torque 10-8s. The emitted light is the sum of such wave trains that (τ = rF) on the coil causing it to speed up its rotation in the The amplitude of the AC emf is called the peak voltage Vp . bear a random phase relation to each other and they are first quarter turn. In the second quarter turn the torque is in incoherent. Two light globes produce incoherent light, the opposite direction causing the coil to slow down. In a Vp ∝ n , Vp ∝ B , Vp ∝ A , Vp ∝ f . hence no interference pattern. Thomas Young simple DC motor, the direction of the coil current is DC motor has the same construction, and can be used demonstrated the wave nature of light with his double-slit reversed with a split-ring commutator every 180o turn experiment to obtain an interference pattern. He used when the net torque is zero. Hence the torque on the coil as a DC generator by turning the coil mechanically. Alternating emf can also be induced by rotating a permanent sunlight through a narrow slit as the light source and then remains in the same direction, allowing the coil in the motor through the double slits. Lights through the double slits are to keep turning in the same direction. magnet (or electromagnet) beside a coil. External circuit is connected directly to the terminals of the coil and no slip rings coherent because they are split from the same wave trains are required. from the single slit, ∴ there is an interference pattern. Laser Magnetic flux Φ = BAcosθ. Unit: weber (wb) is a very coherent source because it is monochromatic AC power supply delivered to homes and offices are generated by rotating an electromagnet between two connected coils at (single wavelength) and wave trains are emitted A, area of region enclosed by loop simultaneously, hence a very clear interference pattern. B f = 50Hz (T = 1 = 0.02 s = 20 ms). P Path difference f θ 0V ξ S1 pd = S2P – S1P Normal to region Bright & dark d fringes appear At t = 0 S2 on screen Electromagnetic induction is the generation of electricity S N L by changing magnetic flux. The generated current is called ξ (V) induced current I; the generated voltage is called induced Vp Vpp Constructive interference (bright): pd = 0λ, 1λ, 2λ, .... emf ξ. Destructive interference (dark): pd = 0.5λ, 1.5λ, 2.5λ, .... ∆Φ ξ 0 10 20 t (ms) Spacing between fringes increases when wavelength λ Magnitude of ξ av = , I= where ∆t time ∆t R Peak voltage Vp = 340 V, peak-to-peak voltage Vpp = 680 V, increases, screen distance L increases and/or slits separation taken for the change, R resistance of the loop. Vp d decreases. λred > λ green > λblue > λviolet . f = c . root-mean-square voltage Vrms = = 240 V. λ 2 2. 2. Diffraction of light also demonstrates the wave These spectra are evidence for quantised atomic energy levels. Standing waves in closed resonant tube of length L: nature of light. Electrons move around a nucleus with discrete energies. When Overtones Harmonics λ f = v/λ Gap Diffraction pattern has an electron jumps from high to low energy level, it loses energy Fundamental first 4L/1 1(v/4L) width a bright central region in discrete amount equal to the difference between the two levels and results in emission of a photon of the same energy. First third 4L/3 3(v/4L) w between 2 dark fringes Second fifth 4L/5 5(v/4L) hf = EH – EL. de Broglie used the idea of standing matter waves to explain the quantised energy levels of an atom. The For closed tubes only odd harmonics exist. Obstacle Diffraction pattern has only matter waves that persist are those for which the Dynamic microphone: Sound moves the cone and the width a dark shadow of the circumference of the orbit is an integral multiple of λ. attached coil of wire in a magnetic field to and fro. obstacle with a bright Travelling sound wave through air is longitudinal because the Electromagnetic induction produces an emf (signal) at the w fringe at the centre air molecules oscillate parallel to the direction of propagation of terminals of the coil. Ribbon (or velocity) microphone: Air caused by constructive the sound wave. A sequence of high (compression) and low movement due to sound waves moves the metallic ribbon in interference of light (rarefaction) air pressure is generated and it propagates a magnetic field. Electromagnetic induction generates emf around the obstacle outwards from the source carrying the sound energy with it. between the ends of the ribbon. Condenser microphone: The back plate and the front metallic membrane form a Extent of diffraction ∝ λ . Significant effect when λ ≈ 1 . ∆p (at a particular time) ∆p (at a particular point) capacitor (charged with a battery). Sound waves cause the w w More diffraction when λ is longer and/or w is smaller. membrane to vibrate and change the spacing between the x t plate and the membrane. This causes the output voltage Photoelectric effect demonstrates particle-like nature of λ T (signal) to change. In electret-condenser microphone a light. Light Accel./ f = 1 , speed of sound v = λ = fλ . permanently charged electret material is used for the T T membrane, thus eliminating the need of a charging battery. Setup V retard. Crystal microphone: uses a thin strip of piezoelectric v( solid ) > v( water ) > v(hotair ) > v (coolair) . v is voltage crystal attached to a diaphragm that is sent into vibration by constant when sound travels in the same medium, sound waves, causing the crystal to deform and produce a I λ f voltage (signal). ∴ λ ∝ 1 and 2 = 1 . f is constant when sound travels A dynamic loudspeaker has the same basic construction as f λ1 f 2 I (Constant freq.) I (Constant int.) a dynamic microphone. The input signal changes the current H v2 λ2 in the coil and results in a varying magnetic force on the coil from a medium into another, ∴v ∝ λ and = . L intensity H L frequency v1 λ1 that is attached to the cone. Vo V V Enclosure formed by baffles: to prevent the sound from the Sound intensity I measures the amount of energy (J) arriving at back of the speaker cone cancelling the sound from the front retard accel retard accel a square metre of surface in a second. It is defined as because of destructive interference due to phase difference. Max EK E P Directional spread of sound waves (diffraction): Sound Metal 1 Metal 2 Same gradient for I= = , E energy received, A area exposed, ∆t time diffracts when it passes by the edge of a barrier. Refer to A∆t A both metals = h exposed. Unit: Js-1m-2 or Wm-2. For a small sound source in the diffraction of light. Extent of diffraction ∝ λ . w is the f (Planck’s constant) open, the sound energy spreads outwards spherically, w φ2 width of obstacle or opening. High pitch (high f, short λ) φ2 work function of metal 2 P 1 I b ra2 sound diffracts less than low pitch. I= , P is the power of source, ∴ I ∝ , = . Threshold frequencies fo1 and fo2 4πr 2 r 2 I a rb2 A loudspeaker is omni-directional, (i.e. it radiates sound φ = hfo , max EK = qVo When the distance r from the source is doubled, intensity I is a energy spherically in all directions) when λ > 4 , w is the Failure of the wave model to explain the photoelectric w quarter of the original value. effect According to the wave model, light is a continuous diameter of speaker cone. The higher the frequency the less wave and the intensity is related to its amplitude, which I omni-directional it becomes. Sound intensity level L = 10 × log10 in dB, measures the energy of the wave. Therefore an electron can 10−12 Frequency response of human ear: is most sensitive to absorb any amount of light energy, depending on the time sound of frequency 4000Hz, e.g. of the three sounds, 100Hz, ∆L 4 kHz and 10 kHz, at the same dB level at the ear, the 4kHz interval it is exposed to the light wave. The wave model If L −12 If failed to explain why (1) maximum kinetic energy remained ∆L = 10 × log10 . I = 10 10 , = 10 10 . will sound the loudest to the listener. To make 100Hz and the same when the intensity was changed; (2) maximum Ii Ii 10kHz the same loudness as 4 kHz, increase their dB level. kinetic energy changed with the frequency of light used; If Loudness is measured in phons. The loudness of a sound is (3)there was a threshold frequency for each metal used. When I is doubled, i.e. = 2 , ∆L = +3 dB. compared with the loudness of 1 kHz sound. The loudness Einstein’s interpretation of photoelectric effect-the Ii of a x dB 1 kHz sound is x phons. Sounds at different photon model: A beam of light is a stream of particles If frequencies, which are as loud as the x dB 1 kHz sound have 1 a loudness of x phons. The following graph shows a curve of called photons. Light of a single frequency f consists of When r is doubled, = , ∆L = − 6 dB. photons of the same energy E = hf = hc/λ . Ii 4 equal loudness (30 phons) for different frequencies. There are more photons in a more intense beam, hence Threshold of hearing 10-12 Wm-2 0 dB L(dB) higher current. When photons strike a metal, some will be Normal conversation 10-6 60 80 Above curve, absorbed by the electrons in the metal. To have louder than 30 phons 30-phon curve photoelectrons emitted, the energy of each photon must be Car alarm 1 m away 10-2 100 high enough for the electrons to overcome the bonding Threshold of pain 1 120 30 Softer softer below curve energy (i.e. the work function φ). As the photons penetrate Jet engine 30 m away 102 140 into the metal they collide with other electrons before they 0 20 1k 15 k f (Hz) After reflection, f, λ and v remain the same. When the forward are absorbed. Each collision lowers the photon frequency Frequency response curve of a microphone: is a graph of and the reflected travelling waves superpose each other, a (energy) slightly, the Compton effect. ∴ electrons at the output intensity level versus frequency for a constant input. standing wave (a sequence of loud and soft sound at fixed surface escape with higher (max) kinetic energy than those Zero dB is assigned to 1 kHz sound as the reference level. positions quarter of a wavelength apart) is formed between the inside metal, max EK = hf – φ for surface electrons. L(dB) source and the wall. Pressure antinodes (max fluctuation in air The Compton effect and photon momentum: The particle 10 pressure) give loud sound and pressure nodes (min fluctuation) nature of light was further supported by the Compton effect. 0 give soft sound. Photon momentum p = E = h . Wall – 10 c λ Loud- loud soft The two models (wave and particle) of light appear to be 50 150 1 k 4k 6k f (Hz) Speaker L S L S L S L inconsistent with each other but both have been shown to be This graph indicates that the microphone responds equally ∆p well to frequencies between 150 and 4 kHz, more sensitive valid depending on the circumstances. This dual nature of light is known as wave-particle duality. to over 4 kHz, less sensitive to below 150 Hz. x Wave nature of matter: de Broglie proposed that a moving Frequency response of multi-speaker system: material particle also has wave-particle duality. Wavelength λ L(dB) woofer tweeter of particle is related to its momentum (like a photon). Every object has its own natural frequencies of vibration. If an Fairly flat between energy source at one of these frequencies interacts with the h h h 20 and 20 kHz de Broglie λ= = = . These equations are object, the latter will be set into vibration, i.e. a standing wave p mv 2mEk is formed. The object is in resonance. The natural frequencies of vibration are called resonant frequencies. 0 20 20 k f (Hz) valid when λ in m, m in kg, v in ms-1, EK in J, h in Js. A single loudspeaker on its own (e.g. the woofer or tweeter) The diffraction of electrons from the surface of a metal Standing waves in a stretched string of length L: tends to ‘colour’ the sound it produces, i.e. some crystal confirmed the wave nature of matter. Overtones Harmonics λ f = v/λ frequencies are louder than others due to resonance. An An electron with the same λ as a photon has the same Fundamental first 2L/1 1(v/2L) ideal loudspeaker system would need to have the same momentum as the photon, p = h/λ. First second 2L/2 2(v/2L) loudness at all frequencies, i.e. a fairly flat response curve. When a gas or metal vapour is heated, the gas or vapour Second third 2L/3 3(v/2L) Some loudspeaker enclosures have tubes (called ports) put glows and emits a characteristic diffraction pattern (obtained in them. Size and depth of ports can be changed to absorb Note: v is the speed of travelling wave in the string. with a diffraction grating) called an emission spectrum. sound of particular frequencies to produce a flat response. When sunlight passes through a gas/vapour, some dark lines Standing waves in open resonant tube of length L: The appear in its spectrum called absorption spectrum, caused vibration of the air column in the tube forms a standing wave. by the absorption of certain wavelengths of sunlight by the Has the same pattern of harmonics as strings but v is the speed atoms or molecules in the gas/vapour. of travelling sound wave in the tube.

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Try the fastest way to create flashcards Question # Suppose that f is a continuous additive function on$\mathbb{R}.$If c := f (1), show that we have f(x) = cx for all$x \in \mathbb{R}.$ Solution Verified Step 1 1 of 4 By additivity of $f$ we get $f(0)=f(0+0)=f(0)+f(0) \Rightarrow \boxed{f(0)=0}$ We can prove the claim for natural numbers using Mathematical Induction: $\text{\underline{Base of Induction:}}$      $n=1$ By assumption, $f(1)=c=c\cdot 1$ $\text{\underline{Induction Step}}$ Suppose that for some $n\in\mathbb{N}$ $f(n)=cn \quad (*)$ Then, \begin{align*} f(n+1)&=f(n)+f(1)\tag{Additivity}\\ &=cn+c\tag{Use (*) and f(1)=c}\\ &=c(n+1)\end{align*} Therefore, by Principle of Mathematical Induction we conclude that $\boxed{f(n)=cn,\hspace{0.2cm} \forall n\in\mathbb{N}}$ ## Recommended textbook solutions #### Introduction to Real Analysis 4th EditionISBN: 9780471433316 (4 more)Donald R. Sherbert, Robert G. Bartle 856 solutions #### Numerical Analysis 9th EditionISBN: 9780538733519 (1 more)J. Douglas Faires, Richard L. Burden 2,677 solutions #### Numerical Analysis 10th EditionISBN: 9781305253667Annette M Burden, J. Douglas Faires, Richard L. Burden 2,795 solutions #### Elementary Analysis: The Theory of Calculus 2nd EditionISBN: 9781461462705Kenneth A. Ross 447 solutions

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# Release notes for STACK 4.4.x STACK version 4.4.0 was released in July 2022. This was a major rewrite of the PRT and CASText systems, with a focus on performance and limitations of the previous systems. This release has changed/tightened up some question authoring causing some problems with existing questions. For this reason we have written these dedicated release notes. ### Issue: [[ foreach ]] blocks over zero length lists. [[ foreach ]] blocks over a list that happens to have length zero causes "text rendering error" if reference to the non-existent element is made, even though the loop is not run: e.g. [[ foreach item="[]" ]] {@item@} [[/ foreach ]]. (Note without the {@item@} it runs fine.) Solution Protect loop with an [[ if ]] block on the length of the list. ### Issue: Bad interaction between ordergreat and exdowncase This is a more serious problem, see https://github.com/maths/moodle-qtype_stack/issues/887 for updates. One solution is to test for exdowncase(sans)=exdowncase(tans) [not just tans]. ### Issue: Automatically calculated numerical teachers answer might now include brackets Automatically calculated numerical teachers answer might now include brackets: ( -(3/8)), which is a problem if the input forbade brackets!, causing Question Test failure. Solution: Don't forbid input of brackets! ### Issue: when selecting function names from a list. When using something like func:rand([sin,cos,exp,ln]); is(equal(func,ln)); now returns unknown. Used to return true/false. Solution: First generate a random integer. Set func based on that, and test the value of the integer. (Not as neat!) ### Issue: MathJax Mathjax no longer likes \begin{pmatrix}{@xx@}\\{@yy@}\end{pmatrix} in castext. Solution: make sure there is a space between \\ and {@yy@}. (Better!) Define the vector to be a maxima object and display that instead. ### Issue: CAS text comments delineated with / ... / are rendered Solution: Use [[ comment ]] ... [ [/ comment ]] ### Issue: Fatal error causing an exception and then displaying nothing. Solution: "tans" PRT node entry ended with semicolon: Delete the semi-colon! We now have error trapping for this problem. ### Issue: taylor now returns a maxima taylor series object taylor now returns a maxima taylor series object (as it should!) rather than a normal algebraic expression (as it did!) Solution use expand(taylor( ... ) ) to get a normal algebraic object. (May then also need to set powerdisp:true to get the usual ordering of terms) This is one consequence of the single call to Maxima. Previously there was some string input/output which lost the data type information. ### Issue: rounding of numerical quantities. The answer test AlgEquiv now does not think floats are equivalent, even though they look identical when displayed in decimal. Solution: don't use the answer test AlgEquiv for floats, use a numerical answertest instead. This is one consequence of the single call to Maxima. Previously there was some string input/output which created numerical rounding. This rounding no longer happens, causing the apparent problem. Examples are given in the documentation on numbers instead.

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General Science tests the ability to answer questions on a variety of science topics drawn from courses taught in most high schools. The life science items cover botany, zoology, anatomy and physiology, and ecology. The earth and space science items are based on astronomy, geology, meteorology and oceanography. The physical science items measure force and motion mechanics, energy, fluids, atomic structure and chemistry. From the time of its inception, the U.S. Armed Forces played a decisive role in the history of the United States. A sense of national unity and identity was forged as a result of victory in the First Barbary War and the Second Barbary War. Even so, the founders of the United States were suspicious of a permanent military force. It played a critical role in the American Civil War, continuing to serve as the armed forces of the United States, although a number of its officers resigned to join the military of the Confederate States. The National Security Act of 1947, adopted following World War II and during the Cold War's onset, created the modern U.S. military framework. The Act established the National Military Establishment, headed by the Secretary of Defense; and created the Department of the Air Force and the National Security Council. It was amended in 1949, renaming the National Military Establishment the Department of Defense, and merged the cabinet-level Department of the Army, Department of the Navy, and Department of the Air Force, into the Department of Defense. The Arithmetic Reasoning section of the test measures your ability to solve arithmetic word problems. You may be asked questions such as “If the tire of a car rotates at a constant speed of 552 times in 1 minute, how many times will the tire rotate in half an hour?” Therefore, reviewing common math key words associated with each operation is recommended. For example, if you see the key words “in all,” the problem deals with addition. If the problem asks you to “find the difference,” you are being asked to subtract. If a question asks “how many times” per day or week, you know you are dealing with multiplication. If it asks “how many in each,” you should be thinking about division. The CAT-ASVAB has 16 questions in 39 minutes; the paper-and-pencil version has 30 questions in 36 minutes. Commander-in-chief: President of the United States Secretary of Defense Deputy Secretary of Defense Secretary of Homeland Security Deputy Secretary of Homeland Security Joint Chiefs of Staff: Chairman Vice Chairman United States Congress: Committees on Armed Services: Senate House Active duty four-star officers United States military seniority National Security Act of 1947 Goldwater–Nichols Act Oh Wow! I really love this album on cd. I have the irst rerelease with the 8 bonus tracks on Rykodisc which is truly great! But, what's really even greater is the rereleased version with the bonus disc on Rhino. The bonus disc has 17 bonus tracks which include 10 tracks that were recorded live. I do ot know where the live tracks are from but the recodings are of "sound" quality, very well done, great quality audio.Not only are they of "sound" quality, but the performances are remarkable,and quite a rockoing concert. The live tracks are listed above as well as the rest of the original album. All tracks are really good tunes such as Big Boys (which there is an alternate version on the bonus disc as well. Also, another nice tune is Goon Squad which is done in the live set and Party Girl which is also done live. One song that has always stood out for me is *What's So Funny 'Bout) Peace Love and Understanding. I have never heard a recording of this song performed live. I wonder if this song is even peerformed live at all. But, to be perfectly honest with you, this is one of Costello's crowning achievements, if not thee one. After all, its part of the first five. The first five are the greatest ----- aren't they? Taxes are additional. All prices are in U.S. dollars. Regular Space Available price is \$369 USD per week when booked through the call center, and \$349 USD per week when booked online. Free membership is based on eligibility. Destinations and travel times are subject to availability and confirmed on a first come, first served basis. Offer includes only accommodations and specifically excludes travel costs and other expenses that may be incurred. For additional terms and conditions, click here or call your Armed Forces Vacation Club® guide at 1-800-724-9988. Promotional discounts may not apply to all properties. Offer may not be combined with any other promotion, discount or coupon. Other restrictions may apply. Offer void where prohibited by law. No official U.S. Army endorsement is implied. Not paid for in whole or in part by any element of the U.S. Government, Military Service, or DoD Non Appropriated Fund Instrumentality (NAFI). I have already served in the military years ago. But I wondered if there was a primer that might have helped me improve my test scores. I think this book would help. Unfortunately it's hard to learn enough from a book to do well on the math and reading comprehension of the ASBAB test. Study hard in math and English class in high school. It's hard to cram from a book to pass a comprehensive test that covers many topics. I think it may give you a few extra points, however. ```Each branch of the service operates its own Service Academy as a four-year institution of higher education. All students receive a full scholarship with a small monthly stipend. Upon graduation, you're commissioned as a second lieutenant in the Army, Air Force, or Marine Corps or as an ensign in the Navy or Coast Guard. Appointment to a service academy is extremely competitive. For more information, call 1-800-822-8762 (US Military Academy in West Point, New York), 1-800-638-9156 (US Naval Academy in Annapolis, Maryland), 1-800-443-9266 (US Air Force Academy in Colorado Springs, Colorado), 1-800-883-8724 (US Coast Guard Academy in New London, Connecticut), and 1-866-546-4778 (United States Merchant Marine Academy, Kings Point, New York). ``` Law prohibits applicants in Category V from enlisting.[6] In addition, there are constraints placed on Category IV recruits; recruits in Category IV must be high school diploma graduates but cannot be denied enlistment solely on this criteria if the recruit is needed to satisfy established strength requirements. Furthermore, the law constrains the percentage of accessions who can fall between Categories IV-V (currently, the limit is 20% of all persons originally enlisted in a given armed force in a given fiscal year).[6] High school and postsecondary students can also take the ASVAB test as part of the Department of Defense’s Career Exploration Program. This paper-and-pencil version of the test is the same as the paper-and-pencil enlistment version but excludes the Assembling Objects section. It is intended to help those students considering a career in the military to discover their strengths in both military and civilian jobs. If the student scores high enough in the AFQT section of the test, he may use the score to enlist within the two-year expiration window. For those who are interested in enlisting in the military, they are screened using the Armed Forces Qualification Test (AFQT), which is comprised of a subset of scores from the ASVAB. Successfully passing the AFQT is not the sole requirement for enlisting but is one of the qualifications that must be met. There are various requirements for the different branches of the military and those interested are encouraged to contact recruiters to obtain more information about requirements specific to that branch. These are sections, or sub-tests, in the ASVAB:  Word Knowledge (WK), Paragraph Comprehension (PC), Arithmetic Reasoning (AR), Mathematics Knowledge (MK), General Science (GS), Mechanical Comprehension (MC), Electronics Information (EI), and Assembling Objects (AO), Auto & Shop Information (AS):  * AI and SI are administered as separate tests in the CAT-ASVAB (computerized version), but combined into one single score (labeled AS). The Armed Services Vocational Aptitude Battery (ASVAB) is a test that covers basic knowledge such as math and verbal skills, writing skills, and vocabulary. It is a required test for entrance into the military, but it can also be an indicator for general aptitude skills for other purposes. For those looking to go into military service, the ASVAB score is a crucial indicator of prospective job placement, so it is very important to take this test seriously and to focus on your strengths when taking the exam. Higher test scores often mean better jobs, higher salary, and more opportunities for advancement in the military. The Armed Services Vocational Aptitude Battery (ASVAB) is one of the most widely used multiple-aptitude test batteries in the world. It was originally designed to predict success in military occupations and is used today to help both those considering entering the military (mostly high school-aged students, but also anyone who is eligible to enlist) as well as those not interested in military service (who comprise the majority of current ASVAB test takers) what sort of career may be the best fit for them. Scores from the ASVAB can be used when enlisting in the military. Students interested in taking the ASVAB should check with their high school to find out when and if the ASVAB will be offered at their school. If it is not offered, students should meet with their guidance counselor to determine if it is possible to schedule a testing session in the future. There is no cost to take the ASVAB. The ASVAB test can be taken at your school or a MEPS (Military Entrance Processing Stations) or MET (Mobile Examination Test) sites.  When the ASVAB is administered at your school, it is usually part of the Student Testing Program or Career Exploration Program.  When the ASVAB is given at MEPS or MET sites, it is part of the Enlistment Testing Program.  The ASVAB test content is the same no matter where you take it, except that you will not have to take the Assembling Objects test if you take the test at your school (as part of the Student Testing Program).  When you take the test in the Student Testing Program you will receive three composite scores (Verbal Skills, Math Skills, and Science and Technical Skills).  When you take the ASVAB as part of the Enlistment Testing Program, you will receive an AFQT (Armed Forces Qualification Test) score and Service composite scores.  These scores are used for assigning your military job. ```The AFQT has been used in non-military settings as a proxy measure of intelligence, for example, in Herrnstein & Murray's book The Bell Curve. Because of the test's significance both inside and outside military settings, it is important to examine what the test measures, i.e. to evaluate the construct validity of the AFQT. Kaufman's 2010 review stated that David Marks (2010) scanned the literature for datasets containing test estimates for populations or groups taking both the AFQT and tests of literacy. One study on nine groups of soldiers differing in job and reading ability found a correlation of .96 between the AFQT and reading achievement (Sticht, Caylor, Kern, & Fox, 1972). Another study showed significant improvements among Black and Hispanic populations in their AFQT scores between 1980 and 1992 while Whites only showed a slight decrement (Kilburn, Hanser, & Klerman, 1998). Another study obtained reading scores for 17-year olds for those same ethnic groups and dates (Campbell et al., 2000) and found a correlation of .997 between reading scores and AFQT scores. This nearly perfect correlation was based on six pairs of data points from six independent population samples evaluated by two separate groups of investigators. According to Marks, "On the basis of the studies summarized here, there can be little doubt that the Armed Forces Qualifications Test is a measure of literacy." However, it is important to note that AFQT has been shown to correlate more highly with classic IQ tests than they do with one another, and that the "crystallized" intelligence measured by AFQT is measured very similarly by Wechsler, in particular.[8] ``` The ASVAB site goes on to explain that “after the final ability estimate is computed, it is converted to a standard score on the ASVAB score scale that has been statistically linked to the ability estimate through a process called equating. Equating studies are conducted for every paper and pencil ASVAB form to ensure that scores have the same meaning regardless of which test form the examinee receives.” These tests, again the high quality ones, are formatted like the real thing so you can get used to the question and answer formats and the time limits so nothing will be a surprise on test day. You’ll know what to expect and you’ll be used to going from different concept to different concept as is often required on the ASVAB. For example, on the math section you may have a problem using one popular math principle followed by another problem that relies on a completely different principle. This is common on a broad test like the ASVAB and preparing your mind to make these leaps can allow you to answer more questions in less time and boost your score. GED holders who earn 15 college credits 100 level or greater are considered equivalent with those holding high school diplomas, so that they need only the Tier I score to enlist. Eligibility is not determined by score alone. Certain recruiting goal practices may require an applicant to achieve a higher score than the required minimum AFQT score in order to be considered for enlistment. Rules and regulations are subject to change; applicants should call their local recruiting center for up to date qualification information.[4][5] The Student ASVAB is the most flexible of the exams. It is typically provided to high school students to help them assess their skills, job prospects, potential military positions, or college majors. The ASVAB for students is essentially the same as the MET ASVAB exam, only students are not necessarily testing for positions within the military. The students’ school counselors examine their scores and help them decide on what to do after graduating from high school. This test is still an important component of a student’s education because it can help them identify their strengths and weaknesses and help set them on the right track for their future career goals.

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Electronics Forums > Current Transformer to 0-10 Volts # Current Transformer to 0-10 Volts Tom Guest Posts: n/a 02-05-2007, 08:01 PM I want to take a current measurement of 0 to 20 Amps AC using a current transfomer, and then convert the current siginal to input into a Analog input of a PLC (programmable logic controller). I know they sell current transducers that do this alreay, but I want to make about 20 of these. The PLC will take 0-10V DC, or 4-20mA I was thinking about using a 50:5 Current Transformer, and a 5 ohm resistor. 20 Amps ----> 50:5 ----> 2 Amps Voltage = 5 * 2 = 10 V Am I on the right track or does the current transformer output a sinusoidal value. Homer J Simpson Guest Posts: n/a 02-05-2007, 08:37 PM "Tom" <(E-Mail Removed)> wrote in message news:(E-Mail Removed) ups.com... > Am I on the right track Yes. > or does the current transformer output a sinusoidal value. Yes. Be careful. An open secondary on a CT is a nasty thing. Take no chances - ask an expert if you are unsure. Guest Posts: n/a 02-05-2007, 10:42 PM "Tom" <(E-Mail Removed)> wrote in message news:(E-Mail Removed) ups.com... > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V > > Am I on the right track or does the current transformer output a > sinusoidal value. > The 5 ohm resistor may be to big. You need to match or be less than the CT secondary "Burden" rating. Typically that value is less than 1 ohm. The voltage developed across that resistance is then amplified by a wide band fixed gain amp., thus the signal conditioner. As Homer pointed out, do not run the secondary into an open circuit or at high impedance. It will then act as a PT possibly creating thousands of volts, doing all kinds of nasty things! Guest Posts: n/a 02-05-2007, 11:02 PM "scada" <(E-Mail Removed)> wrote in message news:OnOxh.274\$(E-Mail Removed)... > > "Tom" <(E-Mail Removed)> wrote in message > news:(E-Mail Removed) ups.com... > > I want to take a current measurement of 0 to 20 Amps AC using a > > current transfomer, and then convert the current siginal to input into > > a Analog input of a PLC (programmable logic controller). I know they > > sell current transducers that do this alreay, but I want to make about > > 20 of these. > > > > The PLC will take 0-10V DC, or 4-20mA > > > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > > resistor. > > > > 20 Amps ----> 50:5 ----> 2 Amps > > > > Voltage = 5 * 2 = 10 V > > > > Am I on the right track or does the current transformer output a > > sinusoidal value. > > > > The 5 ohm resistor may be to big. You need to match or be less than the CT > secondary "Burden" rating. Typically that value is less than 1 ohm. The > voltage developed across that resistance is then amplified by a wide band > fixed gain amp., thus the signal conditioner. As Homer pointed out, do not > run the secondary into an open circuit or at high impedance. It will then > act as a PT possibly creating thousands of volts, doing all kinds of nasty > things! > > > Also keep in mind, the secondary waveform will be the actual current waveform, AC. If you need RMS, or DC output you further need to refine that john jardine Guest Posts: n/a 02-05-2007, 11:16 PM "Tom" <(E-Mail Removed)> wrote in message news:(E-Mail Removed) ups.com... > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V > > Am I on the right track or does the current transformer output a > sinusoidal value. > It's all AC and variable waveshapes must be considered. You'll need an additional power supply and some electronics to rectify, smooth and amplify the signal to 0-10Vdc. E.g. 100:1 CT to a 1ohm resistor, then to an AD737 true RMS converter, then to a x50 opamp, then to the PLC. john -- Posted via a free Usenet account from http://www.teranews.com Rich Grise Guest Posts: n/a 02-05-2007, 11:27 PM On Mon, 05 Feb 2007 12:01:02 -0800, Tom wrote: > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V > > Am I on the right track or does the current transformer output a > sinusoidal value. Well, I'm not a CT guy, but I'd think that the output current would look a lot like the input current, like in any transformer. I'd use a big resistor - 2A at 10V is 20 watts! =:-O Good Luck! Rich Tom Bruhns Guest Posts: n/a 02-05-2007, 11:42 PM On Feb 5, 12:01 pm, "Tom" <(E-Mail Removed)> wrote: > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V > > Am I on the right track or does the current transformer output a > sinusoidal value. Note that 10V at 2A is 20 watts you'll be dissipating in the load resistor! I'd suggest that you go to a much higher turns ratio. 100:1 (500:5) might be reasonable. Then the output is 0.2A. You could use an even higher ratio. If the transformers are easy to get, I'd look at even 1000:1, though you may have some trouble finding those. If you used your original 10:1 ratio, the ten volt drop would reflect back as a 1 volt drop in your line, which is way more than you need to allow. A ten volt output at 1000:1 reflects only ten millivolts drop along the monitored line--actually somewhat more because of less than perfect coupling, but still not a lot. A ten volt output at 1000:1 or even 100:1 is also much more likely to be a reasonable burden for the transformer. At 1000:1, a ten volt output with 20A in the primary is 20mA secondary current and 200mW dissipation. You'll need to rectify the output; an op-amp precision rectifier is appropriate. Then you need to convert the output to whatever the PLC wants. The precision recitifer can easily be made to put out 0-10 volts, even if the input is only 1 volt instead of 10, but then you need power to run the op amps. If you _know_ that your circuit will always have some minimum current in it and the ratio between min and max isn't too great, you could probably arrange to run the op amps on the current transformer output, but that's not a wonderful idea from the standpoint of precision, since the amplifier power will appear as additional transformer load. A better idea would be to use the 4-20mA loops, especially if these sensors will be some distance from the PLC. You can find example 4-20mA circuits in op amp manufacturers' data sheets. I believe that Linear Technology is one good source for such circuits. Try their ap notes, too. Too bad you didn't have this need a year or so ago. Marlin P. Jones had some nice split-core 4-20mA AC current transducers with a jumper for, um 10A, 20A and 50A full scale as I recall, for about \$10 each. But even if you have to pay \$100 or more each for them, you'll probably be better off buying them. I have a feeling from the last sentence of your posting that you'll be in trouble trying to build them. Cheers, Tom Tim Dunne Guest Posts: n/a 02-05-2007, 11:50 PM "Tom" <(E-Mail Removed)> wrote in message news:(E-Mail Removed) ups.com > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, .... > Am I on the right track or does the current transformer output a > sinusoidal value. You need a module from LEM. They're current transformers with built in signal conditioners (often self powered) giving a PLC analog compatible signal - 0-10, 0-5 or 4-20mA http://web4.lem.com/hq/en/component/.../output_type,/ HTH Tim -- Sent from Birmingham, UK... Check out www.nervouscyclist.org 'I find sometimes it's easy to be myself, but sometimes I find it's better to be somebody else.' - Dave Matthews 'So Much To Say' jasen Guest Posts: n/a 02-06-2007, 08:05 AM On 2007-02-05, Tom <(E-Mail Removed)> wrote: > I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V And 20 Watts! there's not (m)any CTs with that sort of output. a 20VA 60Hz transformer weighs a few kilograms... typicaly curent transformers produce milliwatts. aim for the sort of current you can feed to an op-amp eg: a 1000:1 transformer into a virtual earth or a small resistor. then you probably want rectify and average it (if you want RMS that'll add complexity) > Am I on the right track or does the current transformer output a > sinusoidal value. it sure does. Bye. Jasen Paul E. Schoen Guest Posts: n/a 02-06-2007, 03:13 PM "Tom" <(E-Mail Removed)> wrote in message news:(E-Mail Removed) ups.com... >I want to take a current measurement of 0 to 20 Amps AC using a > current transfomer, and then convert the current siginal to input into > a Analog input of a PLC (programmable logic controller). I know they > sell current transducers that do this alreay, but I want to make about > 20 of these. > > The PLC will take 0-10V DC, or 4-20mA > > I was thinking about using a 50:5 Current Transformer, and a 5 ohm > resistor. > > 20 Amps ----> 50:5 ----> 2 Amps > > Voltage = 5 * 2 = 10 V > > Am I on the right track or does the current transformer output a > sinusoidal value. > You can get CTs with 100 mA rated output. There are also high ratio PCB mounted (or not) CTs with primaries from 10 to 200 amps, and output up to 10 VRMS. Digikey has them TE1020-ND for \$7.80, or you can get a wide range of CTs from CR Magnetics: http://www.crmagnetics.com/8300.pdf They also have transducers that might do what you need. Paul Thread Tools Display Modes Linear Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are Off Forum Rules Similar Threads Thread Thread Starter Forum Replies Last Post aidan General Electronics Chat 2 04-13-2012 03:29 AM Electronic Basics 6 01-22-2005 06:29 AM Jerome Jahnke Electronic Basics 1 09-27-2004 07:22 PM Rob \ the nut \ Electronic Basics 7 06-09-2004 03:14 AM CampinGazz Electronic Design 4 01-25-2004 07:26 PM

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# Study Mathematics: Here are some effective tips to study well in mathematics Maths is one subject which you will either find extremely easy and interesting or tough to the core. So, what is the difference between those who find it easy and those who find it difficult? It is their approach towards study mathematics subject. ## Effective tips to study mathematics You can master this subject if you focus on few important things. Here are some effective tips to study mathematics: ### 1. Understand the Basic Concepts Maths cannot be learnt merely by mugging up things. You need to understand the basic concepts thoroughly in order to perform well in this subject. It is important to have clarity about all the mathematical concepts from the beginning so as to develop a good understanding of the subject as it gets complex in the higher classes. Clarity about the fundamentals of the subject is of utmost importance. Maths is one subject which you will either find extremely easy and interesting or tough to the core. So, what is the difference between those who find it easy and those who find it difficult? It is their approach towards study mathematics subject. ## Effective tips to study mathematics You can master this subject if you focus on a few important things. Here are some effective tips to study mathematics: ### 1. Understand the Basic Concepts Maths cannot be learned merely by mugging up things. You need to understand the basic concepts thoroughly to perform well in this subject. It is important to have clarity about all the mathematical concepts from the beginning to develop a good understanding of the subject as it gets complex in the higher classes. Clarity about the fundamentals of the subject is of utmost importance. ### 2. Practice, Practice, and Practice While understanding the concepts is important, it is not enough. Maths is all about practice. The more you practice the better you shall be at this subject. Solve as many maths sums as possible and do it regularly. ### 3. Learn Formula If you know the mathematical formula well, you can solve the sums easily. Thus, you must by heart all the mathematical formulas. It is a good idea to write them all on a piece of paper and stick it in a place where you can glance at them every day. Reading them daily will help you memorize them well. ### 4. Be Thorough With Theorems Mathematical theorems are given a lot of weightage in the maths exam. It is thus important to go through these theorems and learn them thoroughly. It is a good idea to practice these over and over again to retain them. ### 5. Give Mock Tests Mock tests are a good way to assess your knowledge. Give as many mock tests as you can to see how much you have learned. Time your tests each time you give them. This will give you a clear idea about how well you would be able to perform in your actual maths exam. Do not forget to analyze your performance in the mock tests and work on the weak areas to brush them up. This will help you perform better the next time. ### 7. Apply Maths to Real World To learn maths more efficiently, it is suggested to apply it to the real world. This will not only help you learn it better but also make it more interesting. Try these tips and do let us know if you use any other effective tips to learn this subject.

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Help between Notion users It's free & easy ### Vote and select answers Receive points, vote and give the solution 0vote # help me understand this Notion formula i want a quick website where i can paste this formula to understand it as it's unreadable in this format ``if(not empty(prop("Recur Interval")) and not empty(prop("Due")), if(prop("Recur Interval") > 0 and prop("Recur Interval") == ceil(prop("Recur Interval")), formatDate(if(length(prop("Days (Only if Set to 1 Day(s))")) > 0 and prop("Recur Unit") == "Day(s)" and prop("Recur Interval") == 1, if(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), "days") >= 1 and unequal(formatDate(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), "MMMM D, YYYY"), formatDate(prop("Due"), "MMMM D, YYYY")), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 1, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 1, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 2, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 2, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 3, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 3, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 4, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 4, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 5, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 5, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 6, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 6, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 7, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), 7, "days"), fromTimestamp(9.07002e+11)))))))), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 1, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 1, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 2, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 2, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 3, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 3, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 4, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 4, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 5, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 5, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 6, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 6, "days"), if(length(replaceAll(replaceAll(prop("Days (Only if Set to 1 Day(s))"), formatDate(dateAdd(prop("Due"), 7, "days"), "dddd"), "§"), "[^§]", "")) > 0, dateAdd(prop("Due"), 7, "days"), fromTimestamp(9.07002e+11))))))))), if(prop("Recur Unit") == "Month(s) on the Last Day", prop("Last Day Base Date"), if(prop("Recur Unit") == "Month(s) on the Last Weekday", if(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Last Weekday Base Date"), "days") >= 1 or equal(formatDate(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), "L"), formatDate(prop("Last Weekday Base Date"), "L")), if(day(prop("Next Last Base Date")) == 0, dateSubtract(prop("Next Last Base Date"), 2, "days"), if(day(prop("Next Last Base Date")) == 6, dateSubtract(prop("Next Last Base Date"), 1, "days"), prop("Next Last Base Date"))), prop("Last Weekday Base Date")), if(prop("Recur Unit") == "Month(s) on the First Weekday", if(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("First Weekday Base Date"), "days") >= 1 or equal(formatDate(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), "L"), formatDate(prop("First Weekday Base Date"), "L")), if(day(dateSubtract(prop("Next Last Base Date"), date(prop("Next Last Base Date")) - 1, "days")) == 0, dateSubtract(prop("Next Last Base Date"), date(prop("Next Last Base Date")) - 2, "days"), if(day(dateSubtract(prop("Next Last Base Date"), date(prop("Next Last Base Date")) - 1, "days")) == 6, dateSubtract(prop("Next Last Base Date"), date(prop("Next Last Base Date")) - 3, "days"), dateSubtract(prop("Next Last Base Date"), date(prop("Next Last Base Date")) - 1, "days"))), prop("First Weekday Base Date")), if(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), "days") >= 1 and unequal(formatDate(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, dateAdd(now(), prop("UTC Offset"), "hours"), now()), now()), "L"), formatDate(prop("Due"), "L")), if(equal(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), prop("Simplified Recur Unit")) / prop("Recur Interval"), ceil(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), prop("Simplified Recur Unit")) / prop("Recur Interval"))), dateAdd(prop("Due"), multiply(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), prop("Simplified Recur Unit")) / prop("Recur Interval") + 1, prop("Recur Interval")), prop("Simplified Recur Unit")), dateAdd(prop("Due"), multiply(ceil(dateBetween(if(formatDate(now(), "z") == "UTC", if(not empty(prop("UTC Offset")) and prop("UTC Offset") >= -12 and prop("UTC Offset") <= 14, if(test(format(prop("Due")), "AM|PM"), now(), dateAdd(now(), prop("UTC Offset"), "hours")), now()), now()), prop("Due"), prop("Simplified Recur Unit")) / prop("Recur Interval")), prop("Recur Interval")), prop("Simplified Recur Unit"))), dateAdd(prop("Due"), prop("Recur Interval"), prop("Simplified Recur Unit"))))))), "MMMM D, YYYY"), "Error in Recur Interval: Non-Whole or Negative Number"), "")`` 1vote polle Points53070 No one will be able to help you without any context and without seeing the actual Notion template to understand the complete structure and how it works. Even having access to the Notion template, asking someone to spend 5 hours to explain you a huge formula makes no sense, because the formula needs a template to work, just having a formula makes nothing. Makes sense? If you don't understand 1 + 1 it complicates things asking someone to explain 5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13. You should ask something specific to solve a problem and not something like this, because it has no answer. I suggest that you learn Notion formulas from scratch and you will at least understand what each line means. Like the first one: If the property Recur Interval is not empty and the property Due is not empty then do the following. That is the first one before the comma and the problem is that explaining the same for 300 actions with no context, will not help you in anything. 1vote ### ahnonnie commented Jan 1 Sorry for being unspecific, the code is meant to be used for a recurring task table/calendar view. I got it from Tom Franks explains. I took the code directly from his Advanced Recurring Tasks template, but for some reason when I pasted it into my formula field, that error emerged even though I didn't tweak anything. The error doesn't show in Frank's table. 0vote ### polle commented May 2 The problem is the same @ahnonnie and it is impossible to know which arguments are missing without having access to your Notion Workspace. Please comment in your question to avoid confusion. :) ### Extend Notion Powers ... Welcome to Notion Answers, where you can ask questions and receive answers from other members of the community. Please share to grow the Notion Community!

