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# Microsoft Interview Experience | Set 132 (Software Engineer for Bing Team) Last Updated : 20 Dec, 2018 I recently attended Microsoft Interview for Software Engineer role in Bing Team. Round 1: Microsoft Interview Experience | Set 131 Its initial screening round. It has happened through skype. 1. Given n*n matrix with some elements in each cell. If there is “0” in any cell then we have to make that corresponding row and column to “0” Time complexity: O(n*n) Space complexity: O(1) 2. Given an array of elements with size n. You should find the number which is repeated more than n/2 times Time complexity: O(n) 3. After screening round, they asked me to come for 4 F2F rounds. I have visited Microsoft IDC hyderabad. Round 2: 1. Given sorted array of numbers and a sum. we have to find any two numbers whose sum is equal to the given sum. Time Complexity: O(n) 2. Given Binary tree with parent pointer and two nodes. Find LCA of the given two nodes in a given binary tree `struct` `TreeNode ` `{ ` `int` `data; ` `TreeNode *left,*right,*parent; ` `}; ` Parent pointer of each node points to its parent. Root node’s parent pointer points to NULL Time Complexity: O(logn) Round 3: 1. Given two linked lists. Find the intersection point of those two linkedlists 2. Its based on Binary tree. I forgot the question 🙂 3. Design discussion on Search functionality available in smart phones Round 4: 1. Given a linkedlist with random pointer for each node which points to some random number in the given list. Clone the linkedlist `struct` `ListNode ` `{ ` ` ``int` `data; ` ` ``ListNode *next,*random; ` `}; ` 2. Design and implement DNS Cache. Requirements: Cache must be fixed in size and it will be decided by the user who wants to use this cache. If the entry is not available in Cache then it should call server to get the details of ipAddress and store it in cache. Round 5: 1. Print given matrix in spiral order 2. I forgot the question. It is related to arrays 3. Design discussion on Top Trends feature available in facebook. Previous Article Next Article Article Tags : Practice Tags :

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https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-3-logic-3-6-negations-of-conditional-statements-and-de-morgan-s-law-exercise-set-3-6-page-178/47

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## Thinking Mathematically (6th Edition) Published by Pearson # Chapter 3 - Logic - 3.6 Negations of Conditional Statements and De Morgan's Law - Exercise Set 3.6 - Page 178: 47 See below. #### Work Step by Step The sentence in "if...then" form is: If there is no pain, there is no gain. The contrapositive of $p\rightarrow q$ is $\sim q\rightarrow \sim p$. The converse of $p\rightarrow q$ is $q \rightarrow p$. The inverse of $p\rightarrow q$ is $\sim p\rightarrow \sim q$. The negation of $p\rightarrow q$ is $p\land \sim q$. Hence here the converse is: If there is no gain, then there is no pain. The inverse: If there is pain, then there is gain. The contrapositive: If there is gain, then there is pain. The negation: There is no pain and there is gain. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

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# How to concatenate numerical vectors and a string to return a string in R? In general, the concatenation of numerical vectors and string results in a vector of strings in R. For example, if we want to concatenate 1, 2, 3 with Tutorialspoint using paste function then it will result in a vector as: "Tutorialspoint 1" "Tutorialspoint 2" "Tutorialspoint 3". But if we want it to return as "Tutorialspoint 1 2 3" then we need to use collapse argument with paste function. ## Example1 > x1 ## Output [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" > y1 ## Output [1] 1 9 6 3 8 1 8 5 9 1 2 8 3 8 4 5 10 1 6 3 9 8 2 2 3 [26] 7 5 5 1 5 7 10 5 4 8 7 6 4 5 4 10 8 4 7 1 1 3 9 2 3 > paste(c(x1,y1),collapse="") ## Output [1] "ABCDEFGHIJ19638185912838451016398223755157105487645410847113923" ## Example2 Live Demo > x2<-"TutorialsPoint" > x2 [1] "TutorialsPoint" Live Demo > y2<-rnorm(50) > y2 ## Output [1] -0.56450438 -0.87409683 -0.45545334 -1.92794565 -0.46204738 1.57181642 [7] -0.98986601 0.79975012 1.03634852 0.40356248 -0.34070839 -0.92796566 [13] 0.77889388 -1.29986590 0.26185934 0.36384901 1.28980906 0.13354925 [19] 0.51731334 0.26331224 -1.12768065 1.00102322 0.14566609 -1.79023868 [25] 0.56832540 -0.30686295 1.42981171 -2.22294595 -0.13630659 -1.66825359 [31] -0.90014165 1.30602557 -0.60606615 -0.08894799 -0.36974716 1.74791307 [37] -1.06738971 0.55717065 0.44214527 1.37510547 -0.33059281 0.09155202 [43] -0.52415542 0.12080025 0.52308841 1.23751663 0.04092456 0.45909642 [49] -0.92586032 1.88577081 > paste(c(x2,y2),collapse="") ## Output [1] "TutorialsPoint-0.564504382978389-0.87409682529276-0.455453344480808- 1.92794564994394-0.4620473763837751.57181641618727- 0.989866012956110.7997501231403411.03634851576550.403562482080398- 0.340708391515938-0.9279656644528410.778893880606269- 1.299865900879470.2618593419490970.3638490122278811.28980906119370.1335492 515560880.5173133396863840.263312236133718- 1.127680650369891.001023218744370.145666090450948- 1.790238680828030.568325403613886-0.306862949111771.42981170973405- 2.22294594835457-0.136306593294414-1.66825359470097- 0.9001416508373761.30602557188284-0.606066145406716-0.0889479853435373- 0.3697471568802411.74791306928163- 1.067389713621220.5571706471840320.4421452735967551.37510547035707- 0.3305928129508030.0915520241487435- 0.5241554231974670.1208002530584250.5230884092939871.237516628051970.04092 456035507360.459096416150022-0.9258603224075091.88577080883107" ## Example3 Live Demo > x3<-"TutorialsPoint" > y3<-1:10 > paste(c(x3,y3),collapse="") ## Output [1] "TutorialsPoint12345678910" ## Example4 Live Demo > x4<-"E-learning" > x4 ## Output [1] "E-learning" Live Demo > y4<-rpois(50,5) > y4 ## Output [1] 5 6 3 7 6 3 7 7 6 4 5 3 5 7 4 5 5 7 2 5 1 3 7 10 6 [26] 2 3 3 5 6 4 3 3 2 9 7 5 6 6 4 5 4 8 5 4 5 8 5 10 9 > paste(c(x4,y4),collapse="") ## Output [1] "E-learning5637637764535745572513710623356433297566454854585109" ## Example5 Live Demo > x5<-"Simply-Easy-Learning" > x5 ## Output [1] "Simply-Easy-Learning" Live Demo > y5<-sample(1:5,50,replace=TRUE) > y5 ## Output [1] 5 5 3 3 3 1 5 4 4 1 2 1 4 4 5 5 1 3 1 3 2 3 2 2 3 3 4 1 5 1 2 5 2 5 5 4 4 1 [39] 3 4 2 5 1 1 3 5 2 3 2 1 > paste(c(x4,y4),collapse=" ") ## Output [1] "E-learning 5 6 3 7 6 3 7 7 6 4 5 3 5 7 4 5 5 7 2 5 1 3 7 10 6 2 3 3 5 6 4 3 3 2 9 7 5 6 6 4 5 4 8 5 4 5 8 5 10 9" ## Example6 Live Demo > x6<-"Programming" > x6 ## Output [1] "Programming" Live Demo > y6<-rpois(100,5) > y6 ## Output [1] 3 5 3 5 7 7 3 3 4 9 4 3 2 8 3 3 7 5 5 2 6 4 2 4 3 [26] 5 5 3 4 7 10 3 6 6 6 4 4 10 1 4 6 4 8 7 8 4 8 6 3 6 [51] 1 6 2 7 4 5 4 4 1 5 5 5 4 5 4 6 5 6 3 6 4 3 8 3 5 [76] 2 3 2 4 5 1 2 2 5 4 4 7 7 4 9 3 6 6 2 2 11 2 7 3 6 > paste(c(x6,y6),collapse="-") ## Output [1] "Programming-3-5-3-5-7-7-3-3-4-9-4-3-2-8-3-3-7-5-5-2-6-4-2-4-3-5-5-3-4-7-10-3-6- 6-6-4-4-10-1-4-6-4-8-7-8-4-8-6-3-6-1-6-2-7-4-5-4-4-1-5-5-5-4-5-4-6-5-6-3-6-4-3-8-3-5- 2-3-2-4-5-1-2-2-5-4-4-7-7-4-9-3-6-6-2-2-11-2-7-3-6"

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https://www.tutorialspoint.com/tpcg.php?p=mhO7tDyA

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# Permutation Sequence in C++ My Projects My Profile Logout Undo Redo Cut Copy Paste Delete Select All Find Find and Replace Editor Theme Crimson Eclipse Github Solarized Cobalt krTheme Monokai Terminal Textmate Twilight Vibrant Ink Font Size 8px 9px 10px 11px 12px 13px 14px 15px 16px 17px 18px 20px 22px 24px Tab Size 1 2 3 4 5 6 7 8 Show Invisible Hide Invisible Show Line Numbers Hide Line Numbers Ace Editor (Default) Vim Editor Emacs Editor Open New Project Save Project Save As New Project Share Project Search Project #include <bits/stdc++.h> using namespace std; typedef long long int lli; class Solution { public: string getPermutation(int n, int k) { string ans = ""; vector <char> candidates(n); for(lli i = 0; i < n; i++) candidates[i] = ((i + 1) + '0'); vector <lli> fact(n + 1); fact[0] = 1; for(lli i = 1; i <= n; i++) fact[i] = fact[i - 1] * i; k--; for(lli i = n - 1; i >= 0; i--){ lli idx = k / fact[i]; ans += candidates[idx]; for(lli j = idx; j + 1< candidates.size(); j++) candidates[j] = candidates[j + 1]; k = k % fact[i]; } return ans; } }; main(){ Solution ob; cout << ob.getPermutation(4, 9); } # Permutation Sequence in C++ (GNU GCC v7.1.1) Permutation Sequence in C++ (GNU GCC v7.1.1) helps you to Edit, Run and Share your C++ Code directly from your browser. This development environment provides you version GNU GCC v7.1.1. ## How to give program Input? The latest version of Coding Ground allows to provide program input at run time from the termnial window exactly the same way as you run your program at your own computer. So simply run a program and provide your program input (if any) from the terminal window available in the right side. ## Keyboard Shortcuts ShortcutDescription ⌘ + EnterRun the program ⌘ + SSave Project (Login Required) ⇧ + ⌘ + SSave As Project ⌘ + PNew Project ⌘ + GShare Project ⌘ + ZUndo Editing ⌘ + YRedo Editing ⌘ + ASelect All Text ⌘ + XCut Selected Text ⌘ + CCopy Selected Text ⌘ + VPaste Copied Text ⌘ + FSearch Text ⌘ + ⌥ + FReplace Text ShortcutDescription Ctrl + EnterRun the program Ctrl + SSave Project Shift + Ctrl + SSave As Project Ctrl + GShare Project Ctrl + ZUndo Editing Ctrl + YRedo Editing Ctrl + ASelect All Text Ctrl + XCut Selected Text Ctrl + CCopy Selected Text Ctrl + VPaste Copied Text Ctrl + FSearch Text Ctrl + HReplace Text ## Save C++ Project You can save your C++ Project with us so that you can access this project later on. To save a project you will need to create a login Id with us. So before you save a project, please create a login Id using a link given at the top right corner of this page. ## Share C++ Project You can use this feature to share your C++ Code with your teachers, classmates and colleagues. Just click Share Button and it will create a short link, which can be shared through Email, WhatsApp or even through Social Media. A shared link will be deleted if it has been passive for almost 3 months.

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http://www.homeownershub.com/uk-diy/theromstat-spec-28911-.htm

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Theromstat Spec • posted on November 11, 2003, 10:58 am Thanks to advice from this group I have successfully fitted a room thermostat to my central heating system. I noticed however on reading the spec sheet that came with the unit (Drayton Digistat 1) that there is a spec for "Differential <0.6 degrees c at 4 degrees c per hour" just curious to know what this means if anyone knows? Thanks Marc <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on November 11, 2003, 11:24 am My guess is that the hysteresis is set for 0.6 degrees, provided that the temperature changes at or below 1C per 15 minutes. I may be wrong. Christian. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on November 11, 2003, 11:30 am I can only guess! The differential is the amount of in-built hysteresis - i.e. the difference in temperature between opening and closing. This is less than 0.6 deg C. For example, if the stat opens at 20 degC, the room would have to cool to something approaching 19.4 degC before it would close again. The 4 degC per hour bit seems to be referring to the rate at which the room temperature is changing. It seems to suggest that the differential is <0.6 at a rate of 4 deg/Hr - but may be different at a different room temperature change rate (for reasons which are not immediately apparent to me!). Maybe someone who knows about these things rather than guessing can explain this better? Roger <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on November 11, 2003, 11:34 am They're telling you the conditions of the test: The chamber in which the thermostat was tested was heated at a rate of 4 degrees per hour until the thermostat switched (off) and the temperature was recorded, the room was (perhaps heated further) then cooled at a rate of 4 degrees per hour until the thermostat switched again (on) and the temperature was recorded. The difference between the two temperatures was less than 0.6 degrees. At a higher or lower rate of change temperature the thermostat may behave differently, eg. at a high rate of change the differential may be lower, or at a lower rate of change, the differential may be higher - or vice versa. HTH -- fred <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on November 11, 2003, 1:46 pm Marc Jennings wrote: A thermostat with a very low hysteresis and a quick response can cause the boiler to short cycle. In the one I have there is a switch inside to limit the number of boiler cycles per hour.. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • Share To HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.

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Instructions For 1040ez - 2016 Page 33 2016 Tax Table Example. Mr. Brown is single. His At But Single Married taxable income on line 6 of Form least less ling 1040EZ is \$26,250. He follows two easy than jointly steps to figure his tax: 1. He finds the \$26,250-26,300 taxable income line. 2. He finds the Single filing status column 26,200 26,250 3,470 3,006 and reads down the column. The tax amount shown where the taxable income 26,250 26,300 3,478 3,014 line and the filing status line meet is 26,300 26,350 3,485 3,021 \$3,478. He enters this amount on line 10 26,350 26,400 3,493 3,029 of Form 1040EZ. If Form 1040EZ, If Form 1040EZ, If Form 1040EZ, If Form 1040EZ, And you are– And you are– And you are– And you are– line 6, is– line 6, is– line 6, is– line 6, is– At But Single Married At But Single Married At But Single Married At But Single Married least less filing least less filing least less filing least less filing than jointly than jointly than jointly than jointly 1,000 2,000 3,000 0 5 0 0 5 15 1 1 15 25 2 2 1,000 1,025 101 101 2,000 2,025 201 201 3,000 3,050 303 303 25 50 4 4 1,025 1,050 104 104 2,025 2,050 204 204 3,050 3,100 308 308 50 75 6 6 1,050 1,075 106 106 2,050 2,075 206 206 3,100 3,150 313 313 75 100 9 9 1,075 1,100 109 109 2,075 2,100 209 209 3,150 3,200 318 318 100 125 11 11 1,100 1,125 111 111 2,100 2,125 211 211 3,200 3,250 323 323 125 150 14 14 3,250 3,300 328 328 1,125 1,150 114 114 2,125 2,150 214 214 150 175 16 16 3,300 3,350 333 333 1,150 1,175 116 116 2,150 2,175 216 216 175 200 19 19 3,350 3,400 338 338 1,175 1,200 119 119 2,175 2,200 219 219 3,400 3,450 343 343 200 225 21 21 1,200 1,225 121 121 2,200 2,225 221 221 3,450 3,500 348 348 225 250 24 24 1,225 1,250 124 124 2,225 2,250 224 224 250 275 26 26 3,500 3,550 353 353 1,250 1,275 126 126 2,250 2,275 226 226 275 300 29 29 3,550 3,600 358 358 1,275 1,300 129 129 2,275 2,300 229 229 300 325 31 31 3,600 3,650 363 363 1,300 1,325 131 131 2,300 2,325 231 231 3,650 3,700 368 368 325 350 34 34 1,325 1,350 134 134 2,325 2,350 234 234 3,700 3,750 373 373 350 375 36 36 1,350 1,375 136 136 2,350 2,375 236 236 3,750 3,800 378 378 375 400 39 39 3,800 3,850 383 383 1,375 1,400 139 139 2,375 2,400 239 239 400 425 41 41 3,850 3,900 388 388 1,400 1,425 141 141 2,400 2,425 241 241 425 450 44 44 3,900 3,950 393 393 1,425 1,450 144 144 2,425 2,450 244 244 3,950 4,000 398 398 450 475 46 46 1,450 1,475 146 146 2,450 2,475 246 246 4,000 475 500 49 49 1,475 1,500 149 149 2,475 2,500 249 249 500 525 51 51 1,500 1,525 151 151 2,500 2,525 251 251 525 550 54 54 1,525 1,550 154 154 2,525 2,550 254 254 550 575 56 56 4,000 4,050 403 403 1,550 1,575 156 156 2,550 2,575 256 256 4,050 4,100 408 408 575 600 59 59 1,575 1,600 159 159 2,575 2,600 259 259 4,100 4,150 413 413 600 625 61 61 1,600 1,625 161 161 2,600 2,625 261 261 4,150 4,200 418 418 625 650 64 64 4,200 4,250 423 423 1,625 1,650 164 164 2,625 2,650 264 264 650 675 66 66 4,250 4,300 428 428 1,650 1,675 166 166 2,650 2,675 266 266 675 700 69 69 4,300 4,350 433 433 1,675 1,700 169 169 2,675 2,700 269 269 4,350 4,400 438 438 700 725 71 71 1,700 1,725 171 171 2,700 2,725 271 271 4,400 4,450 443 443 725 750 74 74 1,725 1,750 174 174 2,725 2,750 274 274 4,450 4,500 448 448 750 775 76 76 1,750 1,775 176 176 2,750 2,775 276 276 775 800 79 79 4,500 4,550 453 453 1,775 1,800 179 179 2,775 2,800 279 279 800 825 81 81 4,550 4,600 458 458 1,800 1,825 181 181 2,800 2,825 281 281 4,600 4,650 463 463 825 850 84 84 1,825 1,850 184 184 2,825 2,850 284 284 4,650 4,700 468 468 850 875 86 86 1,850 1,875 186 186 2,850 2,875 286 286 4,700 4,750 473 473 875 900 89 89 4,750 4,800 478 478 1,875 1,900 189 189 2,875 2,900 289 289 900 925 91 91 4,800 4,850 483 483 1,900 1,925 191 191 2,900 2,925 291 291 925 950 94 94 4,850 4,900 488 488 1,925 1,950 194 194 2,925 2,950 294 294 4,900 4,950 493 493 1,950 1,975 196 196 2,950 2,975 296 296 950 975 96 96 4,950 5,000 498 498 1,975 2,000 199 199 2,975 3,000 299 299 975 1,000 99 99 (Continued) - 33 - Instructions for Form 1040EZ