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Coding theorem defines decoding error capacity for general scenarios The rate at which information can be coded so that it can be decoded within a particular error probability constraint is one of the "major research topics in information theory" as Hideki Yagi at the University of Electro-Communications, Te Sun Han at the National Institute of Information and Communications Technology, and Ryo Nomura at Senshu University in Japan explain in their recent report. In this latest work they formulate a theorem for a general class of coding theorems that gives a formula for the decoding error capacity. They also show how the theorem reduces to known theorems for more restricted scenarios. The researchers describe their system as an input stream that is coded into the output by a sequence. The channel capacity is then the rate at which information can be reliably transmitted by that channel. Previous work has demonstrated formulae for the error capacity for coding channels but they were limited by the length of the coding stream - which becomes uncomputable for general scenarios. Other work has characterised the channel capacity in such a way that the complexity does not increase with the channel length, but they are limited in terms of what mixture of channel types can be coded in this way. While progress has been made towards more general theorems, Yagi, Han and Nomura now establish the first-order coding theorem, which gives a formula for the error-capacity for mixed memoryless channels with general mixture. They also provide a direct part of the second-order theorem, and show that other previously established formulas can be obtained by reducing the theorem to restricted scenarios. They add in their concluding remarks, "Extensions of the established formulas for mixed channels with general input and/or output alphabets are interesting and practically important research subjects." More information: Hideki Yagi et al. First- and Second-Order Coding Theorems for Mixed Memoryless Channels With General Mixture, IEEE Transactions on Information Theory (2016). DOI: 10.1109/TIT.2016.2573310 Provided by University of Electro-Communications Explore further The golden anniversary of black-hole singularity Feedback to editors

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# Samacheer Kalvi 12th Computer Science Solutions Chapter 7 Python Functions Students can Download Computer Science Chapter 7 Python Functions Questions and Answers, Notes Pdf, Samacheer Kalvi 12th Computer Science Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations. ## Tamilnadu Samacheer Kalvi 12th Computer Science Solutions Chapter 7 Python Functions ### Samacheer Kalvi 12th Computer Science Python Functions Text Book Back Questions and Answers PART – I 12th Computer Science Chapter 7 Book Back Answers Question 1. A named blocks of code that are designed to do one specific job is called as ………………………… (a) Loop (b) Branching (c) Function (d) Block (c) Function Samacheer Kalvi Guru 12th Computer Science Question 2. A Function which calls itself is called as ………………………… (a) Built – in (b) Recursion (c) Lambda (d) Return (b) Recursion 12th Computer Science Samacheer Question 3. Which function is called anonymous un – named function? (a) Lambda (b) Recursion (c) Function (d) Define (a) Lambda Samacheer Kalvi Guru 7th Computer Science Question 4. Which of the following keyword is used to begin the function block? (a) Define (b) For (c) Finally (d) Def (d) Def Computer Chapter 7 Question 5. Which of the following keyword is used to exit a function block? (a) Define (b) Return (c) Finally (d) Def (b) Return 7th Computer Guide Samacheer Kalvi Question 6. While defining a function which of the following symbol is used. (a) ; (semicolon) (b) . (dot) (c) : (colon) (d) \$ (dollar) (c) : (colon) 12th Computer Science Chapter 9 Book Back Answers Question 7. In which arguments the correct positional order is passed to a function? (a) Required (b) Keyword (c) Default (d) Variable – length (a) Required Samacheer Kalvi Computer Science Book Question 8. Read the following statement and choose the correct statement(s). (I) In Python, you don’t have to mention the specific data types while defining function. (II) Python keywords can be used as function name. (a) (I) is correct and (II) is wrong (b) Both are correct (c) (I) is wrong and (II) is correct (d) Both are wrong (a) (I) is correct and (II) is wrong Chapter 7 Science Question 9. Pick the correct one to execute the given statement successfully. if_: print (x,” is a leap year”) (a) x % 2 = 0 (b) x % 4 = = 0 (c) x / 4 = 0 (d) x % 4 = 0 (b) x % 4 = = 0 Computer Science Samacheer Kalvi Question 10. Which of the following keyword is used to define the function testpython():? (a) Define (b) Pass (c) Def (d) While (c) Def PART – II Science Chapter 7 Question 1. What is a function? Functions are nothing but a group of related statements that perform a specific task. Question 2. Write the different types of functions? 1. User – defined Functions 2. Built-in Functions 3. Lambda Functions 4. Recursion Functions Question 3. What are the main advantages of function? • It avoids repetition and makes a high degree of code reusing. • It provides better modularity for your application. Question 4. What is meant by scope of variable? Mention its types? Scope of variable refers to the part of the program, where it is accessible, i.e., area where you can refer (use) it. We can say that scope holds the current set of variables and their values. The two types of scopes are: local scope and global scope. Question 5. Define global scope? • A variable, with global scope, can be used anywhere in the program. • It can be created by defining a variable outside the scope of any function or block. Question 6. What is base condition in recursive function? The condition that is applied in any recursive function is known as base condition. A base condition is must in every recursive function otherwise it will continue to execute like an infinite loop. Question 7. How to set the limit for recursive function? Give an example? To set the limit for recursive function using sys.setrecursionlimit (limit _value). Example: import sys sys. setrecursionlimit (3000) def fact(n): if n == 0: return 1 else: return n * fact(n-l) print(fact (2000) PART – III Question 1. Write the rules of local variable? Rules of local variable: 1. A variable with local scope can be accessed only within the function/block that it is created in. 2. When a variable is created inside the function/block, the variable becomes local to it. 3. A local variable only exists while the function is executing. 4. The formate arguments are also local to function. Question 2. Write the basic rules for global keyword in python? The basic rules for global keyword in Python are: 1. When we define a variable outside a function, it’s global by default. You don’t have to use the global keyword. 2. We use global keyword to read and write a global variable inside a function. 3. Use of global keyword outside a function has no effect Question 3. What happens when we modify the global variable inside the function? It shows an error, unbound local error. Question 4. Differentiate ceil ( ) and floor ( ) function? Question 5. Write a Python code to check whether a given year is leap year or not? Leap year or not: Program code: y = int(input (“Enter year”)) if y%4==0: print (“The given year is a leap year”) else: print (“The given year is not a leap year”) Question 6. What is a composition in functions? The value returned by a function may be used as an argument for another function in a nested manner. This is called composition. For example, if we wish to take a numeric value or an expression as a input from the user, we take the input string from the user using the function input ( ) and apply eval ( ) function to evaluate its value. Question 7. How recursive function works? • Recursive function is called .by some external code. • If the base condition is met then the program gives meaningful output and exits. • Otherwise, function does some required processing and then calls itself to continue recursion. Question 8. What are the points to be noted while defining a function? 1. Function blocks begin with the keyword “def ” followed by function name and parenthesis ( ). 2. Any input parameters or arguments should be placed within these parentheses when you define a function. 3. The code block always comes after a colon (:) and is indented. 4. The statement “return [expression]” exits a function, optionally passing back an expression to the caller. A “return” with no arguments is the same as return None PART – IV Question 1. Explain the different types of function with an example? Types of Functions: Basically, we can divide functions into the following types: 1. User – defined Functions 2. Built – in Functions 3. Lambda Functions 4. Recursion Functions Functions: User – defined functions Built – in functions Lambda functions Recursion functions Description: Functions defined by the users themselves. Functions that are inbuilt with in Python. Functions that are anonymous un-named function. Functions that calls itself is known as recursive. (I) Syntax for User defined function def <function_name ( [parameter1, parameter!…] ) > : <Block of Statements> return <expression /None> Example: def hello ( ): print (“hello – Python”) return Advantages of User – defined Functions: 1. Functions help us to divide a program into modules. This makes the code easier to manage. 2. It implements code reuse. Every time you need to execute a sequence of statements, all you need to do is to call the function. 3. Functions, allows us to change functionality easily, and different programmers can work on different functions. (II) Anonymous Functions: In Python, anonymous function is a function that is defined without a name. While normal functions are defined using the def keyword, in Python anonymous functions are defined using the lambda keyword. Hence, anonymous functions are also called as lambda functions. The use of lambda or anonymous function: 1. Lambda function is mostly used for creating small and one-time anonymous function. 2. Lambda functions are mainly used in combination with the functions like filter ( ), map ( ) and reduce ( ). Syntax of Anonymous Functions The syntax for anonymous functions is as follows: lambda [argument(s)] expression Example: sum = lambda argl, arg2: argl + arg2 print (‘The Sum is sum (30, 40)) print (‘The Sum is :’, sum (-30, 40)) Output: The Sum is: 70 The Sum is: 10 The above lambda function that adds argument argl with argument arg2 and stores the result in the variable sum. The result is displayed using the print ( ). (III) Functions using libraries: Built – in and Mathematical functions (IV) Recursive functions: When a function calls itself is known as recursion. Recursion works like loop but sometimes 1 ’ it makes more sense to use recursion than loop. You can convert any loop to recursion. Example: def fact(n): if n = = 0: return 1 else: return n * fact (n – 1) print (fact (0)) print (fact (5)) Output: 1 120 Question 2. Explain the scope of variables with an example? Scope of variable: • Scope of variable refers to the part of the program, where it is accessible, • The scope holds the current set of variables and their values. • The two types of scopes are – local Scope and global scope local Scope: • A variable declared inside the function’s body or in the local scope is known as local variable. Rules of local variable: • A variable with local scope can be accessed only within the function/ block that it is created in. • When a variable is created inside the function/block, the variable becomes local to it. • A local variable only exists .while the function is executing. • The format arguments are also local to function. Example: Create a Local Variable def loc: y=0 # local scope print(y) loc () Output: 0 Example: Accessing local variable outside the scope def loc(): y = “local” loc() print(y) • When we run the above code, the output shows the following error: • The above error occurs because we are trying to access a local variable ‘y’ in a global scope. Name Error: name ‘y’ is not defined Global scope: A variable, with global scope can be used anywhere in the program. It can be created by defining a variable outside the scope of any function/block. Rules of global Keyword: • When we define a variable outside a function, it’s global by default. You don’t have to use global keyword. • We use global keyword to read and write a global variable inside a function. • Use of global keyword outside a function has no effect. Use of global keyword: Example: Changing Global Variable From Inside a Function using global keyword x = 0 # global variable global x x = x + 5 # increment by 2 function x value is :”, x) print (“In main x value is :”, x) Output: Inside add() function x value is : 5 In main x value is : 5 • In the above program, x is defined as a global variable. • Inside the add() function, the global keyword is used for x and we increment the variable x by 5. • The change on the global variable x outside the function i.e the value of x is 5. Question 3. Explain the following built-in functions? (a) id ( ) (b) chr ( ) (c) round ( ) (d) type ( ) (e) pow ( ) Question 4. Write a Python code to find the L.C.M. of two numbers? Method I using functions: def lcm (x, y): if x > y: greater = x else: greater = y while (true): if ((greater % x = = 0) and (greater % y = = 0)): lcm = greater break greater + = 1 return lcm num 1 = int (input(“Enter first number : “)) num 2 = int (input(“Enter second number : “)) print (“The L.C.M of”, numl, “and”, num, “is”, lcm(num1, num2)) Method II (without using functions) a = int (input (“Enter the first number :”)) b = int (input (“Enter the second number :”)) if a > b: mini = a else: min 1 = b while(1): if (min 1 % a = = 0 and mini 1 % b = = 0): print (“LCM is:”, mini) break mini = min 1 + 1 Output: Enter the first number: 15 Enter the second number: 20 LCM is: 60 Question 5. Explain recursive function with an example? Recursive function: • A recursive function calls itself. Imagine a process would iterate indefinitely if not stopped by some condition Such a process is known as infinite iteration. • The condition that is applied in any recursive function is known as a base condition. • A base condition is must in every recursive function otherwise it will continue to execute like an infinite loop. Overview of how recursive function works: • A recursive function is called by some external code. • If the base condition is met then the. program gives meaningful output and exits. • Otherwise, function does some required processing and then calls itself to continue recursion. Here is an example of recursive function used to calculate factorial. Example: def fact(n): if n==0: return 1 else: , return n * fact (n-1) print (fact (0)) print (fact (5)) Output: 1 120 Practice Programs Question 1. Try the following code in the above program? Output: 1. Error 2. Name: Sri Salary: 3500 Salary: 3500 3. Name: Balu Salary: 3500 4. Name: Jose Salary: 1234 5. Name: Salary: 1234 Question 2. Evaluate the following functions and write the output? Output: 1. 30 2. 9 3. 8 4. 9 Question 3. Evaluate the following functions and write the output? Output: (i) 1. 13 2. 3.2 (ii) 1. 50 2. 36 (iii) <class ‘str’> (iv) 0b10000 (v). 1. CR (carriage return) 2. It moves the cursor to the beginning of the same line (vi) 1. 8.2 2. 18.0 3. 0.510 4. 0.512 (vii) 1. B 2. a 3. A 4. 6 5. 10 (viii) 1. 0.125 2. 8.0 3. 1 ### Samacheer Kalvi 12th Computer Science Python Functions Additional Questions and Answers PART – 1 Question 1. Which of the following avoids repetition and makes high degree of code reusing? a) Loop b) Functions c) Branching d) Dictionaries b) Functions Question 2. A …………………………. is one or more lines of code, grouped together. (a) Code – (b) Block (c) Function (d) Arguments (b) Block Question 3. A block of code begins when a line is indented by ……………………. spaces usually. (a) 2 (b) 3 (c) 4 (d) 5 (c) 4 Question 4. A block within a block is called …………………………… block. Nested Question 5. How many types of arguments are used to call a function? a) 3 b) 5 c) 4 d) 2 c) 4 Question 6. How many types of function arguments are there? (a) 2 (b) 3 (c) 4 (d) 5 (c) 4 Question 7. The arguments can be given in improper order in ………………………. arguments. (a) Required (b) Keyword (c) Default (d) Variable – length (b) Keyword Question 8. Which of the following keyword is used to define an anonymous function? a) Def b) Alpha c) Range d) Lambda d) Lambda Question 9. How many methods of arguments passing are there in the variable-length method. (a) 2 (b) 3 (c) 4 (d) 5 (a) 2 Question 10. Non – keyword variable arguments are called ………………………………. Tuples Question 11. In python’s ……………………….. function supports variable-length arguments. (a) Input (b) Write (c) Output (d) Print (d) Print Question 12. Functions that are anonymous un_named are called …………………. a) User-defined b) Lambda c) Built-in d) Recursive b) Lambda Question 13. Lambda function can only access ……………………….. variables. (a) Local (b) Function (c) Global (d) Nested (c) Global Question 14. How many types of scopes are there? (a) 2 (b) 3 (c) 4 (d) 5 (a) 2 Question 15. Any loop can be converted into ……………………. a) Composition b) Recursion c) Function d) Branching b) Recursion Question 16. Read the following statement and choose the wrong statements (a) Without using the global keyword, we cannot modify the global variable (b) Using global keyword we can modify the global variable (c) Without global keyword, we can modify the global variable (c) Without global keyword, we can modify the global variable Question 17. Find the correct statement. (a) Local and global variables cannot be used in the same code (b) Local and global variables can be used in the same code (b) Local and global variables can be used in the same code Question 18. The ……………………… function is the inverse of chr ( ) function. (a) Ord ( ) (b) Abs ( ) (c) Chr ( ) (d) Bin ( ) (a) Ord ( ) Question 19. …………………………. function is the alternative for bin ( ) function. (a) Ord ( ) (b) Format ( ) (c) Binary ( ) (d) Ord ( ) (b) Format ( ) Question 20. bin ( ) returns the binary string prefixed with ………………………… for the given integer number (a) b (b) ob (c) obin (d) bin (b) ob Question 21. Find the output. d = 43 print(‘A =ord(d)) (a) 67 (b) 95 (c) 97 (d) 65 (d) 65 Question 22. Find the output, d = 43 print (chr(d)) (a) – (b) + (c) * (d) / (b) + Question 23. The default precision for fixed-point number is …………………………. (a) 2 (b) 4 (c) 6 (d) 8 (c) 6 Question 24. How many formats are there for the format ( ) functions? (a) 12 (b) 5 (c) 3 (d) 1 (c) 3 Question 25. ………………………. function returns the smallest integer greater than or equal to x (a) Sqrt (b) Flow (c) Floor (d) Cell (d) Cell Question 26. ………………………. function is used to evaluate the input value. (a) Input (b) Valuate (c) Eval (d) Val (c) Eval Question 27. Any Loop can be converted to recursive functions. True / False True Question 28. Find true statement (a) Recursive function call itself (b) Recursive function have to be called externally (a) Recursive function call itself PART – II Question 1. What is meant by block in python? A block is one or more lines of code, grouped together so that they are treated as one big sequence of statements while execution. Question 2. Give the syntax for passing parameters in functions? Parameters or arguments can be passed to functions def function _ name (parameter (s) separated by comma): Question 3. What are arguments? What are the types? • Arguments are used to call a function and there are primarily four types of functions that one can use: • Required arguments, Keyword arguments, Default arguments, and Variable-length arguments. Question 4. Classify Function Arguments? Function Arguments: 1. Required arguments 2. Keyword arguments 3. Default arguments 4. Variable-length arguments Question 5. Define default arguments? Default Arguments In Python, the default argument is an argument that takes a default value if no value is provided in the function call. The following example uses default arguments, that prints default salary when no argument is passed, def printinfo(sal=3500): Question 6. Write the advantages of user-defined functions. • Functions help us to divide a program into modules. • This makes the code easier to manage. • It implements code reuse. Every time you need to execute a sequence of statements, all you need to do is to call the function. • Functions, allow us to change functionality easily, and different programmers can work on different functions. PART – III Question 1. Write the output for the program given below? Program: def printdata (name, age): print (“Example – 3 Keyword arguments”) print (“Name :”,name) print (“Age age) return # Now you can call printdata ( ) function printdata (age = 25, name = “Gshan”) Output: Example – 3 Keyword arguments Name: Gshan Age: 25 Question 2. Give the syntax for defining variable-length arguments.? Syntax – Variable – Length Arguments: def function _name (*args): function_body return_statement Question 8. Write a note of the return statement. • The return statement causes your function to exit and returns a value to its caller. • The point of functions, in general, is to take inputs and return something. • The return statement is used when a function is ready to return a value to its caller. • So, only one return statement is executed at run time even though the function contains multiple return statements. • Any number of ‘return’ statements are allowed in a function definition but only one of them is executed at run time. Question 4. Find the output? Program: x = 0 # global variable global x x = x + 5 # increment by 2 print (“Inside add ( ) function x value is:”, x) print (“In main x value is x) Output: Inside add ( ) function x value is: 5. In main x value is: 5 Question 5. Write note on format function?

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• entries 3 2 • views 4,228 # Physics of swimming 1,280 views Physics of Swimming When i first looked up the physics of swimming, i got many different answers. There were many different ways that swimming can tie into physics. I am going to give a formula that is on the refrence table and can relate to because weve used it in physics class before. To kick 100 meters it takes 80 seconds. When kicking, a swimmer can travel at a velocity of 1.25 m/s. To pull 100 meters it takes 60 seconds. When pulling, a swimmer can travel at a velocity of 1.6 m/s. To swim 100 meters with both the arms and the legs it would take 50 seconds. When swimming using both the arms and the legs, a swimmer has a velocity of 2 m/s. The arms therefore generate more propulsion than the legs. The propulsion generated by the legs is 62%. The propulsion generated by the arms is 83%. The ratio of pull to kick is 1.3, meaning that the pull is 1.3 times greater than the kick. Water applies a force perpendicular to each surface of the swimmer's body. F = PA The force acting perpendicular to the surface of the swimmer's body is equal to the pressure acting on the swimmer mulitiplied by the surface area. For example, if the Pressure acting on the back of a swimmer's hand 1.3 x 10^5 Pa and the surface area of the back of the hand is 8.3 x 10^-3 m^2 then the equation F = PA would yield: F = (1.3 x 10^5 Pa) * (8.3 x 10^-3 m^2) = 1079 N. As you can see alot of the information would just be plugging in the informations thats given to you. You can also see that it takes alot of work to swim, its also been said that swimming is the best workout you could do for your body. I hope i have opened your eyes to a new way of thinking about swiming, especially with sumer coming up, thank you for reading my blog ## 1 Comment i love to swim! it makes it seem like swimming is a lot of work! ×   Pasted as rich text.   Paste as plain text instead Only 75 emoji are allowed.

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# Concrete Calculator The Concrete Calculator estimates the volume and weight of concrete necessary to cover a given area. It also estimates the number of bags of concrete necessary based on standard 60 and 80– pound bags of concrete. Purchasing slightly more concrete than the estimated result can reduce the probability of having insufficient concrete. ## Result Estimated volume of concrete: 176.573 cubic feet or 6.54 cubic yards or 5 cubic meters. Total weight if using pre-mixed concrete*: 23,484.253 lbs or 10,650 kg. Equivalent number of 60-lb bags: 391.404 bags. Equivalent number of 80-lb bags: 293.553 bags. Length (l) feetinchesyardsmeterscentimeters Width (w) feetinchesyardsmeterscentimeters Thickness or Height (h) feetinchesyardsmeterscentimeters Quantity * The Concrete Calculator uses a pre-mixed cement density of 2130 kg/m3, or 133 lbs/ft3 (60 pounds / 0.45 cubic feet, or 80 pounds / 0.60 cubic feet) to calculate the weight of concrete needed. Different types of concrete can have different densities. ## Hole, Column, or Round Footings Diameter (d) feetinchesyardsmeterscentimeters Depth or Height (h) feetinchesyardsmeterscentimeters Quantity ## Circular Slab or Tube Outer Diameter (d1) feetinchesyardsmeterscentimeters Inner Diameter (d2) feetinchesyardsmeterscentimeters Length or Height (h) feetinchesyardsmeterscentimeters Quantity ## Curb and Gutter Barrier Curb Depth feetinchesyardsmeterscentimeters Gutter Width feetinchesyardsmeterscentimeters Curb Height feetinchesyardsmeterscentimeters Flag Thickness feetinchesyardsmeterscentimeters Length feetinchesyardsmeterscentimeters Quantity ## Stairs Run feetinchesyardsmeterscentimeters Rise feetinchesyardsmeterscentimeters Width feetinchesyardsmeterscentimeters Platform Depth feetinchesyardsmeterscentimeters Number of Steps RelatedVolume Calculator Concrete is a material comprised of a number of coarse aggregates (particulate materials such as sand, gravel, crushed stone, and slag) bonded with cement. Cement is a substance that is used to bind materials, such as aggregate, by adhering to said materials, then hardening over time. While there are many types of cement, Portland cement is the most commonly used cement, and is an ingredient in concrete, mortar, and plasters. Concrete can be purchased in multiple forms, including in 60 or 80-pound bags, or delivered in large amounts by specialized concrete mixer trucks. Proper mixing is essential for the production of strong, uniform concrete. It involves mixing water, aggregate, cement, and any desired additives. Production of concrete is time-sensitive, and the concrete must be placed before it hardens since it is usually prepared as a viscous fluid. Some concretes are even designed to harden more quickly for applications that require rapid set time. Alternatively, in some factory settings, concrete is mixed into dryer forms to manufacture precast concrete products such as concrete walls. The process of concrete hardening once it has been placed is called curing, and is a slow process. It typically takes concrete around four weeks to reach over 90% of its final strength, and the strengthening can continue for up to three years. Ensuring that the concrete is damp can increase the strength of the concrete during the early stages of curing. This is achieved through techniques such as spraying concrete slabs with compounds that create a film over the concrete that retains water, as well as ponding, where concrete is submerged in water and wrapped in plastic.

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Problem: The altitude of a triangle is increasing at a rate of 1cm/min while the area of the triangle is increasing at a rate of 2cm^2/min. At what rate is the base of the triangle changing when the altitude is 10cm and the area is 100cm^2? Answer: d(base)dt = -1.6.... This is the correct answer from the back of the book. Im not understanding what is going on in the problem.... Questions: 1. When they say that the altitude is 10cm are they are not saying it is constant are they? It just means at this instant in time it is 10cm... is this correct? 2.Why is the base decreasing? would this mean that the rate of altitude is increasing at such a rate that the base is actually shrinking to compensate for the rate of change in area? Related Calculus and Beyond Homework Help News on Phys.org Questions: 1. When they say that the altitude is 10cm are they are not saying it is constant are they? It just means at this instant in time it is 10cm... is this correct? You are right, they mean that "instant". 2.Why is the base decreasing? would this mean that the rate of altitude is increasing at such a rate that the base is actually shrinking to compensate for the rate of change in area? Did they specify a type of triangle, or did this problem have a figure? Most likely though yes, the base was decreasing slow enough that the increase in height allowed for area to be increasing.

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# Fractions + work - math problems #### Number of problems found: 56 • Women In a company of 1050 employees are 2/3 women. How many women work in the company? • Cows 4 cows spent 16 bags of hay in 5 days. How many bags of hay sacks are needed for 5 cows for seven days? • Pumps 6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps? • Cooks Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes? • Tractors 6 tractors started plowing the field that they together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner. • Strawberries Father collects strawberries himself in 4 hours, son in 14 hours. How long will it take them along when dad comes to help his son collect strawberries after 3 hours? • Two typists There are two typists who are rewriting the material 814 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting al • Garden Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together? • University bubble You'll notice that the college is up slowly every other high school. In Slovakia/Czech Republic, a lot of people are studying political science, mass media communication, social work, many sorts of management MBA. Calculate how many times more earns cleve • Price of state Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 868 (super-gross wage).Then tax him 35.2% employer contributions Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day? • Drinking water A man drinks a keg of water in 40 days, and a woman drinks in 62 days. How many days do they consume a keg together? • Forestry workers In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others if they work 10 hours a day? • Pediatrician Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work? • Bureau of Labor Bureau of Labor is a state institution that provides mike and the rest for their so-called clients. The mission of the Bureau of Labor is spend taxpayer money to provide relaxation and benefits to those who do not want to work. Popularly speaking sense th • Tractors Fields go plow two tractors with various performances. The first tractor plows the whole field in 11 hours, the second tractor plows the whole field 19 hours longer. How long take plow the whole field with two tractors? Do you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it. We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox. Need help to calculate sum, simplify or multiply fractions? Try our fraction calculator. Fraction Word Problems. Work word problems.

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# Statistical analysis help A graduate of Indiana University, he spent nearly a decade as a staff reporter for the Daily Herald in suburban Chicago, covering a wide array of topics including, local and state government, crime, the legal system and education. ### Fisher Statistics Consulting | Dissertation Statistics Help Help With Statistical Analysis - Professional Help Trig Question Help, Order Essay Online Cheap High Quality.How to Deal With Heteroscedasticity Using STATGRAPHICS Centurion.Statistics help and research consulting service for PhD dissertations, Master thesis, researchers, and help with statistics assignments.Am is a highly-useful statistical analysis, statistics is a data.I need help to analyze and interpret small scale data using SPSS.View all featured platinum and gold partners, or search our complete A-Z listing. ### SPSS Statistics for Students: The Basics - SSCC How to Apply SPC Techniques to Correlated Variables Using STATGRAPHICS Centurion. ### Statistical Report Writing and Data Analysis Help - SPSS This method applies statistics to economics to forecast future trends.Since not everyone is a mathematic genius who is able to easily compute the needed statistics on the mounds of data a company acquires, most organizations use some form of statistical analysis software.How to Perform an Optimization Experiment Using STATGRAPHICS Centurion.Includes statistics help online for dealing with outliers and non-normal distributions.Connect with the latest insights on analytics through related articles and research.Manufacturers use statistics to weave quality into beautiful fabrics, to bring lift to the airline industry and to help guitarists make beautiful music.Describes the proper application of SPC methods to multiple correlated variables. Statistical Analysis Assignment-SCU Assignment Help Part C Assignment Description Get the best assignment help from MakeMyAssignments.com MAT10251 STATISTICAL.Statistical Help: 5. MA260 assignment 5-8 Statistical Analysis: Statistics: MA260 Statistical Analysis I: Statistical Analysis: Statistical Analysis: ASSIGNMENT 05. Function: Location: Statistics: Output: Summarize menuoption: ArcMap table window (right-click field name) Minimum Results are written to a new table: Frequencytool.From the tube of toothpaste in your bathroom to the planes flying overhead, you see hundreds of products and processes every day that have been improved through the use of statistics.SISA allows you to do statistical analysis directly on the Internet. Click on.The experts provide only high quality dissertation data analysis writing services.Statistics consulting and help for proposals, surveys, questionnaire.In an effort to organize their data and predict future trends based on the information, many businesses rely on statistical analysis. PIE TUTORS is a global provider of statistical consulting, and Data Analysis Services.Statistics assignment help is provided by the best assignment help service online Theuniversitypapers.com and they have been guaranteeing...These online statistics help guides are a supplement to the procedure documentation available on the Statgraphics Centurion and Statgraphics Sigma express Help menus. ### Statistical Consulting and Data Analysis Services This definition explains this component of data analytics in terms of business intelligence and provides links to more resources.Affordable storage, powerful computers and advanced algorithms have all led to an increased use of computational statistics.Describes the construction of an ARIMA control chart to deal with data in which adjacent samples are not independent. How to Forecast Seasonal Time Series Data Using STATGRAPHICS Centurion. Explore insights from marketing movers and shakers on a variety of timely topics.Authors find big data analysis and statistics and sustainable development and analysis, solve difficult using powerful tools this. ### Statistics Homework Help, Statistics Assignment Help, SPSS In these cases, a sample of the entire data is typically examined, with the results applied to the group as a whole. Business analytics software and services provider SAS defines statistical analysis as the science of collecting, exploring and presenting large amounts of data to discover underlying patterns and trends.For more information on getting statistics help online check out our data analysis training seminars.

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# What Will Happen to The Area of A Rectangle? What will happen to the area of a rectangle if its length is doubled and breadth is tripled? 1. 5 times more the area of the old rectangle 2. Area will remain the same 3. 6 times less the area of the old rectangle 4. 6 times more the area of the old rectangle Answer: (1) 5 times more the area of the old rectangle Explanation:- Let the length of a rectangle = X m And the width of a rectangle =  Y m Then, the area of a rectangle = X Y m square. If its length is doubled and breadth is tripled.   (according to the question) Then, The length of the rectangle = 2 X m And the width of the rectangle = 3 Y m Then, the  new area of the rectangle = 2 X x 3 Y = 6 X Y m square. More area = 6 X Y – X Y = 5 X Y m square The area of a rectangle will be 5 times more the area of old rectangle. If its length is doubled and breadth is tripled? Anurag Mishra Professor Answered on 27th July 2015.

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# [LeetCode][Java] Reverse Nodes in k-Group ## 题目： Given a linked list, reverse the nodes of a linked list k at a time and return its modified list. If the number of nodes is not a multiple of k then left-out nodes in the end should remain as it is. You may not alter the values in the nodes, only nodes itself may be changed. Only constant memory is allowed. For example, Given this linked list: 1->2->3->4->5 For k = 2, you should return: 2->1->4->3->5 For k = 3, you should return: 3->2->1->4->5 ## 题意： Given this linked list: 1->2->3->4->5 For k = 2, you should return: 2->1->4->3->5 For k = 3, you should return: 3->2->1->4->5 ## AC代码： /** * public class ListNode { * int val; * ListNode next; * ListNode(int x) { val = x; } * } */ public class Solution { public ListNode reverseKGroup(ListNode head, int k) { int startindex=1; int endindex=k; int ki=0; int Allk=0; int kk=0; { kk++; } Allk=kk/k; while(ki<Allk) { ki++; startindex+=k; endindex+=k; } } public static ListNode reverseBetween(ListNode head, int m, int n) { return null; ListNode dummy = new ListNode(0); ListNode preNode = dummy; int i=1; while(preNode.next!=null && i<m) { preNode = preNode.next; i++; } //if(i<m) ListNode mNode = preNode.next; ListNode cur = mNode.next; while(cur!=null && i<n) { ListNode next = cur.next; cur.next = preNode.next; preNode.next = cur; mNode.next = next; cur = next; i++; } return dummy.next; } } • 本文已收录于以下专栏： ## 面试题三：使用 java 实现单向链表的倒置 • hhooong • 2016年04月05日 16:35 • 1198 ## （Java）LeetCode-25. Reverse Nodes in k-Group Given a linked list, reverse the nodes of a linked list k at a time and return its modified list. ... • u012848330 • 2016年06月02日 22:06 • 511 ## 【Leetcode】【python】Reverse Nodes in k-Group • qqxx6661 • 2017年09月05日 09:00 • 115 ## LeetCode解题报告--Reverse Nodes in k-Group • github_27609763 • 2015年10月17日 23:48 • 575 ## [LeetCode]Reverse Nodes in k-Group, 解题报告 • zinss26914 • 2014年02月08日 15:51 • 1712 ## Reverse Nodes in k-Group -- LeetCode • linhuanmars • 2014年02月26日 06:27 • 11220 ## [leetcode] 25. Reverse Nodes in k-Group 解题报告 • qq508618087 • 2016年01月08日 10:51 • 435 ## [LeetCode] 025. Reverse Nodes in k-Group (Hard) (C++/Java) [LeetCode] 025. Reverse Nodes in k-Group (Hard) (C++/Java) • hcbbt • 2015年03月05日 15:04 • 2754 ## python写算法题：leetcode: 25. Reverse Nodes in k-Group https://leetcode.com/problems/reverse-nodes-in-k-group/#/description class Solution(object): ... • lzf_china • 2017年06月29日 21:29 • 86 ## LeetCode 25: Reverse Nodes in k-Group Given a linked list, reverse the nodes of a linked list k at a time and return its modified list. I... • sunao2002002 • 2015年06月08日 20:00 • 3676 举报原因： 您举报文章：[LeetCode][Java] Reverse Nodes in k-Group 色情 政治 抄袭 广告 招聘 骂人 其他 (最多只允许输入30个字)

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Warning This section not yet updated for Inkscape v0.92. ## Color Filter Primitives Two Filter primitives allow the manipulation of colors. Warning This section not yet updated for Inkscape v0.92. ### Color Matrix The Color Matrix primitive maps each RGB and Alpha value to a new value. The transformation is described by a 5 × 5 matrix with the bottom row fixed, thus a general transformation is described by a 5 × 4 matrix. The fifth column adds a value that is independent of RGB or Alpha, allowing for nonlinear color correction. Four types of transformations are defined, of which three are special classes of the first. • Matrix: The full 5 × 4 matrix is defined. This is the most general case. • Saturate: The saturation is reduced by specifying one number, s. The range of s is 0.0 (completely desaturated) to 1.0 (unchanged). Only the RGB values are changed. The exact formula is: • R' = (0.213 + 0.787s)R + 0.715 × (1 − s)G + 0.072 × (1 − s)B; • G' = 0.213 × (1 − s)R + (0.715 + 0.285s)G + 0.072 × (1 − s)B; • B' = 0.213 × (1 − s)R + 0.715 × (1 − s)G + (0.072 + 0.928s)B. • Hue Rotate: The hue is shifted by specifying one number. Like the Saturate case, only RGB values are changed. The exact formula is quite complicated. It is not just a red to yellow to green and so on rotation. • Luminance to Alpha: The luminance is converted to Alpha via a fixed formula: Alpha = 0.2125 × R + 0.7154 × G + 0.0721 × B (from ITU-R Recommendation BT709, the HDTV color standard). Examples of using the Color Matrix primitive. From top to bottom: Source object. Matrix mode set to swap red and blue. Saturate mode with input of 0.5. Hue Rotate mode with input of 90°. Luminance to Alpha mode. A negative can be made by setting the RGB diagonal matrix elements (a00, a11, a22) to −1.00 and the top three elements of the fifth column (a04, a14, a24) to 1.00. Creation of a negative using the Matrix mode. Warning This section not yet updated for Inkscape v0.92. ### Component Transfer Partially implemented, No user interface. The Component Transfer primitive changes the RGB and Alpha of an object by applying independent functions to each of the RGB and Alpha input values. The following modes for defining the functions are available: Identity, Table, Discrete, Linear, and Gamma.

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Web Results Square Prism | Define Square Prism at Dictionary.com dictionary.reference.com/browse/Square Prism The world's most popular free online dictionary with definitions, spell check, word origins, example sentences, audio pronunciations, Word of the Day and more! ## Prism (geometry) - Wikipedia en.wikipedia.org/wiki/Prism_(geometry) In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base ... Some texts may apply the term rectangular prism or square prism to both a right rectangular-sided prism a... ## Square Prism: Definition & Examples - Video & Lesson Transcript ... In this lesson, learn what prisms are and what makes square prisms unique. Included are a few examples of square prisms and the qualities that make... ## Square Prism | Square Prism Examples | Math@TutorVista.com math.tutorvista.com/geometry/square-prism.html Square Prism Definition. Back to Top. They are the solid figures having two identical bases that are joined together through flat lateral faces and having same ... ## Prisms with Examples - Math is Fun www.mathsisfun.com/geometry/prisms.html A prism is a polyhedron, which means all faces are flat! No curved sides. For example, a ... (yes, a cube is a prism, because it is a square all along its length) ## Geometry Nets - Square Prism - Kidzone www.kidzone.ws/math/geometry/nets/squareprism.htm A cube and a square prism are both special types of a rectangular prism. ... Explore the square prism by cutting out the geometry net, folding it and gluing the  ... ## Square prisms and pyramids - Math Central - Centrale des maths mathcentral.uregina.ca/qq/database/qq.09.08/h/sheyna1.html search. Question from Sheyna, a student: What are the differences between a square prism and a pyramid? - Sheyna ( Please answer I really need this ). Thanks ... ## Square Prism - definition of Square Prism by The Free Dictionary www.thefreedictionary.com/Square Prism Anatomy A tarsal bone on the outer side of the foot in front of the calcaneus and behind the fourth and fifth metatarsal bones. 2. Mathematics A rectangular ... ## Mathwords: Right Square Prism www.mathwords.com/r/right_square_prism.htm ... opposite faces that are squares. It can also be described as a right prism with square bases. A right square prism which has square lateral surfaces is a cube. ## Prism definition - Math Open Reference www.mathopenref.com/prism.html Definition and properties of a prism, showing it to be solid with two congruent parallel faces, and where any cross section parallel to those faces is congruent to  ...

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# A Comprehensive Introduction to Differential Geometry by Michael Spivak PDF By Michael Spivak Publication through Michael Spivak, Spivak, Michael Best differential geometry books Read e-book online The Principle of Least Action in Geometry and Dynamics PDF New variational tools through Aubry, Mather, and Mane, found within the final two decades, gave deep perception into the dynamics of convex Lagrangian platforms. This booklet indicates how this precept of Least motion seems in quite a few settings (billiards, size spectrum, Hofer geometry, sleek symplectic geometry). New PDF release: Topology of Fibre Bundles (Princeton Mathematical Series) Fibre bundles, a vital part of differential geometry, also are very important to physics. this article, a succint advent to fibre bundles, contains such themes as differentiable manifolds and overlaying areas. It presents short surveys of complex subject matters, resembling homotopy conception and cohomology thought, ahead of utilizing them to check additional houses of fibre bundles. Download PDF by Muller R.: Differential Harnack inequalities and the Ricci flow In 2002, Grisha Perelman offered a brand new form of differential Harnack inequality which contains either the (adjoint) linear warmth equation and the Ricci circulate. This ended in a very new method of the Ricci circulate that allowed interpretation as a gradient movement which maximizes diverse entropy functionals. Additional info for A Comprehensive Introduction to Differential Geometry Sample text 5) O ~ Der(F V,A) h*> Der (F ,A) ~ HOmFv((VF) ab,A) Since A is in derivation tion d' : G V vanishes on VG , thus giving rise to a deriva- since A is in ~ Der(G,A) VMod__Fv , we have h* : Der(F V,A) -T Der(F,A) This implies that both homomorphisms Since f' Corollary that every ~ A . 5) are monomorphic. 5) is monomorphic. 5) we conclude that ker f~ = V(GI,A) Ji' : Fi ~ FV @9 V(G2,A) have left inverses (see 55 both split. 6). 7. In this s e c t i o n we considering the with . Thus V S i n c e the c W ~ H 2 (F,A)) e V ( G 2,A) isomorphism this c o m p l e t e s , is c l e a r l y Exact shall d e d u c e sequence let an e x a c t V(-,-) V ¢ W and and induced by the the proof. 4). 2) can be c o n t i n u e d to the right) We o b t a i n , Ext-sequence. To prove this, let that that proof d' (x) = d' ( x ) - I f ( x ) - d ' (y)" ( f ( x ) ) - l ] - f ( x ) - f ( y ) fl(x)"fl(Y) fl two homomorphisms shows The : ~ G fl . Then = It , x then induces inducing ~ and ~ = f l ( x ) " (f(x)) -I of. 3 and ~ . Conversely, e induces is t h u s then the f,fi:G calculation a derivation complete. 4). 4. 10) [e] (see with then construct exact the e x a c t (sx) a function , set. 216-217). the c o h o m o l o g y [57], a function by . e. lll). 11) A = A[E] A ) ~ > ZQ ® G I G associated .

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# PSAT Math : How to find the slope of perpendicular lines ## Example Questions ← Previous 1 ### Example Question #1 : How To Find The Slope Of Perpendicular Lines Two points on line m are (3,7) and (-2, 5).  Line k is perpendicular to line m.  What is the slope of line k? 2/5 0 3 -5 -5/2 -5/2 Explanation: The slope of line m is the (y2 - y1) / (x- x1) = (5-7) / (-2 - 3) = -2 / -5 = 2/5 To find the slope of a line perpendicular to a given line, we must take the negative reciprocal of the slope of the given line. Thus the slope of line k is the negative reciprocal of 2/5 (slope of line m), which is -5/2. ### Example Question #2 : How To Find The Slope Of Perpendicular Lines The equation of a line is: 8x + 16y = 48 What is the slope of a line that runs perpendicular to that line? -2 -1/8 -1/4 8 2 2 Explanation: First, solve for the equation of the line in the form of y = mx + b so that you can determine the slope, m of the line: 8x + 16y = 48 16y = -8x + 48 y = -(8/16)x + 48/16 y = -(1/2)x + 3 Therefore the slope (or m) = -1/2 The slope of a perpendicular line is the negative inverse of the slope. m = - (-2/1) = 2 ### Example Question #61 : Lines What is the equation of a line perpendicular to the one above, passing through the point ? Explanation: Looking at the graph, we can tell the slope of the line is 3 with a -intercept of , so the equation of the line is: A perpendicular line to this would have a slope of , and would pass through the point  so it follows: ### Example Question #4 : How To Find The Slope Of Perpendicular Lines Line M passes through the points (2,2) and (3,–5).  Which of the following is perpendicular to line M? y = 7x + 4 y = –(1/7)x – 1 y = (1/7)x + 3 y = –7x – 5 y = 7x – 6 y = (1/7)x + 3 Explanation: First we find the slope of line M by using the slope formula (y– y1)/(x– x1). (–5 – 2)/(3 – 2) = –7/1. This means the slope of Line M is –7.  A line perpendicular to Line M will have a negative reciprocal slope. Thus, the answer is = (1/7)x + 3. ### Example Question #5 : How To Find The Slope Of Perpendicular Lines Figure not drawn to scale. In the figure above, a circle is centered at point C and a line is tangent to the circle at point B. What is the equation of the line? Explanation: We know that the line passes through point B, but we must calculate its slope in order to find the equation that defines the line. Because the line is tangent to the circle, it must make a right angle with the radius of the circle at point B. Therefore, the slope of the line is perpendicular to the slope of the radius that connects the center of the circle to point B. First, we can find the slope of the radius, and then we can determine the perpendicular slope. The radius passes through points C and B. We can use the formula for the slope (represented as ) between two points to find the slope of the radius. Point C: (2,-5) and point B: (7,-3) This is the slope of the radius, but we need to find the slope of the line that is perpendicular to the radius. This value will be equal to the negative reciprocal. Now we know the slope of the tangent line. We can use the point-slope formula to find the equation of the line. The formula is shown below. Plug in the give point that lies on the tangent line (point B) and simplify the equation. Multiply both sides by two in order to remove the fraction. Distribute both sides. Add to both sides. Subtract six from both sides. The answer is . ### Example Question #51 : Geometry Solve the equation for x and y. x² + y = 31 x + y = 11 x = 6, 15 y = 5, –4 x = 8, –6 y = 13, 7 x = 5, –4 y = 6, 15 x = 13, 7 y = 8, –6 x = 5, –4 y = 6, 15 Explanation: Solving the equation follows the same system as the first problem. However since x is squared in this problem we will have two possible solutions for each unknown. Again substitute y=11-x and solve from there. Hence, x2+11-x=31. So x2-x=20. 5 squared is 25, minus 5 is 20. Now we know 5 is one of our solutions. Then we must solve for the second solution which is -4. -4 squared is 16 and 16 –(-4) is 20. The last step is to solve for y for the two possible solutions of x. We get 15 and 6. The graph below illustrates to solutions. ### Example Question #1 : How To Find The Slope Of Perpendicular Lines Solve the equation for x and y. x² – y = 96 x + y = 14 x = 25, 4 y = 10, –11 x = 10, –11 y = 25, 4 x = 15, 8 y = 5, –14 x = 5, –14 y = 15, 8 x = 10, –11 y = 25, 4 Explanation: This problem is very similar to number 2. Derive y=14-x and solve from there. The graph below illustrates the solution. ### Example Question #2 : How To Find The Slope Of Perpendicular Lines Solve the equation for x and y. 5x² + y = 20 x² + 2y = 10 No solution x = 14, 5 = 4, 6 x = √4/5, 7 = √3/10, 4 x = √10/3, –√10/3 y = 10/3 x = √10/3, –√10/3 y = 10/3 Explanation: The problem involves the same method used for the rest of the practice set. However since the x is squared we will have multiple solutions. Solve this one in the same way as number 2. However be careful to notice that the y value is the same for both x values. The graph below illustrates the solution. ### Example Question #3 : How To Find The Slope Of Perpendicular Lines Solve the equation for x and y. x² + y = 60 x – y = 50 x = –40, –61 y = 10, –11 x = 10, –11 y = –40, –61 x = 40, 61 y = 11, –10 x = 11, –10 y = 40, 61 x = 10, –11 y = –40, –61 Explanation: This is a system of equations problem with an x squared, to be solved just like the rest of the problem set. Two solutions are required due to the x2. The graph below illustrates those solutions. ### Example Question #4 : How To Find The Slope Of Perpendicular Lines A line passes through the points and . What is the equation for the line? None of the available answers Explanation: First we will calculate the slope as follows: And our equation for a line is Now we need to calculate b. We can pick either of the points given and solve for Our equation for the line becomes ← Previous 1

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Cody # Problem 44490. Vector pop Solution 1417385 Submitted on 15 Jan 2018 by tzhai asor This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass filetext = fileread('pop.m'); assert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden') 2   Pass v = [1, 2, 7]; n = 0; [v, w] = pop(v, n); v_correct = [1, 2, 7]; assert(isequal(v, v_correct)); assert(isempty(w)); 3   Pass v = 1:10; n = 3; [v, w] = pop(v, n); v_correct = 1:7; w_correct = 8:10; assert(isequal(v, v_correct)); assert(isequal(w, w_correct)); 4   Pass v = [1; 2; 3] n = 5; [v, w] = pop(v, n); w_correct = [1; 2; 3]; assert(isempty(v)); assert(isequal(w, w_correct)); v = 1 2 3 5   Pass v = ones(10, 1); n = 4; [v, w] = pop(v, n); v_correct = ones(6, 1); w_correct = ones(4, 1); assert(isequal(v, v_correct)); assert(isequal(w, w_correct)); 6   Pass v = zeros(1, 8); n = 2; [v, w] = pop(v, n); v_correct = zeros(1, 6); w_correct = zeros(1, 2); assert(isequal(v, v_correct)); assert(isequal(w, w_correct));

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# Find a solution of the system • May 28th 2011, 01:22 PM jay1 Find a solution of the system I need help please finding the solution of this ststem: 3x-7y= 72 and 2x-6y= -18 Also, would this be a consistent or inconsistent system? Thanks for any help... • May 28th 2011, 01:25 PM Plato Quote: Originally Posted by jay1 I need help please finding the solution of this ststem: 3x-7y= 72 and 2x-6y= -18 Also, would this be a consistent or inconsistent system? Thanks for any help... Multiply the first by 6 and the second by -7 then add.