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# Number 96667 facts The odd number 96,667 is spelled 🔊, and written in words: ninety-six thousand, six hundred and sixty-seven. The ordinal number 96667th is said 🔊 and written as: ninety-six thousand, six hundred and sixty-seventh. The meaning of the number 96667 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 96667. What is 96667 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 96667. ## Interesting facts about the number 96667 ### Asteroids • (96667) 1999 JJ23 is asteroid number 96667. It was discovered by LINEAR, Lincoln Near-Earth Asteroid Research from Lincoln Laboratory, Socorro on 5/10/1999. ## What is 96,667 in other units The decimal (Arabic) number 96667 converted to a Roman number is (XC)(V)MDCLXVII. Roman and decimal number conversions. #### Length conversion 96667 kilometers (km) equals to 60067 miles (mi). 96667 miles (mi) equals to 155571 kilometers (km). 96667 meters (m) equals to 317146 feet (ft). 96667 feet (ft) equals 29465 meters (m). #### Time conversion (hours, minutes, seconds, days, weeks) 96667 seconds equals to 1 day, 2 hours, 51 minutes, 7 seconds 96667 minutes equals to 2 months, 1 week, 4 days, 3 hours, 7 minutes ### Codes and images of the number 96667 Number 96667 morse code: ----. -.... -.... -.... --... Sign language for number 96667: Number 96667 in braille: Images of the number Image (1) of the numberImage (2) of the number More images, other sizes, codes and colors ... ## Share in social networks #### Is Prime? The number 96667 is a prime number. The closest prime numbers are 96661, 96671. #### Factorization and factors (dividers) The prime factors of 96667 Prime numbers have no prime factors smaller than themselves. The factors of 96667 are 1, 96667. Total factors 2. Sum of factors 96668 (1). #### Prime factor tree 96667 is a prime number. #### Powers The second power of 966672 is 9.344.508.889. The third power of 966673 is 903.305.640.772.963. #### Roots The square root √96667 is 310,913171. The cube root of 396667 is 45,89437. #### Logarithms The natural logarithm of No. ln 96667 = loge 96667 = 11,479027. The logarithm to base 10 of No. log10 96667 = 4,985278. The Napierian logarithm of No. log1/e 96667 = -11,479027. ### Trigonometric functions The cosine of 96667 is 0,981231. The sine of 96667 is 0,192834. The tangent of 96667 is 0,196522. ## Number 96667 in Computer Science Code typeCode value 96667 Number of bytes94.4KB Unix timeUnix time 96667 is equal to Friday Jan. 2, 1970, 2:51:07 a.m. GMT IPv4, IPv6Number 96667 internet address in dotted format v4 0.1.121.155, v6 ::1:799b 96667 Decimal = 10111100110011011 Binary 96667 Decimal = 11220121021 Ternary 96667 Decimal = 274633 Octal 96667 Decimal = 1799B Hexadecimal (0x1799b hex) 96667 BASE64OTY2Njc= 96667 SHA18e23d4af3869309934d51e21a19c1b9077aca7d3 96667 SHA22433db306dd94f239971328320c3c79ce9c8dc925e25cd97fd93b405bf 96667 SHA25626fc0d3c6e5d1ced5d8e6fea43c89c50c2ddebc4c15d2e160b5cd50ab938319e More SHA codes related to the number 96667 ... If you know something interesting about the 96667 number that you did not find on this page, do not hesitate to write us here. ## Numerology 96667 ### Character frequency in the number 96667 Character (importance) frequency for numerology. Character: Frequency: 9 1 6 3 7 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 96667, the numbers 9+6+6+6+7 = 3+4 = 7 are added and the meaning of the number 7 is sought. ## № 96,667 in other languages How to say or write the number ninety-six thousand, six hundred and sixty-seven in Spanish, German, French and other languages. The character used as the thousands separator. Spanish: 🔊 (número 96.667) noventa y seis mil seiscientos sesenta y siete German: 🔊 (Nummer 96.667) sechsundneunzigtausendsechshundertsiebenundsechzig French: 🔊 (nombre 96 667) quatre-vingt-seize mille six cent soixante-sept Portuguese: 🔊 (número 96 667) noventa e seis mil, seiscentos e sessenta e sete Hindi: 🔊 (संख्या 96 667) छियानवे हज़ार, छः सौ, सरसठ​ Chinese: 🔊 (数 96 667) 九万六千六百六十七 Arabian: 🔊 (عدد 96,667) ستة و تسعون ألفاً و ستمائة و سبعة و ستون Czech: 🔊 (číslo 96 667) devadesát šest tisíc šestset šedesát sedm Korean: 🔊 (번호 96,667) 구만 육천육백육십칠 Danish: 🔊 (nummer 96 667) seksoghalvfemstusinde og sekshundrede og syvogtreds Hebrew: (מספר 96,667) תשעים ושישה אלף שש מאות שישים ושבע Dutch: 🔊 (nummer 96 667) zesennegentigduizendzeshonderdzevenenzestig Japanese: 🔊 (数 96,667) 九万六千六百六十七 Indonesian: 🔊 (jumlah 96.667) sembilan puluh enam ribu enam ratus enam puluh tujuh Italian: 🔊 (numero 96 667) novantaseimilaseicentosessantasette Norwegian: 🔊 (nummer 96 667) nittiseks tusen seks hundre og sekstisyv Polish: 🔊 (liczba 96 667) dziewięćdziesiąt sześć tysięcy sześćset sześćdziesiąt siedem Russian: 🔊 (номер 96 667) девяносто шесть тысяч шестьсот шестьдесят семь Turkish: 🔊 (numara 96,667) doksanaltıbinaltıyüzaltmışyedi Thai: 🔊 (จำนวน 96 667) เก้าหมื่นหกพันหกร้อยหกสิบเจ็ด Ukrainian: 🔊 (номер 96 667) дев'яносто шість тисяч шістсот шістдесят сім Vietnamese: 🔊 (con số 96.667) chín mươi sáu nghìn sáu trăm sáu mươi bảy Other languages ... ## News to email I have read the privacy policy ## Comment If you know something interesting about the number 96667 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. There are no comments for this topic.

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• Accueil • Science • When will electromagnet attracts magnetic objects?... # When will electromagnet attracts magnetic objects? a. when current flows in the wire b. when there is no current in the wire c. when there is iron core in the wire d. when a compass is placed near the magnet • Réponse publiée par: janalynmae . more 2. lesser and more 3. more and lesser 4. more and lesser 5. lesser Explanation: • Réponse publiée par: nelspas422 1. The current is directly proportional to the voltage and inversely proportional to the resistance. So doubling or tripling it will cause the current to be one-half or one-third the original value. In a linear circuit of fixed resistance, if we increase the voltage, the current goes up, and similarly, if we decrease the voltage, the current goes down. This means that if the voltage is high, so is the current, and if the voltage is low, so is the current... • Réponse publiée par: JUMAIRAHtheOTAKU 1.If you are doubling the current, either you are doing it by increasing the voltage or by decreasing the resistance or by a combination of both. So the resistance will remain constant if current is doubled through doubling the voltage supply. 2.By Ohm's law, V = IR. Current will decrease when voltage decrease, and will do so by a constant proportion. ... And if water's pressure drops, by keeping constant the pipeline diammeter (resistance), then water current will drop too. Explanation: Sana po makatulong • Réponse publiée par: ShairaGailSanchez Electricity electricity electricity electricity Explanation: Watch Dr. Stone • Réponse publiée par: lhadyclaire Koko ni wa minikui mono wa nani mo arimasen Explanation: daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki daisuki • Réponse publiée par: nelspas422 B. Explanation:

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# Europa Universalis IV: Keeping Army Tradition HIgh I just did a difficult economical-challenged achievement (Lucky of the Irish as kildore). It was difficult in the early years to keep army tradition higher than 10-25ish Army Tradition. I was wondering is there an easier first 4 at most idea group order that can reach at least 50ish army tradition hovering ignoring National Ideas (Like Prussian .5 bonus to Army Tradition). Requirements: +Two military ideas in three or four first idea groups at most +possible use of policies is ok +Assuming western tech group country +assume National Idea will not contribute one way or another to army tradition +stuff that indirectly reduce boost army tradition like building cost and less maintenance is ok +Assume growing tall gameplay with few war or mostly defensive mentality +reach hovering 50 army tradition or higher +assume this country will either start small or medium (One province up to 30ish) and grow to afford +1/2 advisers across the board +idea group obviously have to be practical like second idea is military to avoid falling behind +ideally doable before 1600 (Thirty Years' War) +fewer monarchy points used the better I know it is possible to reach 100% hovering (did it for an achievement) but it requires lot of idea group picks to be practical in every possible situation. Duh, I already could figure out the answer myself. I will post here for anyone else who are curious. At the most you only need 1200 military monarch points + lot of admin to unlock the third idea group slot. With updated one fort per each 50 development. You get one army tradition per month. With defensive and quality. You get two army tradition per month from each. Be sure to pick another diplomacy or admin idea group in between. No policies necessary. With decay of 5 percent each month. You will hover at 60 army tradition. • Regarding the hovering AT, I just did the math out of curiosity. Stable condition is `(x+3)*0.95 = x`, solving this for x yields `x = 3*0.95/0.05`, not `3/0.05` as you wrote. The difference is very small, of course (this would only be significant if the decay were larger). Just nitpicking!

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# How far is Uzhhorod from Simferopol? The distance between Simferopol (Simferopol International Airport) and Uzhhorod (Uzhhorod International Airport) is 607 miles / 977 kilometers / 527 nautical miles. The driving distance from Simferopol (SIP) to Uzhhorod (UDJ) is 1487 miles / 2393 kilometers, and travel time by car is about 36 hours 50 minutes. 607 Miles 977 Kilometers 527 Nautical miles 1 h 38 min 114 kg ## Distance from Simferopol to Uzhhorod There are several ways to calculate the distance from Simferopol to Uzhhorod. Here are two standard methods: Vincenty's formula (applied above) • 606.916 miles • 976.736 kilometers • 527.395 nautical miles Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet. Haversine formula • 605.475 miles • 974.418 kilometers • 526.143 nautical miles The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points). ## How long does it take to fly from Simferopol to Uzhhorod? The estimated flight time from Simferopol International Airport to Uzhhorod International Airport is 1 hour and 38 minutes. ## What is the time difference between Simferopol and Uzhhorod? The time difference between Simferopol and Uzhhorod is 1 hour. Uzhhorod is 1 hour behind Simferopol. ## Flight carbon footprint between Simferopol International Airport (SIP) and Uzhhorod International Airport (UDJ) On average, flying from Simferopol to Uzhhorod generates about 114 kg of CO2 per passenger, and 114 kilograms equals 250 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel. ## Map of flight path and driving directions from Simferopol to Uzhhorod See the map of the shortest flight path between Simferopol International Airport (SIP) and Uzhhorod International Airport (UDJ). ## Airport information Origin Simferopol International Airport City: Simferopol Country: Ukraine IATA Code: SIP ICAO Code: UKFF Coordinates: 45°3′7″N, 33°58′30″E Destination Uzhhorod International Airport City: Uzhhorod Country: Ukraine IATA Code: UDJ ICAO Code: UKLU Coordinates: 48°38′3″N, 22°15′48″E

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## Tuesday, November 3, 2015 ### Olympiad Math Problem: Find the maximum and minimum of P (First Attempt) Find the minimum and maximum of $P=\dfrac{y−x}{x+8y}$ for all real $x$ and $y$ that satisfy the equation $y^2(6-x^2)-xy-1=0$. On one hand, this is not a unmanageable Olympiad Mathematics optimization problem, on the other hand, this problem allows us to show students how powerful algebraic manipulation is when we use it diligently and how effective the accurate solution we could have arrived compared to all the alternatives. One might want to try the typical old method (calculus approach) to tackle it, let's see if such an approach would be fruitful. First off, we need to rewrite the function of $P$ such that it is in terms of only one variable for easy referencing and easy working. From the given equation where both real $x$ and $y$ that satisfy, it would be hard to rewrite either $x$ in terms of $y$ or the other way round. $y^2(6-x^2)-xy-1=0$ \begin{align*}y&=\dfrac{x\pm \sqrt{x^2-4(6-x^2)(-1)}}{2(6-x^2)}\\&=\dfrac{x\pm \sqrt{24-3x^2}}{2(6-x^2)}\end{align*} What do you think now? Do you think you want to proceed to find the expression for $y$? Let's assume you want to go ahead to do that...you would end up with the following: Now comes the time to make up your mind and make the good decision based on your finding. Would you think it is useful to substitute the above expression for $y$ into the target expression of $P$? \begin{align*}P&=\dfrac{y−x}{x+8y}\\&=\dfrac{\dfrac{x\pm \sqrt{24-3x^2}}{2(6-x^2)}−x}{x+8\left(\dfrac{x\pm \sqrt{24-3x^2}}{2(6-x^2)}\right)}\\&=\dfrac{x\pm \sqrt{24-3x^2}-x(2)(6-x^2)}{2x(6-x^2)+8x\pm 8\sqrt{24-3x^2}}\\&=\dfrac{2x^3-11x\pm \sqrt{24-3x^2}}{20x-2x^3\pm \sqrt{24-3x^2}}\end{align*} This looks horrible and if you are persistent, you might want to try it so to differentiate $P$ w.r.t. $x$, we get: \small\begin{align*}P'&=\dfrac{(20x-2x^3\pm \sqrt{24-3x^2})\left(6x^2-11\pm\dfrac{(-6x)}{\sqrt{24-3x^2}}\right)-(2x^3-11x\pm \sqrt{24-3x^2})\left(20-6x^2\pm\dfrac{(-6x)}{\sqrt{24-3x^2}}\right)}{(20x-2x^3\pm \sqrt{24-3x^2})^2}\end{align*} What about it now? What's your decision? Do you still want to continue with what you have left off? It's a choice you make, but if I were you, I could stop and try to approach the problem differently. The first derivative is necessarily hard to work with and it seems it's virtually impossible to determine the critical points from it. I will post in the next blog post the different way of approaching the problem and I hope you would attempt at a solution and remember, you learn best from your mistake.

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Quick Python Question This topic is 4361 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. Recommended Posts Can't believe Im asking this but: Some code: terrain = [ [ 1, 1, 1, 1, 1, 1 ],/ [ 1, 0, 0, 0, 0, 1 ],/ [ 1, 0, 0, 0, 0, 1 ],/ [ 1, 0, 0, 0, 0, 1 ],/ [ 1, 0, 0, 0, 0, 1 ],/ [ 1, 0, 0, 0, 0, 1 ],/ [ 1, 1, 1, 1, 1, 1 ],] print terrain When it prints it prints like this [[1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1]] I could have sworn \ would make the it start prining on the next line. I want it to print out like this: [ 1, 1, 1, 1, 1, 1 ] [ 1, 0, 0, 0, 0, 1 ] [ 1, 0, 0, 0, 0, 1 ] [ 1, 0, 0, 0, 0, 1 ] [ 1, 0, 0, 0, 0, 1 ] [ 1, 0, 0, 0, 0, 1 ] [ 1, 1, 1, 1, 1, 1 ] :( Edit: It screwed up. Share on other sites llen = len(terrain)i = 0while i < llen: print terrain i = i + 1 This would be my solution. Share on other sites for i in terrain: print i Thx! Share on other sites New question. Heres what I have: City = [[ 1, 1, 1, 1, 1, 1, 1], [ 1, 2, 0, 2, 0, 0, 1], [ 1, 0, 0, 0, 0, 0, 1], [ 1, 0, 0, 9, 0, 0, 1], [ 1, 0, 0, 0, 0, 0, 1], [ 1, 1, 1, 1, 1, 1, 1]] llen = len(City) i = 0 while i < llen: print City i = i + 1 What I need to know how to do is to be able to reference a specific spot on that. Preferbly in X,Y Form. I want to be able to do this: Pos = X,Y Move = input("move") if Move == W: City(Pos) = 0 Pos = X,Y+1 City(Pos) = 9 elif Move == S: City(Pos) = 0 Pos = X,Y-1 elif Move == A: City(Pos) = 0 Pos = X-1,Y elif Move == D: City(Pos) = 0 Pos = X+1,Y pos = City[X,Y] Share on other sites In X,Y Form: (Y_Position * Width_Of_Map) + X_Position So, to access position (3,6) of your map, which is, say, 15 x 15 grid, you would use: (6 * 15) + 3. If you want to move west of that position, you would simply do (6 * 15) + 4. And you would obviously want to check that that is a valid position before trying to access it. Share on other sites City is a list. It just so happens to only contain lists. To access a specific element in a list contained by City, you must first subscript City to obtain the list in question, then subscript that list to obtain the element: City = [[ ... ], [ ... ], ... ]# access coordinate pair (i, j)element = City[j] Share on other sites Thx for the help, I got that working. I have a new question, do I have to list all my global variables that I want to use in a function? For example: global Strglobal MHpglobal Hpglobal Agilglobal MMnglobal Mnglobal Mpglobal Gglobal Lvlglobal Xpglobal Skpglobal Fstglobal Equipedglobal Buffsglobal BuffsEnglobal Romeglobal Locglobal PosXglobal PosYdef warriorstart( ): global Str global MHp global Hp global Agil global MMn global Mn global Mp global G global Lvl global Xp global Skp global Fst global Equiped global Buffs global BuffsEn print "You have chosen the warrior!" Str = 18 Hp = 150 Mhp = 150 Agil = 10 MMn = 10 Mn = 10 Mp = 0 G = 10 Lvl = 1 Xp = 0 Skp = 1 Fst = 5 Equiped = [ 'W', 'A', 'S', 'T'] stats( )def stats( ): global Str global MHp global Hp global Agil global MMn global Mn global Mp global G global Lvl global Xp global Skp global Fst global Equiped global Buffs global BuffsEn print "Level,", Lvl print "Xp,", Xp print "Skill Points,", Skp print "Free Stat Points,", Fst print "Strength,", Str print "Agility,", Agil print "Magic Power,", Mp print "Health Points,", Hp print "Mana,", Mn print "Gold,", G print "Equiped:", Equiped print "Assign Stats: 1" print "Not now: 0" NowStats = input("Assign Stats Now?") if NowStats == 1: while NowStats == 1: print "Strength: 1" print "Agility: 2" print "Magic Power: 3" print "Mana: 4" print "Health Points: 5" print "None: 0" WhichStat = input("Which Stat") if WhichStat != 0: HowMuch = input("How Much") if HowMuch <= Fst: Fst = Fst - HowMuch if WhichStat == 1: Str = Str + HowMuch if WhichStat == 2: Agil = Agil + HowMuch if WhichStat == 3: Mp = Mp + HowMuch if WhichStat == 4: MMn = MMn + HowMuch Mn = Mn + HowMuch if WhichStat == 5: Hp = Hp + HowMuch MHp = MHp + HowMuch if WhichStat == 0: NowStats = 0 It is annoying to keep having to say global X global Y in each of my functions, when I want to use variables X and Y in that function. Is there anyway I can get around having to list every variable each time? I would much rather have my code look like this: global Strglobal MHpglobal Hpglobal Agilglobal MMnglobal Mnglobal Mpglobal Gglobal Lvlglobal Xpglobal Skpglobal Fstglobal Equipedglobal Buffsglobal BuffsEnglobal Romeglobal Locglobal PosXglobal PosYdef warriorstart( ): print "You have chosen the warrior!" Str = 18 Hp = 150 Mhp = 150 Agil = 10 MMn = 10 Mn = 10 Mp = 0 G = 10 Lvl = 1 Xp = 0 Skp = 1 Fst = 5 Equiped = [ 'W', 'A', 'S', 'T'] stats( )def stats( ): print "Level,", Lvl print "Xp,", Xp print "Skill Points,", Skp print "Free Stat Points,", Fst print "Strength,", Str print "Agility,", Agil print "Magic Power,", Mp print "Health Points,", Hp print "Mana,", Mn print "Gold,", G print "Equiped:", Equiped print "Assign Stats: 1" print "Not now: 0" NowStats = input("Assign Stats Now?") if NowStats == 1: while NowStats == 1: print "Strength: 1" print "Agility: 2" print "Magic Power: 3" print "Mana: 4" print "Health Points: 5" print "None: 0" WhichStat = input("Which Stat") if WhichStat != 0: HowMuch = input("How Much") if HowMuch <= Fst: Fst = Fst - HowMuch if WhichStat == 1: Str = Str + HowMuch if WhichStat == 2: Agil = Agil + HowMuch if WhichStat == 3: Mp = Mp + HowMuch if WhichStat == 4: MMn = MMn + HowMuch Mn = Mn + HowMuch if WhichStat == 5: Hp = Hp + HowMuch MHp = MHp + HowMuch if WhichStat == 0: NowStats = 0 Share on other sites Why don't you use a global class with all your useful vars ? Emmanuel Share on other sites Of course. That would be so much easier in general too. 1. 1 2. 2 3. 3 Rutin 22 4. 4 frob 18 5. 5 • 33 • 13 • 11 • 10 • 12 • Forum Statistics • Total Topics 632572 • Total Posts 3007128 ×