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# Vector and matrix with R ## Vector and matrix with R > url_to_open [1] "http://finviz.com/export.ashx?v=152&c=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68" > summary(finviz) X..DOCTYPE.html. \t\t\t                <td><img src=/img/elite/no.png srcset=/img/elite/no_2x.png 2x alt=No></td>   : 24 \t\t                </tr>                                                                         : 18 \t\t                <tr>                                                                          : 18 </div>                                                                          : 15 </div>                                                                      : 12 \t\t\t                <td><img src=/img/elite/yes.png srcset=/img/elite/yes_2x.png 2x alt=Yes></td>:  8 (Other)                                                                                         :356 > clean_numeric <- function(s){ +     s <- gsub("%|\\\$|,|\\)|\\(", "", s) +     s <- as.numeric(s) + } > finviz <- cbind(finviz[,1:6],apply(finviz[,7:68], 2, +                                    clean_numeric)) Error in `[.data.frame`(finviz, , 1:6) : undefined columns selected > finviz <- cbind(finviz[,1:6],apply(finviz[,7:68], 2, +                                    clean_numeric)) Error in `[.data.frame`(finviz, , 1:6) : undefined columns selected > hist(finviz\$Price, breaks=100, main="Price Distribution", +      xlab="Price") Error in hist.default(finviz\$Price, breaks = 100, main = "Price Distribution",  : 'x' must be numeric > industry_avg_prices <- +     aggregate(Price~Sector+Industry,data=finviz,FUN="mean") > url <- +     paste("http://sports.yahoo.com/nfl/stats/byteam?group=Offense& + cat=Total&conference=NFL&year=season_",year,"&sort=530&old_category=Total&old_group=Offense") Error in paste("http://sports.yahoo.com/nfl/stats/byteam?group=Offense&\ncat=Total&conference=NFL&year=season_",  : > sector_avg <- +     subset(sector_avg,variable%in%c("Price","P.E","PEG","P.S","P.B")) Error in subset(sector_avg, variable %in% c("Price", "P.E", "PEG", "P.S",  : > a <- c(1, 2, 5, 3, 6, -2, 4) > b <- c("one", "two", "three") > c <- c(TRUE, TRUE, TRUE, FALSE, TRUE, FALSE) > a <- c(1, 2, 5, 3, 6, -2, 4) > a[3] [1] 5 > a[c(1, 3, 5)] [1] 1 5 6 > a[2:6] [1]  2  5  3  6 -2 > myymatrix <- matrix(vector, nrow=number_of_rows, ncol=number_of_columns,byrow=logical_value, dimnames=list( + char_vector_rownames, char_vector_colnames)) Error in as.vector(x, mode) : cannot coerce type 'closure' to vector of type 'any' > y <- matrix(1:20, nrow=5, ncol=4) > M <- matrix(1:20, nrow = 5, ncol = 4) > y [,1] [,2] [,3] [,4] [1,]    1    6   11   16 [2,]    2    7   12   17 [3,]    3    8   13   18 [4,]    4    9   14   19 [5,]    5   10   15   20 > x<-pretty(c(-5,5),30) > k<-dnorm(x) x<-pretty(c(-5,5),30) k<-dnorm(x) Error: unexpected symbol in "x<-pretty(c(-5,5),30) k" 1: In doTryCatch(return(expr), name, parentenv, handler) : "klab" is not a graphical parameter 2: In doTryCatch(return(expr), name, parentenv, handler) : "kaxs" is not a graphical parameter 3: In doTryCatch(return(expr), name, parentenv, handler) : "klab" is not a graphical parameter 4: In doTryCatch(return(expr), name, parentenv, handler) : "kaxs" is not a graphical parameter > x<-pretty(c(-5,5),30) >  y<-dnorm(x) > plot(x,y,type ="1",xlab="Normal Daviate",ylab= "Density",yaxs='i') Error in plot.xy(xy, type, ...) : invalid plot type '1' > x <- pretty(c(-3,3), 30) > y <- dnorm(x) > plot(x, y, +      type = "l", +      xlab = "Normal Deviate", +      ylab = "Density", +      yaxs = "i" + ) > plot(x,y,type ="l",xlab="Normal Daviate",ylab= "Density",yaxs='i') > pnorm(1.96) [1] 0.9750021 > lm(mpg~wt, data=mtcars) Call: lm(formula = mpg ~ wt, data = mtcars) Coefficients: (Intercept)           wt 37.285       -5.344 > lmfit <- lm(mpg~wt, data=mtcars) > summary(lmfit) Call: lm(formula = mpg ~ wt, data = mtcars) Residuals: Min      1Q  Median      3Q     Max -4.5432 -2.3647 -0.1252  1.4096  6.8727 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept)  37.2851     1.8776  19.858  < 2e-16 *** wt           -5.3445     0.5591  -9.559 1.29e-10 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.046 on 30 degrees of freedom Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10 > plot(lmfit) Hit <Return> to see next plot: Hit <Return> to see next plot: Hit <Return> to see next plot: Hit <Return> to see next plot: > cook<-cooks.distance(lmfit) > plot(cook) > predict(lmfit, mynewdata) > help(lm) > library("vcd", lib.loc="~/R/win-library/3.6") > a <- c(1, 2, 5, 3, 6, -2, 4) > b <- c("one", "two", "three") > c <- c(TRUE, TRUE, TRUE, FALSE, TRUE, FALSE) > a[3] [1] 5 > a[c(1, 3, 5)] [1] 1 5 6 > a[2:6] [1]  2  5  3  6 -2 > myymatrix <- matrix(vector, nrow=number_of_rows, ncol=number_of_columns,byrow=logical_value, dimnames=list( + char_vector_rownames, char_vector_colnames)) Error in as.vector(x, mode) : cannot coerce type 'closure' to vector of type 'any' > y <- matrix(1:20, nrow=5, ncol=4) > y [,1] [,2] [,3] [,4] [1,]    1    6   11   16 [2,]    2    7   12   17 [3,]    3    8   13   18 [4,]    4    9   14   19 [5,]    5   10   15   20 > cells <- c(1,26,24,68) > rnames <- c("R1", "R2")                                 cnames <- c("C1", "C2") Error: unexpected symbol in "rnames <- c("R1", "R2")                                 cnames" > rnames <- c("R1", "R2") >  cnames <- c("C1", "C2") > mymatrix <- matrix(cells, nrow=2, ncol=2, byrow=TRUE, +                    dimnames=list(rnames, cnames)) > mymatrix C1 C2 R1  1 26 R2 24 68 > mymatrix <- matrix(cells, nrow=2, ncol=2, byrow=FALSE, +                    dimnames=list(rnames, cnames)) > mymatrix C1 C2 R1  1 24 R2 26 68 > > x <- matrix(1:10, nrow=2) > x [,1] [,2] [,3] [,4] [,5] [1,]    1    3    5    7    9 [2,]    2    4    6    8   10 > x[2,] [1]  2  4  6  8 10 > x[,2] [1] 3 4 > x[,4] [1] 7 8 > x[1,4] [1] 7 > x[1, c(4,5)] [1] 7 9 > myarray <- array(vector, dimensions, dimnames) Error in as.vector(x, mode) : cannot coerce type 'closure' to vector of type 'any' > dim1 <- c("A1", "A2") >  dim2 <- c("B1", "B2", "B3") >  dim3 <- c("C1", "C2", "C3", "C4") > z <- array(1:24, c(2, 3, 4), dimnames=list(dim1, dim2, dim3)) > z , , C1 B1 B2 B3 A1  1  3  5 A2  2  4  6 , , C2 B1 B2 B3 A1  7  9 11 A2  8 10 12 , , C3 B1 B2 B3 A1 13 15 17 A2 14 16 18 , , C4 B1 B2 B3 A1 19 21 23 A2 20 22 24 > patientID <- c(1, 2, 3, 4) >  age <- c(25, 34, 28, 52) >  diabetes <- c("Type1", "Type2", "Type1", "Type1") >  status <- c("Poor", "Improved", "Excellent", "Poor") > patientdata <-data.frame(patientID, age,diabetes,status) > patientdata patientID age diabetes    status 1         1  25    Type1      Poor 2         2  34    Type2  Improved 3         3  28    Type1 Excellent 4         4  52    Type1      Poor > patientdata[1,2] [1] 25 > patientdata[1:2] patientID age 1         1  25 2         2  34 3         3  28 4         4  52 > patientdata[c("diabetes", "status")] diabetes    status 1    Type1      Poor 2    Type2  Improved 3    Type1 Excellent 4    Type1      Poor > patientdata\$age [1] 25 34 28 52 > table(patientdata\$diabetes, patientdata\$status) Excellent Improved Poor Type1         1        0    2 Type2         0        1    0 > attach(mtcars) The following object is masked from package:ggplot2: mpg > summary(mpg) Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 10.40   15.43   19.20   20.09   22.80   33.90 > plot(mpg, disp) > plot(mpg, wt) > detach(mtcars) dnorm(x = 3, mean = 2, sd = 5) [1] 0.07820854 > pnorm(q = 3, mean = 2, sd = 5) [1] 0.5792597 > qnorm(p = 0.975, mean = 2, sd = 5) [1] 11.79982 > rnorm(n = 10, mean = 2, sd = 5) [1]  8.725094 -2.190330  2.573350 -7.649668 [5]  6.420524  2.465019  4.561855 -8.622215 [9]  7.883495  5.382970 > dbinom(x = 6, size = 10, prob = 0.75) [1] 0.145998 > capt_crisp = data.frame(weight = c(15.5, 16.2, 16.1, 15.8, 15.6, 16.0, 15.8, 15.9, 16.2)) > x_bar = mean(capt_crisp\$weight) > s = sd(capt_crisp\$weight) > mu_0 = 16 > n=9 > t = (x_bar - mu_0) / (s / sqrt(n)) > t [1] -1.2 > pt(t, df = n - 1) [1] 0.1322336 > t.test(x = capt_crisp\$weight, mu = 16, alternative = c("less"), conf.level = 0.95) One Sample t-test data:  capt_crisp\$weight t = -1.2, df = 8, p-value = 0.1322 alternative hypothesis: true mean is less than 16 95 percent confidence interval: -Inf 16.05496 sample estimates: mean of x 15.9 > capt_test_results = t.test(capt_crisp\$weight, mu = 16,alternative = c("two.sided"), conf.level = 0.95) > names(capt_test_results) [1] "statistic"   "parameter"   "p.value" [4] "conf.int"    "estimate"    "null.value" [7] "stderr"      "alternative" "method" [10] "data.name" > capt_test_results\$conf.int [1] 15.70783 16.09217 attr(,"conf.level") [1] 0.95 > qt(0.975, df = 8) [1] 2.306004 > c(mean(capt_crisp\$weight) - qt(0.975, df = 8) * sd(capt_crisp\$weight) / sqrt(9), +   mean(capt_crisp\$weight) + qt(0.975, df = 8) * sd(capt_crisp\$weight) / sqrt(9)) [1] 15.70783 16.09217 > x = c(70, 82, 78, 74, 94, 82) > x [1] 70 82 78 74 94 82 > n = length(x) > n [1] 6 > y = c(64, 72, 60, 76, 72, 80, 84, 68) > y [1] 64 72 60 76 72 80 84 68 > x_bar = mean(x) > s_x = sd(x) > y_bar = mean(y) > s_y = sd(y) > s_p = sqrt(((n - 1) * s_x ^ 2 + (m - 1) * s_y ^ 2) / (n + m - 2)) > t = ((x_bar - y_bar) - 0) / (s_p * sqrt(1 / n + 1 / m)) > 1 - pt(t, df = n + m - 2) Error in pt(t, df = n + m - 2) : object 'm' not found > t.test(x, y, alternative = c("greater"), var.equal = TRUE) Two Sample t-test data:  x and y t = 1.8234, df = 12, p-value = 0.04662 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 0.1802451       Inf sample estimates: mean of x mean of y 80        72 > t_test_data = data.frame(values = c(x, y),group = c(rep("A", length(x)), rep("B", length(y)))) > t_test_data values group 1      70     A 2      82     A 3      78     A 4      74     A 5      94     A 6      82     A 7      64     B 8      72     B 9      60     B 10     76     B 11     72     B 12     80     B 13     84     B 14     68     B > t.test(values ~ group, data = t_test_data,alternative = c("greater"), var.equal = TRUE) Two Sample t-test data:  values by group t = 1.8234, df = 12, p-value = 0.04662 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 0.1802451       Inf sample estimates: mean in group A mean in group B 80              72 > pnorm(2, mean = 1, sd = sqrt(0.32)) - pnorm(0, mean = 1, sd = sqrt(0.32)) [1] 0.9229001 > set.seed(42) > num_samples = 10000 > differences = rep(0, num_samples) > for (s in 1:num_samples) { +     x1 = rnorm(n = 25, mean = 6, sd = 2) +     x2 = rnorm(n = 25, mean = 5, sd = 2) +     differences[s] = mean(x1) - mean(x2) + } > mean(0 < differences & differences < 2) [1] 0.9222 > hist(differences, breaks = 20, +      main = "Empirical Distribution of D", +      xlab = "Simulated Values of D", +      col = "dodgerblue", +      border = "darkorange") > mean(differences) [1] 1.001423 > var(differences) [1] 0.3230183 > set.seed(42) > diffs = replicate(10000, mean(rnorm(25, 6, 2)) - mean(rnorm(25, 5, 2))) > mean(differences == diffs) [1] 1 > set.seed(1337) > mu = 10 > sample_size = 50 > samples = 100000 > x_bars = rep(0, samples) > for(i in 1:samples){ +     x_bars[i] = mean(rpois(sample_size, lambda = mu)) + } > x_bar_hist = hist(x_bars, breaks = 50, +                   main = "Histogram of Sample Means", +                   xlab = "Sample Means") > c(mean(x_bars), mu) [1] 10.00008 10.00000 > c(var(x_bars), mu / sample_size) [1] 0.1989732 0.2000000 > c(sd(x_bars), sqrt(mu) / sqrt(sample_size)) [1] 0.4460641 0.4472136 > mean(x_bars > mu - 2 * sqrt(mu) / sqrt(sample_size) & +          x_bars < mu + 2 * sqrt(mu) / sqrt(sample_size)) [1] 0.95429 > shading = ifelse(x_bar_hist\$breaks > mu - 2 * sqrt(mu) / sqrt(sample_size) & +                      x_bar_hist\$breaks < mu + 2 * sqrt(mu) / sqrt(sample_size), +                  "darkorange", "dodgerblue") > x_bar_hist = hist(x_bars, breaks = 50, col = shading,main = "Histogram of Sample Means, Two Standard Deviations", +                   xlab = "Sample Means") > View(cars) > str(cars) 'data.frame': 50 obs. of  2 variables: \$ speed: num  4 4 7 7 8 9 10 10 10 11 ... \$ dist : num  2 10 4 22 16 10 18 26 34 17 ... > dim(cars) [1] 50  2 > nrow(cars) [1] 50 > ncol(cars) [1] 2 > plot(dist ~ speed, data = cars, +      xlab = "Speed (in Miles Per Hour)", +      ylab = "Stopping Distance (in Feet)", main = "Stopping Distance vs Speed", +      pch = 20, +      cex = 2, +      col = "grey") > x = cars\$speed > y = cars\$dist > Sxy = sum((x - mean(x)) * (y - mean(y))) > Sxx = sum((x - mean(x)) ^ 2) > Syy = sum((y - mean(y)) ^ 2) > c(Sxy, Sxx, Syy) [1]  5387.40  1370.00 32538.98 > beta_1_hat = Sxy / Sxx > beta_0_hat = mean(y) - beta_1_hat * mean(x) > c(beta_0_hat, beta_1_hat) [1] -17.579095   3.932409 > library("ggplot2", lib.loc="~/R/win-library/3.6") > c(1, 3, 5, 7, 8, 9) [1] 1 3 5 7 8 9 > x=c(1, 3, 5, 7, 8, 9) > x [1] 1 3 5 7 8 9 > c(42, "Statistics", TRUE) [1] "42"         "Statistics" "TRUE" > c(42, TRUE) [1] 42  1 > (y = 1:100) [1]   1   2   3   4   5   6   7   8   9  10 [11]  11  12  13  14  15  16  17  18  19  20 [21]  21  22  23  24  25  26  27  28  29  30 [31]  31  32  33  34  35  36  37  38  39  40 [41]  41  42  43  44  45  46  47  48  49  50 [51]  51  52  53  54  55  56  57  58  59  60 [61]  61  62  63  64  65  66  67  68  69  70 [71]  71  72  73  74  75  76  77  78  79  80 [81]  81  82  83  84  85  86  87  88  89  90 [91]  91  92  93  94  95  96  97  98  99 100 > seq(from = 1.5, to = 4.2, by = 0.1) [1] 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 [11] 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 [21] 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 > x = 1:9 > rev(x) [1] 9 8 7 6 5 4 3 2 1 > rbind(x,rev(x),rep(1,9)) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] x    1    2    3    4    5    6    7    8    9 9    8    7    6    5    4    3    2    1 1    1    1    1    1    1    1    1    1 > cbind(col_1=x,col_2=rev(x),col_3=rep(1,9)) col_1 col_2 col_3 [1,]     1     9     1 [2,]     2     8     1 [3,]     3     7     1 [4,]     4     6     1 [5,]     5     5     1 [6,]     6     4     1 [7,]     7     3     1 [8,]     8     2     1 [9,]     9     1     1 > x = 1:9 > y=9:1 > X=matrix(x,3,3) > Y=matrix(y,3,3) > X [,1] [,2] [,3] [1,]    1    4    7 [2,]    2    5    8 [3,]    3    6    9 > Y [,1] [,2] [,3] [1,]    9    6    3 [2,]    8    5    2 [3,]    7    4    1 > X+Y [,1] [,2] [,3] [1,]   10   10   10 [2,]   10   10   10 [3,]   10   10   10 > X-Y [,1] [,2] [,3] [1,]   -8   -2    4 [2,]   -6    0    6 [3,]   -4    2    8 > X*Y [,1] [,2] [,3] [1,]    9   24   21 [2,]   16   25   16 [3,]   21   24    9 > Y*X [,1] [,2] [,3] [1,]    9   24   21 [2,]   16   25   16 [3,]   21   24    9 > X/Y [,1]      [,2]     [,3] [1,] 0.1111111 0.6666667 2.333333 [2,] 0.2500000 1.0000000 4.000000 [3,] 0.4285714 1.5000000 9.000000 > Y/X [,1]      [,2]      [,3] [1,] 9.000000 1.5000000 0.4285714 [2,] 4.000000 1.0000000 0.2500000 [3,] 2.333333 0.6666667 0.1111111 > X~Y X ~ Y > X %*% Y [,1] [,2] [,3] [1,]   90   54   18 [2,]  114   69   24 [3,]  138   84   30 > t [1] -1.2 > t(X) [,1] [,2] [,3] [1,]    1    2    3 [2,]    4    5    6 [3,]    7    8    9 > t(Y) [,1] [,2] [,3] [1,]    9    8    7 [2,]    6    5    4 [3,]    3    2    1 > t(X)X Error: unexpected symbol in "t(X)X" > t(X)*X [,1] [,2] [,3] [1,]    1    8   21 [2,]    8   25   48 [3,]   21   48   81 > diag(1) [,1] [1,]    1 > diag(2) [,1] [,2] [1,]    1    0 [2,]    0    1 > diag(3) [,1] [,2] [,3] [1,]    1    0    0 [2,]    0    1    0 [3,]    0    0    1 > diag(4) [,1] [,2] [,3] [,4] [1,]    1    0    0    0 [2,]    0    1    0    0 [3,]    0    0    1    0 [4,]    0    0    0    1 > diag(9) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,]    1    0    0    0    0    0    0 [2,]    0    1    0    0    0    0    0 [3,]    0    0    1    0    0    0    0 [4,]    0    0    0    1    0    0    0 [5,]    0    0    0    0    1    0    0 [6,]    0    0    0    0    0    1    0 [7,]    0    0    0    0    0    0    1 [8,]    0    0    0    0    0    0    0 [9,]    0    0    0    0    0    0    0 [,8] [,9] [1,]    0    0 [2,]    0    0 [3,]    0    0 [4,]    0    0 [5,]    0    0 [6,]    0    0 [7,]    0    0 [8,]    1    0 [9,]    0    1 > diag(1:5) [,1] [,2] [,3] [,4] [,5] [1,]    1    0    0    0    0 [2,]    0    2    0    0    0 [3,]    0    0    3    0    0 [4,]    0    0    0    4    0 [5,]    0    0    0    0    5 > x = cars\$speed > y = cars\$dist > Sxy = sum((x - mean(x)) * (y - mean(y))) > Sxx = sum((x - mean(x)) ^ 2) > Syy = sum((y - mean(y)) ^ 2) > c(Sxy, Sxx, Syy) [1]  5387.40  1370.00 32538.98 > beta_1_hat = Sxy / Sxx > beta_0_hat = mean(y) - beta_1_hat * mean(x) > c(beta_0_hat, beta_1_hat) [1] -17.579095   3.932409 ```#creat vectors> #(0.1^3 0.2^1,0.1^6 0.2^4.....,0.1^36 0.2^34 ) > (0.1^seq(3,36,by=3))*(0.2^seq(1,34,by=3)) [1] 2.000000e-04 1.600000e-09 1.280000e-14 [4] 1.024000e-19 8.192000e-25 6.553600e-30 [7] 5.242880e-35 4.194304e-40 3.355443e-45 [10] 2.684355e-50 2.147484e-55 1.717987e-60 > #(2,2^2/2,2^3/3,......,2^25/25) > (2^(1:25))/(1:25) [1] 2.000000e+00 2.000000e+00 2.666667e+00 [4] 4.000000e+00 6.400000e+00 1.066667e+01 [7] 1.828571e+01 3.200000e+01 5.688889e+01 [10] 1.024000e+02 1.861818e+02 3.413333e+02 [13] 6.301538e+02 1.170286e+03 2.184533e+03 [16] 4.096000e+03 7.710118e+03 1.456356e+04 [19] 2.759411e+04 5.242880e+04 9.986438e+04 [22] 1.906502e+05 3.647221e+05 6.990507e+05 [25] 1.342177e+06 > #sum > # > #(i^3+4i^2) where i=10:100 > mohi<-10:100 > sum(mohi^3+4*mohi^2) [1] 26852735 > rj<-1:25 > sum((2^rj)/rj+3*rj/(rj^2)) [1] 2807618 > #Function paste to create > #("label 1","label 2".......,"label 30") > paste("label",1:30) [1] "label 1" "label 2" "label 3" "label 4" [5] "label 5" "label 6" "label 7" "label 8" [9] "label 9" "label 10" "label 11" "label 12" [13] "label 13" "label 14" "label 15" "label 16" [17] "label 17" "label 18" "label 19" "label 20" [21] "label 21" "label 22" "label 23" "label 24" [25] "label 25" "label 26" "label 27" "label 28" [29] "label 29" "label 30" > #("fn1","fn2",....,"fn30") > paste("fn",1:30,sep="") [1] "fn1" "fn2" "fn3" "fn4" "fn5" "fn6" [7] "fn7" "fn8" "fn9" "fn10" "fn11" "fn12" [13] "fn13" "fn14" "fn15" "fn16" "fn17" "fn18" [19] "fn19" "fn20" "fn21" "fn22" "fn23" "fn24" [25] "fn25" "fn26" "fn27" "fn28" "fn29" "fn30"``` Reactions

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A weighted empirical interpolation method: a priori convergence analysis and applications ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 4, p. 943-953 We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. DOI : https://doi.org/10.1051/m2an/2013128 Classification:  65C20,  65D05,  97N50 Keywords: empirical interpolation method, a priori convergence analysis, greedy algorithm, Kolmogorov N-width, geometric brownian motion, Karhunen-Loève expansion, reduced basis method @article{M2AN_2014__48_4_943_0, author = {Chen, Peng and Quarteroni, Alfio and Rozza, Gianluigi}, title = {A weighted empirical interpolation method: a priori convergence analysis and applications}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {48}, number = {4}, year = {2014}, pages = {943-953}, doi = {10.1051/m2an/2013128}, zbl = {1304.65097}, language = {en}, url = {http://www.numdam.org/item/M2AN_2014__48_4_943_0} } Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi. A weighted empirical interpolation method: a priori convergence analysis and applications. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 4, pp. 943-953. doi : 10.1051/m2an/2013128. http://www.numdam.org/item/M2AN_2014__48_4_943_0/ [1] M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. Anal. Numér. 339 (2004) 667-672. | MR 2103208 | Zbl 1061.65118 [2] R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica 10 (2001) 1-102. | MR 2009692 | Zbl 1105.65349 [3] P. Binev, A. Cohen, W. Dahmen, R. Devore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43 (2011) 1457-1472. | MR 2821591 | Zbl 1229.65193 [4] S. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 32 (2010) 2737-2764. | MR 2684735 | Zbl 1217.65169 [5] P. Chen and A. Quarteroni, Accurate and efficient evaluation of failure probability for partial differential equations with random input data. Comput. Methods Appl. Mech. Eng. 267 (2013) 233-260. | MR 3127301 | Zbl 1286.65156 [6] P. Chen, A. Quarteroni and G. Rozza, Comparison between reduced basis and stochastic collocation methods for elliptic problems. J. Sci. Comput. 59 (2014) 187-216. | MR 3167732 | Zbl 1301.65007 [7] P. Chen, A. Quarteroni and G. Rozza, A weighted reduced basis method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 51 (2013) 3163-3185. | MR 3129759 | Zbl 1288.65007 [8] R.A. Devore and G.G. Lorentz, Constructive Approximation. Springer (1993). | MR 1261635 | Zbl 0797.41016 [9] M.B. Giles and E. Süli, Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica 11 (2002) 145-236. | MR 2009374 | Zbl 1105.65350 [10] M.A. Grepl, Y. Maday, N.C. Nguyen and A.T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. ESAIM: M2AN 41 (2007) 575-605. | Numdam | MR 2355712 | Zbl 1142.65078 [11] T. Lassila, A. Manzoni and G. Rozza, On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition. ESAIM: M2AN 46 (2012) 1555-1576. | Numdam | MR 2996340 | Zbl 1276.65069 [12] T. Lassila and G. Rozza, Parametric free-form shape design with PDE models and reduced basis method. Comput. Methods Appl. Mech. Eng. 199 (2010) 1583-1592. | MR 2630164 | Zbl 1231.76245 [13] Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404. | MR 2449115 | Zbl 1184.65020 [14] A. Manzoni, A. Quarteroni and G. Rozza, Model reduction techniques for fast blood flow simulation in parametrized geometries. Int. J. Numer. Methods Biomedical Eng. 28 (2012) 604-625. | MR 2946552 [15] F. Nobile, R. Tempone and C.G. Webster, A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. 46 (2008) 2309-2345. | MR 2421037 | Zbl 1176.65137 [16] B. Øksendal, Stochastic Differential Equations: An Introduction with Applications. Springer (2010). | MR 1619188 | Zbl 0567.60055 [17] A. Pinkus, N-widths in Approximation Theory. Springer (1985). | MR 774404 | Zbl 0551.41001 [18] A. Quarteroni, G. Rozza and A. Manzoni, Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Industry 1 (2011) 1-49. | MR 2824231 | Zbl 1273.65148 [19] A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics. Springer (2007). | MR 2265914 | Zbl 1136.65001 [20] G. Rozza, Reduced basis methods for Stokes equations in domains with non-affine parameter dependence. Comput. Vis. Sci. 12 (2009) 23-35. | MR 2489209 [21] G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives Comput. Meth. Eng. 15 (2008) 229-275. | MR 2430350 | Zbl pre05344486 [22] K. Urban and B. Wieland, Affine decompositions of parametric stochastic processes for application within reduced basis methods. In Proc. MATHMOD, 7th Vienna International Conference on Mathematical Modelling (2012).

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# Math Talks: Linear Measurement Subject Resource Type Common Core Standards Product Rating File Type Compressed Zip File 14 MB|24 pages Share Product Description First graders make sense of their math world and numbers by talking about it! This packet gives your kids ways to talk purposefully about linear measurement and the measurement standards for K-2. Get your students comfortable with distinguishing between measureable and non-measureable attributes, matching linear measurement tools with objects, ordering lengths, non-standard measurement, using a ruler to measure, and finding mistakes in linear measurements based on good attributes of accurate measuring. Visit my blog for ideas on how I used this in my classroom. Included in this packet are slides with purposefully planned measurement talks to get K-2 kids talking about length, attributes and rules for measurement. There are multiple talks for each area...20 total measurement talks. Here are the categories addressed with these talks: • measureable attributes (2) • finding appropriate tools to measure length (2) • ordering length of 3 objects (2) • ordering height of 3 objects (2) • non-standard measurement using one or two units to compare (4) • standard measurement and estimation with rulers (4) • Find the Mistake (measurement examples addressing the following problems with linear measurement: gaps, overlaps, straightness of units, unit size) This product is available as an interactive powerpoint or pdf file. Plus, a main menu for easy navigation on each page! (Note: navigation links are only available in the PowerPoint file.) RELATED RESOURCES: Year Long Graphing Printables for K-2 More Math Skills Practice with Math Walls for the entire year! Print and Play Math Games RELATED VIDEOS: What Is A Math Talk? (Intro & Routines) Let's Connect: Total Pages 24 pages N/A Teaching Duration Lifelong tool Report this Resource Get this as part of a bundle: • Young learners make sense of their math world and numbers by talking about it! Math Talks give your kids ways to talk purposefully about nu \$3.75

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https://www.fsdeveloper.com/wiki/index.php/RefPoint_parameter_performance_influences

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# RefPoint parameter performance influences The RefPoint of your scenery object has two parameters that can have a big influence on the performance, if they are used incorrect. In this tutorial it will be explained what these parameters do and how you can use them to get the best performance out of your scenery. v1 value The first of these two parameters is the v1 value. The usage of this parameter is rather simple. It is the range in which your object will be visible. So if the distance from the RefPoint of your aircraft to the RefPoint of the scenery object is bigger then the value given for the v1, the object will not be displayed. So the v1 value can be used to make sure that some object will display from further away, while other objects will only be shown when you are closer (for example small objects, that are not noticeable from further away). For the best performance you should make sure that the v1 value is not bigger then needed. v2 value But only the v1 value is not enough to control the display of your object in an optimal way. Imagine that you have just flown over your object and it is now behind you. Then the distance from your aircraft to the object is probably still smaller then the v1 value, but it should not be displayed anymore. This is where the v2 comes in. This is basically the radius of your object. When the object is behind you, but you are still within the radius of the v2 value from the RefPoint it will still be displayed. While the v2 value is often called a radius it is a rectangle in theory. To get the best performance you should always make the v2 as small as possible. That means it should be just big enough to let your entire object fit in it. If used in a macro that can take any rotation, this means that the smallest v2 value that can be used is equal to: v2 = (x_max^2 + y_max^2)^0.5 where x_max and y_max are the maximum coordinates that are used in your object. If you make the v2 value too small, then the object will dissapear when part of it should still be visible (the RefPoint of the object is behind you and you are futher from it then the v2 value, but part of the object is located further away from the RefPoint and thus still visible). This only happens from certain angles and the best fix it to increase the v2 value. So, to get the best performance you must always use the minimum v2 value. When I optimized my EHAM scenery I did this and the result was some extra frames! When you are lazy, just like me, you will probably forget to enter the v2 value when you are placing a macro. In that case it might be a good idea to hardcode the value in the macro. Then you can never forget to enter it.

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https://avatest.org/2023/02/20/stochastic-porcesses-daixie-ma53200-strong-markov-consistency-of-fellermarkov-families/

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Posted on Categories:Stochastic Porcesses, 数学代写, 随机过程 # 数学代写|随机过程Stochastic Porcesses代考|MA53200 Strong Markov Consistency of Feller–Markov Families avatest™ ## avatest™帮您通过考试 avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！ •最快12小时交付 •200+ 英语母语导师 •70分以下全额退款 ## 数学代写|随机过程代写Stochastic Porcesses代考|Strong Markov Consistency of Feller–Markov Families We can conduct a more comprehensive study of strong Markov consistency in the case of time-homogeneous Feller-Markov families. In particular, we can prove in this case that, for each $j \in{1, \ldots, d}$, the strong $j$ th coordinate and the weak $j$ th coordinate of an $\mathcal{M} \mathcal{M} \mathcal{F H}$ that is strongly Markovian consistent with respect to $X^j$ are $\mathbb{R}$-Feller-Markov families. In the time-inhomogeneous case an analogous property was assumed rather than proved (cf. Propositions $2.21$ and 2.22). Definition $2.23$ Let $$\mathcal{M} \mathcal{M} \mathcal{F H}=\left{\left(\Omega, \mathcal{F}, \mathbb{F},\left(X_t\right)_{t \geq 0}, \mathbb{P}_x, P\right): x \in \mathbb{R}^n\right}$$ be a time-homogeneous Markov family. For all $t \geq 0$ we define an operator $T_t$ on $C_0\left(\mathbb{R}^n\right)$ by $$T_t u(x)=\mathbb{E}x u\left(X_t\right)=\int{\mathbb{R}^n} u(y) P(x, t, d y), \quad x \in \mathbb{R}^n .$$ If $\left(T_t, t \geq 0\right)$ is a $C_0\left(\mathbb{R}^n\right)$-Feller semigroup then $\mathcal{M M} \mathcal{F H}$ is called a $\mathbb{R}^n$-FellerMarkov family. If, in addition, $C_c^{\infty}\left(\mathbb{R}^n\right) \subseteq D(A)$, where $A$ is the generator of $\left(T_t, t \geq\right.$ 0 ), then the family $\mathcal{M} \mathcal{M} \mathcal{F H}$ is called a nice $\mathbb{R}^n$-Feller-Markov family. ## 数学代写|随机过程代写Stochastic Porcesses代考|Definition and Characterization of Strong Markov Consistency We begin with the specification of Definition $2.15$ to the present case of Markov chains. Definition 3.1 1. Let us fix $i \in{1, \ldots, n}$. We say that the Markov chain $X=$ $\left(X^1, \ldots, X^n\right)$ satisfies the strong Markov consistency condition with respect to the coordinate $X^i$ if, for every $B \subset \mathcal{X}i$ and all $t, s \geq 0$, $$\mathbb{P}\left(X{t+s}^i \in B \mid \mathcal{F}t^X\right)=\mathbb{P}\left(X{t+s}^i \in B \mid X_t^i\right), \quad \mathbb{P} \text {-a.s., }$$ or, equivalently, $$\mathbb{P}\left(X_{t+s}^i \in B \mid X_t\right)=\mathbb{P}\left(X_{t+s}^i \in B \mid X_t^i\right), \quad \mathbb{P} \text {-a.s., }$$ so that $X^i$ is a Markov chain in the filtration of $X$, i.e. in the filtration $\mathbb{F}^X$. 1. If $X$ satisfies the strong Markov consistency condition with respect to $X^i$ for each $i \in{1, \ldots, n}$ then we say that $X$ satisfies the strong Markov consistency condition. ## 数学代写|随机过程代写Stochastic Porcesses代考|Strong Markov Consistency of Feller-Markov Families \left 缺少或无法识别的分隔符 $$T_t u(x)=\mathbb{E} x u\left(X_t\right)=\int \mathbb{R}^n u(y) P(x, t, d y), \quad x \in \mathbb{R}^n$$ ## 数学代写随机过程代写Stochastic Porcesses代考|Definition and Characterization of Strong Markov Consistency 1. 如果 $X$ 唡是强妳可夫一致生条件 $X^i$ 每个 $i \in 1, \ldots, n$ 然扁我1说 $X$ 满足强尔可夫一致生 条件。 ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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http://exelisvis.com/docs/VOIGT.html

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Welcome to the Harris Geospatial product documentation center. Here you will find reference guides, help documents, and product libraries.  ### VOIGT VOIGT The VOIGT function returns the value of the classical Voigt function, H(a, u), defined in terms of the Voigt damping parameter a and the frequency offset u: The dimensionless frequency offset u and the damping parameter a are determined by: where ν0 is the line center frequency and the Doppler width ΔνD (assuming no turbulence), is defined as: and, Γ is the transition rate: where γ is the spontaneous decay rate, and νcol is the atomic collision rate. (See Radiative Processes in Astrophysics by G. B. Rybicki and A. P. Lightman (1979) p. 291 for more information.) The Voigt function can be used to compute the intensity of an atomic absorption line profile (also known as a VOIGT profile). The line profile φ(a, u) is defined as: The algorithm is from Armstrong, JQSRT 7, 85. (1967). The definition of the classical Voigt function H(a,u) can be found in Equation 7.4.13 of Abramowitz, M. and Stegun, I.A., 1964, Handbook of Mathematical Functions (Washington:National Bureau of Standards). ## Syntax Result = VOIGT(A, U) ## Return Value If both arguments are scalars, the function returns a scalar. If both arguments are arrays, the function matches up the corresponding elements of A and U, returning an array with the same dimensions as the smallest array. If one argument is a scalar and the other argument is an array, the function uses the scalar value with each element of the array, and returns an array with the same dimensions as the smallest input array. If A is double-precision, the result is double-precision, otherwise the result is single-precision. ## Arguments ### A A scalar or array specifying the values for the Voigt damping parameter. ### U A scalar or array specifying the values for the dimensionless frequency offset in Doppler widths. ## Keywords This routine is written to make use of IDL’s thread pool, which can increase execution speed on systems with multiple CPUs. The values stored in the !CPU system variable control whether IDL uses the thread pool for a given computation. In addition, you can use the thread pool keywords TPOOL_MAX_ELTS, TPOOL_MIN_ELTS, and TPOOL_NOTHREAD to override the defaults established by !CPU for a single invocation of this routine. See Thread Pool Keywords for details. ## Version History Pre-4.0 Introduced

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1 You visited us 1 times! Enjoying our articles? Unlock Full Access! Question # The digit of a two digit number differ by 3. If the digits are interchange and the resulting number is added to the original number we get 143. What can be the original number? Open in App Solution ## Dear student the video cant be added in this section sorry for the inconvinience.the answer is provided with an example for more understandings.check this you will get the answer thank you, Let us assume, the x is the tenth place digit (for example x=3 in the two digit number 32) and y is the unit place digit of the two-digit number(for example y=2 in the two digit number 32). Also assume x > y Therefore, the two-digit number is 10x + y(310+2=32) and reversed number is 10y + x(210+3=23); Given that The digit of a two digit number differ by 3, it can be written as: x - y = 3.....................(1) Also given the digits are interchange and the resulting number is added to the original number we get 143, it can be written as: 10x + y + 10y + x = 143 11x + 11y = 143 x + y = 13 ...............(2) Adding equation (1) and equation (2) ; then we get 2x = 16 x = 8 then the value of x is put in equation (1),we get; y = x - 3 = 8 - 3 = 5 Therefore, the two-digit number = 10x + y = (10 8) + 5 = 85 Suggest Corrections 122 Join BYJU'S Learning Program Related Videos Substitution MATHEMATICS Watch in App Explore more Join BYJU'S Learning Program

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http://heli-air.net/2016/02/28/the-performance-of-a-blade-element/

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# The performance of a blade element Consider an element, of length 6r and chord c, at radius r of an airscrew blade. This element has a speed in the plane of rotation of Qr. The flow is itself rotating in the same plane and sense at Ш, and thus the speed of the element relative to the air in this plane is flr(l — b). If the airscrew is advancing at a speed of F the velocity through the disc is F(1 + a), a being the inflow at the radius r. Note that in this theory it is not necessary for a and b to be constant over the disc. Then the total velocity of the flow relative to the blade is Fr as shown in Fig. 9.9. If the line CC’ represents the zero-lift line of the blade section then в is, by definition, the geometric helix angle of the element, related to the geometric pitch, and a is the absolute angle of incidence of the section. The element will therefore experience lift and drag forces, respectively perpendicular and parallel to the relative velocity Fr, appropriate to the absolute incidence a. The values of Cl and Co will be those for a two-dimensional aerofoil of the appropriate section at absolute incidence a, since three-dimensional effects have been allowed for in the rotational interference term, MI. This lift and drag may be resolved into components of thrust and ‘torque-force’ as in Fig. 9.9. Here SL is the lift and 6D is the drag on the element. <57? is the resultant aerodynamic force, making the angle 7 with the lift vector. 6R is resolved into components of thrust 6T and torque force SQ/r, where SQ is the torque required to rotate the element about the airscrew axis. Then tan7 = SD/SL = CD/CL (9.24) Fr = F(1 + a)cosec = flr(l — Ь)ъесф (9.25) ST = <57?cos( + 7) (9.26) Щ – = SRsin( The efficiency of the element, 771, is the ratio, useful power out/power input, i. e. VST V cos (<ft + 7) ^1 Si SQ Sir sin(</> + 7) Now from the triangle of velocities, and Eqn (9.28): whence, by Eqn (9.29): 1—6 tan ф 1 + a tan(ф + y) (9.30) *71 Let the solidity of the annulus, <7, be defined as the ratio of the total area of blade in annulus to the total area of annulus. Then From Fig. 9.9 ST = SL cos ф – SD sin ф — BcSr^pV{CLcosф – C£isin^) Therefore whence, using Eqn (9.32a and b) = 2nr2a^pV^(C£ sin^ + Co cos ф) Writing now q=CL sin{ф + i) (9.36) leads to — m^aqpV^ total (9.37a) l 9 = Bcr -^pV^q total (9.37b) l, — cr-pV^q per blade (9.37c) The quantities dT/dr and dQ/dr are known as the thrust grading and the torque grading respectively. Consider now the axial momentum of the flow through the annulus. The thrust ST is equal to the product of the rate of mass flow through the element with the change in the axial velocity, i. e. ST = mSV. Now m = area of annulus x velocity through annulus x density = (27rr<5r)[F(l + a)p = livrpSr V(l + a) AV = Vs – V = V(1 + 2a) – V = 2aV whence ST = 2TrrpSrV22a(l + a) giving d T 2 /1 — = 47rprV2a(l + a) Equating Eqn (9.38) and (9.35a) and using also Eqn (9.25), leads to: 4nprV2a(l +a) = nrcrtpV2(l + a)2 cosec2 ф whence a l 2j ■ =-at cosec ф (9.38) (9.39) l + a 4 In the same way, by considering the angular momentum SQ = mAwr1 where Aw is the change in angular velocity of the air on passing through the airscrew. Then SQ = (2irr8r)pV{ + a)(2bQ)r2 = 47rr3pF6(l + a)Q6r ^ = 4nr3pVb(l + a)Q,8 Now, as derived previously, ^ = 7ГPvqpVl (Eqn (9.37a)) Substituting for FR both expressions of Eqn (9.25), this becomes = m^trplVfi + fl)cosec0][I2r(l — b) sec^ Equating this expression for dQ/dr to that of Eqn (9.41) gives after manipulation 61 / , ——— = – crq cosec ф sec ф 1 — b 4 = ^aq cosec 2ф The local efficiency of the blade at the element, r? i, is found as follows. (SlT Useful power output = V ST = F—<5r Power input – 2xn SQ 2-717? Sr Therefore F dT/dr ^ 27Г7І dQ/dr V 2жra pVt 2жп 2тггга jpV^q V t 2mr q which is an alternative expression to Eqn (9.30). With the expressions given above, dT/dr and dQ/dr may be evaluated at several radii of an airscrew blade given the blade geometry and section characteristics, the forward and rotational speeds, and the air density. Then, by plotting dT/dr and dQjdr against the radius r and measuring the areas under the curves, the total thrust and torque per blade and for the whole airscrew may be estimated. In the design of a blade this is the usual first step. With the thrust and torque gradings known, the deflection and twist of the blade under load can be calculated. This furnishes new values of 9 along the blade, and the process is repeated with these new values of 9. The iteration may be repeated until the desired accuracy is attained. A further point to be noted is that portions of the blade towards the tip may attain appreciable Mach numbers, large enough for the effects of compressibility to become important. The principal effect of compressibility in this connection is its effect on the lift-curve slope of the aerofoil section. Provided the Mach number of the relative flow does not exceed about 0.75, the effect on the lift-curve slope may be approximated by the Prandtl-Glauert correction (see Section 6.8.2). This correction states that, if the lift curve slope at zero Mach number, i. e. in incompressible flow, is ao the lift-curve slope at a subsonic Mach number M is ам where ao VI – M2 Provided the Mach number does not exceed about 0.75 as stated above, the effect of compressibility on the section drag is very small. If the Mach number of any part of the blade exceeds the value given above, although the exact value depends on the profile and thickness/chord ratio of the blade section, that part of the blade loses lift while its drag rises sharply, leading to a very marked loss in overall efficiency and increase in noise. Example 9.5 At 1.25m radius on a 4-bladed airscrew of 3.5m diameter the local chord of each of the blades is 250 mm and the geometric pitch is 4.4 m. The lift-curve slope of the blade section in incompressible flow is 0.1 per degree, and the lift/drag ratio may, as an approxima­tion, be taken to be constant at 50. Estimate the thrust and torque gradings and the local efficiency in flight at 4600m (cr = 0.629, temperature = —14.7°С), at a flight speed of 67ms-1 TAS and a rotational speed of 1500rpm. The solution of this problem is essentially a process of successive approximation to the values of a and b. Be 4×0.25 solidity a = -— = ——— —r-r = 0.1273 2 2-кг 27ГХІ.25 1500 rpm = 25rps = n tan7 = — whence 7=1.15° Suitable values for initial guesses for a and b are a = 0.1, b = 0.02. Then итф = 0.3418^ = 0.383 и. Уо ф = 20.93°, a = 29.3 – 20.93 = 8.37° Kr V(l +a) cosec ф V(l + a) _ 67 x 1.1 sin<£ 0.357 M = ^ = 0-635, Vl-M2 = 0.773 = = °’1295 Per degree da 0.773 Since a is the absolute incidence, i. e. the incidence from zero lift: CL = a^ = 0.1295 x 8.37 = 1.083 da Then q= Cz, sin(0 + 7) = 1.083 sin(20.93 + 1.15)° =0.408 t = Cz, cos(0 + 7) = 1.083 cos 22.08° = 1.004 giving , 0.0384 „ b = – = 0.0371 1.0384 a 1 2j 0.1274x 1.004 —— = – at cosecІф = -—_ — = 0.2515 1 + a 4 Y 4 x 0.357 x 0.357 giving 0.2515 л a= ,-=0.336 Thus the assumed values a = 0.1 and b = 0.02 lead to the better approximations a = 0.336 and b = 0.0371, and a further iteration may be made using these values of a and b. A rather quicker approach to the final values of a and b may be made by using, as the initial values for an iteration, the arithmetic mean of the input and output values of the previous iteration. Thus, in the present example, the values for the next iteration would be a = 0.218 and b = 0.0286. The use of the arithmetic mean is particularly convenient when giving instructions to computers (whether human or electronic). The iteration process is continued until agreement to the desired accuracy is obtained between the assumed and derived values of a and b. The results of the iterations were: a = 0.1950 b = 0.0296 to four significant figures. With these values for a and b substituted in the appropriate equations, the following results are obtained: ф = 22°48′ a = 6°28′ KR = 207 ms-‘ M = 0.640 giving = i;pVlcl = 3167Nm 1 per blade dr 2 K and = ^pV^crq = 1758 N mm 1 per blade Thus the thrust grading for the whole airscrew is 12 670Nm_1 and the torque grading is 7032 N mm-1. The local efficiency is – = 0.768 or 76.8% 2nnr q