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https://mathr.co.uk/blog/2014-07-31_recode_project_topographic_form_animated.html

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# mathr / blog / # ## ReCode Project - Topographic Form animated After I posted topographic form to the #diagrams IRC channel, I got a comment: < luite_> ClaudiusMaximus: have you tried making an animation of that? So that's what I did today, with this Haskell code: import Diagrams.Prelude import Diagrams.Backend.SVG.CmdLine (defaultMain) import System.Environment (withArgs) import Control.Monad (forM_) main = forM_ [0..49] $\f -> withArgs ["-w", "788", "-o", drop 1$ show (f + 100) ++ ".svg"] $defaultMain (diagram (2 * fromIntegral f / 50) (fromIntegral (if f >= 25 then 50 - f else f) / 25)) diagram r s = fromVertices (zigzag r s) # withEnvelope' (fromVertices [p2 (0, 3), p2 (135, 78)]) # bg white withEnvelope' a b = withEnvelope (a asTypeOf b) b zigzag r s = concat$ zipWith (line r (pi/2 * s)) ys (cycle [xs, reverse xs]) line r s y = map (point s (r + y)) point s y x = p2 (x, y + heightMap s x y) heightMap s x y = maximum [ arcH 36 (\t -> t < 0 || pi/2 < t - s) x y , arcH 67.5 (\t -> True) x y , arcH 99 (\t -> -pi/2 < t - s) x y ] arcH x0 f x y | f t && ri < r && r < ro = h0 * cos (pi * (r - r0) / (ro - ri)) | otherwise = 0 where t = atan2 y' x' r = sqrt $x'^2 + y'^2 x' = x - x0 y' = y - y0 y0 = 40.5 r0 = 15.75 ri = r0 * 0.75 ro = r0 * 1.25 h0 = (ro - ri) / 2 xs = [0 .. 135] ys = [0 .. 81] To postprocess the output into an animgif I did this in bash: for i in ??.svg do rsvg$i ${i%svg}png convert${i%svg}png \${i%svg}gif done gifsicle --delay 4 --loop --optimize ??.gif > out.gif

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# Perimeter A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length – it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference. Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool’s perimeter.

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Exploring Fractions Stage: 1 and 2 Published November 2013. Introduction At NRICH, our aim is to offer rich tasks which develop deep understanding of mathematical concepts.  Of course, by their very nature, rich tasks will also provide opportunities for children to work like a mathematician and so help them develop their problem-solving skills alongside this conceptual understanding. Such tasks also provide valuable opportunities for you to assess where children have got to in their thinking and so support the next steps on their learning journey. The current National Curriculum in England, which became statutory in September 2014, contains more content related to fractions than the previous curriculum. To support children in getting to grips with the concept of fractions it is important to make sure they have lots of practical and varied experience using objects, shapes and quantities. This, combined with an experience of rich tasks that stimulate and challenge their thinking; the opportunity to talk and the chance to use models and images rather than 'tricks', will all support their growing understanding of fractions. Why might children find fractions difficult? Difficulties with fractions often stem from the fact that they are different from natural numbers in that they are relative rather than a fixed amount - the same fraction might refer to different quantities and different fractions may be equivalent (Nunes, 2006).  Would you rather have one quarter of £20 or half of £5? The fact that a half is the bigger fraction does not necessarily mean that the amount you end up with will be bigger. The question should always be, 'fraction of what?'; 'what is the whole?'. Fractions can refer to objects, quantities or shapes, thus extending their complexity. In order to be able to develop their understanding and then generalise about fractions, children need to explore many representations and uses over a significant period of time.  In the Early Years, learners will have learnt to generalise the concept of three by having lots of experience of the three-ness of three, yet with fractions we may find in school that their experience is limited to pizzas, sticky paper and chocolate! Do the children have experience of objects, shapes and amounts in equal measure and do they have experience of the whole being something other than 'one'? • The first group gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children’s current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. • The second group of tasks focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills. In this article, we will discuss each group of tasks in turn, outlining further reasons for grouping in this way and explaining why each particular task has been selected. First Group of Tasks - Starting Points As mentioned above, all these tasks could be introduced to children of any age.  They provide a chance for meaningful mathematical discussion and sharing of current understanding, in addition to offering opportunities for challenging misconceptions.  It is important that children build up a vocabulary with which to talk about fractions.  Of course this is a gradual process, but greatly helped by you modeling appropriate language wherever possible and drawing attention to good use of specific vocabulary by children themselves.  All of the following tasks provide contexts in which to encourage learners to talk about their ideas and to work towards refining their vocabulary.  (The article Developing a Classroom Culture That Supports A Problem-solving Approach to Mathematics offers several practical ideas to help your classroom become a classroom that is based on talk.) Paper Halving is a wonderfully rich task which needs only a plentiful supply of plain A4 paper.  Learners are invited to halve pieces of paper in different ways and to articulate how they know that they have created halves.  Talk is key here.  Asking children to explain their ideas will help to reveal their understanding even if their constructions are not quite accurate.  You can facilitate discussion about not all halves being symmetrical and it would also be fruitful to ask how learners think the task would have been affected if they had been given squared paper rather than plain. What Do You See Here? builds on Paper Halving by having a range of sizes of paper along with their related halves.  In a similar way to Paper Halving, this activity encourages learners to explore fractions as area.  Children are invited to ‘say what they see’ to prompt discussion related to statements about the paper.  Here, the teacher’s role is to draw out the idea that the ‘halves’ are different sizes (“I’ll have the bigger half!”), as the idea of a half is meaningless without knowing the whole.  In this way, the task lays the foundations for a deep understanding of the part-whole relationship. (In our Early Fraction Development article, which is also part of the first group of resources in this feature, Bernard Bagnall describes his experiences of using these two tasks, and others, many times with groups of children and suggests further ideas using paper.) And how often do we vary the 'whole'?  Is it always 'one'?  What about sharing two pizzas between three?  In the NRICH task Chocolate, the 'whole' is one, two or three bars of chocolate.  Learners have to make a decision about the best table to stand at if the chocolate on it is shared between everyone at that table.  Encouraging children to record their ideas themselves helps us 'see' their thinking and assess what they are doing. Fractions as a form of division In her research, Nunes (2006) suggests that sharing situations might also be used as a starting point for children's understanding of fractions since she found that primary school children have some insights into fractions when solving division problems: They understand the relative nature of fractions: if one child gets half of a big cake and the other gets half of a small one, they do not receive the same amount. They also realise, for example, that you can share something by cutting it in different ways: this makes it ‘different fractions but not different amounts’. Finally, they understand the inverse relation between the denominator and the quantity: the more people there are sharing something, the less each one will get. Our Early Years Foundation Stage activity Maths Story Time introduces Pirate Panda, who has stolen all the treasure but Cat, Dog and Rabbit want some too.  What do the children think they should do?  In a similar way, the activity Fair Feast offers the context of sharing a picnic and could form the basis of an initial exploratory task.  You could also invite learners to consider other food types – can they choose something that they would like to bring to the picnic and explain how it could be shared? In summary, the tasks that comprise the first group within our Fractions Unpacked Feature … • are applicable to a range of ages; • provide contexts in which to explore the part-whole relationship in depth; • offer opportunities to develop conceptual understanding through talk. Second Group of Tasks – Progression in Fractions Through Problem-solving The second group of tasks in our Fractions Unpacked Feature has been selected to reflect a progression in concepts associated with fractions at the same time as giving learners opportunities to develop their problem-solving and reasoning skills. Being able to recognise, find and name ‘a half’ is often one of the first steps along the fractions journey and the tasks included above in the first group will be useful in that regard.  Also worth mentioning is the activity Halving which focuses on halving in the context of area (of squares).  A Bowl of Fruit, however, explores halving in the context of discrete objects and you could easily tweak the task to create similar problems focusing on slightly more challenging curriculum content by using the language of halves, quarters and/or thirds. The idea of equivalence is a key one to introduce as children's understanding of fractions develops.  Not only are learners encouraged to find families of fractions that are equivalent, but also to recognise decimal equivalents of fractions.  Being able to round decimals to the nearest whole number is a skill that is often taught around this time, and the two tasks Round the Dice Decimals 1 and Round the Dice Decimals 2 offer meaningful practice.  These two exploratory tasks give learners the chance to investigate for themselves, to conjecture and to generalise, meaning that not only will children be getting better at rounding, but they will also be developing their reasoning skills too. In Spiralling Decimals, learners are required to compare decimal numbers and the game context may provide motivation for some.  Trying to beat an opponent demands a higher level of thinking in terms of developing a strategy.  In deciding which number to choose for any one turn, pupils will perform multiple comparisons and select the one they believe is ‘best’ for that move.  Asking a pair to play another pair at this game means that partners can talk to each other about their thinking, which will help clarify their ideas.  (As opposed to an individual playing competitively against another individual when neither will want to give away their strategy!) The activities Linked Chains and Fraction Lengths both offer opportunities to identify, name and write equivalent fractions, as well as to add fractions.  Fraction Lengths is slightly more challenging, as the denominators are not always multiples of the same number.  Both tasks have multiple solutions, so children are encouraged to use a variety of problem-solving skills, such as trial and improvement, and working systematically. If you would like to focus on supporting children to consider how to go about solving a problem, Andy’s Marbles may well fit the bill.  The task involves using fractions to calculate and divide quantities, and it is certainly not straightforward.  The level of challenge it provides means that it lends itself to referring specifically to one or more of the four stages of the problem-solving process (see the article Developing Excellence in Problem Solving with Young Learners). When it comes to calculation of fractions, the danger is that we introduce rules to be memorised and suddenly the conceptual development appears no longer to be valued.  However, in the article Models in Mind, Mike Askew demonstrates that the array is a powerful tool for thinking about multiplication of fractions, giving children a visual image to draw on, rather than relying on 'tricks'.  He begins with an array such as this one, representing 13 x 4: By chunking the 13 into 10 and 3, we can use known facts to solve this multiplication: 13 x 4 = (10 x 4) + (3 x 4) Of course, as the numbers increase, it becomes tedious to draw out all the dots, so we encourage children to make use of a blank array.  For example, 15 x 4 could be represented as: This leads into the grid method for multiplication.  Here is an image showing both the array and grid method for solving 14 x 4: We can then see how multiplication of fractions follows on.  For example, to calculate $\frac{2}{3} \times \frac{2}{5}$, we would start with an array divided into thirds one way and fifths the other way: Learners who have come to think of multiplication in terms of arrays will be comfortable in thinking of the required piece as being the part of the array marked out by the intersection of the $\frac{2}{3}$ and $\frac{2}{5}$: The article is well worth a read and reminds us that “the mark of a good model for/tool for thinking with is that it can help learners gain insight into mathematical structure, not simply get correct answers”. Summary The concept of fractions is a complex one and it takes time, combined with a rich range of experiences and appropriate mathematical models, for children to develop a deep and rigorous understanding. You may like to try out some of the resources we have recommended in this article to see how they can support the development of children's understanding of fractions. You may also want to look to see what the children's 'fraction diet' is like across the whole school and how it could be usefully strengthened to maximise the opportunities children have to develop a meaningful and thorough understanding of fractions.

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DEV Community is a community of 891,295 amazing developers We're a place where coders share, stay up-to-date and grow their careers. Matheus Gomes πŸ‘¨β€πŸ’» Posted on Sup dudes, it's me again!😎 If you are new to this article, i explain everything about the basics of programming in my previous article, this is a series of articles about this topic. Every time i learn about one i come here and write another one. Here you can get to all of my articles of this series! You are here! So... What is a Structured Programming Paradigm?πŸ€” More Technical ExplanationπŸ‘¨β€πŸ’»: According to Ray Toal (see references) structured programming paradigm is defined by a Programming with clean, goto-free, nested control structures. What does it mean? It means that structured programming is a kind of imperative programming where control flow is defined by nested loops, conditionals, and subroutines, rather than via GOTOS. Variables are generally local to blocks (have lexical scope). Early languages emphasizing structured programming: Algol 60, PL/I, Algol 68, Pascal, C, Ada 83, Modula, Modula-2. Structured programming as a discipline is sometimes though to have been started by a famous letter by Edsger Dijkstra entitled Go to Statement Considered Harmful. More practical explanationπŸ˜‹: It's simple a advance or improvement on the clarity, quality and development time of a computer program by making extensive use of the structured control flow constructs of selection (if/then/else) and repetition (while and for), block structures, and subroutines. Graphical representation of the three basic patterns β€” sequence, selection, and repetition β€” using NS diagrams (blue) and flow charts (green). Practical example: ``````result = []; for i = 0; i < length(people); i++ { p = people[i]; if length(p.name)) > 5 { } } return sort(result); `````` In shortπŸ‘ It's a advance in the early programming languages by using if/else/while/for and block structures and subroutines. Imagine programming in something the doesn't even have a if else statement, that was a reality a few years ago in the early beginnings of programming. That's why we need to be thankfully to Dijkstra and his hate to GOTO statements. References: https://en.wikipedia.org/wiki/Structured_programming https://en.wikipedia.org/wiki/Goto#Criticism https://cs.lmu.edu/~ray/ Discussion (2) Marcos Henrique Awesome 🀘 Matheus Gomes πŸ‘¨β€πŸ’» Thanks Marcos!

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• 0 Vote(s) - 0 Average • 1 • 2 • 3 • 4 • 5 Mittag-Leffler series for generating continuum sum? bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 12/11/2009, 11:16 AM (This post was last modified: 12/11/2009, 11:18 AM by bo198214.) So I had a look at E. Borel: Leçons sur les séries divergentes (1901) In chapter V, page 156 he explains the Mittag-Leffler expansion. Mostly I fighted my way through the text with an online translator. I found the following interesting formulas, where $\phi$ is the function we search the expansion of: $g_n(x)=\sum_{\lambda_1=0}^{n^{2n}}\sum_{\lambda_2=0}^{n^{2n-2}} \dots\sum_{\lambda_n=0}^{n^2} \frac{\phi^{(\lambda_1+\dots+\lambda_n)}(0)}{\lambda_1!\dots\lambda_n!} \left(\frac{x}{n}\right)^{\lambda_1+\dots+\lambda_n}$ $G_0(x)=g_0(x)=\phi(0)$ $G_n(x)=g_n(x)-g_{n-1}(x)$ for $n>0$, $\phi(x)=\sum_{n=0}^\infty G_n(x)$ « Next Oldest | Next Newest » Messages In This Thread Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 09:14 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/14/2009, 04:54 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 08:24 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 09:18 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/14/2009, 10:05 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 10:24 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 03:21 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 12:10 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 06:54 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 08:44 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/17/2009, 09:20 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/17/2009, 11:22 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/18/2009, 08:05 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/18/2009, 09:55 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/18/2009, 10:43 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/18/2009, 11:01 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/28/2009, 10:36 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 11/28/2009, 10:56 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/29/2009, 03:48 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/11/2009, 11:16 AM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/11/2009, 11:45 AM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/12/2009, 01:47 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/12/2009, 08:18 PM RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/12/2009, 09:53 PM RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/13/2009, 02:48 AM Mittag-Leffler product ? Ramanujan's master theorem - by tommy1729 - 12/13/2009, 05:41 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by mike3 - 12/13/2009, 08:19 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by tommy1729 - 12/13/2009, 11:15 PM RE: Mittag-Leffler product ? Ramanujan's master theorem - by mike3 - 12/14/2009, 04:40 AM Possibly Related Threads... Thread Author Replies Views Last Post Perhaps a new series for log^0.5(x) Gottfried 3 664 03/21/2020, 08:28 AM Last Post: Daniel Taylor series of i[x] Xorter 12 13,256 02/20/2018, 09:55 PM Last Post: Xorter Recursive formula generating bounded hyper-operators JmsNxn 0 1,713 01/17/2017, 05:10 AM Last Post: JmsNxn Taylor series of cheta Xorter 13 14,318 08/28/2016, 08:52 PM Last Post: sheldonison 2015 Continuum sum conjecture tommy1729 3 3,718 05/26/2015, 12:24 PM Last Post: tommy1729 Another way to continuum sum! JmsNxn 6 7,040 06/06/2014, 05:09 PM Last Post: MphLee [integral] How to integrate a fourier series ? tommy1729 1 2,775 05/04/2014, 03:19 PM Last Post: tommy1729 Continuum sum = Continuum product tommy1729 1 2,880 08/22/2013, 04:01 PM Last Post: JmsNxn applying continuum sum to interpolate any sequence. JmsNxn 1 3,077 08/18/2013, 08:55 PM Last Post: tommy1729 Powerful way to perform continuum sum JmsNxn 7 8,463 08/12/2013, 07:17 PM Last Post: JmsNxn Users browsing this thread: 1 Guest(s)

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# 题目 In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure)) One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order. Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not. ### Input Specification: Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree. ### Output Specification: For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree. Finally print in a line `Max Heap` if it is a max heap, or `Min Heap` for a min heap, or `Not Heap` if it is not a heap at all. # 题解 ## 思路 • 根本是考你堆的存储 • 堆的存储是一个数组，第一个0下标为空。真正的根在下标1。 • 这样就可以保证，任何下标乘以2就是它的左孩子，乘以2+1就是它的右孩子 • 然后题目考你DFS和maxheap还是minheap的判断，分开来都不难 • DFS遍历树就是维护一个路径，能右就右，然后能左就左，注意回溯。 • 判断heap先判断前两项的关系，然后看后面每项和它的父亲比大小即可。 ## 数据结构 • nodes 是一个堆 • path 记录DFS的路径 • isMax 记录是不是大顶堆 • 照着思路走一遍就OK。 ## 代码 • 由于使用Python可以AC，因此只放了Python的题解。

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### Tutor Topics Pivot Tables We have seen how the `GroupBy` abstraction lets us explore relationships within a dataset. A pivot table is a similar operation that is commonly seen in spreadsheets and other programs that operate on tabular data. The pivot table takes simple column-wise data as input, and groups the entries into a two-dimensional table that provides a multidimensional summarization of the data. The difference between pivot tables and `GroupBy` can sometimes cause confusion; it helps me to think of pivot tables as essentially a multidimensional version of `GroupBy`aggregation. That is, you split-apply-combine, but both the split and the combine happen across not a one-dimensional index, but across a two-dimensional grid. ## Motivating Pivot Tables For the examples in this section, we’ll use the database of passengers on the Titanic, available through the Seaborn library (see Visualization With Seaborn):In [1]: ```import numpy as np import pandas as pd import seaborn as sns ``` In [2]: ```titanic.head() ``` Out[2]: 003male22.0107.2500SThirdmanTrueNaNSouthamptonnoFalse 111female38.01071.2833CFirstwomanFalseCCherbourgyesFalse 213female26.0007.9250SThirdwomanFalseNaNSouthamptonyesTrue 311female35.01053.1000SFirstwomanFalseCSouthamptonyesFalse 403male35.0008.0500SThirdmanTrueNaNSouthamptonnoTrue This contains a wealth of information on each passenger of that ill-fated voyage, including gender, age, class, fare paid, and much more. ## Pivot Tables by Hand To start learning more about this data, we might begin by grouping according to gender, survival status, or some combination thereof. If you have read the previous section, you might be tempted to apply a `GroupBy` operation–for example, let’s look at survival rate by gender:In [3]: ```titanic.groupby('sex')[['survived']].mean() ``` Out[3]: survived sex female0.742038 male0.188908 This immediately gives us some insight: overall, three of every four females on board survived, while only one in five males survived! This is useful, but we might like to go one step deeper and look at survival by both sex and, say, class. Using the vocabulary of `GroupBy`, we might proceed using something like this: we group by class and gender, select survival, apply a mean aggregate, combine the resulting groups, and then unstack the hierarchical index to reveal the hidden multidimensionality. In code:In [4]: ```titanic.groupby(['sex', 'class'])['survived'].aggregate('mean').unstack() ``` Out[4]: classFirstSecondThird sex female0.9680850.9210530.500000 male0.3688520.1574070.135447 This gives us a better idea of how both gender and class affected survival, but the code is starting to look a bit garbled. While each step of this pipeline makes sense in light of the tools we’ve previously discussed, the long string of code is not particularly easy to read or use. This two-dimensional `GroupBy` is common enough that Pandas includes a convenience routine, `pivot_table`, which succinctly handles this type of multi-dimensional aggregation. ## Pivot Table Syntax Here is the equivalent to the preceding operation using the `pivot_table` method of `DataFrame`s:In [5]: ```titanic.pivot_table('survived', index='sex', columns='class') ``` Out[5]: classFirstSecondThird sex female0.9680850.9210530.500000 male0.3688520.1574070.135447 This is eminently more readable than the `groupby` approach, and produces the same result. As you might expect of an early 20th-century transatlantic cruise, the survival gradient favors both women and higher classes. First-class women survived with near certainty (hi, Rose!), while only one in ten third-class men survived (sorry, Jack!). ### Multi-level pivot tables Just as in the `GroupBy`, the grouping in pivot tables can be specified with multiple levels, and via a number of options. For example, we might be interested in looking at age as a third dimension. We’ll bin the age using the `pd.cut` function:In [6]: ```age = pd.cut(titanic['age'], [0, 18, 80]) titanic.pivot_table('survived', ['sex', age], 'class') ``` Out[6]: classFirstSecondThird sexage female(0, 18]0.9090911.0000000.511628 (18, 80]0.9729730.9000000.423729 male(0, 18]0.8000000.6000000.215686 (18, 80]0.3750000.0714290.133663 We can apply the same strategy when working with the columns as well; let’s add info on the fare paid using `pd.qcut` to automatically compute quantiles:In [7]: ```fare = pd.qcut(titanic['fare'], 2) titanic.pivot_table('survived', ['sex', age], [fare, 'class']) ``` Out[7]: fare[0, 14.454](14.454, 512.329] classFirstSecondThirdFirstSecondThird sexage female(0, 18]NaN1.0000000.7142860.9090911.0000000.318182 (18, 80]NaN0.8800000.4444440.9729730.9142860.391304 male(0, 18]NaN0.0000000.2608700.8000000.8181820.178571 (18, 80]0.00.0980390.1250000.3913040.0303030.192308 The result is a four-dimensional aggregation with hierarchical indices (see Hierarchical Indexing), shown in a grid demonstrating the relationship between the values. The full call signature of the `pivot_table` method of `DataFrame`s is as follows: ```# call signature as of Pandas 0.18 DataFrame.pivot_table(data, values=None, index=None, columns=None, aggfunc='mean', fill_value=None, margins=False, dropna=True, margins_name='All') ``` We’ve already seen examples of the first three arguments; here we’ll take a quick look at the remaining ones. Two of the options, `fill_value` and `dropna`, have to do with missing data and are fairly straightforward; we will not show examples of them here. The `aggfunc` keyword controls what type of aggregation is applied, which is a mean by default. As in the GroupBy, the aggregation specification can be a string representing one of several common choices (e.g., `'sum'``'mean'``'count'``'min'``'max'`, etc.) or a function that implements an aggregation (e.g., `np.sum()``min()``sum()`, etc.). Additionally, it can be specified as a dictionary mapping a column to any of the above desired options:In [8]: ```titanic.pivot_table(index='sex', columns='class', aggfunc={'survived':sum, 'fare':'mean'}) ``` Out[8]: faresurvived classFirstSecondThirdFirstSecondThird sex female106.12579821.97012116.11881091.070.072.0 male67.22612719.74178212.66163345.017.047.0 Notice also here that we’ve omitted the `values` keyword; when specifying a mapping for `aggfunc`, this is determined automatically. At times it’s useful to compute totals along each grouping. This can be done via the `margins` keyword:In [9]: ```titanic.pivot_table('survived', index='sex', columns='class', margins=True) ``` Out[9]: classFirstSecondThirdAll sex female0.9680850.9210530.5000000.742038 male0.3688520.1574070.1354470.188908 All0.6296300.4728260.2423630.383838 Here this automatically gives us information about the class-agnostic survival rate by gender, the gender-agnostic survival rate by class, and the overall survival rate of 38%. The margin label can be specified with the `margins_name` keyword, which defaults to `"All"`. ## Example: Birthrate Data As a more interesting example, let’s take a look at the freely available data on births in the United States, provided by the Centers for Disease Control (CDC). This data can be found at https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv (this dataset has been analyzed rather extensively by Andrew Gelman and his group; see, for example, this blog post):In [10]: ```# shell command to download the data: # !curl -O https://raw.githubusercontent.com/jakevdp/data-CDCbirths/master/births.csv ``` In [11]: ```births = pd.read_csv('data/births.csv') ``` Taking a look at the data, we see that it’s relatively simple–it contains the number of births grouped by date and gender:In [12]: ```births.head() ``` Out[12]: yearmonthdaygenderbirths 0196911F4046 1196911M4440 2196912F4454 3196912M4548 4196913F4548 We can start to understand this data a bit more by using a pivot table. Let’s add a decade column, and take a look at male and female births as a function of decade:In [13]: ```births['decade'] = 10 * (births['year'] // 10) ``` Out[13]: genderFM 196017536341846572 19701626307517121550 19801831035119243452 19901947945420420553 20001822930919106428 We immediately see that male births outnumber female births in every decade. To see this trend a bit more clearly, we can use the built-in plotting tools in Pandas to visualize the total number of births by year (see Introduction to Matplotlib for a discussion of plotting with Matplotlib):In [14]: ```%matplotlib inline import matplotlib.pyplot as plt sns.set() # use Seaborn styles births.pivot_table('births', index='year', columns='gender', aggfunc='sum').plot() plt.ylabel('total births per year'); ``` With a simple pivot table and `plot()` method, we can immediately see the annual trend in births by gender. By eye, it appears that over the past 50 years male births have outnumbered female births by around 5%. ### Further data exploration Though this doesn’t necessarily relate to the pivot table, there are a few more interesting features we can pull out of this dataset using the Pandas tools covered up to this point. We must start by cleaning the data a bit, removing outliers caused by mistyped dates (e.g., June 31st) or missing values (e.g., June 99th). One easy way to remove these all at once is to cut outliers; we’ll do this via a robust sigma-clipping operation:In [15]: ```quartiles = np.percentile(births['births'], [25, 50, 75]) mu = quartiles[1] sig = 0.74 * (quartiles[2] - quartiles[0]) ``` This final line is a robust estimate of the sample mean, where the 0.74 comes from the interquartile range of a Gaussian distribution (You can learn more about sigma-clipping operations in a book I coauthored with Željko Ivezić, Andrew J. Connolly, and Alexander Gray: ”Statistics, Data Mining, and Machine Learning in Astronomy” (Princeton University Press, 2014)). With this we can use the `query()` method (discussed further in High-Performance Pandas: `eval()` and `query()`) to filter-out rows with births outside these values:In [16]: ```births = births.query('(births > @mu - 5 * @sig) & (births < @mu + 5 * @sig)') ``` Next we set the `day` column to integers; previously it had been a string because some columns in the dataset contained the value `'null'`:In [17]: ```# set 'day' column to integer; it originally was a string due to nulls births['day'] = births['day'].astype(int) ``` Finally, we can combine the day, month, and year to create a Date index (see Working with Time Series). This allows us to quickly compute the weekday corresponding to each row:In [18]: ```# create a datetime index from the year, month, day births.index = pd.to_datetime(10000 * births.year + 100 * births.month + births.day, format='%Y%m%d') births['dayofweek'] = births.index.dayofweek ``` Using this we can plot births by weekday for several decades:In [19]: ```import matplotlib.pyplot as plt import matplotlib as mpl births.pivot_table('births', index='dayofweek', plt.gca().set_xticklabels(['Mon', 'Tues', 'Wed', 'Thurs', 'Fri', 'Sat', 'Sun']) plt.ylabel('mean births by day'); ``` Apparently births are slightly less common on weekends than on weekdays! Note that the 1990s and 2000s are missing because the CDC data contains only the month of birth starting in 1989. Another intersting view is to plot the mean number of births by the day of the year. Let’s first group the data by month and day separately:In [20]: ```births_by_date = births.pivot_table('births', [births.index.month, births.index.day]) ``` Out[20]: ```1 1 4009.225 2 4247.400 3 4500.900 4 4571.350 5 4603.625 Name: births, dtype: float64``` The result is a multi-index over months and days. To make this easily plottable, let’s turn these months and days into a date by associating them with a dummy year variable (making sure to choose a leap year so February 29th is correctly handled!)In [21]: ```births_by_date.index = [pd.datetime(2012, month, day) for (month, day) in births_by_date.index] ``` Out[21]: ```2012-01-01 4009.225 2012-01-02 4247.400 2012-01-03 4500.900 2012-01-04 4571.350 2012-01-05 4603.625 Name: births, dtype: float64``` Focusing on the month and day only, we now have a time series reflecting the average number of births by date of the year. From this, we can use the `plot`method to plot the data. It reveals some interesting trends:In [22]: ```# Plot the results fig, ax = plt.subplots(figsize=(12, 4)) births_by_date.plot(ax=ax); ``` In particular, the striking feature of this graph is the dip in birthrate on US holidays (e.g., Independence Day, Labor Day, Thanksgiving, Christmas, New Year’s Day) although this likely reflects trends in scheduled/induced births rather than some deep psychosomatic effect on natural births. For more discussion on this trend, see the analysis and links in Andrew Gelman’s blog post on the subject. We’ll return to this figure in Example:-Effect-of-Holidays-on-US-Births, where we will use Matplotlib’s tools to annotate this plot. Looking at this short example, you can see that many of the Python and Pandas tools we’ve seen to this point can be combined and used to gain insight from a variety of datasets. We will see some more sophisticated applications of these data manipulations in future sections!

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1 / 10 # Twister Math - PowerPoint PPT Presentation Twister Math. Solve using Order of Operations: 3 x 8 – 14 + 6. Pretty Paws Place Value. Write the following number in each form: Two hundred eighteen thousand, four hundred six and twenty seven hundredths 1. Standard: 2. Expanded:. Fluttering Fractions. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described. ## PowerPoint Slideshow about 'Twister Math' - denzel Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - Presentation Transcript ### Twister Math Solve using Order of Operations: 3 x 8 – 14 + 6 ### Pretty Paws Place Value Write the following number in each form: Two hundred eighteen thousand, four hundred six and twenty seven hundredths 1. Standard: 2. Expanded: ### Fluttering Fractions Tina has two pies. If she gives two-thirds of one pie away and she eats one-third of the other pie. How much pie does she have left? ### Shop Til You Drop! Your mom buys you a computer for Christmas. The original cost was \$2,190.99. Your mom uses a coupon for \$150.00 off. How much did she spend on the computer? • What time is fifteen minutes after 3? • What time is 30 minutes before 2? • What time is half past 9? • What time is quarter past 3? Answer the following questions using the number sentence: 3 x 9 = 27 • What is the math term for 3 and 9? • What is the term for 27? ### Rounding King Round the following number : 2,748,037.92 To the Thousands place To the Hundreds place To the Tens place To the tenths place • How many inches are in 4 feet? • How many feet are in 3 yards? • How many inches are in 8 yards? • How many yards are in 3 miles? • How many feet are in 4 miles? How many red rome apples are sold in food stores? How many Jonathan apples are sold in food stores? How many more red delicious apples are sold than golden delicious apples? If you added 25 more McIntosh apples, what pictures would you need to add to the graph? ### Hand Shaking Equations Solve for n : n x 3 = 36 108 divided by n = 3 The sum of n and 46,887 is 192,008. The difference in 8,237 and n is 309.

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# Singular ### 7.3.10 kbase (plural) `Syntax:` `kbase (` ideal_expression `)` `kbase (` module_expression `)` `kbase (` ideal_expression`,` int_expression`)` `kbase (` module_expression`,` int_expression`)` `Type:` the same as the input type of the first argument `Purpose:` with one argument: computes the vector space basis of the factor-module that equals ring (resp. free module) modulo the ideal (resp. submodule), generated by the initial terms of the given generators. If the factor-module is not of finite dimension, -1 is returned. If the generators form a Groebner basis, this is the same as the vector space basis of the factor-module. when called with two arguments: computes the part of a vector space basis of the respective quotient with degree (of monomials) equal to the second argument. Here, the quotient does not need to be finite dimensional. `Note:` in the non-commutative case, a ring modulo an ideal has a ring stucture if and only if the ideal is two-sided. `kbase` respects module-grading given by the `isHomog` attribute of input modules. `Example:` ```ring r=0,(x,y,z),dp; matrix d[3][3]; d[1,2]=-z; d[1,3]=2x; d[2,3]=-2y; def R=nc_algebra(1,d); // this algebra is U(sl_2) setring R; ideal i=x2,y2,z2-1; i=std(i); print(matrix(i)); // print a compact presentation of i ==> z2-1,yz-y,xz+x,y2,2xy-z-1,x2 kbase(i); ==> _[1]=z ==> _[2]=y ==> _[3]=x ==> _[4]=1 vdim(i); ==> 4 ideal j=x,z-1; j=std(j); kbase(j,3); ==> _[1]=y3 ``` See ideal (plural); module (plural); vdim (plural).