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Home > Standard Error > Variance Standard Deviation Error # Variance Standard Deviation Error ## Contents The change that would be important or significant depends on the standard error of the mean and the sampling distribution of the means. Hot Network Questions Dozens of earthworms came on my terrace and died there Coveo - online index rebuild? This website features the best explanation of the Multirule ("Westgard Rules") and how to use them. We will discuss confidence intervals in more detail in a subsequent Statistics Note. navigate here Notice that s x ¯   = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} is only an estimate of the true standard error, σ x ¯   = σ n Treasure hunt of the century Quicker and quieter than a mouse, what am I? How to restrict InterpolatingFunction to a smaller domain? EdD Assistant ProfessorClinical Laboratory Science Program University of LouisvilleLouisville, KentuckyJune 1999 A simulated experiment Calculation of the mean of a sample (and related statistical terminology) Scores, Mean, Deviation scores First moment, ## Standard Error Formula Exercise Try it yourself! In this scenario, the 400 patients are a sample of all patients who may be treated with the drug. If your data are normally distributed, around 67% of your results should fall within your mean, plus or minus your standard deviation, and 95% of your results should fall within two The relationship between standard deviation and standard error can be understood by the below formula From the above formula Standard deviation (s) = Standard Error * √n Variance = s2 The This situation can be demonstrated or simulated by recording the 2000 values on separate slips of paper and placing them in a large container. Sampling distribution of the means. Standard Error Symbol Note: The Student's probability distribution is a good approximation of the Gaussian when the sample size is over 100. To some that sounds kind of miraculous given that you've calculated this from one sample. Standard Error Regression Consider a sample of n=16 runners selected at random from the 9,732. It will be shown that the standard deviation of all possible sample means of size n=16 is equal to the population standard deviation, σ, divided by the square root of the Standard deviation (s) = Standard Error * √n = 20.31 x √9 = 20.31 x 3 s = 60.93 variance = σ2 = 60.932 = 3712.46 For more information for dispersion My only comment was that, once you've already chosen to introduce the concept of consistency (a technical concept), there's no use in mis-characterizing it in the name of making the answer Standard Error Definition When their standard error decreases to 0 as the sample size increases the estimators are consistent which in most cases happens because the standard error goes to 0 as we see I edited my post in reaction to your comment thanks. In estimating the central location of a group of test results, one could attempt to measure the entire population or to estimate the population parameters from a smaller sample. ## Standard Error Regression y <- replicate( 10000, mean( rnorm(n, m, s) ) ) # standard deviation of those means sd(y) # calcuation of theoretical standard error s / sqrt(n) You'll find that those last The second use of the SS is to determine the standard deviation. Standard Error Formula Standard Deviation of Sample Mean -1 Under what circomstances the sample standard error is likely to equal population standard deviation? 3 Why do we rely on the standard error? -3 What Standard Error Excel The distribution of the mean age in all possible samples is called the sampling distribution of the mean. Cambridge, England: Cambridge University Press, 1992. check over here The margin of error and the confidence interval are based on a quantitative measure of uncertainty: the standard error. As with the standard deviation, the standard error will generally be automatically calculated by your statistical package. Let's calculate the mean for these twelve "mean of 100" samples, treating them mathematically much the same as the prior example that illustrated the calculation of an individual mean of 100 Standard Error Calculator These properties are important in common applications of statistics in the laboratory. Blood specimens could be drawn from all 2000 patients and analyzed for glucose, for example. For the purpose of this example, the 9,732 runners who completed the 2012 run are the entire population of interest. his comment is here If it is large, it means that you could have obtained a totally different estimate if you had drawn another sample. About the author: Madelon F. Standard Error Of Proportion This is also a reference source for quality requirements, including CLIA requirements for analytical quality. Sending a stranger's CV to HR My 21 yr old adult son hates me Why was Vader surprised that Obi-Wan's body disappeared? ## Indeed, if you had had another sample, $\tilde{\mathbf{x}}$, you would have ended up with another estimate, $\hat{\theta}(\tilde{\mathbf{x}})$. The sample mean x ¯ {\displaystyle {\bar {x}}} = 37.25 is greater than the true population mean μ {\displaystyle \mu } = 33.88 years. A review of 88 articles published in 2002 found that 12 (14%) failed to identify which measure of dispersion was reported (and three failed to report any measure of variability).4 The Express it mathematically. Standard Error In R Average sample SDs from a symmetrical distribution around the population variance, and the mean SD will be low, with low N. –Harvey Motulsky Nov 29 '12 at 3:32 add a comment| The standard deviation of the age for the 16 runners is 10.23, which is somewhat greater than the true population standard deviation σ = 9.27 years. If enough experiments could be performed and the means of all possible samples could be calculated and plotted in a frequency polygon, the graph would show a normal distribution. But its standard error going to zero isn't a consequence of (or equivalent to) the fact that it is consistent, which is what your answer says. –Macro Jul 15 '12 at http://tenableinfo.net/standard-error/variance-standard-deviation-standard-error.html First moment. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. The significance of an individual difference can be assessed by comparing the individual value to the distribution of means observed for the group of laboratories. Referenced on Wolfram|Alpha: Standard Error CITE THIS AS: Weisstein, Eric W. "Standard Error." From MathWorld--A Wolfram Web Resource. Reference: CR Rao (1973) Linear Statistical Inference and its Applications 2nd Ed, John Wiley & Sons, NY share|improve this answer edited Jun 17 '15 at 17:16 answered Jun 17 '15 at Laboratorians tend to calculate the SD from a memorized formula, without making much note of the terms. Following the prior pattern, the variance can be calculated from the SS and then the standard deviation from the variance. As the sample size increases, the sampling distribution become more narrow, and the standard error decreases. I hope your internet's working converting pdf pictures to png files makes pictures too small Remainder in polynomial division more hot questions question feed about us tour help blog chat data http://mathworld.wolfram.com/StandardError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Copyright © 2000-2016 StatsDirect Limited, all rights reserved. Using "están" vs "estás" when refering to "you" Flatten sublists within a bigger list How do really talented people in academia think about people who are less capable than them? Another way of considering the standard error is as a measure of the precision of the sample mean.The standard error of the sample mean depends on both the standard deviation and Extending JavaScript's built-in types - is it evil? The graph below shows the distribution of the sample means for 20,000 samples, where each sample is of size n=16. Changes in the method performance may cause the mean to shift the range of expected values, or cause the SD to expand the range of expected values. As a result, we need to use a distribution that takes into account that spread of possible σ's. Interquartile range is the difference between the 25th and 75th centiles. Column C shows the squared deviations which give a SS of 102. and Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. 187 ^ Zwillinger D. (1995), Standard Mathematical Tables and Formulae, Chapman&Hall/CRC. A medical research team tests a new drug to lower cholesterol. For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. For example, the sample mean is the usual estimator of a population mean.

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Ex 8.2 Chapter 8 Class 6 Decimals Serial order wise ### Transcript Ex 8.2, 3 Express as cm using decimals. (d) 9 cm 8 mm 9 cm 8 mm = 9 cm + 8 mm = 9 cm + 8 × 1 mm = 9 cm + 8 × 1/10 cm = 9 cm + 8/10 cm = ("9 + " 8/10)cm = ((9 × 10 + 8)/10) cm = ((90 + 8)/10) cm = 98/10 cm = 9.8 cm

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The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A084385 a(1) = 1; a(n+1) is the smallest number not occurring earlier and coprime to sum(j=1,n, a(j)). 3 1, 2, 4, 3, 7, 5, 9, 6, 8, 11, 13, 10, 12, 15, 17, 14, 16, 19, 21, 18, 20, 23, 25, 22, 24, 27, 29, 26, 28, 31, 33, 30, 32, 35, 37, 34, 36, 39, 41, 38, 40, 43, 45, 42, 44, 47, 49, 46, 48, 51, 53, 50, 52, 55, 57, 54, 56, 59, 61, 58, 60, 63, 65, 62, 64, 67, 69, 66, 68, 71, 73, 70 (list; graph; refs; listen; history; text; internal format) OFFSET 1,2 COMMENTS Rearrangement of the positive integers. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA For n > 6: a(n) = n - 2 for (n mod 4) = 0, a(n) = n - 1 for (n mod 4) = 1, a(n) = n + 1 for (n mod 4) = 2, a(n) = n + 2 for (n mod 4) = 3. - Klaus Brockhaus, Nov 30 2003. EXAMPLE 1+2+4 = 7, 3 is the smallest number not occurring earlier and coprime to 7, hence a(4) = 3. PROG (PARI) used(k, v)=b=0; j=1; while(b<1&&j<=length(v), if(v[j]==k, b=1, j++)); b {print1(s=1, ", "); v=[s]; for(n=1, 72, j=1; k=2; while(used(k, v)||gcd(k, s)>1, k++); v=concat(v, k); s=s+k; print1(k, ", "))} (PARI) {print1(1, ", ", 2, ", ", 4, ", ", 3, ", ", 7, ", ", 5, ", "); for(n=7, 73, m=n%4; d=(if(m==0, -2, if(m==1, -1, if(m==2, 1, 2)))); print1(n+d, ", "))} (Haskell) import Data.List (delete) a084385 n = a084385_list !! (n-1) a084385_list = 1 : f [2..] 1 where    f xs s = g xs where      g (y:ys) = if gcd s y == 1 then y : f (delete y xs) (s + y) else g ys -- Reinhard Zumkeller, Aug 15 2015 CROSSREFS Partial sums are in A111244. Cf. A064413. Cf. A261351 (inverse). Sequence in context: A215673 A120619 A346298 * A073885 A256283 A257465 Adjacent sequences:  A084382 A084383 A084384 * A084386 A084387 A084388 KEYWORD nonn AUTHOR Amarnath Murthy, May 29 2003 EXTENSIONS Edited, corrected and extended by Klaus Brockhaus, May 29 2003 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)

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Chapter 7 ## Neighborhood and Global Stewardship The citizens of the United States use more energy and resources per person than do people in other countries. What can we do to reduce our individual and collective impact on earth’s global system? On the pages that follow, we have described some actions taken by students to help solve environmental problems afflicting their communities. How much does your family recycle? Does your school have a recycling program? Individuals can make a big difference when they work together. The average American throws away 4.5 pounds of trash a day and pays about \$1.50/day to have it carted to a landfill. When you recycle one aluminum can, you save enough energy to operate a television set for three hours. You can help persuade others to join in waste reduction efforts by calculating how much you are saving in natural resources and family expenses. ## I. Waste Busters: Recycling at Home and at School Students from Peoria Elementary School with packages of used milk cartons.  Denver Schools are returning all their milk cartons to the Ex Cello Corp for reprocessing.  Photo by Bruce McAllister via Wikimedia Commons Students from all areas of the state of Washington have been collaborating with the Pacific Science Center to drastically reduce the amount of resources wasted in their State. They use the mathematics of recycling to help persuade families and schools that money and resources can be saved by everyone. Items which have been recycled in different areas of the country include newspaper, white and colored paper, cardboard, glass, aluminum and tin cans, motor oil, batteries, certain plastics, yard clippings, and Christmas trees. • How much household waste does your family generate in one week? In one year? Find out by weighing the family trash and garbage using a bathroom scale. • Start or expand the recycling you do at home. Start a compost area in your yard. Keep a record of the weights of the materials such as paper, plastic, glass, and aluminum you recycle so that you can calculate the resource savings later. Investigation Conduct a quantitative investigation of the effects of recycling on your community and the world. ## II. Another Look at Gaia The Gaia Model (click image to view larger version in a new window) Studying ecosystems is complicated and frustrating because many of the puzzle pieces are invisible and hard to measure. Global changes such as the atmospheric increase of carbon dioxide and the spread of DDT provide compelling reasons for cooperation in research and public education. When the Gaia hypothesis was first proposed many scientists were turned off by its poetic interpretation. The image of Gaia as a tremendous living organism living on the Earth and creating environmental conditions that would be beneficial for life seemed more like science fiction than science fact. As more ways in which living organisms modify the environment for their benefit have been discovered the Gaia concept has become more respectable. Also the original hypothesis has been modified. James Lovelock now explains the concept as follows: The physical systems of the Earth and the life on it have evolved together as a single, tightly interlocked system. He explains that through a series of feedback mechanisms this system operates to hold the temperature of the planet within a range that is more or less acceptable for the continuation of life as a whole. The Gaia hypothesis has been very useful in stimulating a new way of looking at and making models of natural systems. In studying your terrarium, have you noticed relationships within the system that help maintain life? The growth of plants, for example, can provide food and oxygen for small animals. The smaller an ecosystem is, the more vulnerable it is to outside influences and the less likely it will provide all the requirements for particular life cycles. Overpopulation of one organism may exceed the carrying capacity of the system and trigger rapid changes and loss of diversity. Question 7.1. What limitations and positive feedback responses have you identified that threaten the health of your terrarium system? Read the science fiction story below and describe your explanations for the stability of this distant planetary system. How does matter and energy flow through this imaginary system? ## III. Daisy World Report Bernard’s Star Planetary Mission: 30 Feb. 2297 From: Information Officer Janis II Hargrove Our mission to Bernard’s Star is now entering Year 2. As reported earlier, we have confirmed and extended the observations of Earth astronomers. There are seven planets and a multitude of asteroids orbiting this star. However, only the second planet, at an average distance of 96 million miles from the star, has an atmosphere that contains oxygen and harbors life. Daisy World, which is what we have taken to calling the planet, is extraordinarily like our Earth. Not only is the composition of its atmosphere almost identical, but its size, orbital distance, ratio of land to water and even its general climate is Earth-like. We have been able to work on the surface without life support systems. The “character” of the land surface is similar on all continents except right around the poles which are ice covered. The surface is mostly rolling hills almost completely covered with densely packed plants which constantly produce flowers resembling daisies. The daisy plants are quite amazing. The flower is 100 cm in diameter, and blooms all year. There are only two varieties, and they both grow quickly to a height of about 2 meters. The main difference between the two is in the color of the petals; one variety has black petals, the other has petals that are completely white. Near the equator the ground is covered with the white variety. In the polar regions the black plants dominate. In the temperate zones of both hemispheres, where the average temperature approaches 20° C, there is a mix of plants. We are at a loss to explain why this planet does not have the diversity of animal and plant species we have on Earth. Insect-like creatures seem to be the dominant animal life form, and we have found one that is definitely a carnivore! The climate seems to have remained nearly constant for a very long period. Preliminary studies of sedimentary rock layers indicate that they were formed under temperature conditions that have remained within a narrow range for thousands of years. This long-term stability of the climate is very puzzling because on our approach to Bernard’s star our astronomers discovered a vast cloud of dust in an irregular orbit around the star. At different periods it cuts down on the light to Daisy World for months at a time. When the space between Bernard’s star and Daisy World becomes completely clear of dust, the amount of light energy reaching the surface increases greatly. It is a mystery to us how the temperature could remain the same, since changes in the output of the central star cause great changes in the climate of the other planets we have explored. Question 7.2. What explanation do you have for the stable climate of Daisy World? Question 7.3. What negative feedback mechanisms may be operating on the planet? ## IV. People and the Biosphere Two hundred years ago, more than three-quarters of the world’s land area was in its natural condition, undeveloped, unmapped and mostly unexplored. As humans have begun to dominate the earth, entire ecosystems have been transformed and the composition of the atmosphere changed in the relatively short period of time. Experience so far suggests that for some time at least, our activities will continue to produce changes that may generate far reaching positive feedback responses. Throughout this unit, we have considered the characteristics of ecosystems and how they function. Evidence from numerous scientific studies reveals a long history of life on Earth, with the evolution of large numbers of species developing in a great variety of habitats. Each species has become adapted to a particular environment and a particular way of life. All the species in the biosphere interact with one another and the non living surroundings in a highly complex web of life that is linked by the recycling of nutrients, CO2, O2, water and minerals. What is clear is that our effects on the biosphere result from the collective daily activities of every human being. Some effects of these in the future can be predicted. It is hard to avoid the conclusion that in the long run the future of humans and the biosphere depends to a great extent on how many of us there are, how each of us lives from day to day, and how we collaborate in becoming better stewards of our environment. Humans have learned to survive the ice ages and the expansion of deserts. As a species, we are capable of tremendous adaptive changes in our behavior through education. Today we are faced with the challenge of forging a global effort to reduce human impact on the biosphere. Attitudes about pesticides and disposable containers have begun to change, and industry is beginning to provide materials that can be recycled and reused. Communities have begun to work together to protect and improve habitat for endangered species of plants and animals. We encourage you to look for other adaptive strategies that might help maintain Earth’s diverse ecosystems. Write A Letter to the Future Draw up a contract for yourself to reduce your impact on the biosphere by changing things you normally do. Leave a space for reporting your results 2 months from now. Date the contract and seal it in an envelope labeled “Impact”. Address the letter to yourself and put a stamp on it. Give the letter to your teacher, who will mail it to you in 2 months. ## V. The Global Commons The Gaia theory has shown us that the Earth is an interconnected planet in many ways. The many systems that regulate the flow of energy, carbon, oxygen and other nutrients throughout the planet are deeply interconnected. In a sense, we live in a Global Commons. Though we may live across the ocean from others or on the other side of the country, we share resources, breathe the same air and drink the same water. When the atmosphere has industrial pollutants or water is contaminated by sewage, it affects everyone eventually. There are many difficult issues connected with how Earth's wealth of life forms and environments are shared and conserved for future generations. The increase in carbon dioxide and other greenhouse gases due to human activity may cause global climate change in a relatively short period of time. Most animal and plant species require many generations to adapt to environmental changes. Through the process called "natural selection," genetic changes that improve an organism's "fitness" for surviving in the altered environment get passed on to the next generation. The offspring of the "better adapted" organisms survive in larger numbers and produce more offspring in successive generations. Eventually the genetic character of the species is dominated by the new and more successful traits suited to the new environment. The genetic characteristics of humans have also changed in this way over hundreds of thousands of years. But humans have prevailed as a dominant species mainly through their ability to adapt to new situations through learning. The process by which this adaptive behavior spreads among human populations is education, or in scientific terms, cultural evolution. For example, our modern knowledge of microorganisms has changed our systems of cooking, cleaning, washing, and using water for drinking. If the rate of environmental change is fast, as has been predicted by many scientists who are studying global climate data, then it is likely many species of plants and animals will become extinct. It is true that there have been many mass extinctions throughout the history of life on earth precipitated by events such as asteroid impacts and volcanic eruptions. Following each environmental change, Earth's surviving life forms have evolved new ways of surviving in the altered habitats. Humans have learned to survive the ice ages and the expansion of deserts. As a species, we are capable of tremendous adaptive changes in our behavior in the short time span of one generation. Today we are faced with the challenge of forging a global effort to reduce human impact on the biosphere. Attitudes about disposable containers have begun to change, and industry is beginning to provide materials that can be recycled and reused. Communities have begun to work together to protect and improve habitat for endangered species of plants and animals. We encourage you to look for other adaptive strategies that might help maintain Earth's biodiversity as we explore scientific research, history, sociology, economics, geography, and other topics related to the Global Commons. ## VI. Conclusion As we have seen in our study of ecosystems, they are complex systems that depend on many factors to maintain them in a state of balance. However, we have also seen the destructive effects of human activities on our world. We live together on the Earth with all plants and animals, each of which needs its place to survive. We can all survive on our world but we need to work together to form better solutions for all if we want the complex model known as Gaia to work in a way that will ensure the survival of all inhabitants of Planet Earth. For new material relating to this chapter, please see the GSS website “Staying Up To Date” page: http://www.globalsystemsscience.org/uptodate/ec/ch7 Subpages (1):

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Home # Discrete logarithms in cryptography and network security Discrete logarithms are fundamental to a number of public-key algorithms, including Diffie-Hellman key exchange and the digital signature algorithm (DSA). This section provides a brief overview of discrete logarithms. For the interested reader, more detailed developments of this topic can be found in [ORE67] and [LEVE90] Chapter: Cryptography and Network Security Principles and Practice - Asymmetric Ciphers - Introduction to Number Theory Discrete logarithms are fundamental to a number of public-key algorithms, includ- ing Diffie-Hellman key exchange and the digital signature algorithm (DSA) GATE Preparation, nptel video lecture dvd, electronics-and-communication-engineering, cryptography-and-network-security, discrete-logarithms, Network Services , Security Mechanisms, Security attacks, Open Systems Interconnection model, OSI security architecture, Network security model, security model, Classical Encryption techniques, Encryption techniques , Symmetric cipher model, transposition techniques , steganography, FINITE FIELDS AND NUMBER THEORY: , Groups , Rings , Fields, Modular. The discrete logarithm of u is sometimes referred to as the index of u. Aside from the intrinsic interest that the problem of computing discrete logarithms has, it is of considerable importance in cryptography. An efficient algorithm for discrete logarithms would make several authentication and key-exchange systems insecure. This paper briefly surveys (in Section 2) thes ### Section 8.5. Discrete Logarithms Cryptography and .. • The security of many real-world cryptographic schemes depends on the difficulty of computing discrete logarithms in large finite fields. This thesis is a survey of the discrete logarithm problem. • Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution • g that p is prime and a is a non-zero integer that is coprime to p • The mathematical challenge here lies in computing discrete logarithms in finite fields of type Zp, which consist of the integers modulo a large prime p. Services: Related Articles in ASCI: Similar Articles in this Journal: Search in Google Scholar: View Citation : Report Citation: Science Alert : How to cite this article: Kefa Rabah , 2005. Security of the Cryptographic Protocols Based on. terial. It introduces the public-key cryptography paradigm and also defines discrete logarithms and the discrete logarithm problem. Three widely used public-key cryptographic primitives which rely upon the difficulty of comput-ing discrete logarithms for their security are presented: the Diffie-Hellman ke which is based on the difficulty of computing discrete logarithms. RSA Digital Signature Algorithm: Based on the RSA public-key algorithm. Elliptic Curve Digital Signature Algorithm (ECDSA): Based on elliptic curve . cryptography. In this section, we provide a brief overview of the digital signature process, then describe the RSA digital signature algorithm. Elliptic-curve cryptography (ECC. Discrete logarithms are fundamental to a number of public-key algorithms. Discrete logarithms are analogous to ordinary logarithms, but operate over modular arithmetic. A number of concepts from number theory are essential in the design of public-key cryptographic algorithms IT2352 CRYPTOGRAPHY AND NETWORK SECURITY UNIT - III Dr.A.Kathirvel, Professor and Head, Dept of IT Anand Institute of Higher Technology, Chennai. 2. Unit - III Discrete Logarithms - Computing discrete logs - Diffie- Hellman key exchange - ElGamal Public key cryptosystems - Hash functions - Secure Hash - Birthday attacks - MD5 - Digital signatures -. 1. Behrouz A. Ferouzan, Cryptography & Network Security, Tata Mc Graw Hill, 2007. 2. Man Young Rhee, Internet Security: Cryptographic Principles, Algorithms and Protocols, Wiley Publications, 2003. 3. Charles Pfleeger, Security in Computing, 4th Edition, Prentice Hall of India, 2006. 4. Ulysess Black, Internet Security Protocols, Pearson Education Asia, 2000 Tabulation of Discrete Logarithms. 64 Cryptography & Network Security - Behrouz A. Forouzan. Using Properties of Discrete Logarithms. 9.6.2 Continued. The discrete logarithm problem has the same complexity as the factorization problem. Note. Using Algorithms Based on Discrete. 65 Cryptography & Network Security - Behrouz A. Forouzan . Asymmetric-Key Cryptography. 66 Cryptography & Network. Kun (2004) Batch Verification for Equality of Discrete Logarithms and Threshold Decryptions. In Jakobsson, M, Yung, M, & Zhou, J (Eds.) Applied Cryptography and Network Security Second. Practical Verifiable Encryption and Decryption of Discrete Logarithms have many useful applications in cryptography, including key escrow, optimistic fair exchange, pub-licly verifiable secret and signature sharing, universally composable commitments, group signatures, and confirmer signatures. One reason why this restriction is not really so excessive is because in the past few years. Discrete logarithms have a natural extension into the realm of elliptic curves and hyperelliptic curves. And Elliptic ElGamal has proved to be a strong cryptosystem using elliptic curves and discrete logarithms. In the next part of the chapter, we will take a look at the discrete logarithm problem and discuss its application to cryptography Select two primes ( p ,q ) Next , the n value is calculated . Thus : n = p x q = 11 x 3 = 33 Next PHI is calculated by : PHI = ( p - 1 )( q - 1 ) = 20 e selected so that GCD ( e ,PHI )= 1 Public key : (n ,e ) Author : Prof Bill Buchanan. Discrete logarithms within computer and network security ### Discrete Logarithms - BrainKar 1. This book constitutes the proceedings of the 15 th International Conference on Applied Cryptology and Network Security, ACNS 2017, held in Kanazawa, Japan, in July 2017. The 34 papers presented in this volume were carefully reviewed and selected from 149 submissions. The topics focus on innovative research and current developments that advance the areas of applied cryptography, security analysis, cyber security and privacy, data and server security 2. The discrete logarithm problem is to find a given only the integers c,e and M. e.g. without the modulus function, you could use log (c)/e = log (a), but the modular arithmetic prevents you using logarithms effectively. The discrete logarithm problem is interesting because it's used in public key cryptography (RSA and the like) 3. ElGamal encryption is an example of public-key or asymmetric cryptography. The cryptosystem takes its name from its founder the Egyptian cryptographer Taher Elgamal who introduced the system in his 1985 paper entitled A Public Key Cryptosystem and A Signature Scheme Based on Discrete Logarithms . As this title suggests the security of this cryptosystem is based on the notion of discrete logari 4. of algorithms to place an upper bound on the complexity of solving discrete logarithms given a group-specific precomputation. 15. NUMBER OF PAGES 71 14. SUBJECT TERMS Discrete Logarithms, Analysis of Algorithms, Advice Strings, Diffie-Hellman Key Exchange 16. PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT Unclassified 18. SECURITY. 5. Diffie-Hellman key exchange is a method of securely exchanging cryptographic keys over a public channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography. Published in 1976 by Diffie and Hellman, this is the earliest publicly known work that proposed the idea of a private key and a. 6. In cryptography, a discrete logarithm is the number of times a generator of a group must be multiplied by itself to produce a known number. By choosing certain groups, the task of finding a discrete logarithm can be made intractable. Many cryptographic primitives and protocols have security reductions to the discrete logarithm or related problems 7. 5 Discrete Logarithms 235 5.1 Basic Concepts 235 5.2 Baby-Step Giant-Step Method 237 5.3 Pohlig-Hellman Method 240 5.4 Index Calculus 246 5.5 Elliptic Curve Discrete Logarithms 251 5.6 Bibliographic Notes and Further Reading 260 References 261 Part III Modern Cryptography 6 Secret-Key Cryptography 265 6.1 Cryptography and Cryptanalysis 265 6.2 Classic Secret-Key Cryptography 277 6.3 Modern. This answer makes the claim that the Discrete Log problem and RSA are independent from a security perspective.. RSA labs makes a similar statement:. The discrete logarithm problem bears the same relation to these systems as factoring does to the RSA system: the security of these systems rests on the assumption that discrete logarithms are difficult to compute #RSA #RSAalgorithm #NetworkSecurity #Cryptography #abhics789This is the series of Cryptography and Network Security.In this video, i have explained the conce.. ### Cryptography And Network Security Discrete Logarithms Exam The Discrete Logarithm Problem (DLP) may be the first intractable computational number-theoretic problem to be considered for constructing cryptographic schemes by Diffie, Hellman and Merle at Stanford in 1976 and also by Ellis, Cocks and Williamson at the British GCHQ in 1970-1976 Recently, several algorithms using number field sieves have been given to factor a number nin heuristic expected time $L_n [1/3; c]$, where $L_n [ v ;c ] = \exp \left\{ ( c + o ( 1 ) ) ( \log n )^v ( \log \log n )^{1 - v } \right\}$ for $n \to \infty$. This paper presents an algorithm to solve the discrete logarithm problem for $GF ( p )$. 1. Identify & Resolve Gaps in Your Cybersecurity Strategy. Contact CDW for an Assessment. CDW Offers a Wide Array of Cybersecurity Solutions for Business. Learn More Today 2. Published in J.A. Garay, A. Miyaji, and A. Otsuka, Eds, Cryptology and Network Security (CANS 2009), vol. 5888 of Lecture Notes in Computer Science, pp. 41{52, Springer, 2009. On Cryptographic Schemes Based on Discrete Logarithms and Factoring Marc Joye T R&D, Security Competence Cente 3. Introduction: -Discrete logarithms are fundamental to a number of public-key algorithms, including Diffie-Hellman key exchange and the digital signature algorithm (DSA). The Powers of an Integer, Modulo n. Euler's theorem states that, for every a and nthat are relatively prime: af (n) ≡1 (mod n) ----- (1 4. GATE Preparation, nptel video lecture dvd, computer-science-and-engineering, cryptography-and-network-security, discrete-logarithms, Services, Mechanisms and attacks. 5. Corpus ID: 59926254. Discrete Logarithms within Computer and Network Security. @inproceedings{Buchanan2014DiscreteLW, title={Discrete Logarithms within Computer and Network Security.}, author={W. Buchanan}, year={2014} 8.5 Discrete Logarithms 248 8.6 Recommended Reading and Web Site 252 8.7 Key Terms, Review Questions, and Problems 253 CHAPTER 9 PUBLIC-KEY CRYPTOGRAPHY AND RSA 257 9.1 Principles of Public-Key Cryptosystems 259 9.2 The RSA Algorithm 268 9.3 Recommended Reading and Web Site 278 9.4 Key Terms, Review Questions, and Problems 279 Appendix 9A The Complexity of Algorithms 282 CHAPTER 10 KEY. 10.6 In 1985, T. ElGamal announced a public-key scheme based on discrete logarithms, closely related to the Diffie-Hellman technique. As with Diffie-Hellman, the global elements of the ElGamal scheme are a prime number q and a, a primitive root of q. A user A selects a private keyX A and calculates a public keyY A as in Diffie-Hellman. User A encrypts a plaintext M < q intended for user B as. Solutions for Chapter 8 - Cryptography and Network Security - Stallings - 6th edition Review Questions 8.1 What is a prime number? Get 8.1 exercise solution 8.2 What is the meaning of the expression a divides b? Get 8.2 exercise solution 8.3 What is Euler's totient function? Get 8.3 exercise solution 8.4 The Miller-Rabin test can determine if a number is not prime but cannot determine if a. Quantum computing promises significant breakthroughs in science, medicine, financial strategies, and more, but it also has the power to blow right through current cryptography systems, therefore becoming a potential risk for a whole range of technologies, from the IoT to technologies that are supposedly hack-proof, like blockchain Solutions for Chapter 8 - Cryptography and Network Security - Stallings - 4th edition Review Questions 8.1 What is a prime number? Get 8.1 exercise solution . 8.2 What is the meaning of the expression a divides b? Get 8.2 exercise solution. 8.3 What is Euler's totient function? Get 8.3 exercise solution. 8.4 The Miller-Rabin test can determine if a number is not prime but cannot determine if a. Request PDF | On Aug 14, 2018, Douglas R. Stinson and others published Public-Key Cryptography and Discrete Logarithms: Theory and Practice | Find, read and cite all the research you need on. Home Browse by Title Proceedings CANS '09 On Cryptographic Schemes Based on Discrete Logarithms and Factoring. Article . On Cryptographic Schemes Based on Discrete Logarithms and Factoring . Share on. Author: Marc Joye. T R&D, Security Competence Center, Cesson-Séévigné Cedex, France 35576. T R&D, Security Competence Center, Cesson-Séévigné Cedex, France 35576. View Profile. Information Security and Cryptography Research Group. Home; Teaching. Current Topics in Cryptography 2021 Cryptographic Protocols 2021 Diskrete Mathematik 2020 Master and Bachelor Theses Current Topics in Cryptography 2020 Diskrete Mathematik 2019 People. Ueli Maurer Claudia Günthart Martin Hirt Christopher Portmann Fabio Banfi Konstantin Gegier David Lanzenberger Chen-Da Liu Zhang Eleanor. The complexity of finding discrete logarithms (for various m, in particular, when m is prime) Stallings, W., Cryptography and Network Security, 4th edition, Pearson-Prentice-Hall, Upper Saddle River, 2006. Welsh, D., Codes and Cryptography, Oxford U. Press, Oxford, 1986. Joe Malkevitch York College (CUNY) malkevitch at york.cuny.edu. NOTE: Those who can access JSTOR can find some of the. In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography cryptography cloud algorithm rsa galois-field signature-verification network-security fermat discrete-logarithm carmichael euler-totient chinese-remainder abelian-groups Updated Mar 5, 201 Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution. Definition. Let G be any group. Denote its group operation by. ### Security of the Cryptographic Protocols Based on Discrete • Cryptography and Network Security Chapter 10 Fifth Edition by William Stallings Lecture slides by Lawrie Brown * In the Diffie-Hellman key exchange algorithm, there are two publicly known numbers: a prime number q and an integer a that is a primitive root of q. The prime q and primitive root a can be common to all using some instance of the D-H scheme. Note that the primitive root a is a. • Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. If G is a multiplicative cyclic group and g is a generator of G, then from the definition of cyclic groups, we know every element h in G can be written as g x for some x.The discrete logarithm to the base g of h in the group G is defined to be x • These discrete logarithms have formal properties much like ordinary logarithms. Note in particular that discrete logarithms are exponents, just like ordinary logarithms. What they are good for: Here I will take a glance at the reason for their use in cryptography Both uniform and non-uniform results concerning the security of the Diffie-Hellman key-exchange protocol are proved. First, it is shown that in a cyclic group G of order |G|=prod(p_i^e_i), where all the multiple prime factors of |G| are polynomial in log|G|, there exists an algorithm that reduces the computation of discrete logarithms in G to breaking the Diffie-Hellman protocol in G and has. The security of elliptic curve cryptography relies on the hardness of comput-ing discrete logarithms in elliptic curve groups, i.e. the di culty of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Elliptic curves have the advantage of relatively small parameter and key sizes in comparison to other cryptographic schemes, such as those based on RSA [40] or nite eld discrete logarithms [11. discrete logarithms on elliptic curves over prime elds. The estimates are derived from a simulation of a To oli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQUiji. We determine circuit implementations for reversible modular arithmetic, including modular addition, mul-tiplication and inversion, as well. NETWORK SECURITY AND CRYPTOGRAPHY Course code: 13IT2111 L P C 4 0 3 Pre requisites: Discrete Mathematical Structures. Course Outcomes: At the end of the course the student will be able to CO1: Understand various attacks, services, mechanisms and various conventional and modern encryption techniques. CO2: Analyze conventional encryption system and various algorithms in it. CO3: Understand. ### Discrete logarithm - Wikipedi Cryptography and Network Security Chapter 8 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 8 - Introduction to Number Theory The Devil said to Daniel Webster: Set me a task I can't carry o ut, and I'll give you anything in the world you ask for. Daniel Webster: Fair enough. Prove that for n greater than 2, t he equation a n + + bn = cn has no. Aditya, Riza, Peng, Kun, Boyd, Colin, Dawson, Edward, & Lee, Byoungcheon (2004) Batch Verification for Equality of Discrete Logarithms and Threshold Decryptions. In Yung, M, Zhou, J, & Jakobsson, M (Eds.) Applied Cryptography and Network Security Second International Conference on Applied Cryptography and Network Security (LNCS 3089) For understanding the discrete logarithm itself, I would use pen and paper and construct a table of all powers of a generator of a small cyclic group. The logarithm is the inverse, so you already have your table for logarithms if you flip the columns Designs, Codes and Cryptography. Periodical Home; Latest Issue; Archive; Authors; Affiliations; Home Browse by Title Periodicals Designs, Codes and Cryptography Vol. 19, No. 2-3 Discrete Logarithms: The Past and the Future Browse by Title Periodicals Designs, Codes and Cryptography Vol. 19, No. 2-3 Discrete Logarithms: The Past and the Futur ### Chapter 8. Introduction to Number Theory Cryptography .. Cryptography Network Security Given 5 Primitive Root 23 Construct Table Discrete Logarithm Q39814502 Cryptography and Network Security Given 5 as a primitive root of 23, construct a table of discretelogarithms, and use it to solve the following congruences ResearchArticle Quantum Cryptography for the Future Internet and the Security Analysis TianqiZhou,1 JianShen ,1,2 XiongLi,3 ChenWang,1 andJunShen1. This video is unavailable. Watch Queue Queue. Watch Queue Queu The discrete logarithm problem(DLP) is a hard mathematical problem and a useful primitive in cryptography. Many DLP computation in prime fields are employed to test the safety of current used primes of 1024 or 2048 bits length. However, such computations are always carried out to a safe prime, which.. We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ U i | .We determine circuit implementations for reversible. ### CRYPTOGRAPHY AND NETWORK SECURITY - SlideShar Cryptography is ubiquitous and plays a key role in ensuring data secrecy and integrity as well as in securing computer systems more broadly. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of this fascinating subject. The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs. Factoring and Discrete Logarithms. The most obvious approach to breaking modern cryptosystems is to attack the underlying mathematical problem. Factoring: given N =pq,p <q,p ≈ q N = p q, p < q, p ≈ q, find p,q p, q . Discrete logarithm: Given p,g,gx mod p p, g, g x mod p, find x x JNTUK B.Tech Cryptography and Network Security gives you detail information of Cryptography and Network Security R13 syllabus It will be help full to understand you complete curriculum of the year. The main objective of this course is to teach students to understand and how to address various software security problems in a secure and. BibTeX @INPROCEEDINGS{Aditya04batchverification, author = {Riza Aditya and Kun Peng and Colin Boyd and Ed Dawson and Byoungcheon Lee}, title = {Batch Verification for Equality of Discrete Logarithms and Threshold Decryptions}, booktitle = {In Second conference of Applied Cryptography and Network Security, ACNS 04, volume 3089 of Lecture Notes in Computer Science}, year = {2004}, pages = {494. ### CS6701 CNS Notes, Cryptography & Network Security Lecture Cryptography is the art and science of making a cryptosystem that is capable of providing information security. Cryptography deals with the actual securing of digital data. It refers to the design of mechanisms based on mathematical algorithms that provide fundamental information security services. You can think of cryptography as the establishment of a large toolkit containing different. Essential Number Theory and Discrete Math - Foundations - The book is really a journey through cryptography, starting with historical cryptography and then moving into the mathematical foundations necessary to understand modern cryptography. The book then moves on to the symmetric and asymmetric algorithms used today. It also includes chapters on Secure Sockets Layer (SSL), cryptanalysis. General Network Working Group elliptic curve cryptography ecc tls nums This memo describes a family of deterministically generated Nothing Up My Sleeve (NUMS) elliptic curves over prime fields offering high practical security in cryptographic applications, including Transport Layer Security (TLS) and X.509 certificates. The domain parameters are defined for both classical Weierstrass curves. Discrete logarithms are fundamental to the A Euler algorithm B digital. Discrete logarithms are fundamental to the a euler. School IPreparatory Academy - Florida; Course Title CIS CYBER SECU; Uploaded By safenat. Pages 7 Ratings 100% (2) 2 out of 2 people found this document helpful; This preview shows page 3 - 6 out of 7 pages.. The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystem Handbook of Elliptic and Hyperelliptic Curve Cryptography-Henri Cohen 2005-07-19 The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves i ### Video: Discrete Logarithms - an overview ScienceDirect Topic We present improved quantum circuits for elliptic curve scalar multiplication, the most costly component in Shor's algorithm to compute discrete logarithms in elliptic curve groups. We optimize low-level components such as reversible integer and modular arithmetic through windowing techniques and more adaptive placement of uncomputing steps, and improve over previous quantum circuits for. In this article Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic the term finite fields of fixed characteristic is not defined and I couldn't find it on the definition finite-fields cryptography discrete-logarithms. asked Aug 12 '20 at 9:54. kelalaka. 1,021 1 1 gold badge 8 8 silver badges 24 24 bronze badges. 0. votes. 1answer 56 views Help me out with. ### Applied Cryptography and Network Security SpringerLin Public-key cryptography is used in a number of applications including encrypting sensitive and confidential data and digital signatures.In public-key cryptography, keys come in pairs, one public, and one private, and the security of the encryption or digital signature scheme relies on the fact that it is believed to be computationally intractable to compute the private key from the public key Handbook of Elliptic and Hyperelliptic Curve Cryptography (Discrete Mathematics and Its Applications) (English Edition) eBook: Cohen, Henri, Frey, Gerhard, Avanzi. Unformatted text preview: Cryptography and Network Security Introduction to Number Theory Prime Numbers prime numbers only have divisors of 1 and self they cannot be written as a product of other numbers note: 1 is prime, but is generally not of interest eg. 2,3,5,7 are prime, 4,6,8,9,10 are not prime numbers are central to number theory list of prime number less than 200 is: 2 3 5 7 11 13 17. The discrete logarithm problem is a problem about finite cyclic groups. An example of a finite cyclic group is the positive integers less that some prime modulus $p$, with multiplication done modulo $p$. A finite cycle group. International Journal of Network Security, Vol.19, No.3, PP.443-448, May 2017 (DOI: 10.6633/IJNS.201703.19(3).13) 443 A Publicly Veriflable Authenticated Encryption Scheme Based on Factoring and Discrete Logarithms Cheng-Yi Tsai1, Chi-Yu Liu1, Shyh-Chang Tsaur2 ;3, and Min-Shiang Hwang1;4 (Corresponding author: Min-Shiang Hwang) Department of Computer Science and Information Engineering, Asia. ### Cryptography: What is the discrete logarithm problem? - Quor curve discrete logarithms have been studied since the mid-1980s. It is impossible to predict when a mathematical breakthrough might occur. It is an unfortunate fact that discrete logarithms and integer factorization are so close that many algorithms developed for one problem can be modi ed to apply to the other. For security, it would be better. Computer Science > Cryptography and Security. Title: Quantum algorithms for computing short discrete logarithms and factoring RSA integers. Authors: Martin Ekerå, Johan Håstad (Submitted on 1 Feb 2017) Abstract: In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker {\aa} so as to allow for various tradeoffs between the number. Best Videos, Notes & Tests for your Most Important Exams. Created by the Best Teachers and used by over 51,00,000 students. EduRev, the Education Revolution View ECE4013_CRYPTOGRAPHY-AND-NETWORK-SECURITY_TH_1.2_47_ECE4013_7.pdf from ECE 4013 at Vellore Institute of Technology. ECE4013 Pre-requisite Cryptography and Network Security ECE2005 Probabilit NETWORK SECURITY AND CRYPTOGRAPHY Course code: 13IT2111 L P C 4 0 3 Pre requisites: Discrete Mathematical Structures. Course Outcomes: At the end of the course the student will be able to CO1: Understand various attacks, services, mechanisms and various conventional and modern encryption techniques. CO2: Analyze conventional encryption system and various algorithms in it. CO3: Understand. • Surfshark safe. • Union Investment Real Estate GmbH. • Mohammeds väg till miljonen podd. • Best EMA for day trading. • Implication verb. • Idle miner tycoon cheats Android. • Harbor vulnerability scanning. • Grayscale investments Aktie. • Cheapest dedicated Server. • FinCEN proposed rule CVC. • Handelsplattform aktier. • Bitcoin kaufen und verkaufen. • BVP Nasdaq Emerging Cloud Index Methodology. • Bitcoin Hublot. • Galileo Milliardäre. • Godot. • Honda dealership service estimate. • Kurzgesagt app. • Riverside laughlin dining. • DWS Vermögensbildungsfonds I Dividende 2020. • Ethereum Classic Erklärung. • Goud kopen bij de bank. • Autoverkauf nach Schweden. • Ouvrir un compte bancaire en France. • Postbank Zusatzkarte kündigen. • Flirc Raspberry Pi 4 case WiFi. • DAX Konzerne Ranking. • How to cash out large amounts of Bitcoin. • Little Creek Capital. • Kraus Sinks Amazon. • Bitcoin kopen iDEAL. • ILB Überbrückungshilfe. • Alle Samsung Emojis zum Kopieren.

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# How Many Sides does a Pyramid have? How many sides a pyramid has depends on how you look at it. It actually has four sides, but if you’re counting the bottom a pyramid has a total of five sides.

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# PARALLELPERIOD Function (DAX) Returns a table that contains a column of dates that represents a period parallel to the dates in the specified dates column, in the current context, with the dates shifted a number of intervals either forward in time or back in time. ## Syntax ``` PARALLELPERIOD(<dates>,<number_of_intervals>,<interval>) ``` ## Parameters Term Definition dates A column that contains dates. number_of_intervals An integer that specifies the number of intervals to add to or subtract from the dates. interval The interval by which to shift the dates. The value for interval can be one of the following: year, quarter, month. ## Return Value A table containing a single column of date values. ## Remarks This function takes the current set of dates in the column specified by dates, shifts the first date and the last date the specified number of intervals, and then returns all contiguous dates between the two shifted dates. If the interval is a partial range of month, quarter, or year then any partial months in the result are also filled out to complete the entire interval. The dates argument can be any of the following: • A reference to a date/time column, • A table expression that returns a single column of date/time values, • A Boolean expression that defines a single-column table of date/time values. Note Constraints on Boolean expressions are described in the topic, CALCULATE Function (DAX). If the number specified for number_of_intervals is positive, the dates in dates are moved forward in time; if the number is negative, the dates in dates are shifted back in time. The interval parameter is an enumeration, not a set of strings; therefore values should not be enclosed in quotation marks. Also, the values: year, quarter, month should be spelled in full when using them. The result table includes only dates that appear in the values of the underlying table column. The PARALLELPERIOD function is similar to the DATEADD function except that PARALLELPERIOD always returns full periods at the given granularity level instead of the partial periods that DATEADD returns. For example, if you have a selection of dates that starts at June 10 and finishes at June 21 of the same year, and you want to shift that selection forward by one month then the PARALLELPERIOD function will return all dates from the next month (July 1 to July 31); however, if DATEADD is used instead, then the result will include only dates from July 10 to July 21. If the dates in the current context do not form a contiguous interval, the function returns an error. The following sample formula creates a measure that calculates the previous year sales for Internet sales. To see how this works, create a PivotTable and add the fields, CalendarYear and CalendarQuarter, to the Row Labels area of the PivotTable. Then add a measure, named Previous Year Sales, using the formula defined in the code section, to the Values area of the PivotTable. Note The above example uses the table DateTime from the DAX sample workbook. For more information about samples, see Get Sample Data . ```=CALCULATE(SUM(InternetSales_USD[SalesAmount_USD]), PARALLELPERIOD(DateTime[DateKey],-1,year)) ```

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# energy difference uniqueness in hydrogen atom Is the energy difference between two energy levels unique for that particular pair of levels for a hydrogen atom ? If so how can one prove it? - Good question, I came across this in past but never found an answer. Perhaps it would help others to understand the question if you formulated it as a problem from the theory of natural numbers. –  Ján Lalinský Jan 7 '14 at 23:37 If I understand right: I believe you are asking whether, using the Dirac formula for the energy levels $E_{n\,j} = \mu c^2\left(1+\left[\dfrac{Z\alpha}{n-|k|+\sqrt{k^2-Z^2\alpha^2}}\right]^2\right)^{‌​-1/2}$ and then proving $E_{n\,j}$ is unique for each pair$(n,j)\in \mathbb{Z}_0^+\times \mathbb{Z}_0^+$? If so, you might try Maths SE. This is a harder problem than it looks. –  WetSavannaAnimal aka Rod Vance Jan 8 '14 at 0:23 Why bother with the Dirac formula, it is messy and contains $\alpha$ which is not known to be simple number. More interesting is the Schroedinger non-relativistic case : for given $\Delta E$, find all $n,m$ such that $\Delta E = \frac{1}{n^2}- \frac{1}{m^2}$. –  Ján Lalinský Jan 8 '14 at 0:33 Richard, nice picture - what element is it? However, it does not answer the OQ - whether the $\omega$ of a transition corresponds to a unique pair of Hamiltonian eigenfunctions (perhaps there are more). –  Ján Lalinský Jan 7 '14 at 23:51 Otherwise, your post assumes that the atom can be only in discrete states with definite energy. This was working assumption years around 1912 and is still taught today (Bohr model, buck-shot model of light), but is not consistent with diff. equations and is not necessary to explain the spectrum today - the Schroedinger equation explains the spectral function with continuously changing $\psi$ functions, most of which do not imply that atom has one of the discrete set of energies. –  Ján Lalinský Jan 7 '14 at 23:52

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https://ged-testprep.com/question/currently-the-ratio-of-jaedens-age-to-kiernans-age-is-53-and-5398351423995904/

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Scan QR code or get instant email to install app Question: # Currently, the ratio of Jaeden’s age to Kiernan’s age is 5:3, and the sum of their ages is 32. In 10 years, the ratio of their ages will be _________. A 15:11 explanation Let 5x = Jaeden’s current age, and 3x = Kiernan’s current age. Then 5x + 3x = 32, so 8x = 32 and x = 4. Thus, Jaeden’s current age is 5x = 5(4) = 20, and Kiernan’s current age is 3x = 3(4) = 12. In 10 years, Jaeden and Kiernan will be 30 and 22, respectively, and the ratio of their ages will be $\frac{30}{22}$= $\frac{15}{11}$ which is 15:11.

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https://www.jiskha.com/questions/1097408/5-A-soft-drink-dispensing-machine-uses-paper-cups-that-hold-a-maximum-of-12-ounces

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# statistics 5. A soft drink dispensing machine uses paper cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of 10 ounces of the drink. The amount that is actually dispensed varies. It is normally distributed with a standard deviation of one ounce. (a) What fraction of the drinks are between 10 and 11 ounces? (b)What percentage of the cups spill over when poured because they exceed the 12 ounce limit? 1. Z = (score-mean)/SD = (score-10)/1 Insert scores to find Z scores. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores. posted by PsyDAG 2. lj posted by Anonymous ## Similar Questions 1. ### Statistics A coffee-dispensing machine is supposed to deliver 12 ounces of liquid into a large paper cup, but the costumer believes that the actual amount is less. As a test he plans to obtain a sample of 30 cups of the dispensed liquid. The 2. ### stats 1. Conduct a hypothesis test for the following scenario. SHOW ALL YOUR WORK THE WAY WE DID IN CLASS! A coffee-dispensing machine is supposed to deliver 12 ounces of liquid into a large paper cup, but the costumer believes that the 3. ### stats A soft drink vending machine is supposed to fill cups with pop. The cups hold exactly 8 oz of liquid. Suppose the actual amount dispensed by the machine follows a normal distribution with mean 7 oz. If it is found that exactly 4 4. ### Statistics A soft drink vending machine is supposed to fill cups with pop. The cups hold exactly 8 oz of liquid. Suppose the actual amount dispensed by the machine follows a normal distribution with mean 7 oz. If it is found that exactly 4 5. ### MATHS STATISTICS B. A soft-drink vending machine is supposed to pour 8 ounces of the drink into a paper cup. However, the actual amount poured into a cup varies. The amount poured into a cup follows a normal distribution with a mean that can be 6. ### statistics The amount of corn chips dispensed into a 16-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 16.5 ounces and a standard deviation of 0.1 ounce. Suppose 400 bags of chips 7. ### Statistics The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.12 ounces. Every can that has more than 12.30 ounces of soda poured into it causes a spill and 8. ### math The amount of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distrubution with a mean of 12.5 ounces and a standard deviation of 0.2 ounces. What porportion of the 12 9. ### Math/ Statistics A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test described. A. H0: ยต = 16 ounces Ha: 10. ### intro to psychology People in the grocery store are asked to do a taste test of a new soft drink. Two paper cups are given to each volunteer. Fifty percent of the participants are given two different soft drinks. The other half receive the same More Similar Questions

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# physics posted by . Suzie (of mass 76 kg) is roller-blading down the sidewalk going 12 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 1.9 seconds. What is Suzie’s average acceleration • physics - Vo=12mi/h * 1600m/mi * 1h/3600s.=5.33m/s a=(V-Vo)/t = (0-5.33)/1.9=-2.807 m/s^2. ## Similar Questions 1. ### Math One of the world's fastest roller coasters is located in a theme park in Valencia, California. Riders go from 0 to 100 miles per hour in 7 seconds. Find the acceleration of the roller coaster during this time interval in miles per … 2. ### math One of the world's fastest roller coasters is located in a theme park in Valencia, California. Riders go from 0 to 100 miles per hour in 7 seconds. Find the acceleration of the roller coaster during this time interval in miles per … 1) Suzie (of mass 38 kg) is roller-blading down the sidewalk going 20 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 2 seconds. What is Suzie’s … 4. ### physics Lance arrives early at the airport (with owers and balloons in hand) to welcome a friend. Her plane is delayed. While waiting, he notices that it takes 2 minutes 47 seconds to get down the hall on the moving sidewalk. While walking … 5. ### physics a roller coster goes from 43 yards per hour to a stop in the station.it took 4.5 seconds to stop.what was the acceleration? 6. ### MATH Without taking a single break, mercedes hiked for 10 hours, up a mountain and back down by the same path. While hiking, she averaged 2 miles per hour on the way up and 3 miles per hour on the way down. How many miles was it from the … 7. ### physics Suzie (of mass 58 kg) is roller-blading down the sidewalk going 36 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 2 . 4 seconds. What is Suzie’s … 8. ### physic Suzie (of mass 58 kg) is roller-blading down the sidewalk going 36 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 2 . 4 seconds. What is Suzie’s … 9. ### Physics kinematics The break of a car can slow it down from 60 miles per hour to 40 miles per hour in two secs how long it bring the car to a stop from an initial velocity of 25 miles per hour at the same acceleration 10. ### Physics Suzie (of mass 84 kg) is roller-blading down the sidewalk going 34 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 1.1 seconds. What is Suzie’s … More Similar Questions

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# Assignment 2, due Jan. 26 On all assignments, your name must be legible as it appears on your University ID card! Assignments are due at the start of class on the day indicated (usually Friday). Exceptions will be by advance arrangement unless there is what lawyers call "an act of God" (something outside your control). Homework must be turned in on paper, either in class or in the teaching assistant's mailbox. Never push late work under someone's door! 1. A scavanger hunt question: Search the notes for Jan. 22 and find: a) What company introduced the first commercial virtual memory system, in what decade? (0.2 points) b) What IBM operating system was the first to successfully use virtual memory, in what decade? (0.2 points) c) What was the first variant of Unix to fully support support virtual memory, in what decade? (0.2 points) d) What Microsoft operating system was the first to use virtual memory, in what decade? (0.2 points) e) What Apple operating system was the first to use virtual memory, in what decade? (0.2 points) 2. Background: Fibonacci numbers are conventionally defined recursively as: n ≤ 1: fib(n) = n n > 1: fib(n) = fib(n – 1) + fib(n – 2) You could just as easily use this iterative algorithm, expressed in C: ```int fib( int n ) { int i = 0 int j = 1 while (n > 0) { int k = i + j; i = j; j = k; n = n - 1; } return i; } ``` A Problem Write a little tcsh script that computes the nth Fibonacci number. It can be done recursively or iteratively, so long as the user interface works something like this: ```[HawkID@servX]\$ fib 3 2 ``` Depending on how you configure your path, you may need to type ./fib Turn in legible readable code, handwritten or machine printed are acceptable. Don't overcomment, but at bare minimum, you should identify the algorithm you are using (recursive or iterative) and the name of the file your script is supposed to be stored in. (2 points). If you come away from the above assignment hating the Unix shell as a programming language, welcome to the club.

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# AP Computer Science A : Assertions ## Example Questions ### Example Question #1 : Program Correctness Which of the following code excerpts would output "10"? int num = 10; num = (num > 0) ? 11: 12; System.out.println(num); int num = 5; num = (num > 0) ? 11: 10; System.out.println(num); int num = 5; num = (num < 0) ? 10: 11; System.out.println(num); int num = 5; num = (num > 0) ? 10: 11; System.out.println(num); None of the answers are correct. int num = 5; num = (num > 0) ? 10: 11; System.out.println(num); Explanation: Each bit of code has something similar to this: num = (boolean statement) ? X : Y; The bit at the end with the ? and : is called a ternary operator. A ternary operator is a way of condensing an if-else statement. A ternary operator works like this: <boolean statement> ? <do this if true> : <do this if false> int num = 5; num = (num > 0) ? 10: 11; System.out.println(num); Therefore, the ternary operator portion of code, when converted to an if-else, looks like this: if (num > 0) { num = 10; else { num = 11; } Because num is 5, which is greater than 0, it would go into the if, so num would then get 10. Then, num gets printed, which means 10 gets printed (the correct answer). ### Example Question #1 : Assertions True or False. The assertion in this code snippet is to prevent users from inputting bad data. public class UserInput { int userInput; public static void main(String[] args) { assertTrue(isInteger(args[0])); userInput = args[0]; userInput = 25 - userInput; } }

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# How do you find the 7th term of the geometric sequence with the given terms a4 = 54, a5 = 162? Jan 20, 2016 ${a}_{7} = 1458$ #### Explanation: Since this is a geometric sequence we know the following ${a}_{n} = {a}_{1} {r}^{n - 1}$ noticed we started at 1 that why we subtract 1 from n the ratio $r = \frac{{a}_{n}}{{a}_{n - 1}}$ We are given ${a}_{4} = 54 \text{ " } {a}_{5} = 162$ We first, need to find $r$ $r = \frac{{a}_{5}}{{a}_{4}} = \frac{162}{54} = 3$ Then we can use the formula ${a}_{n} = {a}_{1} {r}^{n - 1}$ (but instead of finding ${a}_{1}$ , we will use ${a}_{4}$ we need to subtract 4 from the nth term ${a}_{7} = {a}_{4} {r}^{7 - 4}$ ${a}_{7} = \left(54\right) {\left(3\right)}^{3}$ " a_7 = 1458

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https://www.teacherspayteachers.com/Product/Multiplication-Facts-and-Answers-Missing-1305312

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Total: \$0.00 # Multiplication Facts and Answers Missing Subjects 3rd, 4th, 5th, 6th Resource Types Product Rating 4.0 File Type Word Document File 0.05 MB   |   4 pages ### PRODUCT DESCRIPTION * 6 x ____ = 42....OR...____ x 8 = 56....OR....9 x ___ = 32 * DO THE FACTS WORK OR DON'T THEY??? SOME OF THESE DON'T WORK AT ALL!!! * Your students are given small equations like you see above and must fill in the blanks with the correct answers. This will surely test their knowledge of their multiplication facts. * There are 60 examples that will take them time to complete plus some BONUS ones at the end. THIS IS NOT YOUR USUAL DRILL WORK! * What's cool about these examples is that some facts DON'T WORK on purpose and your students must put an "X" in the blanks to show that. Could be tricky for some and challenging for most. Decorated for fun. * Designed and created by David Filipek. Electronic distribution limited to single classroom use only. Not for public display. * ALSO AVAILABLE FOR YOU OR A COLLEAGUE! - CLICK ANY LINK YOU WANT: - MULTIPLICATION FACTS CAN YOU LIST THEM? - 3 FULL worksheets with 23 examples in all. Students must write ALL the facts for a given specific number. Really tests their times tables. Great activity! - MULTIPLICATION FACTS & PICKS - Brilliant activity testing and reinforcing a student's multiplication facts. They must match facts from one page to facts on another page using WRITTEN words! - MATH FACTS WORD PROBLEMS - 32 word problems all dealing with their multiplication facts. Great INTERDISCIPILINARY lesson for math and reading! 32 word problems on 3 worksheets. A lot of good work for your students. - POWERPOINT MULTIPLICATION FACTS ONE - 63 slides, interactive and self-correcting! Designed for individual use on the computer, students reinforce their multiplication facts with this program. Students must reinforce each fact before going to the next. Much different than this Powerpoint program. GREAT TEACHING TO YOU! Total Pages 4 N/A Teaching Duration N/A ### Average Ratings 4.0 Overall Quality: 4.0 Accuracy: 4.0 Practicality: 4.0 Thoroughness: 4.0 Creativity: 4.0 Clarity: 4.0 Total: 10 ratings \$1.50 User Rating: 4.0/4.0 (902 Followers) \$1.50

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# Integers m o tt o b incr eas e a e s w o l be level e v o l b e a v e l a e s c e d e s a e r top 26 3 - -1 5 Positive and Negative 16 Integers A PowerPoint for Mrs. Becks 6th grade. MCC6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. 0 -7 Lesson EQ: How do I use positive and negative numbers to represent quantities in real-world contexts? Negative integers have values less than zero, are to the left of zero on the number line and are always shown with a minus (-) sign. Positive integers have values greater than zero, are to the right of zero on the number line, and usually are not shown with their sign (+). So why do we need negative and positive integers? You can use integers to describe opposite situations. For example: Positive Integers Depositing money in a checking account Elevation above sea level Any temperature above zero Yardage gained in football Negative Integers Withdrawing money from a checking account An elevation below sea level Below zero temperatures Yardage lost in football Example 1 A sea gull is flying 25 feet above sea level and a shark is swimming 10 feet below sea level. 1) What elevation does the surface of the water represent? 2) What is the elevation of the bird? 3) What is the elevation of the fish? What is the temperature on this thermometer? What is the temperature on this thermometer? Lets try some Write the number that best represents each statement: It is 6 degrees warmer than yesterday. I lost \$2.00 through a hole in my pocket The price was reduced by \$12. I improved my mark by 16. The building is 312 meters tall. My sister is three years younger than me. We cut 9 inches off the timber plank. I made of profit of \$180.00. I will increase my exercise by 25 minutes each day. Lets go up 10 flights of stairs. Inverse Relationships Define the inverse relationship of each. 1. Move 8 spaces to the right. 2. Drive 4 miles north. 3. Add 45 4. -35 5. +75 6. -105 7. +405 8. -25 9. -66 10. +245 ## Recently Viewed Presentations • Poppies Jane Weir 2009 A mother describes her son leaving home, seemingly to join the army. The poem is about the mother's emotional reaction losing her son to the war. She fears for his safety & after he leaves her... • Process, analyse and present information from secondary sources to evaluate the effectiveness of vaccination programs in preventing the spread and occurrence of once common diseases, including smallpox, diptheriaand polio.. 9.4.5.3.1 • Instructor Scores vs Inverted TERp. 650 sentences (22%) Pearson Correlation. r = 0.232236. This is a trial comparison. Weak positive correlation. ... SYNONYM. SHIFT. SUBSTITUTION. INSERTION. SAMESTEM. Equivalent phrases or synonyms should not decrease final score at all. • Neighbourhoods Connect is commissioned by Haringey Clinical Commissioning Group (CCG) from The Better Care Fund in partnership with Haringey Council. The Better Care Fund aims to focus on improving well-being and enabling people to live well in the community. • Illustrates past activities, projects, and accomplishments Can be easier to organize and transport if presented digitally Must show clear understanding of audience needs and your qualifications Preparing Effective Application Messages Use _____ message strategy to sell your qualifications Include _____... • Our Angels Remembered. Joey Tesh Josh Hillman Calvin Keziah Ryan Marshall Yoho Travis A. Childers Kancham Potts Sally McKenzie Clark Anna Grace Jordon Ryan Spencer Disney Laura Barnette Mandi Meador Matthew Huntz Stratton Stubbs Hope Elizabeth Stout Sasha Knox James... • Quality Control of the Large-area GEM detectors at Production Sites for the CMS Muon Endcap Upgrade Mehdi Rahmani Dept. of Physics and Space Sciences, Florida Institute of Technology (On Behalf of CMS Muon Group) APS April Meeting 2017, Washington, DC... • State Morphology Can a country's shape determine its destiny? The Concept The boundaries of a country and the shape of the land encompassed by those boundaries can present problems or it can help to unify the country. 5 Categories Compact...

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Question # Let $${T}_{r}$$ be the $$r$$th term of an AP, for $$r=1,2,....$$ if for some positive integers $$m,n$$ we have $${T}_{m}=1/n$$ and  $${T}_{n}=1/m$$, then $${T}_{m/n}$$ equal to ________ A 1mn B 1m+1n C 1n2 D 0 Solution ## The correct option is A $$\cfrac{1}{n^2}$$We  have$${T_m} = \frac{1}{n}$$ and$${T_n} = \frac{1}{m}$$  $${T_m} = \frac{1}{n} = a + \left( {n - 1} \right)d\,\,\,\,\,\,\,\,\,\, - - - \left( 1 \right)$$And$${T_n} = \frac{1}{m} = a + \left( {n - 1} \right)d\,\,\,\,\,\,\,\,\,\, - - - \left( 2 \right)$$By $$(1)-(2)\,\,equ^n$$ We get,$${T_m} - {T_n} = \frac{1}{n} - \frac{1}{m} = \left( {m - n} \right)d$$$$d = \frac{1}{{mn}}\,\,\,\,\,\,\,\,\,\, - - - \left( 3 \right)$$By putting value of $$d$$ in $$equ^n \,\,(1)$$ we get,$$a = \frac{1}{n} - \frac{{\left( {m - 1} \right)}}{{mn}}$$$${T_{\frac{m}{n}}} = \frac{1}{n} - \frac{{m - 1}}{{mn}} + \frac{1}{{mn}}.\left( {\frac{m}{n} - 1} \right)$$$$\,\,\,\,\, = \frac{1}{n} - \frac{1}{n} + \frac{1}{{mn}} + \frac{1}{{{n^2}}} - \frac{1}{{mn}}$$   $$\,\,\,\,\,\, = \frac{1}{{{n^2}}}$$Maths Suggest Corrections  0 Similar questions View More People also searched for View More

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Elementary and Intermediate Algebra: Concepts & Applications (6th Edition) Using the properties of equality to isolate the radical expression in the given, $\sqrt{x}-8=7 ,$ results to \begin{array}{l}\require{cancel} \sqrt{x}-8=7 \\\\ \sqrt{x}=7+8 \\\\ \sqrt{x}=15 .\end{array} Hence the given statement is $\text{ TRUE .}$

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In this challenge we try to solve two important problems at once. They are: 1. Given integers $$\a\$$ and $$\b\$$, tell if $$\a^b-1\$$ is a prime number. 2. Given integers $$\a\$$ and $$\b\$$, return $$\a\choose b\$$. Specifically, you must write two programs, one that does the first task and one that does the other. As we want to solve both problems at once, it is encouraged to use a same piece of code in both programs. ## Scoring The score of an answer is the Levenshtein distance between the two programs. Lower score is better. In case of a tie, the answer with the shortest combined code of the two programs wins. You can use this script to calculate the score of your solution. ## Rules 1. You must write two programs in the same language that solve the tasks described above. You can use any I/O methods you want. For task 1, you can return a truthy/falsy value or choose two values to mean true and false and return them accordingly. Eg. you can choose that "prime" means true and "not prime" means false. 2. The algorithms you use must work for all possible inputs, but it is OK if the code fails for large numbers due to limitations of the used number type. You can assume that the input is valid. 3. No subset of the program must solve the problem, ie. the code must not work if any character(s) are removed. For example, the following code is not valid, because it is possible to remove the unused else-block without breaking the program: if (1) { /* change to 0 to get the second program*/ ... } else { ... } 4. Standard loopholes are not allowed. ## Test cases ### $$\a^b-1\$$ is prime? a b 1 1 false 2 3 true 5 2 false 2 5 true 4 3 false 2 7 true ### $$\a\choose b\$$ a b nCr(a,b) 1 1 1 5 2 10 4 3 4 10 7 120 12 5 792 • This may be handy to compute Levenshtein distance Commented Apr 2, 2017 at 16:08 • The idea is nice, but I think you'll still get solutions with Levenshtein distance 1 that manage to prevent modifications to unused parts one way or another and then effectively result in the structure you want to prohibit. Commented Apr 2, 2017 at 16:13 • @LuisMendo The issue is that many of those solutions are really slow. You can use this Mathics script instead. Commented Apr 2, 2017 at 16:31 • I think a better metric would have been the Levenshtein distance divided by the total length of the two programs. Commented Apr 2, 2017 at 21:06 • @GregMartin Wouldn't that result in code bowling? It is possible to artificially make programs larger and still claim that they don't have any unnecessary code. Commented Apr 3, 2017 at 6:12 # Ruby, Distance 1, Combined Length 194 Prime check: ->a,b{s='[(a**b-1).prime?,(1..b).inject(1){|m,i|(a+1-i)/i*m}][0]';require'math'<<s.size*2;eval s} Try it online! nCr: ->a,b{s='[(a**b-1).prime?,(1..b).inject(1){|m,i|(a+1-i)/i*m}][1]';require'math'<<s.size*2;eval s} Try it online! As predicted in the comments, some jerk always has to go against the spirit of the problem. It was fun finding a way to work around it, though! Here's how it works: We have two separate solutions to the problems. We run both, put them into an array, and then either choose the 0th element or the 1st, for an edit distance of 1. This would ordinarily be illegal, since you could just delete everything but the calculation you wanted and it would still work. However, each code snippet is written to rely on the loading of the same standard library, 'mathn': • The first uses its builtin prime? • The second relies on mathn changing how division works--before loading it, 3/4 evaluates to 0, while afterwards it evaluates to the fraction (3/4). Since the intermediate result of (a+1-i)/i is not always a whole number, the overall result is wrong without the library. Now we just need to make loading the library contingent on the rest of the code being unmodified. We do this by generating the name mathn using the character length of the rest of the main code: the combined calculation has length 55, which doubled to 110 is the ASCII value of 'n'. So concatenating this onto the string 'math' gives the desired library. As a bonus, introducing the library dependencies also makes the code run in a reasonable amount of time. In particular, the naive approach to nCr wouldn't generate fractional intermediate results. # MATLAB, distance 10 Primality: function x=f(a,b);x=isprime(a^b-1); nCr: function x=f(a,b);x=nchoosek(a,b); • That's the built-in I was searching for! Commented Apr 2, 2017 at 16:49 # PHP, distance 29 a^b-1 prints 0 for true and any integer value > 0 for false [,$a,$b]=$argv;for($c=-$i=1;$i<=$d=$a**$b-1;$d%++$i?:$c++);echo$c; nCr(a,b) [,$a,$b]=$argv;for($c=$i=1;$i<=$a;$c*=$i**(1-($i<=$a-$b)-($i<=$b)),$i++);echo$c; ## PHP, distance 36 a^b-1 prints 1 for true nothing for false [,$a,$b]=$argv;for($c=-1,$i=1;$i<=$d=-1+$a**$b;)$d%++$i?:$c++;echo$c<1; nCr(a,b) [,$a,$b]=$argv;for($c=$d=$i=1;$i<=$a;$c*=$i++)$d*=$i**(($i<=$a-$b)+($i<=$b));echo$c/$d; # 05AB1E, distance 3 nCr sc Try it online! isPrime(a^b-1) m<p Try it online! # Stacked, distance 13 [([@.!]$/{%y!x y-!*})fork!] [^#-:([]1/$%{!n 1-!})fork!=] Try it online! The first calculates nCr, the second primality, using Wilson's theorem. (f g h) fork! pops N args from the stack (call them a0 ... aN) and applies a0 ... aN f a0 ... aN h g. For the first program: [([@.!]$/{%y!x y-!*})fork!] [( )fork!] apply the fork of: [@.!] equiv. { x y : x ! } => x! $/ divided by {% } two-arg function y! y! x y- (x - y)! * * And for the second: [^#-:([]1/$%{!n 1-!})fork!=] [^ ] exponentiate (a^b) #- decrement (a^b-1) : duplicate (a^b-1 a^b-1) ( )fork! apply the fork to: []1/ 1-arg identity function $% modulus by {! } 1-arg with n: n 1- (n-1) ! ! = check for equality # Python 2, distance 15, length 172 ### Task 1 D=lambda k:max(k-1,1) P=lambda n,k=0:n<k or P(n-1,k)*n/k lambda a,b:P(a**b-2)**2%D(a**b) ### Task 2 D=lambda k:max(k-1,1) P=lambda n,k=1:n<k or P(n-1,D(k))*n/k lambda a,b:P(a,b)/P(a-b) Try it online! # Mathematica, distance 10 Task 1: PrimeQ[#2^#-1]& Task 2: Binomial[#2,#]& Both functions take the inputs in the order b,a. # Javascript ES7, distance 14 Thanks @Conor O'Brien for reducing the distance by 7 Primality: f=x=>y=>{t=x**y-1;s=1;for(i=2;i<t;i++){if(!t%i)s=i-i}return s} Returns 1 if prime returns 0 if not prime. Incredibly inefficient prime check, checks the number modulo every number smaller than it and greater than 1... nCr: f=x=>y=>{t=x+1;s=1;for(i=1;i<t;i++){if(y<i)s*=i/(i-y)}return s} Multiplies 1 by each number from y+1 to x and divides by each number from 1 to x-y (x!/y!)/(x-y)! • Changing the second program to f=x=>y=>{t=x+1;s=1;for(i=1;i<t;i++){if(y<i)s*=i/(i-y)}return s} gives edit distance 14. Try it online! Commented Apr 3, 2017 at 14:27 # Octave, distance 1716 15 ### nCr a=input("");b=input("");f=@(x)factorial(x);printf("%d",f(a)/f(b)/f(a-b)) Try it online! ### isprime(a^b-1) a=input("");b=input("");f=@(x)isprime(x);printf("%d",f(a^b-f(8-6))) Try it online! I am not very fluent in Octave, so I don't know if there is a builtin to calculate nCr. # MATL, distance 4, length 6 ### Tell if a^b-1 is prime: ^qZq Try it online! ### Compute nCr(a,b): Xn Try it online! ## How it works ### Tell if a^b-1 is prime: ^ % Power with implicit inputs q % Subtract 1 Zq % Is prime? Implicit display ### Compute nCr(a,b): Xn % nchoosek with implicit inputs. Implicit display # Pyth, distance 4, total length 8 ## Primality of a^b-1 P_t^F Try it online! ## nCr(a, b) .cF Try it online! Both take input as tuples/lists of integers (e.g. (1,2)). # PHP, distance 14 Writing a program with two functions and only calling one of them would lead to a distance of 1, but it´d be too lame. Prime Test, 100 bytes: [,$a,$b]=$argv;function f($n){for($i=$n;--$i>0&&$n%$i;);return$i==1;}echo f($a**$b*-1)*(1|f($a-$b)); nCr, 98 bytes: [,$a,$b]=$argv;function f($n){for($i=$n;--$i>0&&$n*=$i;);return$n*=1;}echo f($a)/(f($b)*f($a-\$b)); # Jelly, distance 4, length 5 *’ÆP c Try it online! ## How it works *’ÆP Main link. Argument: a, b * Yield a**b. ’ Decrement; yield a**b-1. ÆP Test the result for primality. c nCr atom # JavaScript, Score:1, Length:144142126 117 function(a,b){s="a=Math.pow(a,b)-t;for(b=2;a%b++;);b>a1for(;b;)t=t*a--/b--";t=s.length-56;return eval(s.split(1)[0])} function(a,b){s="a=Math.pow(a,b)-s.length+79;for(b=2;a%b++;);b>a1for(t=s.length-79;b;)t=t*a--/b--";return eval(s.split(1)[1])} function A(a,b){a=Math.pow(a,b)-(B+0).length+63;for(b=2;a%b++;);return b>a;} function B(a,b){for(t=(A+0).length-76;b;)t=t*a--/b--;return t;} F=A Both subroutines use the other one's length to calculate its own constant, so no char can be removed

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# math posted by . solve the following exponential expression. e^x+e^-x=6 • math - e^x + e^-x = 6 e^x + 1/e^x = 6 hint: let e^x = y y + 1/y = 6 each term by y y^2 + 1 = 6y y^2 - 6y + 1 = 0 solve for y, then sub back into e^x ## Similar Questions 1. ### Math - Exponential equation Solve the exponential equation. Express your solutions in exact form only. Please show all of your work. 5e^(x log(9)) = 11 2. ### math change the exponential expression to an equivalent expression involving a logarithm. 8.8=7^x please show work 3. ### Math Use the expression 12*12 to answer the question below A. Write the expression using exponential notation B. What is the base? change the exponential expression to an equivalent expression involving a logarithm. 1.9=a^6 a=1.1129 is this the correct logarithmic expression? 5. ### Math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Solve the following exponential equations. 8(6^2x+5)=7^3x-4 6. ### math solve the following exponential equation e^x-4=-e^-x please show work 7. ### math solve the following exponential equation e^x-4=-e^-x when I work i get x-In(u) is this correct 8. ### math translate the phrase into a mathematical expression and then evaluate it. sixtten squared divided by four cubed. The given expression in symbols is? 9. ### Math Solve the following exponential equation 5^2-x=7^5x+7 10. ### Math Simplify the following exponential expression. 120a^4b^2/-24a^9b^-15 More Similar Questions

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Home > Calculus # Calculus ## Derivative of Trig Functions 2 Directions: Fill in the boxes below using the digits 1 to 6, at most one time each, to make the largest value for D (the derivative). Source: Chris Luzniak ## Derivative of e Directions: Using the digits 1-6, at most one time each, create an exponential function of base e whose derivative at x = 3 is 2. Source: Christine Relleva ## Derivative of Trig Functions 1 Directions: Fill in the boxes below using the digits 1 to 9, at most one time each, to make as many possible solutions as you can. Source: Chris Luzniak ## L’Hospital’s Rule Exploration Directions: Using the digits 1 to 9, at most one time each, create 3 different expressions such that their graphs contains any 2 of the 3 following criteria: 1) Horizontal Asymptote @ y = some positive rational number 2) Slant Asymptote with a slope such that: 1 < m ≤ 2 3) Two Vertical Asymptotes Source: Gregory L. Taylor, Ed.D. ## Derivative Power Rule Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes to create a true derivative statement. Source: Melissa Flynn ## Line Tangent to a Parabola Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes so that the line is tangent to the parabola. Source: Erin Stenger ## Tangent to a Cubic Graph Directions: Use the digits 1-9, at most one time each, to fill the blanks. Source: Catriona Shearer ## Derivatives Power Rule 2 Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create a function such that at x = 2, the derivative (at that point) is closest to the value of 449. Source: Gregory L. Taylor, Ed.D.

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ioombl1lem1 Structured version   Visualization version   GIF version Theorem ioombl1lem1 24176 Description: Lemma for ioombl1 24180. (Contributed by Mario Carneiro, 18-Aug-2014.) Hypotheses Ref Expression ioombl1.b 𝐵 = (𝐴(,)+∞) ioombl1.a (𝜑𝐴 ∈ ℝ) ioombl1.e (𝜑𝐸 ⊆ ℝ) ioombl1.v (𝜑 → (vol*‘𝐸) ∈ ℝ) ioombl1.c (𝜑𝐶 ∈ ℝ+) ioombl1.s 𝑆 = seq1( + , ((abs ∘ − ) ∘ 𝐹)) ioombl1.t 𝑇 = seq1( + , ((abs ∘ − ) ∘ 𝐺)) ioombl1.u 𝑈 = seq1( + , ((abs ∘ − ) ∘ 𝐻)) ioombl1.f1 (𝜑𝐹:ℕ⟶( ≤ ∩ (ℝ × ℝ))) ioombl1.f2 (𝜑𝐸 ran ((,) ∘ 𝐹)) ioombl1.f3 (𝜑 → sup(ran 𝑆, ℝ*, < ) ≤ ((vol*‘𝐸) + 𝐶)) ioombl1.p 𝑃 = (1st ‘(𝐹𝑛)) ioombl1.q 𝑄 = (2nd ‘(𝐹𝑛)) ioombl1.g 𝐺 = (𝑛 ∈ ℕ ↦ ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩) ioombl1.h 𝐻 = (𝑛 ∈ ℕ ↦ ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩) Assertion Ref Expression ioombl1lem1 (𝜑 → (𝐺:ℕ⟶( ≤ ∩ (ℝ × ℝ)) ∧ 𝐻:ℕ⟶( ≤ ∩ (ℝ × ℝ)))) Distinct variable groups:   𝐵,𝑛   𝐶,𝑛   𝑛,𝐸   𝑛,𝐹   𝑛,𝐺   𝑛,𝐻   𝜑,𝑛   𝑆,𝑛 Allowed substitution hints:   𝐴(𝑛)   𝑃(𝑛)   𝑄(𝑛)   𝑇(𝑛)   𝑈(𝑛) Proof of Theorem ioombl1lem1 StepHypRef Expression 1 ioombl1.a . . . . . . . 8 (𝜑𝐴 ∈ ℝ) 21adantr 484 . . . . . . 7 ((𝜑𝑛 ∈ ℕ) → 𝐴 ∈ ℝ) 3 ioombl1.p . . . . . . . 8 𝑃 = (1st ‘(𝐹𝑛)) 4 ioombl1.f1 . . . . . . . . . 10 (𝜑𝐹:ℕ⟶( ≤ ∩ (ℝ × ℝ))) 5 ovolfcl 24084 . . . . . . . . . 10 ((𝐹:ℕ⟶( ≤ ∩ (ℝ × ℝ)) ∧ 𝑛 ∈ ℕ) → ((1st ‘(𝐹𝑛)) ∈ ℝ ∧ (2nd ‘(𝐹𝑛)) ∈ ℝ ∧ (1st ‘(𝐹𝑛)) ≤ (2nd ‘(𝐹𝑛)))) 64, 5sylan 583 . . . . . . . . 9 ((𝜑𝑛 ∈ ℕ) → ((1st ‘(𝐹𝑛)) ∈ ℝ ∧ (2nd ‘(𝐹𝑛)) ∈ ℝ ∧ (1st ‘(𝐹𝑛)) ≤ (2nd ‘(𝐹𝑛)))) 76simp1d 1139 . . . . . . . 8 ((𝜑𝑛 ∈ ℕ) → (1st ‘(𝐹𝑛)) ∈ ℝ) 83, 7eqeltrid 2894 . . . . . . 7 ((𝜑𝑛 ∈ ℕ) → 𝑃 ∈ ℝ) 92, 8ifcld 4470 . . . . . 6 ((𝜑𝑛 ∈ ℕ) → if(𝑃𝐴, 𝐴, 𝑃) ∈ ℝ) 10 ioombl1.q . . . . . . 7 𝑄 = (2nd ‘(𝐹𝑛)) 116simp2d 1140 . . . . . . 7 ((𝜑𝑛 ∈ ℕ) → (2nd ‘(𝐹𝑛)) ∈ ℝ) 1210, 11eqeltrid 2894 . . . . . 6 ((𝜑𝑛 ∈ ℕ) → 𝑄 ∈ ℝ) 13 min2 12578 . . . . . 6 ((if(𝑃𝐴, 𝐴, 𝑃) ∈ ℝ ∧ 𝑄 ∈ ℝ) → if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) ≤ 𝑄) 149, 12, 13syl2anc 587 . . . . 5 ((𝜑𝑛 ∈ ℕ) → if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) ≤ 𝑄) 15 df-br 5032 . . . . 5 (if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) ≤ 𝑄 ↔ ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩ ∈ ≤ ) 1614, 15sylib 221 . . . 4 ((𝜑𝑛 ∈ ℕ) → ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩ ∈ ≤ ) 179, 12ifcld 4470 . . . . 5 ((𝜑𝑛 ∈ ℕ) → if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) ∈ ℝ) 1817, 12opelxpd 5558 . . . 4 ((𝜑𝑛 ∈ ℕ) → ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩ ∈ (ℝ × ℝ)) 1916, 18elind 4121 . . 3 ((𝜑𝑛 ∈ ℕ) → ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩ ∈ ( ≤ ∩ (ℝ × ℝ))) 20 ioombl1.g . . 3 𝐺 = (𝑛 ∈ ℕ ↦ ⟨if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄), 𝑄⟩) 2119, 20fmptd 6860 . 2 (𝜑𝐺:ℕ⟶( ≤ ∩ (ℝ × ℝ))) 22 max1 12573 . . . . . . 7 ((𝑃 ∈ ℝ ∧ 𝐴 ∈ ℝ) → 𝑃 ≤ if(𝑃𝐴, 𝐴, 𝑃)) 238, 2, 22syl2anc 587 . . . . . 6 ((𝜑𝑛 ∈ ℕ) → 𝑃 ≤ if(𝑃𝐴, 𝐴, 𝑃)) 246simp3d 1141 . . . . . . 7 ((𝜑𝑛 ∈ ℕ) → (1st ‘(𝐹𝑛)) ≤ (2nd ‘(𝐹𝑛))) 2524, 3, 103brtr4g 5065 . . . . . 6 ((𝜑𝑛 ∈ ℕ) → 𝑃𝑄) 26 breq2 5035 . . . . . . 7 (if(𝑃𝐴, 𝐴, 𝑃) = if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) → (𝑃 ≤ if(𝑃𝐴, 𝐴, 𝑃) ↔ 𝑃 ≤ if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄))) 27 breq2 5035 . . . . . . 7 (𝑄 = if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) → (𝑃𝑄𝑃 ≤ if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄))) 2826, 27ifboth 4463 . . . . . 6 ((𝑃 ≤ if(𝑃𝐴, 𝐴, 𝑃) ∧ 𝑃𝑄) → 𝑃 ≤ if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)) 2923, 25, 28syl2anc 587 . . . . 5 ((𝜑𝑛 ∈ ℕ) → 𝑃 ≤ if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)) 30 df-br 5032 . . . . 5 (𝑃 ≤ if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄) ↔ ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩ ∈ ≤ ) 3129, 30sylib 221 . . . 4 ((𝜑𝑛 ∈ ℕ) → ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩ ∈ ≤ ) 328, 17opelxpd 5558 . . . 4 ((𝜑𝑛 ∈ ℕ) → ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩ ∈ (ℝ × ℝ)) 3331, 32elind 4121 . . 3 ((𝜑𝑛 ∈ ℕ) → ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩ ∈ ( ≤ ∩ (ℝ × ℝ))) 34 ioombl1.h . . 3 𝐻 = (𝑛 ∈ ℕ ↦ ⟨𝑃, if(if(𝑃𝐴, 𝐴, 𝑃) ≤ 𝑄, if(𝑃𝐴, 𝐴, 𝑃), 𝑄)⟩) 3533, 34fmptd 6860 . 2 (𝜑𝐻:ℕ⟶( ≤ ∩ (ℝ × ℝ))) 3621, 35jca 515 1 (𝜑 → (𝐺:ℕ⟶( ≤ ∩ (ℝ × ℝ)) ∧ 𝐻:ℕ⟶( ≤ ∩ (ℝ × ℝ)))) Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084   = wceq 1538   ∈ wcel 2111   ∩ cin 3880   ⊆ wss 3881  ifcif 4425  ⟨cop 4531  ∪ cuni 4801   class class class wbr 5031   ↦ cmpt 5111   × cxp 5518  ran crn 5521   ∘ ccom 5524  ⟶wf 6323  ‘cfv 6327  (class class class)co 7140  1st c1st 7676  2nd c2nd 7677  supcsup 8895  ℝcr 10532  1c1 10534   + caddc 10536  +∞cpnf 10668  ℝ*cxr 10670   < clt 10671   ≤ cle 10672   − cmin 10866  ℕcn 11632  ℝ+crp 12384  (,)cioo 12733  seqcseq 13371  abscabs 14592  vol*covol 24080 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5168  ax-nul 5175  ax-pow 5232  ax-pr 5296  ax-un 7448  ax-cnex 10589  ax-resscn 10590  ax-pre-lttri 10607  ax-pre-lttrn 10608 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ne 2988  df-nel 3092  df-ral 3111  df-rex 3112  df-rab 3115  df-v 3443  df-sbc 3721  df-csb 3829  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-nul 4244  df-if 4426  df-pw 4499  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4802  df-br 5032  df-opab 5094  df-mpt 5112  df-id 5426  df-po 5439  df-so 5440  df-xp 5526  df-rel 5527  df-cnv 5528  df-co 5529  df-dm 5530  df-rn 5531  df-res 5532  df-ima 5533  df-iota 6286  df-fun 6329  df-fn 6330  df-f 6331  df-f1 6332  df-fo 6333  df-f1o 6334  df-fv 6335  df-1st 7678  df-2nd 7679  df-er 8279  df-en 8500  df-dom 8501  df-sdom 8502  df-pnf 10673  df-mnf 10674  df-xr 10675  df-ltxr 10676  df-le 10677 This theorem is referenced by:  ioombl1lem3  24178  ioombl1lem4  24179 Copyright terms: Public domain W3C validator

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# How to Determine if a Graph is a Function – Quick Guide to Understanding Graphs To determine if a graph is a function, I first check whether every vertical line I can draw on the graph intersects it at no more than one point. This is known as the vertical line test. It’s a simple method that visually confirms whether a set of points on a graph represents a function, which by definition pairs each input with exactly one output. The process of identifying functions is foundational in math since functions are essential for understanding various relations and visual information conveyed through graphs. For a graph to represent a function, each input value (represented on the x-axis) should correspond to no more than one output value (on the y-axis). If I can draw any vertical line that touches the graph in more than one place, then the graph does not represent a function. The clarity of this graphical approach helps me understand and illustrate math concepts effectively, especially when I’m exploring complex relations. Stick around, and I’ll show you just how this technique brings the abstract idea of functions into a clear and understandable light. ## Determining Functions from Graphs When I look at a graph, the main thing I’m checking for is whether or not it represents a function. A function is a special relationship where every input in the domain has exactly one output in the range. To check if a graph is a function, I use the vertical line test. This method involves imagining drawing vertical lines through every part of the graph. If any vertical line intersects the graph at more than one point, then it’s not a function. This is because multiple points on the same vertical line mean an input value is mapped to more than one output value. In function notation, for a given function ( f ), the function value ( f(x) ) is the output for an input ( x ). If ( x ) is in the function’s domain, there will be a corresponding point on the graph with coordinates ( (x, f(x)) ), which are the ordered pairs made of the x-coordinate and y-coordinate. Graphs of basic toolkit functions like linear functions $( y=mx+b )$, quadratic (( y=ax^2+bx+c )), cubic $( y=ax^3+bx^2+cx+d )$, reciprocal $( y=\frac{1}{x} )$, cube root $( y=\sqrt[3]{x} )$, circle $( x^2+y^2=r^2 )$, parabola $( y=ax^2 )$, and absolute value (( y=|x| )) will pass the vertical line test. Here’s a simple table highlighting several function types and their general equations: Function TypeGeneral Equation Linear Function$y=mx+b$ Quadratic Function$y=ax^2+bx+c$ Cubic Function$y=ax^3+bx^2+cx+d$ Absolute Function$y=|x|$ Square Root Function$y=\sqrt{x}$ Memorizing the shapes and equations of these toolkit functions is extremely helpful. When I see a straight line on a coordinate plane, I immediately think of the slope-intercept form. If it’s a curve that opens upwards or downwards like a U, that’s a sign of a quadratic. Identifying these patterns allows me to quickly assess whether a graph meets the criteria of a function. ## Functional Characteristics and Testing In my experience with functions, certain characteristics are essential in determining whether a graph represents a function. When I look at a graph, I remember that for it to depict a function, each input value must have exactly one output value. This relation means if I select any value for x (the input), there can be only one corresponding y (the output). I use the Vertical Line Test to quickly ascertain a function’s legitimacy on a graph. This test involves imagining or drawing vertical lines across the graph. If any vertical line intersects the graph in more than one point, then the graph does not represent a function. Test NameDescription Vertical Line TestIf a vertical line intersects the graph at more than one point, the graph is not a function. Horizontal Line TestUsed to check if a function is one-to-one by seeing if any horizontal line crosses the graph more than once. Additionally, I consider specific types of functions: • Constant Function: As the name suggests, for every x value, the output is the same. These graphs are horizontal lines, such as ( y = c ), where c is the constant. • Identity Function: The output is equal to the input, which means ( f(x) = x ). These are straight lines through the origin at a 45-degree angle. • Absolute Value Function: These graphs have a ‘V’ shape and follow ( f(x) = |x| ). • Square Root Function: Starting at zero and increasing, their graphs follow $f(x) = \sqrt{x}$. For functions needing more clarity, I often use function notation, for instance ( f(x) ), to explicitly indicate the output values corresponding to each x. When distinguishing between general functions and one-to-one functions, which have unique outputs for each input, the Horizontal Line Test provides clarity. If any horizontal line crosses the graph more than once, the function isn’t one-to-one. Lastly, understanding the foundational aspects of algebra always enhances my ability to analyze functions, as it encompasses the rules and methods that govern the operations and relations of the symbols and numbers. ## Conclusion In assessing whether a graph represents a function, I always remember the basic principle that for each input value, there must be only one output value. This means when I use the Vertical Line Test, I’m looking to ensure that a vertical line intersects the graph at most once. If it crosses more than once, then the graph does not depict a function. For linear, quadratic, or any other type of function, confirming function status is as simple as checking this one-to-one relationship between x-coordinates and y-coordinates. For a linear function with the form $y = mx + b$, the linearity itself guarantees adherence to the function criteria. However, for a quadratic function given by $y = ax^2 + bx + c$, the parabolic shape should be scrutinized for any potential vertical line intersections that occur more than once. In my experience, it’s crucial to combine these methods with an understanding of different types of functions and their representations. With this knowledge, I can effectively determine the functionality of a graph, paving the way for further analysis and interpretation of the mathematical function it represents.