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# Question: What Is The Difference Between Velocity And Momentum? ## How do you find velocity with mass and momentum? The equation that represents this concept is written: momentum = mass x velocity. And because physics uses the symbol ‘p’ to indicate quantity momentum, the equation can be rewritten as: p = m’xv; where,m’ = mass and v=velocity.. ## What is the difference between velocity and momentum How are velocity and momentum similar? velocity is the rate of change of position of a body while momentum is mass times velocity of the body. Impacts of both the quantities on a body are completely different. … So, to change the velocity of a body, we always need a force but to change the momentum, we can vary the mass also. ## How do you find velocity in momentum? The Momentum Calculator uses the formula p=mv, or momentum (p) is equal to mass (m) times velocity (v). The calculator can use any two of the values to calculate the third. Along with values, enter the known units of measure for each and this calculator will convert among units. ## How do you explain velocity and acceleration? Velocity is the rate of change of position with respect to time, whereas acceleration is the rate of change of velocity. Both are vector quantities (and so also have a specified direction), but the units of velocity are meters per second while the units of acceleration are meters per second squared. ## What are the similarities and differences between speed velocity and acceleration? Velocity and acceleration both use speed as a starting point in their measurements. Speed, which is the measurement of distance traveled over a period of time, is a scalar quantity. Both velocity and acceleration are vector quantities, meaning that they use both magnitudes and a specified direction. ## What is the formula for total momentum? Solution: The momentum, p, of the object is simply the product of its mass and its velocity: p = mv. Because no direction is specified, we are only interested in determining the magnitude of p, or p. ## Which has two velocity or acceleration? Answer: It is the velocity which decides the direction of motion of a body. The acceleration simply tells the rate of change of velocity. For example, when a body is thrown vertically upwards, its direction of velocity is upwards, that is why the body goes upward, where as its acceleration is downwards. ## Does momentum change with direction? Notice that momentum does not just depend on the object’s mass and speed. Velocity is speed in a particular direction, so the momentum of an object also depends on the direction of travel. This means that the momentum of an object can change if: the object speeds up or slows down. ## Does direction matter measuring momentum? Two objects with the same mass will always have the same momentum. … Direction does not matter when you are measuring momentum. ## What is the difference between velocity and acceleration? Instantaneous velocity refers to an object’s velocity in an exact moment in time. Acceleration is the change in the velocity of an object, either as it increases or decreases. Acceleration is also a vector and will have both a value and a direction. ## Does Momentum have direction? Momentum is a derived quantity, calculated by multiplying the mass, m (a scalar quantity), times velocity, v (a vector quantity). This means that the momentum has a direction and that direction is always the same direction as the velocity of an object’s motion. ## What is momentum in your own words? Momentum is a physics term; it refers to the quantity of motion that an object has. … If an object is in motion (on the move) then it has momentum. Momentum can be defined as “mass in motion.” All objects have mass; so if an object is moving, then it has momentum – it has its mass in motion. ## How do you use the word momentum? Momentum sentence exampleUsing her momentum , he swung her over his head. … Her body continued its momentum down the hill and she fell, twisting so that she wouldn’t fall on the kid. … Hence the angular momentum of the part between A and B remains constant, or as much enters at B as leaves at A.More items… ## How do you explain momentum to a child? Momentum is a measurement of mass in motion. Any object that is moving has momentum. In physics, momentum of an object is equal to the mass times the velocity. ## What is meant by momentum? Momentum, product of the mass of a particle and its velocity. Momentum is a vector quantity; i.e., it has both magnitude and direction. Isaac Newton’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle. ## What unit is momentum in? The standard units for momentum are k g ⋅ m / s \mathrm{kg \cdot m/s} kg⋅m/sk, g, dot, m, slash, s, and momentum is always a vector quantity. This simple relationship means that doubling either the mass or velocity of an object will simply double the momentum. ## Is momentum the same as inertia? Inertia is the resistance offered by a body to the motion whereas momentum is the tendency of a body to continue moving. ## Are momentum and velocity the same? Momentum is in the same direction as velocity. Scientists calculate momentum by multiplying the mass of the object by the velocity of the object. ## What are the two types of momentum? There are two kinds of momentum, linear and angular. A spinning object has angular momentum; an object traveling with a velocity has linear momentum. ## What do force velocity and momentum have in common? Force, velocity and momentum are all vectors. Vectors are quantities that have magnitude and direction. Force is a measure of how much an object… ## How do you determine velocity? Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt. Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (Δt), represented by the equation r = d/Δt.

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Home Electricity Electronics Engineering # What is the smallest way to power a small light bulb? 123 A small battery. ๐ŸŽƒ 0 ๐Ÿคจ 0 ๐Ÿ˜ฎ 0 ๐Ÿ˜‚ 0 ## Related Questions yes you can power a light bulb with limes You answer is on the light bulb. Watts is the same as power. The power rating for a light bulb (like "40 W") tells how much electrical power the light bulb uses. All of the power used by the bulb is either converted into light or heat. In an incandescent bulb, most of the energy becomes heat. In a fluorescent bulb, more of it becomes light. When the power incresaes the light bulb glows brighter. It depends on the Wattage of the light bulb. One kWh will power a 100-Watt light bulb for ten hours. It is impossible to power a light bulb with a carrot. This is because a carrot contains no electricity. A D or a M battery can power a 60 watt light bulb. A D or a M battery can power a 60 watt light bulb. yes it is it is the part that gives the light bulb power The quantity of power consumed by a light bulb is dependant on the wattage of the bulb. The power the amount of energy per unit time, that the bulb uses. Power (in watts) = Volts X Amperes, for a resistive circuit like an incandescent light bulb. yes, you can power a light bulb using fruit. You must use a type of fruit. It has to be citrus. A lemon can power a light bulb because of the acid in it. The acid is used as a conductor and powers the lemon. Yes, you can power a light bulb with fruit, it only depends an how much citric acid the fuit has. It takes at least 4 lemons to light a small light bulb. It describes the amount of electric power the bulb uses. bulb absorbs some power. this power is desipated as heat The minimum requirements for an electric circuit that will make a light bulb glow is a power source and conductors from the power source to the light bulb. ###### Home ElectricityAtoms and Atomic StructureMath and ArithmeticBatteriesEnergyScienceLight Bulbs and Artificial LightingChild SafetyHistory, Politics & SocietyHeadlights Tail and Brake Lights Copyright ยฉ 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.

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Aguarde... # PRAXIS CORE TEST PREP GEOMETRY REVIEW--EXAMBUSTERS FLASH CARDS--WORKBOOK 8 OF 8 ### R\$ 19,32 Produto disponível no mesmo dia no aplicativo Kobo, após a confirmação  do pagamento! ## Sinopse "PRAXIS Core Prep Flashcard Workbook 8: GEOMETRY REVIEW" 450 questions and answers (ILLUSTRATED) that focus on essential geometry theorems, postulates, concepts, and definitions. Includes complementary diagrams. Topics: Lines and Angles, Triangles, Proofs, Perpendicular Lines, Parallel Lines, Angle Sums, Quadrilaterals, Medians, Altitudes and Bisectors, Circles, Ratio and Proportion, Similar Polygons, Circles and Regular Polygons, Coordinate Geometry [==================] ADDITIONAL WORKBOOKS: "PRAXIS 1/PPST Prep Flashcard Workbook 4: WORDS COMMONLY CONFUSED" Do you know the difference between "fewer" and "less," when to use "it's" or "its," or how to distinguish between "historical" and "historic" or "tortuous" and "torturous?" This course contains 500 pairs of commonly confused words, some so frequently misused that their wrong application has become acceptable to many ears. Includes part of speech, pronunciation, simple definition, and usage example. Mastering the differences will improve your written grammar, verbal communication, and most importantly, your PRAXIS 1/PPST test score! _______________ "PRAXIS 1/PPST Prep Flashcard Workbook 6: ARITHMETIC REVIEW" 600 questions and answers highlight essential arithmetic definitions, problems, and concepts. Topics: Addition, Subtraction, Multiplication, and Division of Whole Numbers; Fractions and Decimals, Multiplication Tables, Word Problems, Percents, Measurement, Metric System, Square Roots and Powers, Real Numbers, Properties of Numbers ======================================= "EXAMBUSTERS PRAXIS Prep Workbooks" provide comprehensive, fundamental PRAXIS review--one fact at a time--to prepare students to take practice PRAXIS tests. Each PRAXIS study guide focuses on one specific subject area covered on the PRAXIS exam. From 300 to 600 questions and answers, each volume in the PRAXIS series is a quick and easy, focused read. Reviewing PRAXIS flash cards is the first step toward more confident PRAXIS preparation and ultimately, higher PRAXIS exam scores! ## Detalhes do Produto • Ano de Edição: 2017 • Ano:  2017

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1,183 Pages The constant of integration is an unknown constant that must be taken into account when taking an indefinite integral. Since the derivative of any constant is 0, any constants will be "lost" when differentiating. The constant of integration is usually represented with , or, in the case of a differential equation where there are multiple constants, In integral calculus, the constant of integration is usually added to the end of a function; for example: However, in differential equations, the constant of integration is often used in other operations on the final function (the most common is multiplication). For example: There can also be multiple constants of integration. In the case of partial derivatives, the constant of integration is not a constant, but a function of all the independent variables save for the one being integrated (in this case, we'll say this is ). This is necessary because any independent variables that are not will be treated as constants, so any function that does not have an in them will be lost. For example, Community content is available under CC-BY-SA unless otherwise noted.

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# the difference between the entropy and the heat capacity? they are very similar!! by su214 Tags: capacity, difference, entropy, heat, similar P: 3 hello ... as we all know that specific heat capacity = joule/ k entropy = joule/k they are same in units Q= m Cv dT Q/dT=m Cv................1 dS= dQ/T .....2 from 1 & 2 dS= m Cv ..............??????????????????????????… i'm now confused ,,entropy can't equal mCv i know i'm wrong ,,but don't know why? and in the same time what does it mean that they have the same units ? and if entropy measuers the chaos in the system and the specific heat capacity is the amount of heat to raise one Kg of the matter one degree of tempreture aren't the entropy and the heat capacity related somehow ? PF Patron HW Helper P: 2,532 Quote by su214 aren't the entropy and the heat capacity related somehow ? Sure, the heat capacity for a given constraint X (like constant volume or constant pressure) is defined as $C_X=T(\partial S/\partial T)_X$. In your derivation, dQ/T doesn't equal Q/dT, so this can't be used to show that entropy is the same as heat capacity. And it doesn't mean anything that they have the same units; work, heat, and torque are fundamentally different parameters that also share the same units (N-m), for example. HW Helper Thanks P: 4,260 You all have confused entropy with enthalpy. Enthalpy is a measure of the total heat content of a substance. Entropy is a much more subtle concept, and its description and use form the basis for the Second Law of Thermodynamics. PF Patron HW Helper P: 2,532 ## the difference between the entropy and the heat capacity? they are very similar!! Quote by SteamKing You all have confused entropy with enthalpy. Enthalpy is a measure of the total heat content of a substance. Entropy is a much more subtle concept, and its description and use form the basis for the Second Law of Thermodynamics. Who is the "all" you're addressing? Nobody is discussing enthalpy. P: 748 Quote by SteamKing You all have confused entropy with enthalpy. Enthalpy is a measure of the total heat content of a substance. Entropy is a much more subtle concept, and its description and use form the basis for the Second Law of Thermodynamics. Son, please. Do not give wrong information on here. and in the same time what does it mean that they have the same units ? It means nothing. Also, manipulating some symbols doesn't really give any insight into what entropy is. Actually, the "engineering thermo" education will never explain what entropy or temperature are. For that you have to study on your own http://en.wikipedia.org/wiki/Entropy...rmodynamics%29 HW Helper Thanks P: 4,260 If you still think you have not confused enthalpy with entropy, check out the following link: http://en.wikipedia.org/wiki/Enthalpy And, Curl, I'm not your son. PF Patron HW Helper P: 2,532 Quote by SteamKing If you still think you have not confused enthalpy with entropy, check out the following link: http://en.wikipedia.org/wiki/Enthalpy It's not clear what you're talking about. What statement do you have a problem with, and how would you revise it? P: 7 Quote by su214 hello ... as we all know that specific heat capacity = joule/ k entropy = joule/k they are same in units Q= m Cv dT Q/dT=m Cv................1 dS= dQ/T .....2 from 1 & 2 dS= m Cv ..............??????????????????????????… i'm now confused ,,entropy can't equal mCv i know i'm wrong ,,but don't know why? and in the same time what does it mean that they have the same units ? and if entropy measuers the chaos in the system and the specific heat capacity is the amount of heat to raise one Kg of the matter one degree of tempreture aren't the entropy and the heat capacity related somehow ? I think is a good question. The Fourier law you started: Q= m Cv dT, I think is missing a dot over the Q which means is the heat flux (derivate with respect to time). The heat capacity has a subindex V which means it is a process at constant volume. However, it would still be valid to say: Q = mCT (1) Notice Q (without point) refers just to the internal energy in the system, C would be the heat capacity -without specifying if is at constant pressure or volume- and of course, m stands for mass and T for temperature (the units of temperature should be consistent with those of C and should be in kelvin units to make the relationship with entropy concept). From Eq. (1) it can find out Q/T= mC = entropy In my opinion is correct, entropy can be deducted from mC, considering C is not a constant anymore, but a parameter that changes with respect to volume and pressure. However, remember that entropy itself is not useful, instead we always find out the change of entropy (dS) from one state to another. This is the reason why I mentioned before that in order to make a comparison with entropy we should use kelvin temperature units. So entropy can be seen as a disorder parameter, or the capacity to store energy of each component of a system of mass m. PF Patron HW Helper P: 2,532 Hi jonsayago, welcome to PF, but please note that personal theories are not appropriate here; your posts should be based on consensus physics. Quote by jonsayago The Fourier law you started: Q= m Cv dT, I think is missing a dot over the Q which means is the heat flux (derivate with respect to time). No, this would make the units inconsistent. dQ is measured in Joules, so that dQ = mcVdT has units [J] = [kg][J/kg/°C][°C]. Note that in this equation, dQ must be an infinitesimal quantity to match dT. Quote by jonsayago However, it would still be valid to say: Q = mCT (1) No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different. Quote by jonsayago From Eq. (1) it can find out Q/T= mC = entropy Eq. (1) is not correct, so this does not hold. P: 7 First comment I accept Q shouldn't be a derivative with respect to time. It is simply the change with respect to one state and another. However, Ec. (1) stands under equilibrium conditions. I mean in just one state. The rest of my derivation should be fine. P: 7 Quote by Mapes Hi jonsayago, welcome to PF, but please note that personal theories are not appropriate here; your posts should be based on consensus physics. No, this would make the units inconsistent. dQ is measured in Joules, so that dQ = mcVdT has units [J] = [kg][J/kg/°C][°C]. Note that in this equation, dQ must be an infinitesimal quantity to match dT. No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different. Eq. (1) is not correct, so this does not hold. "No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different" How did you integrate this??? I am sure you did a mistake here. PF Patron HW Helper P: 2,532 Quote by jonsayago "No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different" How did you integrate this??? I am sure you did a mistake here. $$\int dQ=\int_{U_1}^{U_2}dU=\int_{T_1}^{T_2}mc_VdT$$ $$\Delta U = Q=mc_V\Delta T$$ where ΔU=U2-U1 is the difference in energy due to the addition of thermal energy Q at constant volume, and where ΔT=T2-T1 is the temperature difference. See here for the differential version and here for the integrated version, for example. What other way is there to integrate it? P: 7 You evaluated the right part of the integral (from T1 to T2) and not left part... You have to evaluate left part too from Q1 to Q2. Someone else out there to comment??? P: 7 By the way which software you use to write equations? PF Patron HW Helper P: 2,532 Quote by jonsayago You evaluated the right part of the integral (from T1 to T2) and not left part... You have to evaluate left part too from Q1 to Q2. dQ is not an exact differential, and there is no such thing as Q1 or Q2. (A state can have an associated energy U or an associated temperature T, but not an associated heat Q; heat describes a path-dependent transfer of energy between two states.) See equation 15.11 here or equation 5.6(a) here, for example, where in this case the work W is zero because of the constant-volume constraint. If you think I'm wrong, please show a reference from the literature. PF Patron HW Helper

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## Statistics (12th Edition) $P(x \leq a) = 0.2$ $P(x \leq a) = ∫_{-∞}^{a} f(x).dx$ = $∫_{-∞}^{a} \frac{1}{d-c}.dx$ = $∫_{-∞}^{a} \frac{1}{2}.dx$ = $∫_{-∞}^{2} \frac{1}{2}.dx + ∫_{2}^{a} \frac{1}{2}.dx$ = 1/2 (0) + 1/2 (a-2)= (a-2)/2 Since $P(x \leq a) = 0.2$ (a-2)/2 = 0.2 a-2 = .4 a = 2 + .4 = 2.4

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ECON1193_A2.docx # ECON1193_A2.docx - ECON 1193 Business Statistics Assessment... This preview shows pages 1–4. Sign up to view the full content. ECON 1193 Business Statistics Assessment 2: Individual Reflection Stratified Sampling Method Definition Stratified sampling method is a multistage sampling method which requires the split of a population into smaller non-overlapping subpopulations known as strata. The strata are set up based on shared attributes and sorting criteria. Moreover, the strata make up the entire population so that each sampling component is located in precisely one stratum (Lohr, 2010) . Then independent samples from each stratum are drawn in numbers corresponding to the size of each stratum in the population (CFA Institute, 2016). These samples are then put together to acquire general population estimates. Examples One real life example of stratified sampling method is when the American Council of Learned Societies (ACLS) used this sampling method to study the membership pattern along with computer and library usage. They had drawn sample from selected ACLS societies stratifying by disciplines. The data are presented in Table 1.1 Table 1.1 Data from ACLS Survey Discipline Membership Number Mailed Valid Returns Female Members (%) Literature 9,100 9115 636 38 Classics 1,950 633 452 27 Philosophy 5,500 658 481 18 History 10,850 855 611 19 Linguistics 2,100 667 493 36 Political Science 5,500 833 575 13 Sociology 9,000 824 588 26 Totals 44,000 5,385 3,835 Source: ACLS (Morton and Price, 1989) One more example using stratified random sampling is the Labour Force Survey (2013) conducted by the General Statistics of Vietnam. Regarding the survey about the labour force participation rate in 2013, the sample is stratified by gender and socio-economic region. The data are shown in table 1.2. Table 1.2: Labour force participation rate in 2013 Unit: Percentage Residence/Socio-economic region Total Male Female Male- female Gap This preview has intentionally blurred sections. Sign up to view the full version. View Full Document Entire country 77.5 82.1 73.2 8.8 Urban 70.3 76.3 64.8 11.5 Rural 81.1 84.8 77.5 7.3 Socio-economic region Northern Midlands and Mountains 85.9 87.4 84.4 3.0 Red River Delta (*) 77.3 79.0 75.7 3.3 North and South Central Coast 79.4 82.4 76.6 5.9 Central Highlands 83.4 86.2 80.6 5.5 Southeast (*) 77.6 83.8 71.9 11.9 Mekong River Delta 77.2 85.1 69.7 15.4 Ha noi city 70.9 74.7 67.4 7.3 Ho Chi Minh city 64.8 74.4 56.5 17.8 (*) Red River Delta excludes Hanoi City and Southeast excludes Ho Chi Minh City. Source: General Statistics Office of Vietnam Another example about the usage of stratified random sampling method is the Enterprise Survey in Vietnam (World Bank and General Statistics Office of Vietnam, 2015). There are three levels of stratification in this sample which are industry stratification (Food and Beverages, Garments,...), establishment size (Small, Medium, Big) and region (Red River Delta, Southeast,...). Data are presented in Table 1.3. Table 1.3: Vietnam Enterprise Survey 2015 Food and Beve rage s Garm ents Non metal lic mine ral prod ucs Fabric atd metal produ cts Other manu factu ring Ret ail Other Servic es Gra nd Tota l Red River Delta Small 56 145 74 93 174 91 148 2,04 5 Medium 50 78 63 59 301 41 144 Large 53 66 80 129 92 51 57 North Central area and Central coastal area Small 48 40 148 60 72 50 117 1,17 6 Medium 52 48 64 40 43 48 62 Large 53 53 57 22 35 25 39 South East Small 215 220 178 135 261 379 337 3,53 2 Medium 128 117 147 75 207 49 243 Large 116 257 101 72 158 89 48 Mekong River Delta Small 137 21 33 66 67 44 90 1,14 2 Medium 122 45 37 46 48 45 37 Large 145 59 18 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. {[ snackBarMessage ]} ### What students are saying • As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. Kiran Temple University Fox School of Business ‘17, Course Hero Intern • I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero. Dana University of Pennsylvania ‘17, Course Hero Intern • The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time. Jill Tulane University ‘16, Course Hero Intern

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# Number 1279150279 ### Properties of number 1279150279 Cross Sum: Factorization: Divisors: Count of divisors: Sum of divisors: Prime number? No Fibonacci number? No Bell Number? No Catalan Number? No Base 3 (Ternary): Base 4 (Quaternary): Base 5 (Quintal): Base 8 (Octal): 4c3e48c7 Base 32: 163si67 sin(1279150279) -0.76960314627635 cos(1279150279) 0.63852251114705 tan(1279150279) -1.205287414055 ln(1279150279) 20.969461849904 lg(1279150279) 9.1069215698942 sqrt(1279150279) 35765.210456532 Square(1279150279) ### Number Look Up Look Up 1279150279 (one billion two hundred seventy-nine million one hundred fifty thousand two hundred seventy-nine) is a very special figure. The cross sum of 1279150279 is 43. If you factorisate 1279150279 you will get these result 11 * 116286389. 1279150279 has 4 divisors ( 1, 11, 116286389, 1279150279 ) whith a sum of 1395436680. The number 1279150279 is not a prime number. 1279150279 is not a fibonacci number. The number 1279150279 is not a Bell Number. The figure 1279150279 is not a Catalan Number. The convertion of 1279150279 to base 2 (Binary) is 1001100001111100100100011000111. The convertion of 1279150279 to base 3 (Ternary) is 10022010221120022021. The convertion of 1279150279 to base 4 (Quaternary) is 1030033210203013. The convertion of 1279150279 to base 5 (Quintal) is 10104430302104. The convertion of 1279150279 to base 8 (Octal) is 11417444307. The convertion of 1279150279 to base 16 (Hexadecimal) is 4c3e48c7. The convertion of 1279150279 to base 32 is 163si67. The sine of the number 1279150279 is -0.76960314627635. The cosine of the number 1279150279 is 0.63852251114705. The tangent of 1279150279 is -1.205287414055. The root of 1279150279 is 35765.210456532. If you square 1279150279 you will get the following result 1636225436265777841. The natural logarithm of 1279150279 is 20.969461849904 and the decimal logarithm is 9.1069215698942. I hope that you now know that 1279150279 is very unique number!