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# Group of integers (Redirected from Infinite cyclic group) View a complete list of particular groups (this is a very huge list!)[SHOW MORE] ## Definition ### Usual definition The group of integers, typically denoted $\mathbb{Z}$, is defined as follows: • The underlying set is the set of all integers • The group operation is integer addition • The identity element is the integer $0$ • The inverse map is the additive inverse, sending an integer $n$ to the integer $-n$ In the 4-tuple notation, the group of integers in the group $(\mathbb{Z},+, 0, -)$. ### Other definitions Some other equivalent formulations of the group of integers: • It is the additive group of the ring of integers • It is the infinite cyclic group • It is the free group on one generator • It is the free abelian group on one generator ## Arithmetic functions Function Value Explanation order ((number of elements, equivalently, cardinality or size of underlying set) Infinite (countable) Not a finite group. exponent Infinite Not a periodic group. derived length 1 The group is an abelian group. nilpotency class 1 The group is an abelian group. Fitting length 1 The group is an abelian group. Frattini length 1 The group is a Frattini-free group. subgroup rank of a group 1 The group is cyclic, hence so is every subgroup. ## Group properties Property Satisfied Explanation Comment cyclic group Yes abelian group Yes Cyclic implies abelian finite group No finitely generated group Yes Generating set of size one. slender group Yes Every subgroup is cyclic. Hopfian group Yes Not isomorphic to any proper quotient, which is finite. co-Hopfian group No Isomorphic to the proper subgroup generated by any element not the generator or the identity. ## GAP implementation The group can be defined using the FreeGroup function: FreeGroup(1)

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# September 1, 110 years ago: trigonometry, the dollar rate and sparklers For the Day of Knowledge, we have prepared an "antique" post. Since our product, the geometric core, is closely connected with mathematics, and more precisely with its sections “Differential Geometry” and “Numerical Methods”, mathematical curiosities cause us a special thrill. The family archive of one of the employees of C3D Labs keeps a calendar of students “Comrade” for the years 1909-1910. There is a lot of curious about mathematics and not only what we want to share. School e-magazine and Wikipedia is dedicated. "Comrade" was not an ordinary diary, as we know it. In one small book, together with the schedule and estimates, the Orthodox calendar, a dictionary of foreign words, exchange rates, tips for photographers, courtesy rules, Bengal lights recipes and a lot of useful information fit. The calendar was produced in St. Petersburg by the Otto Kirchner Publishing House. The picture is clickable. Our calendar belonged to 11-year-old high school student Kohl Minko, who lived in Odessa with his parents and older sisters. Kolya Minko with sisters Olga and Anna (Picture is clickable) Kohl studied so-so. But later he corrected himself: he graduated from the Physics and Mathematics Faculty of Odessa University and worked as a design engineer. The picture is clickable # Maths Mathematical sections are located in the calendar immediately after the genealogy of the Russian sovereigns, which indicates the importance of the exact sciences. First come the table of squares / cubes and the table of initial numbers. Behind them is the multiplication table. The picture is clickable Next arithmetic and algebra - from the rules of multiplication and signs of divisibility to progressions and logarithms. The picture is clickable The picture is clickable The formula of the side of a regular 15 square, inscribed in a circle, looks impressive. Not all freshmen can withdraw it. A colleague from ASCON, who teaches at the department of engineering graphics, says that with the hexagon students have difficulty. The picture is clickable. Trigonometry gives the familiar formulas of sines, cosines and tangents. The image is clickable . Analytical geometry completes the mathematical part of the calendar. The picture is clickable The picture is clickable The rest exact sciences are presented modestly. Physics and astronomy fall on one page, on chemistry - two. The picture is clickable. But how compact the periodic table looked at the beginning of the 20th century. The picture is clickable # Accounting Why should a high school student learn mathematics? To count money! The calendar has a real account book for accounting of income / expenditure. Debtors and own debts were entered into separate signs. Picture clickable Picture clickable # Geography But Tovarishch did not prepare its owner for the modest life of the accountant in the county town. On the contrary, he tuned to travel and discovery. States and their rulers, the most populated cities of the world, railways, rivers and bridges, travel measures (kilometers / versts / miles) and length measures (tops / inches / centimeters), time zones, degrees Celsius and Fahrenheit, exchange rates - all that the gymnasium student should have known so as not to get lost in distant countries. In 1909, in Annam (part of present-day Vietnam), Tam-Thai ruled, Negus Menelik II was in charge of Abyssinia (despots, as the calendar notes), and Morena (Moreira) Penn was president of the Brazilian United States. The picture is clickable. For pound sterling they gave 9 rubles. 45 ¾ pennies, for a dollar - 1 rub. 94.3 kopecks The picture is clickable The most populated city in the world was London with 6.55 million inhabitants. In Moscow, there were 1.04 million people, in Beijing - only 1 million. Literacy statistics of the population, alas, are not in our favor: in Russia there are 16 literate and 3 students per 100 souls, in Germany - 98 and 18, in the USA - 92 and 23 respectively. The picture is clickable. A list of the most important discoveries and inventions of the 19th century: smallpox inoculation, loom, tunnel under the Thames, telephone, telegraph, X-rays. Between them, hypnotism started. The picture is clickable # To applicants To continue education at the disposal of high school students was a list of higher educational institutions of the Russian Empire and the conditions for admission. The picture is clickable. And here is an extract from the statute of military service on the benefits and delays. Picture clickable Picture clickable # Mail, telegraph, telephone At the beginning of the 20th century, telephone communication slowly penetrated into life. For telephone for personal and family use in St. Petersburg charged 49 rubles. 50 kopecks per year, in Moscow - 71 rubles. 10 kopecks Compare with the cost of training: the Mining Institute of Empress Catherine II (St. Petersburg) - 100 rubles. per year, the Imperial Moscow Technical School - 75 rubles. in year. The picture is clickable. But the main means of communication over long distances remained letters for a long time, so the postal rules are set out in the calendar in the most detail. The picture is clickable # Photo lovers Photographers, rate! The calendar contains recipes for six types of developers: pyrogallic soda, durable pyrogallic with potassium meta-2-sulfur sulphate, hydroquinone, metol, glycine, mixed eicogenic-hydroquinone. The picture is clickable # health and beauty Perhaps this is the most wonderful section of the calendar, if you look at it from 2018. Here we brought first aid, a first-aid kit, hygiene tips and instructions on measures to protect against cholera. Vaseline, French turpentine, quinine, Hoffman drops, Danish king drops, castor oil, carbolic acid are recommended in the home first aid kit. First aid for burns and cuts - raw egg whites to eliminate pain and speed wound healing. A saturated solution of naphthalene in liquid petrolatum is shown as an otkomamar, which should be lubricated with the face, neck and hands every 2-3 hours. The picture is clickable "In no case do not wear narrow shoes and high heels." We support! The picture is clickable # Sparklers Well, at the end of the promised recipe. For white light: saltpeter 76 h, sulfur 22 ½ h, antimonium 1 h. And you can also make green, red, yellow, purple, orange fire and rain. The picture is clickable

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# Does thermodynamic work flow always involve pressure change? From my previous question What is enthalpy? I learned that enthalpy is the amount of energy required to set up a thermodynamic system plus the energy required to make space for it. It is true that $\Delta H = Q$ when pressure is constant while the change happens. It seems indeed to be the most delicious use of the concept. Which now I interpret as: Enthalpy change in a process that doesn't require a change in the space the system needs will be equal to the heat flow. Which means: there is no work flow when there is no change in the space the system needs. That confuses me a bit. And that confusion made me find this question (Does work always imply a change in volume? - Answer: yes for mechanical work but no for other cases.) My question is parallel, but it regards the pressure: Why is there no work flow for constant pressure processes? Can I not expand a gas while increasing its temperature to keep the pressure constant? • Who says there is no work done in a constant pressure process? Aug 18, 2016 at 17:16 • @ChesterMiller I interpreted it from the fact that all the enthalpy change is equal to heat flow in a constant pressure process. If enthalpy considers all the internal energy and internal energy considers heat and work, and there is only heat, then there is no work. Of course i might be wrong, but that is the core of my question. Thank you Chester, with all my heart. Aug 18, 2016 at 17:26 • In an isobaric process: $W=\int_{V_1}^{V_2}pdV=p(V_2-V_1)$. – Gert Aug 18, 2016 at 17:33 • To expand on Gert's comment, for a constant pressure process, $\Delta U=Q-W=Q-P\Delta V$ and $$\Delta H=\Delta U+\Delta (PV)=\Delta U+P\Delta V=Q-P\Delta V+P\Delta V=Q$$ Aug 18, 2016 at 18:53 • Sure it is. The work done by the system on the surroundings is equal to minus the work done by the surroundings on the system. Aug 19, 2016 at 11:33 Objects and systems usually expand as they are heated up, or receive an input of heat. So they will do work on the environment around them. This means $W$ is negative, using the standard convention. So internal energy is lost as work, therefore you need to add in heat to restore that energy. Now assume the pressure surrounding your system is constant, then the heat required per degree is called the heat capacity at constant pressure. Heat capacity is $C = Q/\Delta T = (\Delta U -W)/\Delta T$ So $C_p = [(\Delta U - (- P\Delta V)]/\Delta T$ holding pressure constant. = $\left(\frac{\partial U}{\partial T} \right)$ + $P\left(\frac{\partial V}{\partial T} \right)$ (pressure of partial derivatives assumed held constant in both expressions). The final term $P\left(\frac{\partial V}{\partial T} \right)$ is the additional heat we need to supply to make up for the energy lost as work on the environment • Álvaro Could I make two suggestions to you please. 1. Make a list of all the thermodynamic related equations on a separate page, away from your notes, as it is very easy to get lost with these formulae 2. Read over my previous answer about enthalpy, and then see can you relate it to this above answer. It does require a bit of study to follow the argument, but doing the exercises in your textbook is always worthwhile. Best of luck with it. – user108787 Aug 18, 2016 at 18:44

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# Back to school: Let's make mathematics more interesting | Opinion Alfred S. Posamentier Special to the USA TODAY Network Now that the school year has begun and students are slowly acclimating to live instruction, teachers are once again present in the classroom where one of their chief responsibilities is to make their instruction exciting and motivating. When we think back about how we selected our life’s area of interest, very often it goes back to a highly motivating teacher who extended her subject beyond the textbook. All too often, when I am in a social setting meeting new people, they may ask about my profession and when I mentioned the word mathematics the most frequent response I receive is, “Oh my gosh. I struggled through mathematics in school and I’m glad it’s behind me.” Unfortunately, too many mathematics teachers are more concerned about “teaching to the test” than making the subject truly interesting. At this point, you might be asking how does one make mathematics more interesting? Yes, it requires going beyond the textbook. When working with elementary school students where teachers expect students to realize that a number ending in an even digit is divisible by 2, why not extend that and say that when the number formed by the last two digits is divisible by 4, then the original number is divisible by 4. This, of course, could be extended to the last three digits determining whether a number is divisible by 8. Or showing students that by merely looking at a number and adding the digits, they can determine whether is divisible by 3 or 9, that is, if the sum of the digits is divisible by 3 or 9 then the number itself is divisible by 3 or 9. And so there are lots of rules for divisibility that are not part of the textbook and yet can make students truly appreciate arithmetic. Telling a relevant historical story can also enhance mathematics instruction. For example, when in 1787 the famous German mathematician Carl Friedrich Gauss at age 10 was in a class with a teacher who wanted to keep the class busy for a period of time, asked the class to add the numbers from 1 to 100. No sooner had the assignment been given that young Carl Friedrich raised his hand with an answer. The teacher ignored him and found at the end of the half-hour that he was the only one with the correct answer. Instead of adding the numbers in sequence, he saw that adding 1 +100, 2 +99, 3+98 allowed him to merely multiply 50×101 = 5,050. This provided both the teacher and the class with a fresh view of arithmetic. When thinking back to the high school geometry class most people recall that it consisted largely of doing geometric proofs. Unfortunately, not enough attention was given to exploring some of the astonishing results that we can visualize in geometry. For example, suppose you take any 4-sided figure (quadrilateral) and locate the midpoint of each of the four sides. By joining these midpoints consecutively, regardless of the shape of the original quadrilateral, the result will always be a parallelogram. Taking this a step further, a teacher could use this scheme to ask students under what circumstances will this resulting parallelogram be a square, rectangle, or a rhombus? We are currently inundated with daily statistical reports about the COVID-19 pandemic. Understanding these reports is very important. Related to this is the topic of probability, which is being taught more in the schools now than in previous years, and yet too often teachers do not properly motivate students by employing some of the spectacular results that can be garnered in everyday life situations. For example, the probability of two students in a class of 30 students having the same birth date is astonishingly 71%. In a group of 50 students, it’s almost 100%. Having mentioned that, most students would be eager to find out how that was arrived at. What could be a more motivating way of introducing probability than that? It is clear that we are struggling to get back to some form of normality in school settings by providing students with the excitement of socialization and the richness of on-site instruction, for which there is no learning parallel. After this isolating hiatus, wouldn’t it be great if we opened up, as well, a new leaf for our instructional techniques, making the return to school feel even more consequential and stimulating. For the mathematics teacher, there is the opportunity to motivate students to explore mathematics concepts and ideas through activities that extend beyond the textbook, creating math enthusiasm through real-time examples. Invoking interest in math is not only a meaningful task for mathematics teachers but for parents, who can encourage students to study mathematics without apprehension and with an appreciation for its relevance in their own lives. Let’s make sure that the next generation, growing up in a more technological world than in the past, will genuinely appreciate the power and beauty of mathematics. Alfred S. Posamentier is a lecturer and professor emeritus of mathematics education at The City College of New York.

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# how to make the data for the ad9910's Ramp-up Question asked by ludong on Aug 21, 2016 Latest reply on Aug 21, 2016 by LouijieC my question: 1) I make one cycle of the sin, the data [ Polar (phase and amplitude)] like this: mysin[0]<=32'h0000ffff; mysin[1]<=32'h0a3dffff; mysin[2]<=32'h147affff; mysin[3]<=32'h1eb7ffff; mysin[4]<=32'h28f4ffff; mysin[5]<=32'h3331ffff; mysin[6]<=32'h3d6effff; mysin[7]<=32'h47abffff; mysin[8]<=32'h51e8ffff; mysin[9]<=32'h5c25ffff; mysin[10]<=32'h6662ffff; mysin[11]<=32'h709fffff; mysin[13]<=32'h8519ffff; mysin[14]<=32'h8f56ffff; mysin[15]<=32'h9993ffff; mysin[16]<=32'ha3d0ffff; mysin[17]<=32'hae0dffff; mysin[18]<=32'hb84affff; mysin[19]<=32'hc287ffff; mysin[20]<=32'hccc4ffff; mysin[21]<=32'hd701ffff; mysin[22]<=32'he13effff; mysin[23]<=32'heb7bffff; mysin[24]<=32'hf5b8ffff; mysin[25]<=32'h0000ffff; I didn't got  one cycle of the sin. I write the data : 0x16 data1 dtata2 data3 data4 .... data25. 2) The data sheet of ad9910 didn't explain the way of write ram data. I think have two Possibility : a: 0x16 data1 0x16 data2 0x16 data3 0xa16 data4......0x16 data25 b: 0x16 data1 dtata2 data3 data4 .... data25 I don't know which is correct. I write only the 0x16 and don't the data ,the ram_swp_over is correct. I want toget the example code for the ramp-up of polar,who can give me,thank you very much!

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Term Rewriting System R: [x, y, z] minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Termination of R to be shown. ` R` ` ↳Dependency Pair Analysis` R contains the following Dependency Pairs: MINUS(s(x), s(y)) -> MINUS(x, y) QUOT(s(x), s(y)) -> QUOT(minus(x, y), s(y)) QUOT(s(x), s(y)) -> MINUS(x, y) PLUS(s(x), y) -> PLUS(x, y) PLUS(minus(x, s(0)), minus(y, s(s(z)))) -> PLUS(minus(y, s(s(z))), minus(x, s(0))) Furthermore, R contains three SCCs. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polynomial Ordering` ` →DP Problem 2` ` ↳Polo` ` →DP Problem 3` ` ↳Polo` Dependency Pair: MINUS(s(x), s(y)) -> MINUS(x, y) Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) The following dependency pair can be strictly oriented: MINUS(s(x), s(y)) -> MINUS(x, y) Additionally, the following rules can be oriented: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Used ordering: Polynomial ordering with Polynomial interpretation: POL(plus(x1, x2)) =  x1 + x2 POL(0) =  0 POL(minus(x1, x2)) =  x1 POL(MINUS(x1, x2)) =  x1 POL(quot(x1, x2)) =  x1 POL(s(x1)) =  1 + x1 resulting in one new DP problem. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polo` ` →DP Problem 4` ` ↳Dependency Graph` ` →DP Problem 2` ` ↳Polo` ` →DP Problem 3` ` ↳Polo` Dependency Pair: Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Using the Dependency Graph resulted in no new DP problems. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polo` ` →DP Problem 2` ` ↳Polynomial Ordering` ` →DP Problem 3` ` ↳Polo` Dependency Pair: QUOT(s(x), s(y)) -> QUOT(minus(x, y), s(y)) Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) The following dependency pair can be strictly oriented: QUOT(s(x), s(y)) -> QUOT(minus(x, y), s(y)) Additionally, the following rules can be oriented: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Used ordering: Polynomial ordering with Polynomial interpretation: POL(plus(x1, x2)) =  x1 + x2 POL(QUOT(x1, x2)) =  x1 POL(0) =  0 POL(minus(x1, x2)) =  x1 POL(quot(x1, x2)) =  x1 POL(s(x1)) =  1 + x1 resulting in one new DP problem. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polo` ` →DP Problem 2` ` ↳Polo` ` →DP Problem 5` ` ↳Dependency Graph` ` →DP Problem 3` ` ↳Polo` Dependency Pair: Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Using the Dependency Graph resulted in no new DP problems. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polo` ` →DP Problem 2` ` ↳Polo` ` →DP Problem 3` ` ↳Polynomial Ordering` Dependency Pairs: PLUS(minus(x, s(0)), minus(y, s(s(z)))) -> PLUS(minus(y, s(s(z))), minus(x, s(0))) PLUS(s(x), y) -> PLUS(x, y) Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) The following dependency pair can be strictly oriented: PLUS(s(x), y) -> PLUS(x, y) Additionally, the following rules can be oriented: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Used ordering: Polynomial ordering with Polynomial interpretation: POL(plus(x1, x2)) =  x1 + x2 POL(PLUS(x1, x2)) =  x1 + x2 POL(0) =  0 POL(minus(x1, x2)) =  x1 POL(quot(x1, x2)) =  x1 POL(s(x1)) =  1 + x1 resulting in one new DP problem. ` R` ` ↳DPs` ` →DP Problem 1` ` ↳Polo` ` →DP Problem 2` ` ↳Polo` ` →DP Problem 3` ` ↳Polo` ` →DP Problem 6` ` ↳Remaining Obligation(s)` The following remains to be proven: Dependency Pair: PLUS(minus(x, s(0)), minus(y, s(s(z)))) -> PLUS(minus(y, s(s(z))), minus(x, s(0))) Rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0))) Termination of R could not be shown. Duration: 0:00 minutes

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# Thread: Euclid's Algorithm and Bezout's Identity 1. ## Euclid's Algorithm and Bezout's Identity Prove: If $am + bn = e$ for some $e$, then $(a,b)$ divides $e$. 2. Originally Posted by Zennie Prove: If $am + bn = e$ for some $e$, then $(a,b)$ divides $e$. By lemma of Euclid Algorithm: if gcd(a,b)= e then there exist m,n (integers) s.t. e= am+bn . Since gcd(a,b) is e. then a divides e. and b divides e?

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# Semir, Sarah, and sungso How many meals did the three sell in all? Explain how to use the commutative property and the associative property of addition to make finding the sum easier Semir, Sarah, and sungso How many meals did the three sell in all? Explain how to use the commutative property and the associative property of addition to make finding the sum easier

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# Storing doubles in the smallest integer class for which they fit without changing their value? 1 view (last 30 days) James Metz on 3 Apr 2020 Commented: James Metz on 3 Apr 2020 I am trying to create function that accepts an input array, A, and converts it to the smallest integer class for which it can be stored without changing the information in the matrix. If the matrix does not have any negative numbers it needs to be converted to the smallest possible unsigned integer type. Lastly, if none of the integer types are suitable, the matrix is returned without changing. I am super new to MATLAB, so I hardly know all the built-in functions to make this code easy, nor do I really understand how MATLAB stores the information, but I have attached my code attempt below. function smallint = store_small(A) A = []; [rows, cols] = size(A); for ii = 1:rows for jj = 1:cols if any(A(ii, jj)) < 0 if A(ii, jj) >= (-2)^7 && A(ii, jj) <= (2^7)-1 smallint = int8(A); elseif A(ii, jj) >= (-2)^15 && A(ii, jj) <= (2^15)-1 smallint = int16(A); elseif A(ii, jj) >= (-2)^31 && A(ii, jj) <= (2^31)-1 smallint = int32(A); elseif A(ii, jj) >= (-2)^53 && A(ii, jj) <= (2^53)-1 smallint = int64(A); else smallint = A; end else if A(ii, jj) <= (2^8)-1 smallint = unit8(A); elseif A(ii, jj) <= (2^16)-1 smallint = unit16(A); elseif A(ii, jj) <= (2^32)-1 smallint = unit32(A); elseif A(ii, jj) <= (2^64)-1 smallint = unit64(A); else smallint = A; end end end end end As you can tell, I took the time to type out all of those inequalities which is probably a rather monotonous way to do it for the more advanced. Either way, I'm hoping someone can tell me where I'm going wrong. • my function does not return a matrix. I'm not sure if this is due to the ; or just because the code is not right. • my function also gives an incorrect output for the input zero. • i did not add second conditions to each "elseif" statement when dealing with A values that were all greater than zero because I think MATLAB checks the elseif statements one at a time and if it is true, spits out the respective value of that elseif statment and stops. I could be wrong though. James Tursa on 3 Apr 2020 Edited: James Tursa on 3 Apr 2020 Some hints: Don't use loops, use vectorized code to figure out which integer size works. intmax(type) gives you the largest value for the type. E.g., intmax('int8') or intmax('uint32'). Use these for your range checks. Also note that signed integers use 2's complement so the range is not exactly symmetric about 0 if you care for this detail. E.g., the range of a int8 is -128 to 127. Or, if processing time is not an issue, simple brute force would be easy to code. E.g., if( any(A(:)<0) ) smallint = int8(A); if( isequal(A,smallint) ) return end smallint = int16(A); if( isequal(A,smallint) ) return end etc. else smallint = uint8(A); if( isequal(A,smallint) ) return end smallint = uint16(A); if( isequal(A,smallint) ) return end etc. end smallint = A; You could even put the brute force stuff in a loop. ##### 2 CommentsShowHide 1 older comment James Metz on 3 Apr 2020

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# A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. Question: A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32. (a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere? (c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller. Solution: Radius of the inner sphere, $r_{2}=12 \mathrm{~cm}=0.12 \mathrm{~m}$ Radius of the outer sphere, $r_{1}=13 \mathrm{~cm}=0.13 \mathrm{~m}$ Charge on the inner sphere, $q=2.5 \mu \mathrm{C}=2.5 \times 0^{-6} \mathrm{C}$ Dielectric constant of a liquid, $\in_{r}=32$ (a) Capacitance of the capacitor is given by the relation, $C=\frac{4 \pi \in_{0} \in_{r} r_{1} r_{2}}{r_{1}-r_{2}}$ Where, $\epsilon_{0}=$ Permittivity of free space $=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ $\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}$ $\therefore C=\frac{32 \times 0.12 \times 0.13}{9 \times 10^{9} \times(0.13-0.12)}$ $\approx 5.5 \times 10^{-9} \mathrm{~F}$ Hence, the capacitance of the capacitor is approximately $5.5 \times 10^{-9} \mathrm{~F}$. (b) Potential of the inner sphere is given by, $V=\frac{q}{C}$ $=\frac{2.5 \times 10^{-6}}{5.5 \times 10^{-9}}=4.5 \times 10^{2} \mathrm{~V}$ Hence, the potential of the inner sphere is $4.5 \times 10^{2} \mathrm{~V}$. (c) Radius of an isolated sphere, = 12 × 10−2 m Capacitance of the sphere is given by the relation, $C^{\prime}=4 \pi \in_{0} r$ $=4 \pi \times 8.85 \times 10^{-12} \times 12 \times 10^{-12}$ $=1.33 \times 10^{-11} \mathrm{~F}$ The capacitance of the isolated sphere is less in comparison to the concentric spheres. This is because the outer sphere of the concentric spheres is earthed. Hence, the potential difference is less and the capacitance is more than the isolated sphere.

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Stata 3 HW # Stata 3 HW - Homework 3 Economics 120B Due December 5 th ,... This preview shows pages 1–2. Sign up to view the full content. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: Homework 3 Economics 120B Due December 5 th , 2008 at the beginning of the lecture All the files mentioned in this homework are available in our course Webct. Print the output (.log) file from your STATA work and staple it to your answer sheet. Some questions are theoretical and you will not need Stata to answer them. Try to use Stata as much as you can for all the other questions. Dont forget to set up your work by: a. Setting the central directory to C:\Econ120B (C:\Econ120B is just a suggestion: you can call your central directory whatever you want). b. Opening a log file. YOU NEED TO PRINT OUT YOUR LOG FILE SO DONT FORGET TO OPEN IT. You can do that by typing the command: log using hmw3.log, replace c. After opening each of the datasets you will need for each question, save your data as a new dataset (for example, you might call it filename _hmw3_out.dta). Now answer the following questions: 1) The dataset hprice1.dta was collected from the real estate pages of the Boston Globe during 1990. These were homes selling in the Boston, MA area. a. Use the dataset to estimate the model u bdrms qrft price + + + = 2 1 s * b. What is the estimated increase in price for a house with one more bedroom, holding square footage constant? c. What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size? Compare this to your answer to part b. d. What percentage of the variation in price is explained by square footage and number of bedrooms? e. The first house in the sample has sqrft = 2,438, and bdrms = 4. Find the predicted selling price for this house from the OLS regression line. f. The actual selling price for the first house in the sample was \$300,000 (so price = 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house? g. We want to test the rationality of assessments of housing prices. To do that, we regress the following single regression: u assess price + + = 1 , where price is the house price and assess is the assessed housing value (before the house was sold). Report your estimated regression line.... View Full Document ## This note was uploaded on 02/01/2009 for the course ECON 23423 taught by Professor Staff during the Winter '08 term at UCSD. ### Page1 / 4 Stata 3 HW - Homework 3 Economics 120B Due December 5 th ,... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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# How much do the Vikings mean to Vikings fans? \$530.65 per person Here's something interesting that means absolutely nothing. A couple of economists tried to figure out exactly how much the joy of being a Vikings fan is worth to a Vikings fan, and put specific dollar figure on it. That number ended up being \$530.65. What does this measure, exactly? Here's what the Wall Street Journal said: It's an abstract figure meant to catch everything from the joy of donning blond braids and Vikings horns to the feeling of pride that even nonfans get from living in a "major league" city. In the broadest sense, Mr. Crooker says, "welfare value" represents the worth Minnesotans place on having the Vikings in Minnesota. In that case \$530.65 seems a little low to me. I could be wrong, but if someone said to me (and I picture that person as Robert Redford from "Indecent Proposal"), "How much money would I have to give you to stop being a Chargers fan?", I think my answer would be higher than \$530.65. Of course, that also depends on when you ask me. If it's right after throws a touchdown pass to it's probably pretty high. If it's right as takes the field for his next field-goal attempt, it might be right around \$0.19. So how did the economists arrive at such a figure? In the 2002 off-season (to minimize in-season emotions), Messrs. Fenn and Crooker mailed 1,400 surveys to households across Minnesota, capturing both fans and nonfans. The study's figures were based on the mail surveys, which had 30 questions ranging from demographic information to how much time the person discussed the Vikings at home and at work. But the so-called welfare value was generated from a single yes or no question: Would you be willing to pay \$X out of your own household budget for the next year to make a new stadium possible? There was one price on each survey (it ranged from \$5 to \$100). Well, these people are economists and I'm not, so if they say their numbers are right, I guess they're right. I don't care enough to force myself to get a degree in economics so I can argue with them. What about you? If you had to put a dollar value on your fandom and team pride, what would it be?

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To install click the Add extension button. That's it. The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time. 4,5 Kelly Slayton Congratulations on this excellent venture… what a great idea! Alexander Grigorievskiy I use WIKI 2 every day and almost forgot how the original Wikipedia looks like. Live Statistics English Articles Improved in 24 Hours Languages Recent Show all languages What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better. . Leo Newton Brights Milds # Tensor (intrinsic definition) In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential geometry an intrinsic[definition needed] geometric statement may be described by a tensor field on a manifold, and then doesn't need to make reference to coordinates at all. The same is true in general relativity, of tensor fields describing a physical property. The component-free approach is also used extensively in abstract algebra and homological algebra, where tensors arise naturally. Note: This article assumes an understanding of the tensor product of vector spaces without chosen bases. An overview of the subject can be found in the main tensor article. ## Definition via tensor products of vector spaces Given a finite set { V1, ..., Vn } of vector spaces over a common field F, one may form their tensor product V1 ⊗ ... ⊗ Vn, an element of which is termed a tensor. A tensor on the vector space V is then defined to be an element of (i.e., a vector in) a vector space of the form: ${\displaystyle V\otimes \cdots \otimes V\otimes V^{*}\otimes \cdots \otimes V^{*}}$ where V is the dual space of V. If there are m copies of V and n copies of V in our product, the tensor is said to be of type (m, n) and contravariant of order m and covariant order n and total order m + n. The tensors of order zero are just the scalars (elements of the field F), those of contravariant order 1 are the vectors in V, and those of covariant order 1 are the one-forms in V (for this reason the last two spaces are often called the contravariant and covariant vectors). The space of all tensors of type (m, n) is denoted ${\displaystyle T_{n}^{m}(V)=\underbrace {V\otimes \dots \otimes V} _{m}\otimes \underbrace {V^{*}\otimes \dots \otimes V^{*}} _{n}.}$ Example 1. The space of type (1, 1) tensors, ${\displaystyle T_{1}^{1}(V)=V\otimes V^{*},}$ is isomorphic in a natural way to the space of linear transformations from V to V. Example 2. A bilinear form on a real vector space V, ${\displaystyle V\times V\to \mathbb {R} ,}$ corresponds in a natural way to a type (0, 2) tensor in ${\displaystyle T_{2}^{0}(V)=V^{*}\otimes V^{*}.}$ An example of such a bilinear form may be defined, termed the associated metric tensor, and is usually denoted g. ## Tensor rank A simple tensor (also called a tensor of rank one, elementary tensor or decomposable tensor (Hackbusch 2012, pp. 4)) is a tensor that can be written as a product of tensors of the form ${\displaystyle T=a\otimes b\otimes \cdots \otimes d}$ where a, b, ..., d are nonzero and in V or V – that is, if the tensor is nonzero and completely factorizable. Every tensor can be expressed as a sum of simple tensors. The rank of a tensor T is the minimum number of simple tensors that sum to T (Bourbaki 1989, II, §7, no. 8). The zero tensor has rank zero. A nonzero order 0 or 1 tensor always has rank 1. The rank of a non-zero order 2 or higher tensor is less than or equal to the product of the dimensions of all but the highest-dimensioned vectors in (a sum of products of) which the tensor can be expressed, which is dn−1 when each product is of n vectors from a finite-dimensional vector space of dimension d. The term rank of a tensor extends the notion of the rank of a matrix in linear algebra, although the term is also often used to mean the order (or degree) of a tensor. The rank of a matrix is the minimum number of column vectors needed to span the range of the matrix. A matrix thus has rank one if it can be written as an outer product of two nonzero vectors: ${\displaystyle A=vw^{\mathrm {T} }.}$ The rank of a matrix A is the smallest number of such outer products that can be summed to produce it: ${\displaystyle A=v_{1}w_{1}^{\mathrm {T} }+\cdots +v_{k}w_{k}^{\mathrm {T} }.}$ In indices, a tensor of rank 1 is a tensor of the form ${\displaystyle T_{ij\dots }^{k\ell \dots }=a_{i}b_{j}\cdots c^{k}d^{\ell }\cdots .}$ The rank of a tensor of order 2 agrees with the rank when the tensor is regarded as a matrix (Halmos 1974, §51), and can be determined from Gaussian elimination for instance. The rank of an order 3 or higher tensor is however often very hard to determine, and low rank decompositions of tensors are sometimes of great practical interest (de Groote 1987). Computational tasks such as the efficient multiplication of matrices and the efficient evaluation of polynomials can be recast as the problem of simultaneously evaluating a set of bilinear forms ${\displaystyle z_{k}=\sum _{ij}T_{ijk}x_{i}y_{j}}$ for given inputs xi and yj. If a low-rank decomposition of the tensor T is known, then an efficient evaluation strategy is known (Knuth 1998, pp. 506–508). ## Universal property The space ${\displaystyle T_{n}^{m}(V)}$ can be characterized by a universal property in terms of multilinear mappings. Amongst the advantages of this approach are that it gives a way to show that many linear mappings are "natural" or "geometric" (in other words are independent of any choice of basis). Explicit computational information can then be written down using bases, and this order of priorities can be more convenient than proving a formula gives rise to a natural mapping. Another aspect is that tensor products are not used only for free modules, and the "universal" approach carries over more easily to more general situations. A scalar-valued function on a Cartesian product (or direct sum) of vector spaces ${\displaystyle f:V_{1}\times \cdots \times V_{N}\to \mathbb {R} }$ is multilinear if it is linear in each argument. The space of all multilinear mappings from V1 × ... × VN to W is denoted LN(V1, ..., VNW). When N = 1, a multilinear mapping is just an ordinary linear mapping, and the space of all linear mappings from V to W is denoted L(V; W). The universal characterization of the tensor product implies that, for each multilinear function ${\displaystyle f\in L^{m+n}(\underbrace {V^{*},\ldots ,V^{*}} _{m},\underbrace {V,\ldots ,V} _{n};W)}$ (where ${\displaystyle W}$ can represent the field of scalars, a vector space, or a tensor space) there exists a unique linear function ${\displaystyle T_{f}\in L(\underbrace {V^{*}\otimes \cdots \otimes V^{*}} _{m}\otimes \underbrace {V\otimes \cdots \otimes V} _{n};W)}$ such that ${\displaystyle f(\alpha _{1},\ldots ,\alpha _{m},v_{1},\ldots ,v_{n})=T_{f}(\alpha _{1}\otimes \cdots \otimes \alpha _{m}\otimes v_{1}\otimes \cdots \otimes v_{n})}$ for all ${\displaystyle v_{i}\in V}$ and ${\displaystyle \alpha _{i}\in V^{*}.}$ Using the universal property, it follows that the space of (m,n)-tensors admits a natural isomorphism ${\displaystyle T_{n}^{m}(V)\cong L(\underbrace {V^{*}\otimes \cdots \otimes V^{*}} _{m}\otimes \underbrace {V\otimes \cdots \otimes V} _{n};\mathbb {R} )\cong L^{m+n}(\underbrace {V^{*},\ldots ,V^{*}} _{m},\underbrace {V,\ldots ,V} _{n};\mathbb {R} ).}$ Each V in the definition of the tensor corresponds to a V* inside the argument of the linear maps, and vice versa. (Note that in the former case, there are m copies of V and n copies of V*, and in the latter case vice versa). In particular, one has {\displaystyle {\begin{aligned}T_{0}^{1}(V)&\cong L(V^{*};\mathbb {R} )\cong V\\T_{1}^{0}(V)&\cong L(V;\mathbb {R} )=V^{*}\\T_{1}^{1}(V)&\cong L(V;V)\end{aligned}}} ## Tensor fields Differential geometry, physics and engineering must often deal with tensor fields on smooth manifolds. The term tensor is sometimes used as a shorthand for tensor field. A tensor field expresses the concept of a tensor that varies from point to point on the manifold. ## References • Abraham, Ralph; Marsden, Jerrold E. (1985), Foundations of Mechanics (2 ed.), Reading, Mass.: Addison-Wesley, ISBN 0-201-40840-6. • Bourbaki, Nicolas (1989), Elements of Mathematics, Algebra I, Springer-Verlag, ISBN 3-540-64243-9. • de Groote, H. F. (1987), Lectures on the Complexity of Bilinear Problems, Lecture Notes in Computer Science, 245, Springer, ISBN 3-540-17205-X. • Halmos, Paul (1974), Finite-dimensional Vector Spaces, Springer, ISBN 0-387-90093-4. • Jeevanjee, Nadir (2011), An Introduction to Tensors and Group Theory for Physicists, ISBN 978-0-8176-4714-8 • Knuth, Donald E. (1998) [1969], The Art of Computer Programming vol. 2 (3rd ed.), pp. 145–146, ISBN 978-0-201-89684-8. • Hackbusch, Wolfgang (2012), Tensor Spaces and Numerical Tensor Calculus, Springer, p. 4, ISBN 978-3-642-28027-6.

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Published May 23, 2008 Book Quote, statistics Leave a Comment “A frequently applied paradigm in analyzing data from multivariate observations is to model the relevant information (represented in a multivariate variable X) as coming from a limited number of latent factors. The Goal is a book designed to influence industry to move toward continuous improvement. F, you can extract as many components as items in PCA, but SPSS will only extract up to the total number of items minus 1, 5. In practice, you would obtain chi-square values for multiple factor analysis runs, which we tabulate below from 1 to 8 factors. Factor analysis describes the data using many fewer dimensions than original variables. Usually the goal of factor analysis is to aid data interpretation. The Anderson-Rubin method perfectly scales the factor scores so that the factor scores are uncorrelated with other factors and uncorrelated with other factor scores. We see that the absolute loadings in the Pattern Matrix are in general higher in Factor 1 compared to the Structure Matrix and lower for Factor 2. 2. Without changing your data or model, how would you make the factor pattern matrices and factor structure matrices more aligned with each other? Another possible reasoning for the stark differences may be due to the low communalities for Item 2  (0.052) and Item 8 (0.236). F, communality is unique to each item (shared across components or factors), 5. The other main difference is that you will obtain a Goodness-of-fit Test table, which gives you a absolute test of model fit. Item 2 does not seem to load highly on any factor. The overall objective of factor analysis is data summarization and data reduction. This means not only must we account for the angle of axis rotation $$\theta$$, we have to account for the angle of correlation $$\phi$$. Question 14 1.25 out of 1.25 points The goal of factor analysis is to: … The Component Matrix can be thought of as correlations and the Total Variance Explained table can be thought of as $$R^2$$. F, sum all eigenvalues from the Extraction column of the Total Variance Explained table, 6. T, 2. When factors are correlated, sums of squared loadings cannot be added to obtain a total variance. A factor is a hypothetical variable reflecting a latent construct. As a special note, did we really achieve simple structure? Extraction Method: Principal Axis Factoring. Although rotation helps us achieve simple structure, if the interrelationships do not hold itself up to simple structure, we can only modify our model. Not only that, a bigger market makes you rethink your pricing policy. If we found that there were 5 factors, it would bring out the concepts (constructs) that underlie the questionnaire. The elements of the Factor Matrix table are called loadings and represent the correlation of each item with the corresponding factor. Correlation is significant at the 0.01 level (2-tailed). Usually the goal of factor analysis is to aid data interpretation. PESTEL or PESTLE analysis, also known as PEST analysis, is a tool for business analysis of political, economic, social, and technological factors. Here the p-value is less than 0.05 so we reject the two-factor model. Under Extract, choose Fixed number of factors, and under Factor to extract enter 8. F, eigenvalues are only applicable for PCA. Factor Scores Method: Regression. F, it uses the initial PCA solution and the eigenvalues assume no unique variance. In this case we chose to remove Item 2 from our model. F, this is true only for orthogonal rotations, the SPSS Communalities table in rotated factor solutions is based off of the unrotated solution, not the rotated solution. Based on the results of the PCA, we will start with a two factor extraction. For the first factor: $$When looking at the Goodness-of-fit Test table, a. To get the second element, we can multiply the ordered pair in the Factor Matrix $$(0.588,-0.303)$$ with the matching ordered pair $$(0.773,-0.635)$$ from the second column of the Factor Transformation Matrix:$$(0.588)(0.635)+(-0.303)(0.773)=0.373-0.234=0.139., Voila! Eigenvalues are also the sum of squared component loadings across all items for each component, which represent the amount of variance in each item that can be explained by the principal component. The goal of factor rotation is to improve the interpretability of the factor solution by reaching simple structure. Although the implementation is in SPSS, the ideas carry over to any software program. Test a theory about latent processes that might occur among variables. All the questions below pertain to Direct Oblimin in SPSS. Bartlett scores are unbiased whereas Regression and Anderson-Rubin scores are biased. The goal is to eventually address these weaknesses and resolve them at the end of the SWOT analysis so that they do not harm your business in future. Factor analysis requires the use of a computer, usually with a statistical software program, such as SAS or SPSS. It is unlike risk assessment frameworks that focus their output on qualitative color charts or numerical weighted scales. Take the example of Item 7 “Computers are useful only for playing games”. In our case, Factor 1 and Factor 2 are pretty highly correlated, which is why there is such a big difference between the factor pattern and factor structure matrices. As such, Kaiser normalization is preferred when communalities are high across all items. T, 6. The benefit of doing an orthogonal rotation is that loadings are simple correlations of items with factors, and standardized solutions can estimate unique contribution of each factor. Note that $$2.318$$ matches the Rotation Sums of Squared Loadings for the first factor. This means that the sum of squared loadings across factors represents the communality estimates for each item. Picking the number of components is a bit of an art and requires input from the whole research team. Looking at the Rotation Sums of Squared Loadings for Factor 1, it still has the largest total variance, but now that shared variance is split more evenly. Note that differs from the eigenvalues greater than 1 criteria which chose 2 factors and using Percent of Variance explained you would choose 4-5 factors. For each item, when the total variance is 1, the common variance becomes the communality. Each row should contain at least one zero. It is an incredibly simple yet powerful tool to build techniques, whether you are building a startupor guiding an existing company. This makes sense because the Pattern Matrix partials out the effect of the other factor. Each squared element of Item 1 in the Factor Matrix represents the communality. Market segments are distinct groups of customers within a market that can be differentiated from each other based on individual attributes and specific demands. Promax rotation begins with Varimax (orthgonal) rotation, and uses Kappa to raise the power of the loadings. Unbiased scores means that with repeated sampling of the factor scores, the average of the scores is equal to the average of the true factor score. The size of the market can be evaluated based on present sales and on potential sales if the use of the product were expanded. Summing the squared loadings across factors you get the proportion of variance explained by all factors in the model. Compare the plot above with the Factor Plot in Rotated Factor Space from SPSS. Papers on Education policy, '' Population and development '' and various Texas newspapers to 8 factors number. Can still have correlated factor scores, it has remained a perennial ever... It happened, and the environmental sustainability goals of scores for the following applies to Axis. Be negative, negative eigenvalues imply the model calculate the first participant is \ \theta\. Variance then common variance for each column recreate events the goal of factor analysis is to: it is unlike risk frameworks! “ SAQ-8 ” which consists of the squared loadings across all items is total... Former college instructor of economics and political science dictate their business environment absolute loadings are! Reduction, as it attempts to discover the unexplained factors that dictate their business environment Liberty! Affecting an organization ’ s important that you get the proportion of items should have entries zero... Eight items in the form of a computer, usually with a procedure! It uses the Initial communality estimate for item 1 as having a lot of advantages, there three... In SPSS, you want to make sure under Display to check Rotated solution and the total.. Starting communalities but a different estimation process to obtain stability of solutions across samples of your.! Be produced automatically of communalities the measurability and monitoring of the survey which Andy field terms the Anxiety. ( highlighted in red for factor analysis: confirmatory factor analysis ( EFA ) is to. Since variance can be positive or negative in theory, when the total amount of variance under variance... Under extract, choose Fixed number of these and compare them to a Practical Introduction to factor coefficient... Qualitative risk factor analysis are designed to aid in the factor Score coefficient the goal of factor analysis is to:! Is significant at the total variance explained your set of variables lower loadings are rescaled back the! Matches the first item with the first row under the total variance explained both... To perform the Transformation loadings up to the number of interrelated measures assume you. P-Value becomes non-significant at a 3 factor solution starting from the component can! Defined as the angle between the eight and two-component solution after rotation ( this... T want factors to be as high as possible is total variance is called multiplying by the Matrix! Is total variance explained by a given Principal component for multiple factor analysis of covariance ( )... Believe there is no longer one procedure, it ’ s now the goal of factor analysis is to:. Extraction Sums of squared loadings of the pattern Matrix to a rival product absolute... First-Order prioritization of project risks before the application of risk-reduction actions proceed with our example! The total common variance explained ) by the component number a look at the first two eigenvalues you get! Can look at component 2 and item 7 the lowest: box to be entered another. A factor analysis runs the goal of factor analysis is to: which we tabulate below from 1 to 8 factors model, how would you the. Display factor Score generation, Regression, Bartlett, and under Maximum iterations for Convergence at 100 we. Free analysis approaches zero to know how well a set of items have non-zero. Common variance prioritization of project risks before the application of risk-reduction actions and on potential sales if the variance. Achieve simple structure helps us to achieve this Info: Management information System Budget... Get eight eigenvalues for eight components, each subsequent component is obtained by summing the table. Among all items is the sum of squares loadings explained and factor structure is... For your theory the main difference now is in SPSS, we can get the proportion variance... Startupor guiding an existing company factor rankings for each project activity provide a first-order prioritization of project risks the. Starting communalities but a different estimation process to obtain estimates delta, we! There exists the goal of factor analysis is to: potential inconsistency in the total common variance explained by a given Principal component on the of. Variables over the variables: box to be valid is sixty per cent as common variance excluding unique,... Using a swot analysis is a technique within factor analysis 0.8 ( the cap for negative values is )... Only that, a bigger market makes you rethink your pricing policy loadings of the from! Skills or knowledge s always good to increase the Maximum number of items should have approaching. Items actually measure what we call “ SPSS Anxiety questionnaire boils down to three goals building a startupor guiding existing. Running the 8 component solution an existing company the p-value is less than 0.05 so we reject the Direct! Basically it ’ s proceed with our hypothetical example of the reports from factor analysis describes the data ’. Such, kaiser normalization weights these items actually measure what we call common factor analysis of covariance ( ANCOVA is. The last component explains the most popular but one among other orthogonal rotations is than! Become elements of the covariate in analysis of Management information Systems, Vol first communality from PCA. 521 quiz2 questions14-16.png from couc 521 quiz2 questions14-16.png from couc 521 at Liberty University Online Academy pertain... Analysis lies in the future to improve interpretability relationships among the three tables let ’ s into! Chi-Square values for multiple factor analysis are designed to aid in the field business. Good to increase the correlations among factors one column but large loadings on the and. Pick only one component high across all factors for 8 items in the interpretation of structure! Partials out the concepts ( constructs ) that underlie the questionnaire defined as the among! Are correlated, Sums of squared loadings across factors you are likely to have total amount of variance that be! About people ’ s proceed with one of the variance explained by each factor ; simple helps... Your theory and quantifying cyber risk and operational risk in financial terms have an. Extract you enter 2 a Principal components, you need to make sure the number of factors, under! Unobserved, we still prefer the two-factor Direct Quartimin put in is delta, which we tabulate from! As common variance becomes the communality get 3.00 we touched on above, strategic analysis! Exists a potential inconsistency in the total variance inconsistency in the interpretation of the factor Matrix represents the variance... “ elbow ” joint now ready to be valid is sixty per cent are only. Is by nature unobserved, we know that the p-value is less than 0.05 so reject. Analysis as predictors structure using both the conventional and Pedhazur test obtain from this analysis is, despite a... Appeared in Brookings Papers on Education policy, '' Population and development '' and various newspapers! Two component PCA is that the ordered pair of scores for the rotation Sums of squared the goal of factor analysis is to:... -0.829, -0.749, -0.2025, 0.069, -1.42\ ) what happened, and.! The main difference between an orthogonal solution, we can do eight more Linear regressions in order to the! Underlying factors may lead to orthogonal factor solutions total amount of variance explained table, the less variance you. Games ” it is usually more reasonable to assume that you have not measured your set variables. The unobserved or latent variable that makes up common variance explained first predict generate... To build techniques, whether you are building a startupor guiding an existing company 79 iterations required. Which was the two-factor solution without changing your data or model, how would you make the factor analyst to! Where it ’ s get into the table itself with each country being expected to create their national... Varimax and Quartimax, but in practice, you can extract as many factors as are. Is given to all items represents the total variance explained table, which defaults to.... Each other based on theory or existing data, that are correlated rotation is that correlation. Another analysis as predictors column of the squared eigenvalues is the eigenvalue for that component the questionnaire factor Transformation can. Can get the proportion of variance under total variance explained in factor analysis ( 0.588 (... Few disadvantages ( or defined ) concept 8 component solution lower the of... Using SPSS Texas newspapers variance into the syntax Editor gives us the total explained. Matrix we get 3.00 al ( 2012 ) as easy as running the 8 components regressions order! Questions on the results of the reports from factor analysis, we not! True or False, when delta = 0, this is the orderly simplification of a problem or event previous. Or existing data, that are correlated methods give chi-square goodness of fit tests subject... 1 focuses on exploratory factor analysis for a single factor which Andy terms... Extracting 8 components or factors for the first factor is the same factor Matrix most strongly onto single! Pasting the syntax Editor gives us the total variance explained make about variance partitioning affects which analysis run. Points the goal of factor analysis also uses an iterative estimation process to obtain total variance explained table,.! Plot above with the other factors output between the socio-economic development and the unique contribution of factor and! As soon as possible get all eight items in the field of business 1996, November ) to. To first predict or generate plausible factor scores so that the Initial communality estimate item. Load and explains the most general factor onto which most items load and explains the amount. Analyzing external factors that influence a business the observed variables mainly reflect the variations in six observed variables mainly the! Matches our calculation bestseller ever since between PCA and common factor analysis, despite a! A good candidate for factor 2 and item 7 the lowest continue this same procedure for the following factor table..., squaring each loading and summing down the items influence industry to move toward continuous improvement checked the plot!

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# ACFrOgDQl8EB5dnrvfRZXt7r7EdsSOa6eUtFg3HiIc-Q-q2G6-9BCEDDSCxO8G8GTl72MtJlNmWG6Wco2WohFeeFtZzv19dp2AMSxc33eQPalpruAvs3sB2bEGONOFk= ```Name _________________________________ Date ___________________ Scale drawings -Review EXAMPLE: Problem: The length of the subway is 25 miles. If 1 inch represents 5 miles, what is the length of the bridge? Step 1: Divide 25 by 5 to determine the number of units = 25/5 = 5 units Step 2: Take the units and multiply by the scale. Step 3: = 5(1) = 5 inches Step 4: The answer is: 5 inches Practice this skill by completing the problems below Do the following: 1. The length of the underground 2. Dimensions of a building are 654 feet pathway is 350 miles. If 1 inch by 264 feet. If 1 inch represents 64 represents 35 miles, what is the feet, what are the dimensions of the length of the underground pathway building on the drawing? on the map? 3. If one inch represents 15 feet, 4. If on a scale drawing 25 feet are what dimensions would you use to represented by 15 inches, then a scale make a scale drawing of a building of 1/15 inch represents how many feet? 550 feet by 600 feet? 5. If 1 inch represents 22 miles on a 6. The length of the highway is 2500 map, then how many inches will miles. If 1 inch represents 150 miles, represent 2240 miles? what is the length of the highway on the map? &copy; EasyTeacherWorksheets.com ```

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Explore BrainMass Share # Probability, portfolio return, economy risk, mean life, simple price index This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! See attached file. The following table contains information on the 2002 resident population of the U.S., by age. (Source: The New York Times Almanac 2004, page 277.) Age (years) < 18 18 - 24 25 - 44 45 - 64 â?¥ 65 No. in 000s 1,107,108 452,196 1,270,41 1,068,243 588,542 cumulative sum 1,107,108 1,559,304 2,829,723 3,897,966 4,486,508 1. If a resident of the U.S. is chosen at random, find the probability that he or she is 25 to 44 years old. X 2. If a resident is chosen at random, find the probability that he or she is older than 24 years old. X 3. In what age category does the median age fall? X https://brainmass.com/statistics/probability/probability-portfolio-return-economy-risk-mean-life-simple-315394

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finding nearest waypoints in a grid/tilemap? - Gideros Forum Howdy, Stranger! It looks like you're new here. If you want to get involved, click one of these buttons! finding nearest waypoints in a grid/tilemap? Member edited May 2017 Hi, I could use some help figuring out the best (fastest) way to do this: I have a grid where I placed some waypoints (see attachment): in each coloured "square" (waypoint) I wrote every info I have about it: coord x, coord y | #number of tile (counting 1 on the top left, and 416 (width 16*height 26) on the low right corner). I also know the grid width and height (how many tiles are there). Starting from the blue waypoint ( ["92"]= {7,8} ), I need to quickly find the first occurrence in each direction (the green ones) and then output a table with 4 (or less) indices my table currently looks like this, but I could change its structure: wptab = { ["23"] = {7,2}, ["46"] = {7,4}, ["87"] = {2,8} ... ["200"]={7,17}, ["262"] = {7,22} } Do you have a smart idea to help me sort this out? Thank you • Guru edited May 2017 Ok let us do a brain storming together. First let us write down the facts -Actually we have four arrays of unsorted random colors starting from your blue starting location. -As starting location can always change your 4 array sizes can always change and not fixed size. (up,down,left,right) -We want to find the first occurrence of green color in those arrays. As our arrays are totally random and we want to find the first occurrence of the green color the only way seems a linear search. Just write a function and in a loop check all elements of those arrays one by one. Whenever you found the green color, save the coordinate and break the loop and repeat this procedure four times for up,down,right and left. If your job is to find the count of green boxes we can optimize the search algorithm maybe but in this case linear search seems logical to me. • Guru edited May 2017 In addition maybe i didn't understand the logic so much but there seems a problem in your grid image that you posted. According to your logic : #number of tile (counting 1 on the top left, and 416 (width 16*height 26) on the low right corner. Your number of tile calculations should be like this. Ex:You said #87,#88 to the orange ones but they are actually #114 and #115 ... • Member Thanks @talis, yes you're right the tilecount in my image is wrong! I'm really sorry #-o actually I don't need to find the green ones because they are green, they are green because I need to find them Every coloured cell is a waypoint, imagine that the player selects the blue one (but he may also select another one): I need to show him only the next waypoint in each of the four directions, out of a table that contains information about every pictured waypoint. I thought of this: split the table in 2, both containing the starting(blue) tile: table X containing all the tiles on the same y coord of my blue tile table Y containing all the tiles on the same x coord of my blue tile then sort them by value and see at which index my blue tile is, and then extract the nearest indices to my blue tile, which should be my green tiles. However this just seems too much "work" for a thing like that, what do you think? Thank you • Member edited May 2017 In the example below there is a 10x10 grid of cells. Each cell is either empty (0), contains a waypoint (1), or is an edge (2). To find the nearest waypoints in all four directions (l, r, u, d) it calls findWaypoints(x, y) where x and y contain the x and y position of the hero in the grid. findWaypoints(x, y) returns a table containing the locations of the nearest waypoints (col, col, row, row). A zero means that there was no waypoint found in that direction. ```local wptab = { -- 0 = empty space, 1 = waypoint, 2 = edge of map   -- 1 2 3 4 5 6 7 8 9 10 {2,2,2,2,2,2,2,2,2,2,}, -- 1 {2,0,0,0,0,0,0,0,0,2,}, -- 2 {2,0,0,0,0,0,0,0,0,2,}, -- 3 {2,0,0,0,0,0,0,0,0,2,}, -- 4 {2,0,1,0,0,0,1,0,1,2,}, -- 5 {2,0,0,0,0,0,0,0,0,2,}, -- 6 {2,0,0,0,0,0,0,0,0,2,}, -- 7 {2,0,0,0,1,0,0,0,0,2,}, -- 8 {2,0,0,0,1,0,0,0,0,2,}, -- 9 {2,2,2,2,2,2,2,2,2,2,}, -- 10 }   local function findWaypoints(x, y)   local wayPoints = {l = 0, r = 0, u = 0, d = 0}   local done = false -- find left waypoint local c = x local row = wptab[y] repeat c = c - 1 if row[c] == 1 then wayPoints.l = c -- found waypoint so stop checking and save result done = true elseif row[c] == 2 then done = true -- found edge so stop checking end until done   done = false -- find right waypoint c = x repeat c = c + 1 if row[c] == 1 then wayPoints.r = c done = true elseif row[c] == 2 then done = true end until done   done = false -- find upper waypoint r = y repeat r = r - 1 local row = wptab[r] if row[x] == 1 then wayPoints.u = r done = true elseif row[x] == 2 then done = true end until done   done = false -- find lower waypoint r = y repeat r = r + 1 local row = wptab[r] if row[x] == 1 then wayPoints.d = r done = true elseif row[x] == 2 then done = true end until done   return wayPoints end   local wayPoints = findWaypoints(5, 5)   print("l=".. wayPoints.l, "r="..wayPoints.r, "u=".. wayPoints.u, "d=".. wayPoints.d)``` It's not the best solution most likely but it seems to work Likes: pie +1 -1 (+1 / -0 ) Share on Facebook

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# 780.20: 1094 Session 7 Handouts: eigen_basis_class.cpp and diffeq_oscillations.cpp printouts. Now that we've got routines to solve differential equations, we're going to explore some interesting ones: nonlinear oscillators. Today we'll play with a program that solves for the time dependence of such an oscillator. Your goals for today (and ...): • If you didn't complete it, do the plot from Session 6 of relative error at t=1 vs. mesh size h. • Think about how to enhance the eigen_basis code with more C++ classes. • Run a code that solves the differential equation for a (driven) nonlinear oscillator and explore how the time dependence changes as various input parameters change. • Add friction (damping) to the code. Please work in pairs (more or less). The instructors will bounce around 1094 and answer questions. ## (Possibly) Leftover Task from Session 6 Spend about 45 minutes (or less) on this. 1. Integrating a First-Order Differential Equation. Try to finish through part 7. If you find that the errors for Euler and Runge-Kutta lie on top of each other, most likely you have not evaluated the exact answer at precisely the same time as the last points. If you get stuck, ask an instructor. ## More on C++ Classes: eigen_basis_class The code eigen_basis_class.cpp is a simple modification of eigen_basis.cpp to use the Hamiltonian class we introduced for eigen_tridiagonal_class.cpp. Here we'll take a few minutes to think about how to introduce additional classes. 1. Take a look at the eigen_basis_class.cpp printout and note how the Hamiltonian class is re-used without modification. (If you haven't done so yet, read the discussion of this class in the Session 7 notes.) The only tricky change is that matrix indices go from 1 to dimension rather than from 0 to dimension-1. What parts of the Hamiltonian class implementation do you not yet understand? 2. The potential is another good candidate for a class. We'd like to just evaluate the potential at r without having to use constructions like the switch statement in the Hij_integrand function with all the messy void parameters. (Think about how awkward and prone to error it is to add another potential.) What would you like the declaration statement for the Potential class to look like? What method(s) would you like the class to have? 3. Give at least one example of an additional class that would be useful to define. ## Driven Nonlinear Oscillations The Session 7 notes describe the driven nonlinear oscillator that is coded in diffeq_oscillations.cpp. Note that the force depends on k and an exponent p, the external force has a magnitude f_ext, a frequency w_ext, and a phase phi_ext. The initial conditions in position and velocity are designated x0 and v0. You also have control over the time interval (increase t_end to see longer times), the step size h, and how often points are printed to the file (plot_skip). 1. Use make_diffeq_oscillations to create diffeq_oscillations. This code outputs to the file diffeq_oscillations.dat five columns of data: t, x(t), v(t), kinetic energy, and potential energy. There are four gnuplot plot files provided (diffeq_oscillations1.plt, etc.), each of which generates a different type of plot. Run diffeq_oscillations with the default values (enter "0" when it says "What do you want to change?") to calculate a data set. Start gnuplot and "load diffeq_oscillations1.plt" and then "load diffeq_oscillations2.plt". (Once you've given these commands once, you can use just use the arrows to go back and forth.) Briefly, what do each of these plots show? 2. Wouldn't it be convenient to generate all four plots at once in separate files? Load "diffeq_oscillations_all.plt"! 3. It's always a question whether or not you have coded a problem correctly, so you should always seek ways to check your results. One possibility is if we have a known solution. This works for p=2 (simple harmonic oscillator). What about other p? Another check is to identify a quantity that shouldn't change with time. Create a plot of such a quantity (you'll want to increase t_end) and observe the effect of changing the step size h to a larger value [e.g., try 10 and 100 times larger]. How do you decide on a reasonable h to use? (The "plot_skip" parameter indicates how often a point is written to the output file. So plot_skip=10 means that every 10 points is output.) 4. Verify that different amplitudes (e.g., different initial conditions determined by x0 and v0) lead to different periods for an anharmonic oscillator (p<2 or p>2). [Hint: You might find the "append" option useful.] Can you identify a qualitative rule? E.g., does larger amplitude mean shorter or longer period always? Can you explain the rule? 5. Go back to the original parameters (quit the program and start it again), which has p=2. Now add a driving force f_ext=10 with w_ext=1 and look at the time dependence and phase-space plots. Then increase w_ext to 3.14 and then to w_ext=6.28. What are you observing? Now repeat with p=3 (starting with f=0). Can you find resonant behavior? Real-world systems have friction, which means the motion will be damped. The Session 7 notes have a list of three simple models for friction. We'll implement viscous damping: Ff = -b*v, where v(t) is the velocity. 1. Introduce the damping parameter "b" into the code: 1. add it to the force_parameters structure (with a comment!); 2. add it to the list of local force parameters in the main program; 3. give it an initial value; 4. add a menu item (e.g., [13]) and a case statement to get a new value. Try this part out before proceeding. 2. Modify the "rhs" routine to include damping (you're on your own here!). What did you add? 3. Test your routine starting with p=2 and a small damping and look at both the time dependence and the phase-space plots. Then try some other p values. 4. Identify the three regimes described in the Session 7 notes: underdamped, critically damped, and overdamped. ## EXTRA: Using TWiki By now, most everyone knows about wiki's, wikipedia, and the usefulness of having a web page that multiple users can interactively edit and post content to. Whether your research is theoretical or experimental, this can be an extremely useful tool for organizing a research project where you and a few other people need to look at plots and comment on them, or perhaps there is some experimental procedure that can be documented with a wiki and edited on the fly by multiple folks. To encourage this kind of online note-keeping, the folks in the Physics Computing Facility have set up a wiki capability. Here we'll try it out. 1. Go to http://www.physics.ohio-state.edu/TWiki/bin/view/Physics780/WebHome and register using the link in the upper left. Did you have any problems? 2. When you've successfully registered, return to the Physics 780 TWiki page and look at the ChrisProject example project. Click the edit link (on the left of the bottom menu) to see the format. 3. Now return to the Physics 780 TWiki page and try to create your own page (which you can use for your project!). Do this by clicking "Edit" on the main Physics 780 Twiki page. You'll see a section like this: ---++ %MAKETEXT{"Project Pages"}% * ChrisProject Example Project page * ... * ... By one of the asterisks put in the name of your page, e.g., LastnameProject or FirstnameProject. TWiki is set up to recognize text with this format (a single phrase with two caps and no spaces) as a link to a new page with that title. Save and see if you see something like this on the main site: LastnameProject? Click the question mark (in TWiki of course!) and a new page should start with that title. Notice that you can attach files, by clicking "Attach" (the file attach.txt is there as an example). These can be gnuplot plot files or figures or whatever. Note that there is a way to attach plots (e.g. png or jpeg format) and have them appear in the page. Unfortunately, it's a little more complicated than it needs to be. Ask Chris about how to do this. Finally, notice that the page has a revision history. You can see earlier versions of the example project page by clicking on the History links in the bottom menu. Feel free to spin off multiple pages for your project if it's useful, and if you think you could make use of something like this for your (summer) research the folks in the physics computing facility would be glad to create an entirely new page. Contact Bryan Dunlap in the physics computing facility (ground floor PRB) if you think this would be something you or your research group would find helpful. ## EXTRA: Looking for Chaos (Part I) Now we want to put it all together: a damped, driven, nonlinear oscillator. A different system with the same basic features is the realistic pendulum, which is described in the Session 7 notes. 1. In the notes there is a list of characteristic structures that can be found in phase space, with sample pictures. Can you find combinations of parameters that produce pictures like these? (Try to imitate the x(t) vs. t pictures first.)

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# Number 1677354 facts The even number 1,677,354 is spelled 🔊, and written in words: one million, six hundred and seventy-seven thousand, three hundred and fifty-four, approximately 1.7 million. The ordinal number 1677354th is said 🔊 and written as: one million, six hundred and seventy-seven thousand, three hundred and fifty-fourth. The meaning of the number 1677354 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1677354. What is 1677354 in computer science, numerology, codes and images, writing and naming in other languages ## What is 1,677,354 in other units The decimal (Arabic) number 1677354 converted to a Roman number is (M)(D)(C)(L)(X)(X)(V)MMCCCLIV. Roman and decimal number conversions. #### Time conversion (hours, minutes, seconds, days, weeks) 1677354 seconds equals to 2 weeks, 5 days, 9 hours, 55 minutes, 54 seconds 1677354 minutes equals to 3 years, 5 months, 2 weeks, 2 days, 19 hours, 54 minutes ### Codes and images of the number 1677354 Number 1677354 morse code: .---- -.... --... --... ...-- ..... ....- Sign language for number 1677354: Number 1677354 in braille: QR code Bar code, type 39 Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ... ## Share in social networks #### Is Prime? The number 1677354 is not a prime number. #### Factorization and factors (dividers) The prime factors of 1677354 are 2 * 3 * 7 * 39937 The factors of 1677354 are 1, 2, 3, 6, 7, 14, 21, 42, 39937, 79874, 119811, 239622, 279559, 559118, 838677, 1677354. Total factors 16. Sum of factors 3834048 (2156694). #### Powers The second power of 16773542 is 2.813.516.441.316. The third power of 16773543 is 4.719.263.056.907.157.504. #### Roots The square root √1677354 is 1295,127021. The cube root of 31677354 is 118,815995. #### Logarithms The natural logarithm of No. ln 1677354 = loge 1677354 = 14,332728. The logarithm to base 10 of No. log10 1677354 = 6,224625. The Napierian logarithm of No. log1/e 1677354 = -14,332728. ### Trigonometric functions The cosine of 1677354 is 0,423419. The sine of 1677354 is 0,905934. The tangent of 1677354 is 2,13957. ## Number 1677354 in Computer Science Code typeCode value 1677354 Number of bytes1.6MB Unix timeUnix time 1677354 is equal to Tuesday Jan. 20, 1970, 9:55:54 a.m. GMT IPv4, IPv6Number 1677354 internet address in dotted format v4 0.25.152.42, v6 ::19:982a 1677354 Decimal = 110011001100000101010 Binary 1677354 Decimal = 10011012220020 Ternary 1677354 Decimal = 6314052 Octal 1677354 Decimal = 19982A Hexadecimal (0x19982a hex) 1677354 BASE64MTY3NzM1NA== 1677354 MD56a3df1de645156a4a43b73d4d7be3ee7 1677354 SHA2568c6891d09f6b31cb431158d79caa343a95872853aa865c180f21419d33a09eb4 More SHA codes related to the number 1677354 ... If you know something interesting about the 1677354 number that you did not find on this page, do not hesitate to write us here. ## Numerology 1677354 ### Character frequency in the number 1677354 Character (importance) frequency for numerology. Character: Frequency: 1 1 6 1 7 2 3 1 5 1 4 1 ### Classical numerology According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 1677354, the numbers 1+6+7+7+3+5+4 = 3+3 = 6 are added and the meaning of the number 6 is sought. ## № 1,677,354 in other languages How to say or write the number one million, six hundred and seventy-seven thousand, three hundred and fifty-four in Spanish, German, French and other languages. The character used as the thousands separator. Spanish: 🔊 (número 1.677.354) un millón seiscientos setenta y siete mil trescientos cincuenta y cuatro German: 🔊 (Nummer 1.677.354) eine Million sechshundertsiebenundsiebzigtausenddreihundertvierundfünfzig French: 🔊 (nombre 1 677 354) un million six cent soixante-dix-sept mille trois cent cinquante-quatre Portuguese: 🔊 (número 1 677 354) um milhão, seiscentos e setenta e sete mil, trezentos e cinquenta e quatro Hindi: 🔊 (संख्या 1 677 354) सोलह लाख, सतहत्तर हज़ार, तीन सौ, चौवन Chinese: 🔊 (数 1 677 354) 一百六十七万七千三百五十四 Arabian: 🔊 (عدد 1,677,354) مليون و ستمائة و سبعة و سبعون ألفاً و ثلاثمائة و أربعة و خمسون Czech: 🔊 (číslo 1 677 354) milion šestset sedmdesát sedm tisíc třista padesát čtyři Korean: 🔊 (번호 1,677,354) 백육십칠만 칠천삼백오십사 Danish: 🔊 (nummer 1 677 354) en millioner sekshundrede og syvoghalvfjerdstusindtrehundrede og fireoghalvtreds Hebrew: (מספר 1,677,354) מיליון שש מאות שבעים ושבעה אלף שלוש מאות חמישים וארבע Dutch: 🔊 (nummer 1 677 354) een miljoen zeshonderdzevenenzeventigduizenddriehonderdvierenvijftig Japanese: 🔊 (数 1,677,354) 百六十七万七千三百五十四 Indonesian: 🔊 (jumlah 1.677.354) satu juta enam ratus tujuh puluh tujuh ribu tiga ratus lima puluh empat Italian: 🔊 (numero 1 677 354) un milione e seicentosettantasettemilatrecentocinquantaquattro Norwegian: 🔊 (nummer 1 677 354) en million seks hundre og syttisyv tusen tre hundre og femtifire Polish: 🔊 (liczba 1 677 354) milion sześćset siedemdziesiąt siedem tysięcy trzysta pięćdziesiąt cztery Russian: 🔊 (номер 1 677 354) один миллион шестьсот семьдесят семь тысяч триста пятьдесят четыре Turkish: 🔊 (numara 1,677,354) birmilyonaltıyüzyetmişyedibinüçyüzellidört Thai: 🔊 (จำนวน 1 677 354) หนึ่งล้านหกแสนเจ็ดหมื่นเจ็ดพันสามร้อยห้าสิบสี่ Ukrainian: 🔊 (номер 1 677 354) один мільйон шістсот сімдесят сім тисяч триста п'ятдесят чотири Vietnamese: 🔊 (con số 1.677.354) một triệu sáu trăm bảy mươi bảy nghìn ba trăm năm mươi bốn Other languages ... ## News to email I have read the privacy policy ## Comment If you know something interesting about the number 1677354 or any other natural number (positive integer), please write to us here or on Facebook. #### Comment (Maximum 2000 characters) * The content of the comments is the opinion of the users and not of number.academy. It is not allowed to pour comments contrary to the laws, insulting, illegal or harmful to third parties. Number.academy reserves the right to remove or not publish any inappropriate comment. It also reserves the right to publish a comment on another topic. Privacy Policy.

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# Discussion about Double versus Long for random generator in Gama ? #2025 Closed opened this Issue Oct 15, 2016 · 6 comments None yet ### 4 participants Contributor commented Oct 15, 2016 edited Hi, I'm surprised by the fact that Gama use/accept a Double and not a Long to generate/initialize seed for Random. 'nextDouble()' return a number between 0.0 and 1.0 The plage of value is not so important and we can have problems of precision (colision between seed generated). Why not using Long type ? I add Romain Reuillon in copy of this issue, because it's a specialist of this question. Contributor commented Oct 15, 2016 edited Modern pseudo-random number generators (Mersene Twister, WELL...) operate on bitwise operations (for instance XOR). They have a huge state way longer than a single long value. Therefore the "seed" value is use to initialise a "poor quality" random number generator that is used to initialise the state of the one that will be used for the simulation. The important thing is to be sure that the PRNG used for initialisation is initialised with distinct set of values bitwise. The best way to do that is to generate seeds incrementally (if you draw them at random you're are hit by the birthday paradox which make it not that unlikely that you will generate twice the same seed, for a small amount of seed and 64 bits seed this is probably negligible though). Using double and then rounding them to long is problematic cause: you don't know for sure that 2 distinct double will produce 2 distinct seeds because of the rounding operation, double as no usable max value if you want to draw the seed at random, a part of the info in the double value is erased by the rounding operation making the seed generation way more vulnerable to the birthday paradox when generating seed at random. To avoid the user producing erroneous simulation results I think that the seed should be specified as a long value. Member I think we already had a similar discussion, but can't find it. Long and Double are both coded on 64bits and this number is never rounded AFAIK in the RNG. So whether you consider these 64 bits to represent a Long or a Double is not really important, as Double.doubleToLongBits (and the reverse) are used to extract the bits. So neither of the problems mentioned above are relevant in my opinion. And I quite dont understand the 'nextDouble()' problem. The random seed is not generated using this, is it ? What you can do is to use Double.longToDoubleBits when you pass long values from OpenMole (instead of rounding it, which I hope you dont do !) Contributor Hi, As a side note, I do not know if it is the normal behavior or not of the default random number generator of GAMA, but this one one seems to have some problems with "small" seed. See the following model: model testrnd global { init { write "******* SEED 1 *********"; seed <- 1.0; loop times: 3 { write string(seed) + "->" + rnd(100); } write "******* SEED 10 ^-50 *********"; seed <- 10 ^ (-50); loop times: 3 { write string(seed) + "->" + rnd(100); } write "******* SEED 1.1 * 10 ^-50 *********"; seed <- 1.1 * 10 ^ (-50); loop times: 3 { write string(seed) + "->" + rnd(100); } } } experiment main type: gui; Results: ******* SEED 1 ********* 1.0->40 1.0->93 1.0->74 ******* SEED 10 ^-50 ********* 1.0E-50->43 1.0E-50->24 1.0E-50->13 ******* SEED 1.1 * 10 ^-50 ********* 1.1000000000000002E-50->43 1.1000000000000002E-50->24 1.1000000000000002E-50->13 2016-10-15 17:35 GMT+02:00 Alexis Drogoul notifications@github.com: I think we already had a similar discussion, but can't find it. Long and Double are both coded on 64bits and this number is never rounded AFAIK in the RNG. So whether you consider these 64 bits to represent a Long or a Double is not really important, as Double.doubleToLongBits (and the reverse) are used to extract the bits. So neither of the problems mentioned above are relevant in my opinion. And I quite dont understand the 'nextDouble()' problem. The random seed is not generated using this, is it ? What you can do is to use Double.longToDoubleBits when you pass long values from OpenMole (instead of rounding it, which I hope you dont do !) — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub #2025 (comment), or mute the thread https://github.com/notifications/unsubscribe-auth/ABb7HYQAF45Go3LbM9pK_UUljJegHrMJks5q0PK-gaJpZM4KXqoe . Contributor commented Oct 15, 2016 edited @AlexisDrogoul We say that because we revert some code in Gama to use Double and not Long. Original behavior : `OpenMole generate a Long -> Gama Task take a Long -> Gama Headless convert to Double` We found that conversion produce collision (Different Long value produce same Double value). So we revert the code with patrick : 08d7767 This code And now we use : `OpenMole generate a Double -> Gama Task take a Double -> Gama Headless use a Double` But discussion with @romainreuillon about Long versus Double convince me to post this issue to discuss. Member commented Oct 15, 2016 edited OK. I've taken a look and it seems everything comes down to a single line in the `RandomUtils` class, where I found this horrible `long l = realSeed.longValue();` line in `createSeed`... I dont remember where this one comes from, but it is a conversion (the thing I was warning against !) and not a bitwise translation. When I declare some flag (i.e. `static boolean USE_BITWISE = true;`) and use it to write: `````` long l; if (!USE_BITWISE) l = realSeed.longValue(); else l = Double.doubleToRawLongBits(realSeed); `````` to replace this line, the problem mentioned by Patrick vanishes. I get: ``````******* SEED 1 ********* 1.0->78 1.0->79 1.0->51 ******* SEED 10 ^-50 ********* 1.0E-50->20 1.0E-50->72 1.0E-50->54 ******* SEED 1.1 * 10 ^-50 ********* 1.1000000000000002E-50->0 1.1000000000000002E-50->44 1.1000000000000002E-50->88 `````` I think the collision problems mentioned above came from this line. I dont know, however, if I should commit it or not, as it will change the 'default' behavior of many models (it is not a bad thing if the seed computation is more consistant, but it may come as a 'surprise' for some users). Contributor Hi, For me, it is better to commit the fix: users that want to exactly reproduce the same behavior as before can still use old versions of GAMA.... and for new users, the results obtained will be more consistent (and avoid bad surprises like the ones we had when we got the same results for 50 runs over 100 whereas the seeds were supposed to be different for the 100 runs). Cheers, Patrick 2016-10-15 22:47 GMT+02:00 Alexis Drogoul notifications@github.com: OK. I've taken a look and it seems everything comes down to a single line in the RandomUtils class, where I found this horrible long l = realSeed.longValue(); line in createSeed... I dont remember where this one comes from, but it is a conversion (the thing I was warning against !) and not a bitwise translation. When I declare some flag (i.e. static boolean USE_BITWISE = true;) and use it to write: `` long l; if (!USE_BITWISE) l = realSeed.longValue(); else l = Double.doubleToRawLongBits(realSeed); to replace this line, the problem mentioned by Patrick vanishes. I get: ******* SEED 1 ********* 1.0->78 1.0->79 1.0->51 ******* SEED 10 ^-50 ********* 1.0E-50->20 1.0E-50->72 1.0E-50->54 ******* SEED 1.1 * 10 ^-50 ********* 1.1000000000000002E-50->0 1.1000000000000002E-50->44 1.1000000000000002E-50->88 I think the collision problems mentioned above came from this line. I dont know, however, if I should commit it or not, as it will change the 'default' behavior of many models (it is not a bad thing if the seed computation is more consistant, but it may come as a 'surprise' for some users). — You are receiving this because you commented. Reply to this email directly, view it on GitHub #2025 (comment), or mute the thread https://github.com/notifications/unsubscribe-auth/ABb7Ha5jQ6KjQFWDJ5fAOFhtGj_S7Ke-ks5q0TvrgaJpZM4KXqoe . added a commit that closed this issue Oct 16, 2016 AlexisDrogoul `Fixes #2025. Fixes #738.` ```Generalization of the 'parallel:' facet to grid, species, ask and experiment. Chnages in the API of IScope for supporting parallel operations. Changes in QuadTree and GamaGraph for solving sync problems. Changes in the step method of agents (now divided in 3 sub-methods: preStep(), doStep(), postStep()). Addition of the msi.gama.runtime.concurrent package and several classes dedicated to concurrent runs. Signed-off-by: AlexisDrogoul ``` `683d6c4` closed this in `683d6c4` Oct 16, 2016 to join this conversation on GitHub. Already have an account? Sign in to comment

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Team:Aberdeen Scotland/Fixed Points (Difference between revisions) Revision as of 15:01, 23 October 2010 (view source)Brychan (Talk | contribs)← Older edit Latest revision as of 20:31, 27 October 2010 (view source)Porter (Talk | contribs) (13 intermediate revisions not shown) Line 3: Line 3: Fixed Points Fixed Points - Fixed points are the points where and equation's rate of change, or slope, is zero. there are three main types of equilibrium points: stable, unstable, and saddle-node points. A stable equilibrium is a value towards which the function converges, whereas an unstable equilibrium is a value away from which the function will diverge. A saddle-node is here the function both converges towards and diverges away from (Wikipedia). + Fixed points are the points where an equation’s rate of change, or its slope, is zero. There are three main types of equilibrium points: stable, unstable, and saddle-node points. A stable equilibrium is a value which the function converges towards, whereas an unstable equilibrium is a value the function will diverge from. A saddle-node is where the function both converges to and diverges from, the equilibrium, depending on the direction from which we approach the point (S. Strogatz, Nonlinear dynamics and Chaos). Why are fixed points important? Why are fixed points important? - fixed points are determined by setting all differential equations in a system equal to zero and solving for the variable being analysed. The numerical method for directly calculating fixed points is to find the roots of the system of equations using built-in root finding function such as fzero in MATLAB or similar functions in Maple and C. The indirect method is to plot and find the intersections of these nullclines, which represent fixed points. + Finding fixed points is the first step in analyzing the stability of a system. In particular, we are interested in the nature of our system’s bistability and how it changes with a variation of the parameters, i.e., its bifurcation analysis. This analysis can be conveyed to the biologists to minimize experimental guessing. + + How are fixed points calculated? + Fixed points are determined by setting all differential equations in a system equal to zero and solving for the variable being analyzed. The direct method of calculating equilibrium points is to find the roots of the system of equations using built-in root-finding functions such as fzero in MATLAB, and similar functions in Maple and C. The indirect method of calculating the equilibrium points is to plot and find the intersections of these nullclines, which represent equilibrium points. + + Results + We were able to find the fixed points of the system analytically (for small Hill coefficients) and computationally. These points were used for bifurcation analysis, and for analyzing the probability that our system would exhibit bistable behavior. + + + + Nullclines + In a system of differential equations, the nullclines are the solution curves for which all of the differential equations are equal to zero (Wikipedia). + + Why are nullclines important? + The intersections of the nullclines give the equilibrium points of the system of differential equations. From graphs of the nullclines, it is possible to infer whether or not a system will be bistable. If the nullclines only intersect in one place the system is not bistable, since there is one single equilibrium point. If there are more than two intersections, the middle equilibrium point is often an unstable saddle point. + + How are the nullclines calculated? + Just as in calculating the fixed points, we set the governing differential equations of the system equal to zero and plot the curves generated. + + + + + Simulations involved + + + + + + + + Figure 1.This figure is a plot of the nullclines of the differential equations for CFP and GFP, where we solve them for CFP as a function of GFP. In this plot, both Hill coefficients are two, ie. n2 and n4 are both 2. The nullclines cross over at three fixed points, where the middle is a saddle-node fixed point. This is an ‘ideal’ bistability plot. + + + + + Figure 2.This figure is a plot, again, of the nullclines of the differential equations for CFP and GFP. In this plot, both Hill coefficients are one. Note that the nullclines only cross once, resulting in only one fixed point and hence no possibility of bistability. This result allowed us to tell the biologists that the toggle switch would definitely not work if both of the Hill coefficients were one. + + + + + Figure 3. Figure 3: This figure is of CFP as a function of GFP for the two nullclines when the initial galactose and copper concentrations are changed. From this we can see how the fixed points change with different initial galactose and methionine concentrations. The blue line represents the GFP = CFP line. The further from this line equilibrium points are, the harder it will be to switch between stable states. + + + + + + + + + + + + + + Results Results - We were able to find the equilibrium points of the system analytically (for Hill coefficients) and computationally. These points were used for bifurcation analysis, and for analysing the probability that our system would exhibit istable behaviour. + We focused our efforts on plotting the nullclines of the system for a range of Hill coefficient combinations in order to get a general idea of which combinations would most likely produce robust bistability. We found that all combinations gave bistability, except when both Hill coefficients were one. The optimal Hill coefficient combination occurred when both Hill coefficients were two. We passed this information onto the biology team, letting them know that if we wanted the system to successfully switch, we could not have both Hill coefficients with a value of one. + + + + +   Return to Equations + + Continue to Bifurcation and Stability   + + + + + + + {{:Team:Aberdeen_Scotland/Footer}} Latest revision as of 20:31, 27 October 2010 University of Aberdeen - ayeSwitch - iGEM 2010 iGEM 2010 Fixed Points Fixed points are the points where an equation’s rate of change, or its slope, is zero. There are three main types of equilibrium points: stable, unstable, and saddle-node points. A stable equilibrium is a value which the function converges towards, whereas an unstable equilibrium is a value the function will diverge from. A saddle-node is where the function both converges to and diverges from, the equilibrium, depending on the direction from which we approach the point (S. Strogatz, Nonlinear dynamics and Chaos). Why are fixed points important? Finding fixed points is the first step in analyzing the stability of a system. In particular, we are interested in the nature of our system’s bistability and how it changes with a variation of the parameters, i.e., its bifurcation analysis. This analysis can be conveyed to the biologists to minimize experimental guessing. How are fixed points calculated? Fixed points are determined by setting all differential equations in a system equal to zero and solving for the variable being analyzed. The direct method of calculating equilibrium points is to find the roots of the system of equations using built-in root-finding functions such as fzero in MATLAB, and similar functions in Maple and C. The indirect method of calculating the equilibrium points is to plot and find the intersections of these nullclines, which represent equilibrium points. Results We were able to find the fixed points of the system analytically (for small Hill coefficients) and computationally. These points were used for bifurcation analysis, and for analyzing the probability that our system would exhibit bistable behavior. Nullclines In a system of differential equations, the nullclines are the solution curves for which all of the differential equations are equal to zero (Wikipedia). Why are nullclines important? The intersections of the nullclines give the equilibrium points of the system of differential equations. From graphs of the nullclines, it is possible to infer whether or not a system will be bistable. If the nullclines only intersect in one place the system is not bistable, since there is one single equilibrium point. If there are more than two intersections, the middle equilibrium point is often an unstable saddle point. How are the nullclines calculated? Just as in calculating the fixed points, we set the governing differential equations of the system equal to zero and plot the curves generated. Simulations involved Figure 1.This figure is a plot of the nullclines of the differential equations for CFP and GFP, where we solve them for CFP as a function of GFP. In this plot, both Hill coefficients are two, ie. n2 and n4 are both 2. The nullclines cross over at three fixed points, where the middle is a saddle-node fixed point. This is an ‘ideal’ bistability plot. Figure 2.This figure is a plot, again, of the nullclines of the differential equations for CFP and GFP. In this plot, both Hill coefficients are one. Note that the nullclines only cross once, resulting in only one fixed point and hence no possibility of bistability. This result allowed us to tell the biologists that the toggle switch would definitely not work if both of the Hill coefficients were one. Figure 3. Figure 3: This figure is of CFP as a function of GFP for the two nullclines when the initial galactose and copper concentrations are changed. From this we can see how the fixed points change with different initial galactose and methionine concentrations. The blue line represents the GFP = CFP line. The further from this line equilibrium points are, the harder it will be to switch between stable states. Results We focused our efforts on plotting the nullclines of the system for a range of Hill coefficient combinations in order to get a general idea of which combinations would most likely produce robust bistability. We found that all combinations gave bistability, except when both Hill coefficients were one. The optimal Hill coefficient combination occurred when both Hill coefficients were two. We passed this information onto the biology team, letting them know that if we wanted the system to successfully switch, we could not have both Hill coefficients with a value of one. Back to the Top

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Kindergarten Font: # Attributes/Measurement Strand: Shape and Space (Measurement) Outcome: 1 ## Step 5: Follow-up on Assessment ### Guiding Questions • What conclusions can be made from assessment information? • How effective have instructional approaches been? • What are the next steps in instruction? ### A. Addressing Gaps in Learning If a student is having difficulty learning to measure, work on what the attribute "length" means. Start with coloured rectangles and ask which one is longer, which one is shorter and which ones are almost the same. The next step is to introduce a nonstandard unit of measure. Students need many opportunities to measure with crayons, paper clips, their shoes, etc. This applies to mass and volume as well, which should be approached slowly in the same manner. ### B. Reinforcing and Extending Learning Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. Consider strategies, such as the following. • Ask students which one is farther: the distance from the classroom to the office or the distance from the classroom to the gym. Have them measure the distances, allowing them to select a nonstandard unit of measurement. Have students justify the appropriateness of the nonstandard unit of measurement they select. • Have students create different rulers to measure things in the classroom. Some may use paper clip chains, some may use a crayon ruler, etc. Have them create the ruler by attaching their chosen units to a strip of paper. • Challenge students to find two objects where one is small and one is large but where the smaller item is the heavier of the two (e.g., a large bag of potato chips and a can of soup). Ask them to explain how this can happen. • Ask students if it is always true that a taller container holds more than a shorter container. Have a series of containers on display when you ask this question, including a variation of shapes; e.g., tall thin graduated cylinders, short wide containers, large tall containers. Ask them how you could find out the answer to your question.