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# Question: What Is The First Overtone? ## What is the difference between an overtone and a harmonic? “Overtone” is a term generally applied to any higher-frequency standing wave, whereas the term harmonic is reserved for those cases in which the frequencies of the overtones are integral multiples of the frequency of the fundamental. Overtones or harmonics are also called resonances.. ## Why third harmonic is dangerous? As seen in the figure, the 3rd harmonic will add constructively across the three phases. This leads to a current in the neutral wire at three times the fundamental frequency, which can cause problems if the system is not designed for it, (i.e. conductors sized only for normal operation.) ## What is the first harmonic? The lowest frequency produced by any particular instrument is known as the fundamental frequency. The fundamental frequency is also called the first harmonic of the instrument. ## What is first frequency and fundamental overtone? In acoustics the basic vibration is the ‘first harmonic’. The term overtone is used to refer to any resonant frequency above the fundamental frequency. The ‘second harmonic’ (twice the fundamental frequency) is the first overtone. Persons who count differently are wrong. In counting − harmonics are not overtones. ## Which overtone is the sixth harmonic? Overtone SeriesHarmonicFreq. HzComments45242 Octaves above fund. and a fourth above G45655A Third above C56786A Fifth above C5 Harms. 4, 5 & 6 form a major chord7917An overtone to avoid3 more rows ## Who discovered the overtone series? Wilfried Kruger”The German musicologist Wilfried Kruger discovered that the eight electrons of the oxygen atom shell and the eight protons of the nucleus of the oxygen atom generate a major scale with the spins of the particles delineating the half tones and whole tones. ## What are overtones vs fundamentals? is that fundamental is a leading or primary principle, rule, law, or article, which serves as the groundwork of a system; essential part, as, the fundamentals of linear algebra while overtone is (physics|music) a tone whose frequency is an integer multiple of another; a harmonic. ## What is the lowest sound of an overtone series called? Vibrating as a whole, it produces its lowest tone. This tone is called the string’s fundamental, or first harmonic. The string also vibrates in halves, producing a sound with twice the frequency (number of vibrations per second) of the fundamental. ## How many overtones are there? So “overtone” is an umbrella term, and there are two types of overtones: (1) “harmonic” overtones (which are integer multiples of the fundamental frequency) and (2) overtones that aren’t integer multiples of the fundamental frequency (I’ll call these disharmonious overtones). ## Which harmonic is the second overtone of an open pipe? This is called as second overtone or fifth harmonic. Therefore the frequency of pth overtone is (2p + 1) n1 where n1 is the fundamental frequency. ## How do overtones affect sound quality? The object’s higher natural frequencies are called overtones. Overtones have frequencies that are two, three, or more times the frequency of the fundamental tone. … But each instrument produces different overtones, so the blending of the fundamental tones and overtones produces different sound qualities. ## Why is overtone series important? …equation (25), known as the overtone series, plays an important part in the analysis of musical instruments and musical tone quality. If the fundamental frequency is the note G2 at the bottom of the bass clef, the first 10 frequencies in the series will correspond closely to the notes shown… ## What is the frequency of the first overtone? 440 HzMusical usage termFrequencyOrderName 21 · f = 440 Hzn = 11st harmonic2 · f = 880 Hzn = 22nd harmonic3 · f = 1320 Hzn = 33rd harmonic4 · f = 1760 Hzn = 44th harmonic ## Are all overtones harmonics? Harmonic: an integer (whole number) multiple of the fundamental frequency of a vibrating object. Overtone: any resonant frequency above the fundamental frequency. Therefore, all harmonics are overtones. ## Can you hear overtones? The reason overtones are hard to hear at first is because they are part of the note – they’re in every note you’ve ever heard, so your brain isn’t looking for them. Try looking “behind” the sound, in a way – listen for a higher pitched sound behind the original sound. ## What is the 11th harmonic? If you play the resonant frequency of a cancer cell and that same frequency 11 times higher (eleventh harmonic of that resonant frequency) then the cancer cells break. This means that the eleventh harmonic is a destructive harmonic. … Skip to 8:50 in this video if you just want to hear about the 11th harmonic. ## What is the meaning of overtone? 1a : one of the higher tones produced simultaneously with the fundamental and that with the fundamental comprise a complex musical tone : harmonic sense 1a. b : harmonic sense 2. 2 : the color of the light reflected (as by a paint)

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# physics posted by on . from what height must a heavy elastic ball be dropped on a floor ,so thatafter reboundingthrice it will reach a height of 16 m?take e=(0.5) • physics - , After the 1st rebounce the speed is v/2, after the 2nd rebounce – v/4, after the third rebounce –v/8, => m(v/8)²/2=mgh₁ v=sqrt(128gh₁) =141.7 m/s mv²/2=mgh h= v²/2g=141.7²/2•9.8=1024 m

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## College Algebra (10th Edition) $\color{blue}{(x-1)^2+(y+2)^2=4}$ The given circle has its center at $(1, -2)$. RECALL: The standard form of a circle's equation is $(x-h)^2+(y-k)^2=r^2$, where $(h, k)$ is the center and $r$ is the radius. Thus, using the standard form above and the center of $(1, -2)$, the tentative equation of the circle whose graph is given is: $(x-1)^2 + (y-(-2))^2=r^2 \\(x-1)^2+(y+2)^2=r^2$ The point $(1, 0)$ is a point on the circle. This means that the x and y coordinates of this point satisfy the equation of the circle. Substitute the x and y coordinates of this point into the tentative equation above to obtain: $(x-1)^2+(y+2)^2=r^2 \\(1-1)^2+(0+2)^2=r^2 \\0^2 + 2^2=r^2 \\0+4=r^2 \\4=r^2$ Therefore, the equation of the circle is : $\color{blue}{(x-1)^2+(y+2)^2=4}$

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# Radius of convergence of product Let $\sum_{i=0}^\infty a_nz^n$ and $\sum_{i=0}^\infty b_nz^n$ be power series, and define the product $\sum_{i=0}^\infty c_nz^n$ by $c_n=a_0b_n+a_1b_{n-1}+\ldots+a_nb_0$. Find an example where the first two series has radius of convergence $R$, while the third (the product) has radius of convergence larger than $R$. The radius of convergence of $\sum_{i=0}^\infty a_nz^n$ is given by $1/R=\limsup{|a_n|^{1/n}}$. I tried some sequences like $a_0=a_1=\ldots=b_0=b_1=\ldots=1$. Then the two sequences have radius $1$. But $c_i=i+1$, and $\lim_{i\rightarrow\infty}(i+1)^{1/i}=1$. So the radius is the same as the original two sequences, which doesn't work. Let $f(x)=(1-x)^{1/2}$ and $g(x)=(1-x)^{-1/2}$. When expanded in a Maclaurin series, we get two series with radius of convergence $1$. The Cauchy product (your product) of the two series is the very simple "infinite" series $1+0\cdot x+0\cdot x^2+\cdots$, which has infinite radius of convergence. Remark: If the example is too simple, we can "doctor" $f(x)$ by mutiplying say it by $h(x)$, where $h(x)=\frac{1}{1-\frac{x}{3}}$. Then the Cauchy product of the Maclaurin series for $f(x)h(x)$ and $g(x)$ has radius of convergence $3$. • I find that it's not easy to compute the radius of convergence of the series expansion for $(1-x)^{1/2}$. It has coefficients $-\dfrac{1}{2}, -\dfrac{1}{2}\cdot\dfrac{3}{2}, -\dfrac{1}{2}\cdot\dfrac32\cdot\dfrac52, \ldots$. And it's not clear what the limsup will be. How do you compute it? – Paul S. Sep 19 '13 at 3:10 • I find the Ratio Test easier to use for this series. Note that once we have the radius of convergence for this one, the radius for the other one is the same, for after one differentiation the series are kind of the same, power of $x$ shifted by $1$, and a missing factor of $\frac{1}{2}$. – André Nicolas Sep 19 '13 at 3:15 • I'm not sure how you use the ratio test to compute the limsup. I've only used it to determine convergence of a series. Could you explain a bit more? – Paul S. Sep 19 '13 at 3:48 • We don't need limsup, the limit of $|a_{n+1}/a_n|$ is $1$. – André Nicolas Sep 19 '13 at 4:03 • It's actually very easy. The only complex singularity is at $x=1$ at distance $1$ from $0$, so the radius of convergence is $1$. – Phira Mar 21 '17 at 12:05 A simpler example: let $$f(z) = \frac{1+z}{1-z} = \frac{1}{1-z} + \frac{z}{1-z}.$$ Note that the first term is just the formula for the geometric sum with first term 1, $$\frac{1}{1-z} = 1 + z + z^2 + z^3 + \cdots, \qquad |z| < 1,$$ and the second term is the formula for a geometric sum with first term equal to the common ratio $z$: $$\frac{z}{1-z} = \frac{1}{1-z} - 1 = z + z^2 + z^3 + \cdots, \qquad |z| < 1.$$ Then the power series for $f(z)$ is given by $$f(z) = \frac{1+z}{1-z} = 1 + 2z + 2z^2 + 2z^3 + \cdots = 1 + 2\sum_{n=1}^\infty z^n, \qquad |z| < 1,$$ and has radius of convergence $R_f = 1$. If we form a new power series $g(z)$ by making the substitution $z \mapsto -z$, we have $$g(z) = \frac{1-z}{1+z} = 1 - 2z + 2z^2 - 2z^3 + \cdots = 1 + 2\sum_{n=1}^\infty (-z)^n, \qquad |z| < 1,$$ also with radius of convergence $R_g = 1$. However, the product series is $$f(z)g(z) = \left( \frac{1+z}{1-z} \right) \left( \frac{1-z}{1+z} \right) = 1 = 1 + 0z + 0z^2 + 0z^3 + \cdots, \qquad \forall z\in\mathbb{C}$$ and has radius of convergence $R_{fg} = \infty$, which is strictly larger than $R_f = R_g = 1$. • How do we prove that radius of convergence of product is atleast minimum of R1 and R2??? – Koro Sep 13 '15 at 8:03

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Accelerating the pace of engineering and science # Documentation Center • Trial Software • Product Updates ### Contents 라이선스가 부여된 사용자만 번역 문서를 볼 수 있습니다. 번역 문서를 보려면 로그인하십시오. # asin Inverse sine in radians Y = asin(X) ## Description Y = asin(X) returns the inverse sine (arcsine) for each element of X. The asin function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians. For real elements of X in the domain [-1,1], asin(X) is in the range For real elements of x outside the range [-1,1], asin(X) is complex. ## Examples expand all ### Graph of Inverse Sine Function Graph the inverse sine over the domain . ```x = -1:.01:1; plot(x,asin(x)), grid on ``` ## More About expand all ### Inverse Sine The inverse sine can be defined as ## See Also Was this topic helpful?

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Community Profile # Mohamed Atyya ### cairo Last seen: 12 months ago Active since 2016 All #### Content Feed View by Submitted knapsack problem this code can solve lage knapsack problem with low hardware capabilities using modified dynamic programming Submitted 01 Knapsack Solution by Dynamic Programming 01 Knapsack Solution by Dynamic Programming Solved Circle/Pentagon Overlap Your function will be provided with the five vertices of a pentagon (p) as well as the center point (cp) and radius (r) of a cir... 5 years ago Solved Recaman Sequence - I Recaman Sequence (A005132 - <http://oeis.org/A005132 - OEIS Link>) is defined as follow; seq(0) = 0; for n > 0, seq(n) ... 5 years ago Solved A Simple Tide Gauge with MATLAB *&#8767 &#8767 &#8767 &#8767 &#8767 &#8767 &#8767 &#8767* You are standing in a few inches of sea water on a beach. You a... 5 years ago Solved Is this is a Tic Tac Toe X Win? For the game of <https://en.wikipedia.org/wiki/Tic-tac-toe Tic Tac Toe> we will be storing the state of the game in a matrix M. ... 5 years ago Solved Basic electricity in a dry situation &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#9889 &#... 5 years ago Solved Pentagonal Numbers Your function will receive a lower and upper bound. It should return all pentagonal numbers within that inclusive range in ascen... 5 years ago Solved Energy of a photon *&#9883 &#9762 &#9883 &#9762 &#9883 &#9762 &#9883* Given the frequency F of a photon in giga hertz. Find energy E of this... 5 years ago Solved How to subtract? *&plusmn &plusmn &plusmn &plusmn &plusmn &plusmn &plusmn &plusmn &plusmn &plusmn &plusmn* * Imagine you need to subtract one... 5 years ago Submitted Nonlinear transformations Gain Scheduling Nonlinear transformations Gain Scheduling Submitted PIDA controller PIDA controller Submitted PDA controller PDA controller Submitted PID controller PID controller Submitted Self-Tuning Regulators (STR) Self-Tuning Regulators (STR) Submitted Concentration Control Gain Scheduling Concentration Control Gain Scheduling Submitted Non-linear valve Gain Scheduling Non-linear valve Gain Scheduling Submitted Tank system Gain Scheduling Tank system Gain Scheduling Submitted Second Order System Adjustment (Lyapunov Theory) Second Order System Adjustment (Lyapunov Theory) Submitted Second Order System Adjustment (Lyapunov Theory) Second Order System Adjustment (Lyapunov Theory) Submitted First Order System Adjustment (Lyapunov Theory) First Order System Adjustment (Lyapunov Theory) Submitted Submitted Second Order System Adjustment with first order controller (Normalized MIT Rule) Second Order System Adjustment with first order controller (Normalized MIT Rule) Submitted Second Order System Adjustment (Normalized MIT Rule) Second Order System Adjustment (Normalized MIT Rule) Submitted First Order System Adjustment (Normalized MIT Rule) First Order System Adjustment (Normalized MIT Rule) Submitted Submitted second order system (Determination of adaptation gain) second order system (Determination of adaptation gain) Submitted first order system (Determination of adaptation gain) first order system (Determination of adaptation gain) Submitted Second Order System Adjustment with first order controller (MIT Rule) Second Order System Adjustment with first order controller (MIT Rule) Submitted Second Order System Adjustment (MIT Rule) Second Order System Adjustment (MIT Rule)

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What is the expected number of marks on a single bingo card to form various common winning patterns? anonymous Here is the average number of marks needed on a card for common winning patterns: • Single bingo — 13.60808351 • Double bingo — 16.37193746 • Triple bingo — 18.02284989 • Single hardway — 15.29273554 • Double hardway — 18.09327842 • Triple hardway — 19.79294406 • Six pack — 14.62449358 • Nine pack — 18.97212394 In the previous Ask the Wizard column, you were asked about the expected number of rolls to achieve a total of 12 with two dice twice in a row. On a related note, I see somebody on your forum is claiming to have witnessed 18 consecutive yo's (total of 11) at the craps table. What is the expected rolls required for that to happen? anonymous 41660902667961039785742 Here is my solution (PDF). This question is asked and discussed in my forum at Wizard of Vegas. The exact answer found with the aid of WizCalc. Henry and Tom decide to bet on a coin flip. Henry wins on heads, Tom wins on tails. It’s \$1 per flip and they are really bored, so they decide to do one million flips. At the end of the session, the loser will write a check to the winner for the final balance. What is the expected value of the check amount? Ace2 797.88456080286535587989211986876373695171726 232986931533185165934131585179860367700250466 781461387286060511772527036537102198390911167 448599242546125101541269054116544099863512903 269161506119450728546416733918695654340599837 28381269120656178667772134093073... The general formula for the answer is the sqrt(variance * (2/pi)). The variance in this case is 1,000,000. So, the expected absolute difference between actual and expected results is sqrt(1,000,000 × (2/pi)) =~ 797.88456080286535587989211986876373695171726 232986931533185165934131585179860367700250466 781461387286060511772527036537102198390911167 448599242546125101541269054116544099863512903 269161506119450728546416733918695654340599837 28381269120656178667772134093073. I ask a related question in Ask the Wizard #358, which will help show where I get the sqrt(2/pi) term. This question was asked and discussed in forum at Wizard of Vegas.

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Home » Bookkeeping articles » Gross Wages What are they and how do you calculate them? # Gross Wages What are they and how do you calculate them? August 22, 2024 Bill Kimball Gross is an employee’s total earnings, such as wages or salary, while net pay is their earnings minus payroll deductions, including taxes, benefits and garnishments. Net pay, or take-home pay, is the amount of an employee’s paycheck after deductions are taken out of their gross pay. Gross pay is noted on a pay stub and should reflect an employee’s salary or hourly wage, plus reimbursements, bonuses, commissions and overtime pay. For example, if their pay is \$20 per hour and they worked 40 hours in a pay period, their gross pay should be \$800 for the pay period. If they’re paid a salary of \$60,000 and paid twice per month, their gross pay per pay period should be \$2,500 (\$60,000 divided into 24 pay periods). When you add gross wages to your labor burden — employer-paid payroll taxes and benefits — you’re given a full picture of the cost of having employees. Calculating gross wages for one or two employees is usually straightforward. If you have many employees, however, calculating gross wages accurately can become more complicated. If you make a mistake, employees may be paid more or less than they should be, or their tax information may be incorrect. To simplify payroll calculations and reporting, consider using payroll software, which we dive into below. ## Which is more―net pay or gross pay? Ensuring that both you and your employees understand what gross pay means and how it affects your employees helps you negotiate clear compensation where both parties are satisfied. Imagine that same individual pays \$1,500 per month in rent, \$450 in student loans, and \$300 towards an auto loan. All three of these expenses are excluded from the calculation of gross income for non-tax purposes. Peter’s wages before taxes and deductions are his hourly pay plus his tips collected. If a salaried employee gets paid semi-monthly, twice per month, 24 times per year — your employee’s total annual income gets divided by 24. ## Gross wages vs. wages included on Form W-2 The easiest way to calculate hourly wages is by the week since most overtime applies to working more than 40 hours in a given week. The calculations for each are slightly different, so we’ll walk through the steps of how to calculate salaried gross pay and hourly gross pay. Social Security is a federal retirement plan that helps provide retirement income to most workers in America. Employers and employees are both required to contribute to Social Security. For example, many sales jobs like real estate include a commission for selling a property or meeting a certain sales quota. Commissions can be a motivating factor for employees to meet the company’s goals. When you calculate gross pay correctly, you’re making the first step in successfully managing your payroll. If you’re running payroll for a restaurant, your employees’ tips get added to the wages you pay them. The offer letter listed my start date and my hourly pay, also called a gross wage rate. Gross pay is the total amount of wages an employer pays to an employee before any taxes or deductions. This is different from net pay, which is the final amount the employee receives after deductions. Understanding gross pay is essential for business budgeting and ensuring your payroll is legally compliant. That’s because some of the money that’s taken out of your account is still subject to tax. If employees are owed commission, reimbursements or bonuses in a given pay period, add the amount owed to their wages to get their overall gross pay. We collaborate with business-to-business vendors, connecting them with potential buyers. There’s also gross profit margin, which is more correctly defined as a percentage and is used as a profitability metric. The gross income for a company reveals how much money it has made on its products or services after subtracting the direct costs to make the product or provide the service. You may be asked to put down your employees’ gross wages for loan applications. Adding the standard hourly wages and overtime pay together, they would receive \$950. Piece rate pay replaces hourly or salaried pay and is sometimes used by employers who want to motivate employees to reach a set quota. Some employees also like piece rate pay because they make a greater amount when they deliver higher output. Some employees like hourly wages because they can receive a greater overall sum if they work a large number of hours. However, the variability of hours worked means that paychecks can sometimes fluctuate. Gross pay is the total amount of wages an employee earns before any deductions are made. Payroll deductions, taxes, and health benefits are deducted from an employee’s gross wages. Understanding gross pay is important for negotiating salary, managing your taxes, and planning a budget. In this article, we’ll go through the components of gross pay, common deductions from gross pay, and how to calculate gross pay for salaried and hourly wages so you can simplify your payroll process. Hourly wages are one type of gross pay that an employer can pay an employee. You must calculate your employees’ gross wages every pay period, whether weekly, bi-weekly, or twice monthly. A base salary is the amount an employee earns prior to other forms of compensation. When the base salary and additional compensation are combined, the total is the employee’s gross wages. 1. That means it’s time to understand the numbers that go into an employee’s paycheck, including the difference between gross pay vs, net pay. 2. The calculations for each are slightly different, so we’ll walk through the steps of how to calculate salaried gross pay and hourly gross pay. 3. Gross income is the annual sum of an employee’s gross pay, such as their earnings for a year when you add up all their paychecks. 4. By using gross income and limiting what expenses are included in the analysis, a company can better analyze what is driving success or failure. Retirement plans aren’t mandatory, but many employees choose to contribute to one. In many cases, employers will offer a retirement plan through the company and may also contribute to retirement contributions as an incentive to draw workers to the company. If an employee elects to pay into a plan like a 401(k), this will be deducted from gross wages. An hourly wage is a fixed amount earned per hour multiplied by the total number of hours worked in each pay period. Gross pay is the total amount of an employee’s paycheck before taxes and deductions, while net pay is the amount an employee takes home after all deductions. Most credit and loan applications ask for your gross annual or monthly income. It’s important to put your gross income, rather than your net income, so that you can provide accurate information on your application and increase your chances of approval. For example, \$70,000 annual salary or \$40 an hour wages are examples of gross pay. To find your personal monthly gross income, calculate the amount of money you earn each month. This will likely be different than the amount of money you take home or receive as payment directly from your employer. A company calculates gross income to understand how the product-specific aspect of its business performed. By using gross income and limiting what expenses are included in the analysis, a company can better analyze what is driving success or failure. An individual’s gross income is used by lenders or landlords to determine whether that person is a worthy borrower or renter. The Social Security tax rate is 1.45% until the employee reaches the wage base limit, after which no further Social Security taxes are withheld for the remainder of the year. Gross wages are important because they provide the basis on which certain payroll calculations are made, including taxes and employee take-home pay. Failure to pay an employee all wages earned when due may lead to expensive wage claims, lawsuits or tax penalties. Although you’ll see your gross pay on a paycheck, you’ll take home a smaller amount (called net pay) after taxes and other deductions. Understanding the difference between gross and net pay helps you plan an accurate budget. When employers discuss salaries and wages, they usually discuss them in terms of gross pay. It’s also the value that’s commonly referred to when discussing compensation with new hires. Understanding the role that gross wages play in payroll processing is essential to paying employees correctly and complying with applicable employment laws. Special considerations go into calculating gross wages for hourly employees who work overtime hours. Hourly employees are generally nonexempt from the Fair Labor and Standards Act (FLSA), which governs overtime. This means you must pay them at least time-and-a-half for all hours over 40 they worked during a workweek. But what exactly is — and isn’t — included in gross wages, and why is it so important to calculate gross wages correctly? We’ll explain exactly what gross wages are, how to calculate them, and why understanding gross wages is critical to managing your small business. For non-tax purposes, individuals can usually use their total wages as gross income. When applying for a loan, individual gross income will equal the amount of money the individual earns prior to any taxes being deducted or any expenses having been paid.

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New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Measurement Conversion Measurement Converter Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC. Conversion Result: ```0.2 gallon = 0.0007570823568 meter^3 (volume) ``` Related Measurements: Try converting from ".2 gallons" to balthazar, bath (Israeli bath), beer gallon (English beer gallon), cc (cubic centimeters), chetvert (Russian chetvert), cord (of wood), cord foot (of wood), cup, displacement ton, gallon, jeroboam, liter, load, noggin, peck (dry peck), pipe, quart (fluid quart), rehoboam, tablespoon, wine bottle, or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: .2 gallons = .32083333 board foot, .02148418 bushel (dry bushel), .00167101 cord foot (of wood), 25,236.08 drop, .68749361 dry quart, 1 fifth, .75708236 liter, .4 magnum, .04 nebuchadnezzar, 6.4 noggin, .06024096 oil arroba (Spanish oil arroba), .19097045 omer (Israeli omer), 1.6 pint (fluid pint), .13333333 rehoboam, .02923977 Roman amphora, 51.2 tablespoon, .02673611 timber foot, .16653483 UK gallon (British gallon), .08326725 UK peck (British peck), .06153846 vedro (Russian vedro). Feedback, suggestions, or additional measurement definitions? Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!

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1. ## Natural Logarithms... Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks 2. Originally Posted by hamnet Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks Use wikipedia for a formal definition. Natural logarithm - Wikipedia, the free encyclopedia Suppose you have e^(2x + 3) = e^(50x) and you wanted to solve for x; In order to negate the e's, you would use ln; ln(e^(2x + 3)) = ln(e^(50x)) 2x + 3 = 5x Further, ln(x) is an exponential function. It crosses the x-axis at (1,0), (whereas e^(x) cross the y axis at (0,1). There are are many uses for the natural log. Take a look at the wikipedia site and then list any questions you have thereafter. 3. Originally Posted by hamnet Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks The natural logarithm is exactly like the average logarithm $\displaystyle \log$. But this one just has a different base. $\displaystyle \log_e = \ln$ The base is a number called $\displaystyle e\approx 2.718$. Thus, $\displaystyle \ln 5 = \log_e 5$ Meaning what does $\displaystyle e$ have to be raised to, to result in 5? You may wonder why such a strange number, but it is important when you learn the Calculus. 4. Originally Posted by AfterShock Use wikipedia for a formal definition. Natural logarithm - Wikipedia, the free encyclopedia Suppose you have e^(2x + 3) = e^(50x) and you wanted to solve for x; In order to negate the e's, you would use ln; ln(e^(2x + 3)) = ln(e^(50x)) 2x + 3 = 5x Further, ln(x) is an exponential function. It crosses the x-axis at (1,0), (whereas e^(x) cross the y axis at (0,1). There are are many uses for the natural log. Take a look at the wikipedia site and then list any questions you have thereafter. Does 50x become 5x? or was that just a typo? --- When it comes to Algebra, when do you know that you need to use a Natural Log?

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Win a copy of Re-engineering Legacy Software this week in the Refactoring forum or Docker in Action in the Agile forum! # Combination Generation... Neville Mehta Greenhorn Posts: 1 Hi, Could someone please refer me to some resource (or be nice enough to explain me here itself ), how we could generate unique combinations of a given set of objects (strings,integers.. whatever). --------------------------------------- Say for eg. here is the set initially A B C Now, we can have 3 (yes... 3C2) number of combinations if we take 2 at a time. Those 3 would be A B B C A C --------------------------------------- A generic algo would be more helpful than an algo in java however even if someone posts an algo in java i could try and understand it myself. If you would be posting code, i request you to please send some little explaination if possible. Neville Michael Dunn Ranch Hand Posts: 4632 Not sure this is what you're after fred rosenberger lowercase baba Bartender Posts: 12085 29 If you're doing combinations, order doesn't matter, right? if you know how many elements you have, and how many you want to choose, you could do this...(i think this works)... write as many nested loops as how many you want to choose. if you have 8 elements and want to choose 3, you'd have 3 nested loops. note: i'm using english, so my elements are numbered 1-8, not 0-7 the outer loop would run from 8 to 4 the first inner loop would run from (outer value -1) to 2 the inner runs from (middle value -1) to 1 inside the inner most loop, you print the elements your on for each loop. you should get 8,7,6 8,7,5 8,7,4 8,7,3 8,7,2 8,7,1 //inner loop done, increment middle loop... 8,6,5 8,6,4... etc i'm not sure how to do it completly generically, where you'd input the number of elelment and the number to choose... but i'm pretty sure it could be done recursively

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Students can download 4th Maths Term 1 Chapter 3 Patterns Ex 3.4 Questions and Answers, Notes, Samacheer Kalvi 4th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. ## Tamilnadu Samacheer Kalvi 4th Maths Solutions Term 1 Chapter 3 Patterns Ex 3.4 Fill in the blanks : i. 90. 180, 270, _____, _____, _____, ii. A9, B18, C27, 836, _____, _____, _____, i. 90. 180, 270, _____, _____, _____, 360, 450, 540. ii. A9, B18, C27, 836, _____, _____, _____, E45 F54, G63. B. Circle the multiples of 9: 25, 27, 35, 36, 45, 46, 54, 55 C. Complete the following sequence: Question 1. 125, 150, 175, _____, _____, _____, 200, 225, 250 Question 2. 100, 400, 700. _____, _____, _____, 1000, 1300, 1600 Question 3. Question 4. Complete the following sequence. Question 1. 9 × 6 = 54 9 × 66 = 594 9 × 666 = 5994 9 × 6666 = 5 ____ 4 9 × 666666 = ______ 9 × 6666 = 59994 9 × 666666 =5999994 Question 2. 9 × 111 = 999 9 × 222 = 1998 9 × 333 = 2997 9 × 444 = ______ 9 × 555 = ______ 9 × 666 = ______ 9 × 444 = 3996 9 × 555 = 4995 9 × 666 = 5994. E. Answer the following Questions: Question 1. The school bell rings once in an hour, to indicate that the session ends/next session begins. And for break, it will be 20 minutes. Shall we try to fill this up. Here is the time table. Question 2. Imagine you are a traffic inspector. You are asked to design the traffic signal timings. Can you design it? Here is the time table.

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• 0 Vote(s) - 0 Average • 1 • 2 • 3 • 4 • 5 Question concerning Aldrovandi/Freitas-article Gottfried Ultimate Fellow Posts: 790 Threads: 121 Joined: Aug 2007 01/19/2008, 09:10 AM (This post was last modified: 01/19/2008, 11:35 AM by Gottfried.) andydude Wrote:So what is the difference between "normality" and "distinct eigenvalues"? I thought that distinct eigenvalues were sufficient for diagonizability... Andrew Robbins "normal": let M be a matrix (we're discussing real matrices for example). Then M is "normal", if M commutes with its transpose M*M' = M'*M This equality is obviously true for symmetric M, but also for some others. It is said, that for normal matrices, if T*M*T^-1 = D , D diagonal, then T is orthogonal, meaning T*T' = T*T^-1=I (I think T is always a rotation) and also T*M*T' = D (from other context I'm used to denote rotation-matrices by letter T) --------------------------- not "normal", but still diagonalizable (the more general case): W*M*W^-1 = D no specific properties on W. Related to current discussion: if M is triangular (and diagonalizable), I think W is also triangular (but I must check this), and the eigenvalues are the entries of its diagonal. ------------------- The question whether eigenvalues are distinct or not is not relevant here; this is only relevant for the description of further properties of W (whether it is unique ... ) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest » Messages In This Thread Question concerning Aldrovandi/Freitas-article - by Gottfried - 01/18/2008, 10:28 PM RE: Question concerning Aldrovandi/Freitas-article - by bo198214 - 01/19/2008, 06:30 AM RE: Question concerning Aldrovandi/Freitas-article - by andydude - 01/19/2008, 08:31 AM RE: Question concerning Aldrovandi/Freitas-article - by bo198214 - 01/19/2008, 08:38 AM RE: Question concerning Aldrovandi/Freitas-article - by Gottfried - 01/19/2008, 09:10 AM Possibly Related Threads... Thread Author Replies Views Last Post Math.Stackexchange.com question on extending tetration Daniel 3 1,593 03/31/2021, 12:28 AM Last Post: JmsNxn Kneser method question tommy1729 9 10,395 02/11/2020, 01:26 AM Last Post: sheldonison A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 11,550 02/18/2019, 10:34 PM Last Post: Micah Math overflow question on fractional exponential iterations sheldonison 4 9,520 04/01/2018, 03:09 AM Last Post: JmsNxn Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 3,365 09/06/2016, 04:23 PM Last Post: tommy1729 [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 21,522 12/28/2014, 10:22 PM Last Post: MphLee Another question! JmsNxn 4 8,213 08/27/2013, 06:57 PM Last Post: JmsNxn Very curious question JmsNxn 3 7,125 08/20/2013, 08:56 PM Last Post: JmsNxn Question about curvature tommy1729 0 3,059 12/15/2012, 11:38 PM Last Post: tommy1729 (MSE) A limit- question concerning base-change Gottfried 0 4,008 10/03/2012, 06:44 PM Last Post: Gottfried Users browsing this thread: 1 Guest(s)

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By choosing I Accept, you consent to our use of cookies and other tracking technologies. # 507 Number 507 (five hundred seven) is an odd three-digits composite number and natural number following 506 and preceding 508. ## Properties of the number 507 Nominal 507 Cardinal five hundred seven Cardinalfive hundred seven Ordinal 507th Number of digits 3 Sum of digits 12 Product of digits 0 Number parity Odd Calculation was done in 0.0000431538 seconds ## Prime Factorization of 507 Prime factorization 3 x 13 x 13 Prime factorization in exponent form 3 x 132 Prime factors 3, 13 Number of distinct prime factors ω(n) 2 Total number of prime factors Ω(n) 3 Sum of prime factors 16 Product of prime factors 39 Calculation was done in 0.0000209808 seconds ## Divisors of 507 List of proper divisors 1, 3, 13, 39, 169 List of all dividers 1, 3, 13, 39, 169, 507 Number of divisors d(n) 6 Sum of all divisors σ(n) 732 Aliquot sum 225 507 is a deficient number , since it is larger than the sum of its proper divisors (225). Its deficiency is 282. Calculation was done in 0.0000169277 seconds ## Prime numbers Is 507 a prime number? No Is 507 a semiprime number? No Is 507 a Chen prime number? No Is 507 a Mersenne prime number? No Calculation was done in 0.0000531673 seconds ## Sequences Is 507 a Catalan number? No Is 507 a Fibonacci number? No Is 507 a Idoneal number? No Calculation was done in 0.0000040531 seconds ## Number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. 507 is not a Happy number 507 is not a Humble number 507 is not a Münchhausen number 507 is not a Perfect number 507 is not a Perfect square 507 is not a Palindrome Calculation was done in 0.0066950321 seconds ## Numeric Bases of 507 In mathematics, a base or radix of a numeral system is the number of unique digits, including zero, used to represent numbers in that system. BaseSystemValue 2Binary1111110112 3Ternary2002103 4Quaternary133234 5Quinary40125 6Senary22036 7Septenary13237 8Octal7738 9Nonary6239 10Decimal507 12Duodecimal36312 20Vigesimal15720 36Base36e336 60Sexagesimal8R60 Calculation was done in 0.0000250340 seconds ## Mathematical operations Mathematical operations are actions that are performed on numbers or mathematical expressions to find a numerical result. Square of 507 (n2) 257049 Cube of 507 (n3) 1.30324e+08 Square root of 507 22.5167 Natural Logarithm (ln) of 507 6.22851 Decimal Logarithm (log) of 507 2.70501 Calculation was done in 0.0000059605 seconds ## Trigonometry Trigonometry is the study of the relationship between the angles and sides of a triangle. Sine of 507 -0.933331 Cosecant of 507 -1.07143 Cosine of 507 -0.359016 Secant of 507 -2.78539 Tangent of 507 2.59969 Cotangent of 507 0.384661 Calculation was done in 0.0000140667 seconds ## Number parity Parity is the property of an integer of whether it is even or odd. No ### Is 507 an Odd Number? Yes, the number 507 is an odd number. Total number of all odd numbers from 1 to 507 is 254 Sum of all the odd numbers from 1 to 507 are 64516 The sum of all odd numbers is a perfect square: 64516 = 254 An odd number is any integer (a whole number) that cannot be divided by 2 evenly. Odd numbers are the opposite of even numbers. Calculation was done in 0.0000081062 seconds ## Ban number In recreational mathematics, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned". The spelling of 507 in words is "five hundred seven", meaning that: 507 is an aban number (a number without the letter a) 507 is not an eban number (as it contains the letter e) 507 is not an iban number (as it contains the letter i) 507 is an oban number (a number without the letter o) 507 is a tban number (a number without the letter t) 507 is not an uban number (as it contains the letter u) Calculation was done in 0.0000040531 seconds ## Numeral systems How to write 507 in other number systems? Bengali numerals ৫০৭ Eastern Arabic numerals ٥٠٧ Hieroglyphs numeralsused in Ancient Egypt 𓍦𓐀 Khmer numerals ៥០៧ Japanese numerals 五百七 Roman numerals DVII Thai numerals ๕๐๗ Calculation was done in 0.0000910759 seconds ## Translation How do you say 507 in 38 different languages? Arabic خمسة مائة و سبعة Croatian petsto sedam Czech pět set sedm Danish fem hundrede syv Dutch vijfhonderd en zeven Estonian alafa atɔ̃ kple adre Faroese fimm­hundrað­og­sjey Filipino limáng daán at pitó Finnish viisi­sataa­seitsemän French cinq cent sept Greek πεντακόσια επτά German fünf­hundert­sieben Hebrew חמש מאות ושבע Hindi पाँच सौ सात Hungarian öt­száz­hét Icelandic fimm­hundrað og sjó Indonesian lima ratus tujuh Italian cinquecentosette Japanese 五百七 Korean 오백칠 Latvian piecsimt septiņi Lithuanian penki šimtai septyni Norwegian fem hundre og sju Persian پانصد و هفت Polish pięćset siedem Portuguese quinhentos e sete Romanian cinci sute şapte Russian пятьсот семь Serbian петсто седам Slovak päť­sto sedem Slovene petsto sedem Spanish quinientos siete Swahili mia tano na saba Swedish femhundrasju Thai ห้า​ร้อย​เจ็ด Turkish beş yüz yedi Ukrainian пʼятсот сім Vietnamese năm trăm lẻ bảy Calculation was done in 0.0181081295 seconds ## Miscellaneous Number 507 reversed 705 Unicode Character U+01FB ǻ Hexadecimal color (shorthand) #550077 Unix Timestamp Thu, 01 Jan 1970 00:08:27 +0000 Calculation was done in 0.0000281334 seconds