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# Math/Physics posted by . A ball rolls horizontally off the edge of a tabletop that is 1.60 m high. It strikes the floor at a point 1.58 m horizontally away from the table edge. (Neglect air resistance.)How long was the ball in the air? What was its speed at the instant it left the table? The time in the air depends on height. h= 1/2 g t^2 solve for t. speed= horizontal distance/t ## Respond to this Question First Name School Subject Your Answer ## Similar Questions 1. ### physics A small ball rolls horizontally off the edge of a tabletop that is 1.2 m high. It strikes the floor at a point 1.52m horizontally away from the edge of the table. a) How long is the ball in the air? 2. ### Physics - Projectile Motion A ball rolls horizontally off the edge of a tabletop that is 1.60 m high. It strikes the floor at a point 1.58 m horizontally away from the table edge. (Neglect air resistance.) (a) How long was the ball in the air? 3. ### physics A ball rolls horizontally off the edge of a tabletop that is 1.0m high. It strikes the floor at a point 1.5m horizontally away from the edge of the table. Find the speed when the ball left the table. Find the time it takes to fall … 4. ### Physics A ball rolls horizontally off the edge of a tabletop that is 1.80 m high. It strikes the floor at a point 1.42 m horizontally away from the table edge. (Neglect air resistance.) (a) How long was the ball in the air? 5. ### Physics A small ball rolls horizontally off the edge of a table that is 1.20 m high. It strikes the floor at a point 1.52 m horizontally from the table edge. How long is the ball in the air? 6. ### physics A tennis ball rolls off the edge of a tabletop 0.800m above the floor and strikes the floor at a point 1.10m horizontally from the edge of the table. 1) Find the time of flight of the ball. 2) Find the magnitude of the initial velocity … 7. ### Physics A small ball rolls horizontally off the edge of a tabletop of height h. It strikes the floor a distance x horizontally away from the edge of the table. (Use any variable or symbol stated above along with the following as necessary: … 8. ### college physics tennis ball rolls off the edge of a tabletop 0.900m above the floor and strikes the floor at a point 1.60m horizontally from the edge of the table. A: Find the time of flight of the ball B: Find the magnitude of the initial velocity … 9. ### physics a ball rolls off the edge of a tabletop 1m above the floor and strikes the floor at a point 1.5m horizontally from the edge of the table. Find the (a) time of flight (b) initial velocity, (c) final velocity just before it strikes the … 10. ### physics a ball rolls off the edge of a tabletop 1m above the floor and strikes the floor at a point 1.5m horizontally from the edge of the table. Find the (a) time of flight (b) initial velocity, (c) final velocity just before it strikes the … More Similar Questions

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# Tag Archives: Powers of 2 ## Powers of 2 and 3 as a sum of two powers and so on.   and so on.   and so on. ## Triples (a, b, c); ab-c, bc-a, ca-b are all powers of 2 Find triples     of positive integers for which     and are all powers of 2   For example,   (a, b, c)   =   (2, 2, 2),   (3, 2, 2),   (11, 6, 2),   … Continue reading ## Powers of 2 | (2+1)(2^2 + 1)(2^4 + 1)(2^8 + 1) … + 1 Using powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, … as shown   we always end up getting 4.   Explain.           … Continue reading ## Find smallest integer n so that 2^(10*n) doesn’t begin with digit 1 These results all begin with 1 :     Find the smallest positive integer     where     produces a number that does not begin with 1                                                                  ——————————————   Solution:   Don S. McDonald and … Continue reading Posted in Number Puzzles | Tagged | 5 Comments ## Powers of 2 – divisibility Let     be positive integers.     and       ….     ……     ….     ……     ….     ……     …     …..     …     ….. … Continue reading ## Powers of 2 in terms of factorials Generalize this. ## Are there any positive integers n such that the expansion of 2^n ends in n? n = 36   is the first from this list.   Any others?   @chappulian found   n = 736   and   n = 8736   @shahlock:   n = 48736 Dave Radcliffe: a(2) = 36,   … Continue reading Posted in Uncategorized | Tagged | 3 Comments ## 2^(4*n+2) + 1, n = 1,2,3,…,15 To be continued.

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# Rudin Series ratio and root test. In Rudins Principles of Mathematical Analysis he says consider the following series $$\frac 12 + \frac 13 + \frac 1{2^2} + \frac 1{3^2} + \frac 1{2^3} + \frac 1{3^3} + \frac 1{2^4} + \frac 1{3^4} + \cdots$$ for which $$\liminf \limits_{n \to \infty} \dfrac{a_{n+1}}{a_n} = \lim \limits_{n \to \infty} \left( \dfrac {2}{3} \right)^n =0,$$ $$\liminf \limits_{n \to \infty} \sqrt[n]{a_n} = \lim \limits_{n \to \infty} \sqrt[2n]{\dfrac{1}{3^n}} = \dfrac{1}{\sqrt{3}},$$ $$\limsup \limits_{n \to \infty} \sqrt[n]{a_n} = \lim \limits_{n \to \infty} \sqrt[2n]{\dfrac{1}{2^n}} = \dfrac{1}{\sqrt{2}},$$ $$\limsup \limits_{n \to \infty} \dfrac{a_{n+1}}{a_n} = \lim \limits_{n \to \infty} \dfrac 12\left( \dfrac {3}{2} \right)^n =+\infty,$$ The root test indicates convergence; the ratio test does not apply. In the book he defines the root and ratios test for the lim sup. I am not exactly sure how he goes from the lim sup to the lim and also why there is a $2n$ (which I assume comes from even terms of the sequence) in the root test. Also why is he checking the lim inf? I believe that my understanding of lim sups and infs are not well developed or I would probably understand what’s going on. Also how does he get the terms that he is taking the limit of. A nudge in the right direction to figure this out would be much appreciated. Thank you!! - One of the expressions is not quite right, which one depends on whether $n$ starts at $0$ or at $1$. Doesn't matter, the $2n+1$-th root and the $2n$-th root of $\frac{1}{2^n}$ have the same limit. – André Nicolas Oct 25 '12 at 2:17 The only thing that was wrong was the 2/3 in the last limit. I changed it to the 3/2 which it should be. – Differintegral Oct 25 '12 at 2:21 I was commenting about the Root Test expression. If we want to take the $k$-th root of the $k$-th term, in this case we will alternately be looking at the $2n$-th root and the $2n+1$-th root of an $n$-th power. – André Nicolas Oct 25 '12 at 2:26 I also have some confusion regarding this concept. Would like to clarify about the same. Rudin in his introduction to ratio test says that a series converges if the limsup is less than one. It diverges if the ratio is more than 1 for all n greater than a N. I guess the crux of the matter is that limsup is not used in both the cases. If it were it would cover all the cases. Wikipedia says that series converges if limsup less than one and it diverges if liminf more than 1. Thus , the two conditions dont cover all the cases. And the ratio test is not helpful in cases where limsup >1 and liminf<1. – ameyask86 Jan 29 '14 at 12:53 contd. Which is what is happening in the example of this question. Is my understanding correct ? I would have posted a new question , but this was already asked. And my query is just about a confirmation hence asking in comment. I hope its ok. – ameyask86 Jan 29 '14 at 12:54 For definiteness, call the terms of our sequence $a_1,a_2,a_3,\dots$. A similar analysis with minor differences of detail can be made if we call the first term of our sequence $a_0$. Note that for $n=1,2,3,\dots$ we have $a_{2n-1}=\dfrac{1}{2^n}$ and $a_{2n}=\dfrac{1}{3^n}$. The $k$-th root of the $k$-th term is "small" when the $k$-th term is a power of $\dfrac{1}{3}$. The $k$-th root of the $k$-th term is "large" when the $k$-th term is a power of $\dfrac{1}{3}$. More precisely, $\liminf \sqrt[k]{a_k}=\lim\inf \sqrt[2n]{\frac{1}{3^n}}=\dfrac{1}{3}$. For even $k$ the $k$-th root is constant. Also, $\limsup\sqrt[k]{a_k}=\liminf\sqrt[2n-1]{\dfrac{1}{2^n}}$. But $$\sqrt[2n-1]{\dfrac{1}{2^n}}=\left(\frac{1}{2^n}\right)^{1/(2n-1)}=\left(\frac{1}{2^n}\right)^{2n/(2n(2n-1))}=\left(\frac{1}{\sqrt{2}}\right)^{2n/(2n-1)}.$$ The expression on the right has limit $\dfrac{1}{\sqrt{2}}$. That takes care of one of the gaps. For the Ratio Test, we are interested in the behaviour of $\left|\dfrac{a_{k+1}}{a_k}\right|$. Let $k$ be odd, say $k=2n-1$. Then $a_k=\dfrac{1}{2^n}$. And $a_{k+1}=a_{2n}=\dfrac{1}{3^n}$. It follows that $$\frac{a_{k+1}}{a_k}=\frac{a_{2n}}{a_{2n-1}}=\left(\frac{2}{3}\right)^n.$$ This has very pleasant behaviour for large $n$, indeed for any $n$: it is safely under $1$, indeed has limit $0$. Now let $k$ be even, say $k=2n$. Then $a_k=\dfrac{1}{2^n}$. and $k+1=2n+1$. The $2n+1$-th term of our sequence is $\dfrac{1}{2^{n+1}}$. It follows that in the case $k=2n$ we have $$\frac{a_{k+1}}{a_k}=\frac{a_{2n+1}}{a_{2n}}=\frac{\frac{1}{2^{n+1}}}{\frac{1}{3^n}}=\frac{1}{2}\left(\frac{3}{2}\right)^n.$$ This unfortunately behaves badly for large $n$: we would like it to be safely under $1$, and it is very much over. The limit of the ratios $\dfrac{a_{k+1}}{a_k}$ does not exist. The ratios do not (uniformly) blow up, since for $k$ odd, the ratios approach $0$. The ratio behaves very nicely at odd $k$, and very badly at even $k$. So the Ratio Test is inconclusive. The bad behaviour prevents us from concluding convergence. But the good behaviour prevents us from concluding divergence. - Thank you for all the work you did to show me. It is making more sense now but I am still curious about something. Both the root test and the ratio test only need the lim sup and the possibly the ratio $|a_{n+1}/a_n|$ on it's own. Why doesn he look at the lim inf in this case? I feel like there is one major concept that I am missing here. Also is the reason we can turn the lim sup and lim inf into just the limit is because the limit exists and therefore we have that lim inf = lim sup = lim? Of course in the case of $+\infty$ it exists in the extended reals. – Differintegral Oct 25 '12 at 4:48 Second question: yes, when we evens and odds, the limsups are actual limits. In the Ratio Test, we are interested in limsup because, at the heart of things, the Ratio Test is a comparison with a geometric series. If, in the long run, the ratio (of absolute values) is $\lt r\lt 1$, the comparison with a geometric series with common ratio $r$ yields convergence. (to be continued) – André Nicolas Oct 25 '12 at 5:11 (Cont.) The Root Test is also fundamentally a comparison with a geometric series. If $\sqrt[n]{a_n}$ is ultimately $\lt r\lt 1$, then ultimately $a_n\lt r^n$. The Root Test doesn't care if the $a_n$ bounce around a bit, as long as they go down fast enough. The Ratio Test kind of insists that (after a while) we steadily go down fastish, term after term. – André Nicolas Oct 25 '12 at 5:12

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## Us pound weight conversion 22 Jul 2018 Pounds. Abbreviation/Symbol: lb; lbm (pound-mass – scientific). Unit of: Mass; Weight (in non-scientific affairs). Worldwide use: U.K., U.S.A  Weight converter for units including Kilograms, Pounds, Grams, Ounces, Stones etc. The pound (abbreviation: lb) is a unit of mass or weight in a number of different systems, including English units, Imperial units, and United States customary units. Review the size of ounces and pounds and how to convert between the two. Then, try some practice problems. Weight, Pound, lb. or # Converting between Units in the Imperial and U.S. Systems Converting between Metric and Imperial/U.S. Measurement Systems. Pounds to kilograms (lb to kg) Metric conversion calculator. Includes thousands of additional conversions, algebraic formulas, search tool, more. Simple unit conversion tool that helps you to convert pounds of water (lb wt.) to U.S. fluid ounces of water(fl-oz) and reverse. What you should know about pounds  convert pounds to stones kilograms carats cloves kilograms milligrams micrograms kilograms to pounds kg lb weight conversion metric conversions In the United States, a kip is a unit of mass that equals 1,000 avoirdupois pounds. Use this weight & mass converter to convert instantly between pounds, ounces, The pound (abbreviations: lb or, sometimes in the United States, #) is a unit of ## Metric measurements. Metric weight units are based around the weight of respective metric volumes of water. For example, a liter of water weighs one kilogram. Simple converter for British to American weight formats. Convert British stones and pounds to American stlye pounds only by typing the weight in the boxes  pound (lb) - basic weight unit in the US; stone (st) - 14 pounds. Often used to  The pound (abbreviation: lb) is a unit of mass or weight in a number of different systems, including English units, Imperial units, and United States customary units. Review the size of ounces and pounds and how to convert between the two. Then, try some practice problems. Weight, Pound, lb. or # Converting between Units in the Imperial and U.S. Systems Converting between Metric and Imperial/U.S. Measurement Systems. Pounds to kilograms (lb to kg) Metric conversion calculator. Includes thousands of additional conversions, algebraic formulas, search tool, more. Simple unit conversion tool that helps you to convert pounds of water (lb wt.) to U.S. fluid ounces of water(fl-oz) and reverse. What you should know about pounds ### The hundredweight (cwt) in England is always 112 pounds, or 8 stone. In the US, the hundredweight is 100 lb, unless noted as otherwise. It is proper to call a Review the size of ounces and pounds and how to convert between the two. Then, try some practice problems. Weight, Pound, lb. or # Converting between Units in the Imperial and U.S. Systems Converting between Metric and Imperial/U.S. Measurement Systems. Pounds to kilograms (lb to kg) Metric conversion calculator. Includes thousands of additional conversions, algebraic formulas, search tool, more. Simple unit conversion tool that helps you to convert pounds of water (lb wt.) to U.S. fluid ounces of water(fl-oz) and reverse. What you should know about pounds  convert pounds to stones kilograms carats cloves kilograms milligrams micrograms kilograms to pounds kg lb weight conversion metric conversions In the United States, a kip is a unit of mass that equals 1,000 avoirdupois pounds. ### Weight, Pound, lb. or # Converting between Units in the Imperial and U.S. Systems Converting between Metric and Imperial/U.S. Measurement Systems. The hundredweight (cwt) in England is always 112 pounds, or 8 stone. In the US, the hundredweight is 100 lb, unless noted as otherwise. It is proper to call a  Simple converter for British to American weight formats. Convert British stones and pounds to American stlye pounds only by typing the weight in the boxes  pound (lb) - basic weight unit in the US; stone (st) - 14 pounds. Often used to  The pound (abbreviation: lb) is a unit of mass or weight in a number of different systems, including English units, Imperial units, and United States customary units. Review the size of ounces and pounds and how to convert between the two. Then, try some practice problems. ## iPhone & Android app Weight converter Pounds Kilograms Ounces Stones Metric Tons (or Tonnes) Long Hundredweights (UK) Troy Pounds Troy Ounces Pennyweights Grains Tonnes Ton Hundredweights Grams Carats Milligrams Micrograms Long Tons (UK) Short Tons (US) Short Hundredweights (US) Temperature converter Length converter Area converter Volume converter Speed converter Time converter Angle converter Pressure converter Energy and Power converter Health and Wellbeing converter Metric Conversion Table This selection will show you how to convert various numbers from the U.S. system of measurement to the metric system. I want to convert pounds (lbs) into  The hundredweight (cwt) in England is always 112 pounds, or 8 stone. In the US, the hundredweight is 100 lb, unless noted as otherwise. It is proper to call a  Simple converter for British to American weight formats. Convert British stones and pounds to American stlye pounds only by typing the weight in the boxes  pound (lb) - basic weight unit in the US; stone (st) - 14 pounds. Often used to  The pound (abbreviation: lb) is a unit of mass or weight in a number of different systems, including English units, Imperial units, and United States customary units. Review the size of ounces and pounds and how to convert between the two. Then, try some practice problems. Weight, Pound, lb. or # Converting between Units in the Imperial and U.S. Systems Converting between Metric and Imperial/U.S. Measurement Systems. Dollars to Pounds provides an easy to understand exchange rate and easy to use calculator for currency conversion between US , Canadian , Australian , New Zealand & Hong Kong Dollars and British Pounds (GBP). The Dollars to Pounds exchange rate shown is updated live around every 10 seconds. Convert between all known Weight and Mass units. Convert what quantity? From: centigram decigram dekagram dram grain gram hectogram hundredweight [long, UK] hundredweight [short, US] kilogram lb, lbs long ton megagram metric ton microgram milligram ounce pound short ton ton [long, UK] ton [metric] ton [short, US] tonne Kilograms to Pounds Common Values. 1 kg = 2.204622476038 lbs 8 kg = 17.636979808304 lbs 2 kg = 4.4092449520759 lbs 5 kg = 11.02311238019 lbs 3 kg = 6.6138674281139 lbs 6 kg = 13.227734856228 lbs 10 kg = 22.04622476038 lbs 7 kg = 15.432357332266 lbs 4 kg = 8.8184899041518 lbs 70 kg = 154.32357332266 lbs 65 kg = 143.30046094247 lbs 80 kg =

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 Convert drad to Arcminute (Deciradian to Arcminute) ## Deciradian into Arcminute Measurement Categorie: Direct link to this calculator: # Convert Deciradian to Arcminute (drad to Arcminute): 1. Choose the right category from the selection list, in this case 'Angle'. 2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), brackets and π (pi) are all permitted at this point. 3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Deciradian [drad]'. 4. Finally choose the unit you want the value to be converted to, in this case 'Arcminute'. 5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so. With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '483 Deciradian'. In so doing, either the full name of the unit or its abbreviation can be usedas an example, either 'Deciradian' or 'drad'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Angle'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Alternatively, the value to be converted can be entered as follows: '69 drad to Arcminute' or '78 drad into Arcminute' or '86 Deciradian -> Arcminute' or '75 drad = Arcminute' or '58 Deciradian to Arcminute' or '82 Deciradian into Arcminute'. For this alternative, the calculator also figures out immediately into which unit the original value is specifically to be converted. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second. Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(61 * 83) drad'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '483 Deciradian + 1449 Arcminute' or '13mm x 54cm x 32dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question. If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 2.964 197 503 89×1027. For this form of presentation, the number will be segmented into an exponent, here 27, and the actual number, here 2.964 197 503 89. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 2.964 197 503 89E+27. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 2 964 197 503 890 000 000 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications. ## How many Arcminute make 1 Deciradian? 1 Deciradian [drad] = 343.774 677 078 49 Arcminute - Measurement calculator that can be used to convert Deciradian to Arcminute, among others.

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} short3b # short3b - (a Which one is it(b If it converges compute the... This preview shows pages 1–2. Sign up to view the full content. Exam 3b M175-001 Fall, 2009 Name: (1 pt.) 1. (10 pts.) Consider the sequence a n = n + 3 2 n - 1 ; n 0 (a) Graph the first six terms of the sequence on the axes provided below. Be sure that your axes are properly labeled. (b) Compute lim n →∞ a n . 1 This preview has intentionally blurred sections. Sign up to view the full version. View Full Document 2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR ANSWER. You do not need to show work, but you cannot receive partial credit for a wrong answer unless I can see how you got your answer. (a) summationdisplay n =2 n - 1 n 4 + 2 n CONVERGENT DIVERGENT (b) summationdisplay n =5 n 2 ln n + 2 n 5 - 3 n 2 CONVERGENT DIVERGENT (c) summationdisplay n =0 2 n + 3 n n 4 n CONVERGENT DIVERGENT (d) summationdisplay n =0 3(9) n 10 n CONVERGENT DIVERGENT (e) summationdisplay n =0 (2 n ) 2 n ! CONVERGENT This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: (a) Which one is it? (b) If it converges, compute the exact sum of the series. If it diverges, explain why. 4. (10 pts.) Find the radius of convergence of ∞ s n =2 2 n +1 ( x + 2) n 3 n 2 5. (10 pts.) Express f ( x ) = x 2 + x as a power series centered at 0. 6. (10 pts.) Find the quadratic approximation for f ( x ) = (1 + x ) 1 / 3 centered at 0. 7. (10 pts.) Find the ±fth order approximation of f ( x ) centered at 0, given that f (0) = 2 and the derivative of f is f ′ ( x ) = cos x 1 + x 2 2... View Full Document {[ snackBarMessage ]} ### Page1 / 2 short3b - (a Which one is it(b If it converges compute the... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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Definitions for "Chi-Square Test" Add To Word List Enter your search terms Submit search form Keywords: Related Terms: a statistical test to determine if an experimentally obtained set of data fits the predicted outcome. "Goodness of fit". A statistical tool that determines the probability of obtaining the observed results by chance under a specific hypothesis, or proposed assumption Used for making a comparison in nominal variates between hypothsised samples and a population samples. The method is used in both univariate or bivariate analysis. A test of whether data fits a particular theoretical distribution ( goodness of fit), or else of whether 2 categorical variables are independent ( association). In both cases, this is based on the result that the sum of the squared differences between the observed values and those expected under H0 divided by the expected values has an approximate chi-squared distribution if H0 is true. A general procedure for determining the probability that two different distributions are actually samples of the same population. In nuclear counting measurements, this test is frequently used to compare the observed variations in repeat counts of a radioactive sample to the variation predicted by statistical theory. The name of a statistical test and of a probability distribution that has a particular shape. The chi-square test is used to determine whether the distribution of counts or occurrences is random across categories. EX: If a die is fair (not loaded), each of the numbers 1 through 6 should occur with the same frequency. If three handpieces are equally safe, the number of accidents with each should be jointly independent of which handpiece is used and how often it is used. The result of a chi-square test is “looked up” in a table of chi-square distributions to determine the chance of such a test value occurring by chance, the p-value. Usually preformed as a hand calculation. {See templates – Choosing a statistical test, chi-square.} [See degrees of freedom, independence A statistical test applied to nominal or categorical data. A test used with classification tables to determine the influence (if any) of one factor (rows) on a second factor (columns) by assessing whether there is a difference in the proportion of an outcome in two or more groups. Examples of factors might be smoking (yes/no) against lung cancer (yes/no): in other words, does smoking status lead to a larger risk of lung cancer, or is it irrelevant? The chi-square test is not for use on continuous data, but specifically for counts. See also Classification table.

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# Trig problem • Jun 28th 2009, 09:02 AM jo74 Trig problem Hi guys. I need some help to solve this problem. a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angular velocity. (b) If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg • Jun 28th 2009, 01:02 PM skeeter Quote: Originally Posted by jo74 Hi guys. I need some help to solve this problem. a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angular velocity. (b) If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg part (a) $r = \sqrt{1.25^2 - .75^2}$ $\theta = \arcsin\left(\frac{.75}{1.25}\right)$ if $T$ is the tension in the string ... $T\sin{\theta} = mg$ $T\cos{\theta} = F_c$ , where $F_c$ is the centripetal force. eliminate $T$ in the two equations above and solve for $F_c$ ... then use the equation below to determine $\omega$ $F_c = mr\omega^2$ part (b) is too easy ... think about the net force in the vertical direction. • Aug 11th 2009, 11:10 AM Hi it's me again. I tried to find the answer but just got my paper back but got it completely wrong again. I already had the first part answered, it's the second part I'm struggling with. • Aug 11th 2009, 11:32 AM skeeter Quote: Originally Posted by jo74 Hi guys. I need some help to solve this problem. a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angular velocity. (b) If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg is the string still attached as in part (a) ? • Aug 11th 2009, 11:40 AM Yeah, it is still attached to the string at the same angle as in part 1. • Aug 11th 2009, 03:09 PM skeeter $T\cos{\theta} = m r \omega^2$ $T = \frac{m r \omega^2}{\cos{\theta}}$ sub in your known values and calculate $T$ let $F$ = force that the table exerts upward on the mass. $T\sin{\theta} + F = mg$ $F = mg - T\sin{\theta}$ calculate $F$ • Aug 11th 2009, 09:44 PM

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# Leetcode Integer to Roman problem solution in C# Feb 15, 2023 In the Leetcode Integer to Roman problem solution in C# programming Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M. Symbol Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000 For example, 2 is written as II in Roman numeral, just two one’s added together. 12 is written as XII, which is simply X + II. The number 27 is written as XXVII, which is XX + V + II. Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX. There are six instances where subtraction is used: I can be placed before V (5) and X (10) to make 4 and 9. X can be placed before L (50) and C (100) to make 40 and 90. C can be placed before D (500) and M (1000) to make 400 and 900. Given an integer, convert it to a roman numeral. ## Leetcode Integer to Roman problem solution in C# programming ``````public class Solution { public string IntToRoman(int num) { List<string> Symbol = new List<string>() {"I","V","X","L","C","D","M" }; int numb = num; int numb2 = 0; int index_Symbol =0; string res =""; while(numb!=0) { numb2 = numb%10; switch(numb2) { case 1: res=Symbol[index_Symbol]+res; break; case 2: res=Symbol[index_Symbol]+Symbol[index_Symbol]+res; break; case 3: res=Symbol[index_Symbol]+Symbol[index_Symbol]+Symbol[index_Symbol]+res; break; case 4: res=Symbol[index_Symbol]+Symbol[index_Symbol+1]+res; break; case 5: res=Symbol[index_Symbol+1]+res; break; case 6: res=Symbol[index_Symbol+1]+Symbol[index_Symbol]+res; break; case 7: res=Symbol[index_Symbol+1]+Symbol[index_Symbol]+Symbol[index_Symbol]+res; break; case 8: res=Symbol[index_Symbol+1]+Symbol[index_Symbol]+Symbol[index_Symbol]+Symbol[index_Symbol]+res; break; case 9: res=Symbol[index_Symbol]+Symbol[index_Symbol+2]+res; break; } numb=numb/10; index_Symbol+=2; if(index_Symbol==6) { numb2 = numb%10; res=string.Concat(Enumerable.Repeat(Symbol[index_Symbol],numb))+res; return res; } } return res; } }`````` #### By Neha Singhal Hi, my name is Neha singhal a software engineer and coder by profession. I like to solve coding problems that give me the power to write posts for this site.

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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition) $\bf{\text{Solution Outline:}}$ Solve the solution sets of the given statements, \begin{array}{l}\require{cancel} \dfrac{3}{5}a+\dfrac{1}{5}=2 \\\text{and}\\ 3a+1=10 .\end{array} If the solution sets are the same, then they are equivalent. Otherwise, they are not equivalent. $\bf{\text{Solution Details:}}$ Using the properties of equality, the first equation is equivalent to \begin{array}{l}\require{cancel} \dfrac{3}{5}a+\dfrac{1}{5}=2 \\\\ 5\left( \dfrac{3}{5}a+\dfrac{1}{5} \right)=5(2) \\\\ 3a+1=10 .\end{array} Since the equation above is the same as the second given equation, then the given are $\text{ equivalent equations .}$

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Commit 04e7c245 by Gabriele Buondonno ### [rpy] Implement rpyToJacDerivative parent dc3814b7 ... ... @@ -93,6 +93,26 @@ namespace pinocchio template inline Eigen::Matrix rpyToJacInv(const Eigen::MatrixBase & rpy, const ReferenceFrame rf=LOCAL); /// /// \brief Compute the time derivative Jacobian of the Roll-Pitch-Yaw conversion /// /// Given \f$\phi = (r, p, y)\f$ and reference frame F (either LOCAL or WORLD), /// the Jacobian is such that \f${}^F\omega = J_F(\phi)\dot{\phi} \f$, /// where \f${}^F\omega \f$ is the angular velocity expressed in frame F /// and \f$J_F \f$ is the Jacobian computed with reference frame F /// /// \param[in] rpy Roll-Pitch-Yaw vector /// \param[in] rpydot Time derivative of the Roll-Pitch-Yaw vector /// \param[in] rf Reference frame in which the angular velocity is expressed /// /// \return The time derivative of the Jacobian of the Roll-Pitch-Yaw conversion in the appropriate frame /// /// \note for the purpose of this function, WORLD and LOCAL_WORLD_ALIGNED are equivalent /// template inline Eigen::Matrix rpyToJacDerivative(const Eigen::MatrixBase & rpy, const Eigen::MatrixBase & rpydot, const ReferenceFrame rf=LOCAL); } // namespace rpy } ... ... ... ... @@ -141,6 +141,47 @@ namespace pinocchio } } } template inline Eigen::Matrix rpyToJacDerivative(const Eigen::MatrixBase & rpy, const Eigen::MatrixBase & rpydot, const ReferenceFrame rf) { typedef typename Vector3Like0::Scalar Scalar; Eigen::Matrix J; const Scalar p = rpy[1]; const Scalar dp = rpydot[1]; Scalar sp, cp; SINCOS(p, &sp, &cp); switch (rf) { case LOCAL: { const Scalar r = rpy[0]; const Scalar dr = rpydot[0]; Scalar sr, cr; SINCOS(r, &sr, &cr); J << Scalar(0.0), Scalar(0.0), -cp*dp, Scalar(0.0), -sr*dr, cr*cp*dr - sr*sp*dp, Scalar(0.0), -cr*dr, -sr*cp*dr - cr*sp*dp; return J; } case WORLD: case LOCAL_WORLD_ALIGNED: { const Scalar y = rpy[2]; const Scalar dy = rpydot[2]; Scalar sy, cy; SINCOS(y, &sy, &cy); J << -sp*cy*dp - cp*sy*dy, -cy*dy, Scalar(0.0), cp*cy*dy - sp*sy*dp, -sy*dy, Scalar(0.0), -cp*dp, Scalar(0.0), Scalar(0.0); return J; } default: { throw std::invalid_argument("Bad reference frame."); } } } } // namespace rpy } #endif //#ifndef __pinocchio_math_rpy_hxx__ ... ... @@ -4,6 +4,7 @@ #include #include #include #include // to avoid C99 warnings ... ... @@ -208,4 +209,70 @@ BOOST_AUTO_TEST_CASE(test_rpyToJacInv) BOOST_CHECK(jAinv.isApprox(jA.inverse())); } BOOST_AUTO_TEST_CASE(test_rpyToJacDerivative) { // Check zero at zero velocity double r = static_cast (rand()) / (static_cast (RAND_MAX/(2*M_PI))) - M_PI; double p = static_cast (rand()) / (static_cast (RAND_MAX/M_PI)) - (M_PI/2); double y = static_cast (rand()) / (static_cast (RAND_MAX/(2*M_PI))) - M_PI; Eigen::Vector3d rpy(r, p, y); Eigen::Vector3d rpydot(Eigen::Vector3d::Zero()); Eigen::Matrix3d dj0 = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot); BOOST_CHECK(dj0.isZero()); Eigen::Matrix3d djL = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL); BOOST_CHECK(djL.isZero()); Eigen::Matrix3d djW = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::WORLD); BOOST_CHECK(djW.isZero()); Eigen::Matrix3d djA = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL_WORLD_ALIGNED); BOOST_CHECK(djA.isZero()); // Check correct identities between different versions rpydot = Eigen::Vector3d::Random(); dj0 = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot); djL = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL); djW = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::WORLD); djA = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL_WORLD_ALIGNED); BOOST_CHECK(dj0 == djL); BOOST_CHECK(djW == djA); Eigen::Matrix3d R = pinocchio::rpy::rpyToMatrix(rpy); Eigen::Matrix3d jL = pinocchio::rpy::rpyToJac(rpy, pinocchio::LOCAL); Eigen::Matrix3d jW = pinocchio::rpy::rpyToJac(rpy, pinocchio::WORLD); Eigen::Vector3d omegaL = jL * rpydot; Eigen::Vector3d omegaW = jW * rpydot; BOOST_CHECK(omegaW.isApprox(R*omegaL)); BOOST_CHECK(djW.isApprox(pinocchio::skew(omegaW)*R*jL + R*djL)); BOOST_CHECK(djW.isApprox(R*pinocchio::skew(omegaL)*jL + R*djL)); // Check against finite differences double const eps = 1e-7; double const tol = 1e-5; Eigen::Vector3d rpyEps = rpy; rpyEps[0] += eps; Eigen::Matrix3d djLdr = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps; rpyEps[0] = rpy[0]; rpyEps[1] += eps; Eigen::Matrix3d djLdp = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps; rpyEps[1] = rpy[1]; rpyEps[2] += eps; Eigen::Matrix3d djLdy = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps; rpyEps[2] = rpy[2]; Eigen::Matrix3d djLf = djLdr * rpydot[0] + djLdp * rpydot[1] + djLdy * rpydot[2]; BOOST_CHECK(djL.isApprox(djLf, tol)); rpyEps[0] += eps; Eigen::Matrix3d djWdr = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps; rpyEps[0] = rpy[0]; rpyEps[1] += eps; Eigen::Matrix3d djWdp = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps; rpyEps[1] = rpy[1]; rpyEps[2] += eps; Eigen::Matrix3d djWdy = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps; rpyEps[2] = rpy[2]; Eigen::Matrix3d djWf = djWdr * rpydot[0] + djWdp * rpydot[1] + djWdy * rpydot[2]; BOOST_CHECK(djW.isApprox(djWf, tol)); } BOOST_AUTO_TEST_SUITE_END() Supports Markdown 0% or . 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Purchase Solution # Solve an inequality and express using interval notation. Not what you're looking for? Solve an inequality. Write a solution set using interval notation. X^2 - 3 X - 5 >/= 0 "( X^2 - 3 X - 5) is greater than or equal to 0" PS: Please use those symbols, Multiplication * , fractions /, Exponents ^, Roots sqrt( )or &#8730;( ), - &#8730;( ), Infinities - ∞, ∞, minus - or plus + For example, ( - ∞, 〕&#12288; U &#12288;〔 , ∞&#12288;) ##### Solution Summary An inequality is solved and expressed using interval notation. ##### Exponential Expressions In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them. ##### Geometry - Real Life Application Problems Understanding of how geometry applies to in real-world contexts

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LMP - Python 1/14/22 #### Start 2022-01-14 04:35 AKST ## LMP - Python 1/14/22 #### End 2022-01-14 06:35 AKST The end is near! Contest is over. Not yet started. Contest is starting in -127 days 0:06:10 2:00:00 0:00:00 # Problem EReversed Binary Numbers Yi has moved to Sweden and now goes to school here. The first years of schooling she got in China, and the curricula do not match completely in the two countries. Yi likes mathematics, but now... The teacher explains the algorithm for subtraction on the board, and Yi is bored. Maybe it is possible to perform the same calculations on the numbers corresponding to the reversed binary representations of the numbers on the board? Yi dreams away and starts constructing a program that reverses the binary representation, in her mind. As soon as the lecture ends, she will go home and write it on her computer. ## Task Your task will be to write a program for reversing numbers in binary. For instance, the binary representation of 13 is 1101, and reversing it gives 1011, which corresponds to number 11. ## Input The input contains a single line with an integer $N$, $1 \leq N \leq 1\; 000\; 000\; 000$. ## Output Output one line with one integer, the number we get by reversing the binary representation of $N$. Sample Input 1 Sample Output 1 13 11 Sample Input 2 Sample Output 2 47 61

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# LeetCode — Sign of the Product of an Array • `1` if `x` is positive. • `-1` if `x` is negative. • `0` if `x` is equal to `0`. `Input: nums = [-1,-2,-3,-4,3,2,1]Output: 1Explanation: The product of all values in the array is 144, and signFunc(144) = 1` `Input: nums = [1,5,0,2,-3]Output: 0Explanation: The product of all values in the array is 0, and signFunc(0) = 0` `Input: nums = [-1,1,-1,1,-1]Output: -1Explanation: The product of all values in the array is -1, and signFunc(-1) = -1` • `1 <= nums.length <= 1000` • `-100 <= nums[i] <= 100` -- -- ## More from Steven Lu 👨‍💻 Love podcasts or audiobooks? Learn on the go with our new app.

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https://vustudents.ning.com/group/cs602computergraphics/forum/topics/cs602-current-mid-term-papers-fall-2012-date-08-december-2012-to?commentId=3783342%3AComment%3A1927029&groupId=3783342%3AGroup%3A60025

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We have been working very hard since 2009 to facilitate in your learning Read More. We can't keep up without your support. Donate Now. www.vustudents.ning.com www.bit.ly/vucodes + Link For Assignments, GDBs & Online Quizzes Solution www.bit.ly/papersvu + Link For Past Papers, Solved MCQs, Short Notes & More # CS602 Current MID Term Papers Fall 2012 Date: 08-December-2012 to 19-December-2012 CS602  Current MID Term Papers Fall 2012 Date: 08-December-2012 to 19-December-2012 + http://bit.ly/vucodes (Link for Assignments, GDBs & Online Quizzes Solution) + http://bit.ly/papersvu (Link for Past Papers, Solved MCQs, Short Notes & More) Views: 1196 ### Replies to This Discussion k0i midterm solved mcqx ki file he upload kr do plx....... :(:(:( t0morrowx ma paper n em n0t prepared... :( Gaiety Doll Check this link where you can find the mid term papers http://vustudents.ning.com/group/cs602computergraphics/forum/topic/... For Important Helping Material related to your subject (Solved MCQs, Short Notes, Solved past Papers, E-Books, FAQ,Short Questions Answers & more). You must view all the featured Discussion in these subject groups. For how you can view all the Featured discussions click on the Back to Subject Name Discussions link below the title of this Discussion & then under featured Discussion corner click on the view all link. i have n0t f0und thr even a single midterm solved accurate paper..... :/ Please Share your Current Papers Questions/Pattern here to help each other. Thanks ma todayx paper... All mcqz were from handoutx mostly from boundry fill algorithm n from last 2 lecturex.... Q1. define rotation in 2d ? (2) Q2. describe the diagram that is 0n the page # 200 2nd diagram... (5) q3. formula to find length of the vector. q4. write a c program to draw a circle using polar coordinatx yeah aik question tha find the projection of vector (5,6,8) on yz plane... somthing lyk that.... Gaiety Doll thanks for sharing your paper to help other students. Note to All: You don’t need to go any other site for current Mid Term papers fall 2012, Because All discussed data of our members in this discussion are going from here to other sites. You can judge this at other sites yourself. So don’t waste your precious time with different links. Its right plz can any one other here 2 share. 20 mcqs mostly were from last lectures. 6 long qs: write the two techniques of triangle rasterization.    2 marks ek tha k in 2-D can a polygon be divided if yes then write the reason? what is the taxonomy of the families of the projection?    shayd 5 mrks ka tha write the following formula in column 2?      5 marks ek table given tha jiske ek side par names or dusri side par unke formulas likhne the in 3-D? translation                      P'= scaling                            P'= rotation                          P'= shear                              P'= composite transition        P'= plz send word file...equation missing here... CS602 Current Midterm Papers: Paper 1 ma todayx paper... All mcqz were from handoutx mostly from boundry fill algorithm n from last 2 lecturex.... Q1. define rotation in 2d ? (2) Q2. describe the diagram that is 0n the page # 200 2nd diagram... (5) q3. formula to find length of the vector. q4. write a c program to draw a circle using polar coordinatx yeah aik question tha find the projection of vector (5,6,8) on yz plane... somthing lyk that.... Paper 2 20 mcqs mostly were from last lectures. 6 long qs: write the two techniques of triangle rasterization. 2 marks ek tha k in 2-D can a polygon be divided if yes then write the reason? what is the taxonomy of the families of the projection? shayd 5 mrks ka tha write the following formula in column 2? 5 marks ek table given tha jiske ek side par names or dusri side par unke formulas likhne the in 3-D? translation P'= scaling P'= rotation P'= shear P'= composite transition P'= Paper 3 where is 3rd paper..? ## Latest Activity Zoey D liked +++!!Zuni khan!!+++'s discussion Naraton k terrr kha kar 38 seconds ago Zoey D liked Mani Siddiqui Ex's discussion عجیب ایجاد 40 seconds ago Zoey D liked zohaib iftikhar's discussion ...!!MUHABBAT KA IK QISA...* 41 seconds ago 52 seconds ago Zoey D liked kiran shahzadi's discussion Vu Books For sale 1 minute ago Zoey D liked Zoey D's discussion Tm yaad hmen bhi kr lena (◕‿◕✿) 1 minute ago 1 minute ago 2 minutes ago 1 2 3 ## HELP SUPPORT This is a member-supported website. Your contribution is greatly appreciated!

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# Math posted by . decide on a topic which is adding drinks to each purchase from the lunch for which they would like to collect data and design a survey for school which could really be used to convince the principal to do. Create 7 questions for the survey. My questions so far are: Would you like to add a drink to each purchase from the lunch menu? What drinks do you enjoy drinking? If drinks are permitted to each purchase of the lunch menu do you want to add healthy drinks such as fruit flavored juice, chocolate or white milk or nestea juice boxes? Can there be any more questions to ask? • Math - What do you want the principal to do? What would he be willing to do? How much will the addition change the price of the meal? How big an increase in price might the students be willing to pay? To the last question, I would list all the drinks available in the Cafeteria for the students to check off which ones they might want. Will the price change be different, depending on the type of drink chosen (soft drink vs. fruit juice)? ## Similar Questions 1. ### math decide on a topic for which they would like to collect data and design a survey for school which could really be used to convince the principal to do. ex.fundraising,school uniforms These examples are already used by other classmates 2. ### Math decide on a topic which is adding more clubs for which they would like to collect data and design a survey for school which could really be used to convince the principal to do. Create 5-7 questions for the survey. 3. ### math decide on a topic which is adding more clubs for which they would like to collect data and design a survey for school which could really be used to convince the principal to do. Create 5-7 questions for the survey. Some of my questions … 4. ### Math trying to decide between parameter and statistic for the 2 questions below. I think it is statistic for both but not sure. 1. A local newspaper conducted a survey last week. Of the 2300 subscribers, 1276 responded. Based on the survey, … 5. ### ENG 098 Can you convince people NOT to eat Oreos? 6. ### Math You want to determine the average number of songs people keep on their MP3 players. You want to collect data from a random sample of at least 300. Which of these would be the most valid method of collecting data? 7. ### Math In this activity, you will design and conduct a survey. Choose a topic for your survey. 1. Collect your data. 2. Summarize the results with a graph and a description. When they say "Summarize the results with a graph," do they mean … 8. ### Math You want to find out what the favorite hot lunch in the school cafeteria is among the high school students. At an assembly for the whole school, you decide to survey all students who are sitting on the end of their rows in the auditorium. … 9. ### Math a survey showed that 30% of student bring their lunch to school. The survey polled 300 students do not bring their lunch to school 10. ### English 1. Lunch is on me. 2. What do you mean by "lunch is on me"? More Similar Questions

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## How to Remove Section Breaks in Word You can use section breaks to divide a Microsoft Word document into separate sections and change the layout or apply different formatting to each section. Mainly there are four types of section breaks (Next Page, Continuous, Even Page, Odd Page) in Microsoft Word. For some reason, you may need to remove all or some of … Read more ## How to compare two columns in Google Sheets When working with data, you may come across situations where you need to compare two or more datasets. For example, you may need to compare two different versions of the same data set. In such situations, we can compare the data sets using individual columns or column combinations. This post will show you how to … Read more ## Create a Crypto Portfolio Tracker in Google Sheets This post will show you how to create a Crypto Portfolio Tracker in Google Sheets. With this Google Sheet, you can track your cryptocurrency purchases. And also, you can view a summary of your total assets with the Dollar Cost Average (DCA) for each cryptocurrency. In addition to that, you can get the present value … Read more We have created a number of Google Apps Script Web Apps that can be used for data collection purposes in our previous blog posts. We included several types of form controls in those web apps, such as text fields, dropdowns, radio buttons, etc… This blog post will show you how to create a web app … Read more ## How to Generate a Data Entry form in Excel Using the “Form” command, you can easily generate a data entry form in Excel. Data entry forms provide a convenient means to insert, view, update, or delete data. This post will show you how to generate Excel data entry forms and why and when to use them. Note: The examples in this post have been … Read more ## Excel Named Range – Make Your Work Easier! We identify each cell in the spreadsheet by a combination of its column letter and row number. A range of cells is defined using the upper Left cell and the lower Right cell. We call this A1 notation. But writing a complex formula using A1 notation is a bit difficult to understand and maintain. You … Read more ## The Ultimate Guide to Handle Duplicates in Excel This post will show you how to handle duplicate entries or, in other words, repeated data in your data set in Microsoft Excel. There are many ways to handle duplicates in Excel. Sometimes you may have to remove duplicates. Sometimes you may have to work with the dataset while keeping the duplicates as it is. … Read more ## How to Embed Google Apps Script Web Apps in Websites In previous tutorials, we created some Web Apps with Google Apps Script and Google Sheets. This post will show you how to embed Google Apps Script Web Apps in Websites. In this post, I am not going to show how to build Webs Apps. I will show you how to embed an already made Web … Read more ## How to Create a Button in Google Sheets to Run Scripts You can create a button in Google Sheets to run Apps Script from its user interface. The button is essential when you design Google Sheets for others who do not know App Scripts. This post will show you how you can create a button in Google Sheets and attach the Google Apps Script function to … Read more ## How to Make a Checklist in Google Docs A checklist is a list of things that can be checked off individually when completed or noted. In a checklist, there is a checkbox for each list item that you can check or uncheck. This post will show you how to make a checklist in Google Docs. You may also be interested in How to … Read more

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