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# How to Convert Metric Bars to Psig? Bars and pounds per square inch gauge are measures of pressure. Bars, sometimes called metric bars, can be abbreviated "b." Pounds per square inch gauge, which measures the difference between the p... Read More » http://www.ehow.com/how_8196622_convert-metric-bars-psig.html Top Q&A For: How to Convert Metric Bars to Psig ## How to Convert an Mpa to a Psig? "MPa" stands for megapascals, a unit of measurement for pressure. One pascal equals one newton of force per square meter. The prefix "mega" means million, and one megapascal equals 1,000,000 pascal... Read More » http://www.ehow.com/how_6530063_convert-mpa-psig.html ## How to Convert Metric to Lb.? The metric system of weights and measures has spread worldwide since it originated during the French Revolution. Its easy-to-handle decimal basis has long supplanted those awkward 12-inch feet and ... Read More » http://www.ehow.com/how_8297480_convert-metric-lb.html ## How to Convert Between Metric & Others? Units in the metric system of measurement are based on powers of 10. Base units -- such as meters for distance, liters for volume and grams for mass -- are used to derive larger and smaller units; ... Read More » http://www.ehow.com/how_8275560_convert-between-metric-others.html ## How to Convert Minutes to Metric? When using metric time, a normal 24-hour day only consists of 10 metric hours. Just like any other measurement in the metric system, each unit is broken into multiples of 10 of the next smaller uni... Read More » http://www.ehow.com/how_8224633_convert-minutes-metric.html Related Questions

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# Which of these is an example of a literal equation Which of these is an example of a literal equation? A. 4x + 7 = 22 B. 5+ 20 = 52 C. ax – by = k D. 2x + 7y

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Teacher2Teacher Q&A #6276 Use of matrices in transformation T2T || FAQ || Teachers' Lounge || Browse || Search || T2T Associates || About T2T View entire discussion [<<prev] [next>>] From: Pat Ballew (for Teacher2Teacher Service) Date: May 06, 2001 at 17:26:17 Subject: Re: Use of matrices in transformation Ghania, If a 2x2 transformation matrix is used to multiply a series of N points written in a 2xN matrix, the only way I can think of that it will map the entire x-y plane to a common point is if the transformation matrix is a zero matrix. If the matrix is dependent (i.e. the second row is a linear multiple of the first) then it will map all points on the plane to a common line. For example, I can map any point x,y to a point 1x+2y, 2x+4y but it is easy to see that 2x+4y is 2(x+2y) and so the y coordinate will always be twice the x-coordinate, and the point will fall on the line y=2x. It is easy to see this from the original first row of the transformation matrix. If the transformation is being applied to a set of points which determine a closed polygon, the determinant of the transformation matrix will also provide clues about the area dilation of the image, as well as orientation. If the determinant is negative, the orientation of the image is the opposite of the original (clockwise or counter-clockwise). The magnitude of the determinant gives the ratio of the areas of the image to pre-image. Hope that helps. -Pat Ballew, for the T2T service Teacher2Teacher - T2T ®

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Hello, Guest! BECOME A MEMBER FOR AN AD FREE EXPERIENCE! Craig Turner died at age 59 on July 3rd, the same date as Richard Swift of The Black Keys, whose frontman is Dan Auerbach. 59 appears to be a number stamped on black celebrities quite often. “Negro”, “Slave”, and “Blues” all sum to 59 in Ordinal. “Five” and “Nine” are the only two numbers to have Ordinal gematria of 42. “Nigger” = 42 (R) In numerology, 109 reflects the number 19. There are 19 years in the Moon’s Metonic cycle, which represents death and rebirth. He died on a date with 19 numerology: The 19th prime number is 67 So it’s interesting they’re calling this an apparent suicide Craig Turner passed away on July 3rd, the date written 7/3 In the Reverse order, Craig Turner sums to 163 163 is the 38th prime number He died 308 days after his birthday: 308 days is exactly 44 weeks The 65th prime number is 313. He died a span of 31 weeks, 3 days after his mother Tina’s birthday: It was also 20 weeks, 6 days before her birthday. He died in Studio City, California on the 184th day of the year: Something else interesting about this – there seems to be some sort of 219 riddle in play. 2×19 = 38, our number for death and killing, and “Two hundred nineteen” = 218 (O), like how “Death” = 218 (EE) He died exactly 219 days after his mom Tina’s birthday. Richard Swift, who died the same day in relation to Dan Auerbach, has his origin listed as simply California, the same state Craig Turner died in. Tina Turner is 78 years old

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• Views : 40k+ • Sol Viewed : 10k+ # Mind Teasers : Picture Cipher Puzzle Difficulty Popularity Solve the picture cipher Discussion Suggestions • Views : 50k+ • Sol Viewed : 20k+ # Mind Teasers : Measuring Time Logic Puzzle Difficulty Popularity You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes. How can you do it? Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature. • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Crossing Bridge Brain Teaser Difficulty Popularity Four friends need to cross a dangerous bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge? • Views : 40k+ • Sol Viewed : 10k+ # Mind Teasers : Cool Equation Riddle Difficulty Popularity If 1 + 9 + 11 = 1, Then what is the value of 12 + 11 + 9 = ? • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Classy Age Riddle Difficulty Popularity Dean Sam and Castiel are three brothers. Interestingly their current age is prime. What's more interesting that difference between their ages is also prime. How old are they ? • Views : 50k+ • Sol Viewed : 20k+ # Mind Teasers : Logical Maths Gold Bar Brain Teaser Difficulty Popularity A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day? • Views : 50k+ • Sol Viewed : 20k+ # Mind Teasers : Popular Logical Brain Teaser Difficulty Popularity A couple had to take shelter in a hotel for they could not proceed their journey in the rain. Having nothing to do at all, they started playing cards. Suddenly there was a short circuit and the lights went off. The husband inverted the position of 15 cards in the deck (52 cards normal deck) and shuffled the deck. Now he asked his wife to divide the deck into two different piles which may not be equal but both of them should have equal number of cards facing up. There was no source of light in the room and the wife was unable to see the cards. For a certain amount of time, she thought and then divided the cards in two piles. To the husband’s astonishment, both of the piles had equal number of cards facing up. How did she do it? • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Who Are We Difficulty Popularity Without being called, we came out at night. Without being stolen, we get lost in the day. Who are we? • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Photo Riddle Brain Teaser Difficulty Popularity In the given picture, there is a fly in the wine glass depicted by the sticks. You have to remove the fly from the glass. You can move only two sticks. Also, you can’t touch the fly • Views : 50k+ • Sol Viewed : 20k+ # Mind Teasers : Statement Puzzle Difficulty Popularity Christanio Ronaldo is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days: Day 1: 'I lie on Monday and Tuesday.' Day 2: 'Today, it's Thursday, Saturday, or Sunday.' Day 3: 'I lie on Wednesday and Friday.' On which day does Christanio Ronaldo tell the truth? • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Unsolvable Problem Difficulty Popularity In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly. How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly ### Latest Puzzles 27 March ##### Unique Words Riddle What is the unique property of the below... 26 March ##### Passcode Riddle You forgot the three digit code of your ... 25 March ##### 3+3!=8 MatchStick Equation Puzzle Can you move one matchstick to make belo... 24 March ##### Harry Potter And Prisonor of Azkaban Riddle Think of a person living in a disguise 23 March ##### Popular Fill In The Blanks Puzzle A ______ Surgeon was _______ to perform ... 22 March

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How to calc. your age in days..? • 03-11-2002 Gugge How to calc. your age in days..? Does anybody have a good idea, to how the easiest way to calc you age in days. ------------------------------------code until now. int yearcalc_how_many_y, yearcalc_how_many_days; int date, month, birthyear, age; int calc_age_i_dage(int date, int month, int birthyear) { int currentyear = 2002; printf("plz key you birthday<dd>: "); scanf("%d", &date); printf("Plz key in month <mm>: "); scanf("%d", &month); printf("plz key in birthyear <yyyy>: "); scanf("%d", &birthyear); age = date+month+birthyear; yearcalc_how_many_y = (currentyear - birthyear); printf("%d",yearcalc_how_many_y); yearcalc_how_many_days = (yearcalc_how_many_y * 365)+((yearcalc_how_many_y/4)-1); printf("%d",yearcalc_how_many_days); return age; } int main() { struct date d; getdate(&d); printf("The current year is: %d\n", d.da_year); printf("The current day is: %d\n", d.da_day); printf("The current month is: %d\n", d.da_mon); calc_age_i_dage(date, month, birthyear); printf("Age: %d", age); getch(); return 0; } /* Which year is leap year. <2000>-1996-1992-1988-1984-1980-1976-1972-1968-1964-1960-1956-1952-1948 Year 2000 didn't count, because, year which divides with 400 is not a leap year */ • 03-11-2002 Prelude What kind of precision do you need? If it doesn't matter then just multiply the age in years by the number of days in a standard year. -Prelude • 03-11-2002 ygfperson imho, your program's flawed. scrap it, and think up a new one. try to limit your variables as much as possible • 03-11-2002 quzah You can simplify this, as Prelude stated: days_alive = (int)(365.25 * years_alive); Actually, you could also use standard 'time' functions and do a bit of subtraction also... Quzah. • 03-11-2002 Gugge yes prob, but is that precis enough, it's has to be 99% correct.. • 03-12-2002 quzah > yes prob, but is that precis enough, it's has to be 99% correct.. If it only hast to be 99% correct, you don't even have to bother using .25 on the end. Hell, you can bee over 3 days off PER YEAR Quzah. • 03-12-2002 Prelude >yes prob, but is that precis enough, it's has to be 99% correct.. 99% correct in this context is way off and gives you a lot of breathing room. Calculate the current number of days that have passed in the current year then just totalDays = ( totalYears - 1 ) * 365 + currentDays; and you'll still be very accurate without having to bother with leap year and all of that junk. The hardest part will be counting the days that have passed in the current year, which should tell you how easy this can be. ;) -Prelude • 03-13-2002 Carlos My opinion is: if you do something, then do it right. If the algorythm you're using is not 100% accurate, well, don't call it algorythm.

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Algebra Tutorials! Friday 2nd of December Home Exponential Decay Negative Exponents Multiplying and Dividing Fractions 4 Evaluating Expressions Involving Fractions The Cartesian Coordinate System Adding and Subtracting Fractions with Like Denominators Solving Absolute Value Inequalities Multiplying Special Polynomials FOIL Method Inequalities Solving Systems of Equations by Graphing Graphing Compound Inequalities Solving Quadratic Equations by Completing the Square Addition Property of Equality Square Roots Adding and Subtracting Fractions The Distance Formula Graphing Logarithmic Functions Fractions Dividing Mixed Numbers Evaluating Polynomials Power of a Product Property of Exponents Terminology of Algebraic Expressions Adding and Subtracting Rational Expressions with Identical Denominators Solving Exponential Equations Factoring The Difference of 2 Squares Changing Fractions to Decimals Solving Linear Equations Using Patterns to Multiply Two Binomials Completing the Square Roots of Complex Numbers Methods for Solving Quadratic Equations Conics in Standard Form Solving Quadratic Equations by Using the Quadratic Formula Simplifying Fractions 2 Exponential Notation Exponential Growth The Cartesian Plane Graphing Linear Functions The Slope of a Line Finding Cube Roots of Large Numbers Rotating Axes Common Mistakes With Percents Solving an Equation That Contains a Square Root Rational Equations Properties of Common Logs Composition of Functions Using Percent Equations Solving Inequalities Properties of Exponents Graphing Quadratic Functions Factoring a Polynomial by Finding the GCF The Rectangular Coordinate System Adding and Subtracting Fractions Multiplying and Dividing Rational Expressions Improper Fractions and Mixed Numbers Properties of Exponents Complex Solutions of Quadratic Equations Solving Nonlinear Equations by Factoring Solving Quadratic Equations by Factoring Least Common Multiples http: Solving Exponential Equations Solving Linear Equations Multiplication Property of Equality Multiplying Mixed Numbers Multiplying Fractions Reducing a Rational Expression to Lowest Terms Literal Numbers Factoring Trinomials Logarithmic Functions Adding Fractions with Unlike Denominators Simplifying Square Roots Adding Fractions Equations Quadratic in Form Dividing Rational Expressions Slopes of Parallel Lines Simplifying Cube Roots That Contain Variables Functions and Graphs Complex Numbers Multiplying and Dividing Fractions 1 Composition of Functions Intercepts of a Line Powers http: Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10 Factoring Trinomials Exponents and Polynomials Decimals and their Equivalent Fractions Negative Integer Exponents Adding and Subtracting Mixed Numbers Solving Quadratic Equations Theorem of Pythagoras Equations 1 Subtracting Fractions Solving Quadratic Equations by Graphing Evaluating Polynomials Slope Angles and Degree Measure Try the Free Math Solver or Scroll down to Tutorials! Depdendent Variable Number of equations to solve: 23456789 Equ. #1: Equ. #2: Equ. #3: Equ. #4: Equ. #5: Equ. #6: Equ. #7: Equ. #8: Equ. #9: Solve for: Dependent Variable Number of inequalities to solve: 23456789 Ineq. #1: Ineq. #2: Ineq. #3: Ineq. #4: Ineq. #5: Ineq. #6: Ineq. #7: Ineq. #8: Ineq. #9: Solve for: Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg: root features of ti-83 Related topics: greatest polar equations | algebra with pizzazz!- creative publications | ask dr. math video game +algerbra | trinomial calculator | free online intermediate algebra for dummies | a quadratic equation in baseball | solving fraction problem calculation | mathematics exercisese sseven grade | absolute value worksheets | on line maths test papers for year 10-11 Author Message seroaletj Registered: 13.08.2005 From: Posted: Thursday 28th of Dec 17:16 Can someone help me with my assignment questions ? Most of them are based on root features of ti-83. I have read a few articles on equivalent fractions and ratios but that didn’t go a long way helping me in finding solutions to the questions on my homework . I didn’t sleep last night since I have a deadline to meet . But the problem is no matter how much time I invest, I just don’t seem to be getting the hang of it. Every question poses a new challenge, one which seems to be tougher than climbing Mt.Everest! I need some help as soon as possible. Somebody please guide me. oc_rana Registered: 08.03.2007 From: egypt,alexandria Posted: Friday 29th of Dec 17:18 Algebrator is a good software to solve root features of ti-83 questions. It gives you step by step solutions along with explanations. I however would warn you not to just copy the solutions from the software. It will not help you in understanding the subject. Use it as a reference and solve the problems yourself as well. Double_J Registered: 25.11.2004 From: Netherlands Posted: Sunday 31st of Dec 08:58 Hi Dude, Algebrator assisted me with my assignments last week. I got the Algebrator from https://mathisradical.com/evaluating-expressions-involving-fractions.html. Go ahead, check that and let us know your opinion. I have even recommended Algebrator to a couple of my friends at college. Baohz Registered: 13.05.2002 From: gxmwt0 Posted: Monday 01st of Jan 11:01 You both have got to be joking! How could this software not be overall information or published in periodicals? Where could I acquire additional data for testing Algebrator? Pardon one for being a bit skeptical , but do you know whether or not one can find a trial copy to apply this ? sxAoc Registered: 16.01.2002 From: Australia Posted: Wednesday 03rd of Jan 08:10 Gools Registered: 01.12.2002 From: UK Posted: Thursday 04th of Jan 10:12 I am a regular user of Algebrator. It not only helps me finish my homework faster, the detailed explanations given makes understanding the concepts easier. I strongly recommend using it to help improve problem solving skills.

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or or taken why Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account. Don't know Know remaining cards Save 0:01 Flashcards Matching Hangman Crossword Type In Quiz Test StudyStack Study Table Bug Match Hungry Bug Unscramble Chopped Targets Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page. Normal Size     Small Size show me how # prop of cong. and eq ### Properties of congruence and equality If a = b, then a+b=b+c Addition property of Equality If a = b, then a-c=b-c Subtraction property of Equality If a = b, then ac = bc Multiplication Property of Equality If a = b, then a/c = b/c provided c not 0 Division Property of Equality a = a Reflexive property of Equality If a = b and b = c, then a = c Transitive Property of Equality If a = b, then b = a Symmetric Property of Equality If a = b and x+a = c, then x+b = c Substitution Property of Equality Angle A is congruent to Angle A Reflexive property of Congruence If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C Transitive Property of Congruence If angle A is congruent to angle B then angle B is congruent to angle A Symmetric Property of Congruence Created by: jbenecke

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# Microcontroller self-shutdown with MAX682 I have read How to implement a soft power switch controllable by microcontroller? and am wondering if something similar would be possible with a MAX682. What I want, is a device that is turned on by pressing a single button, and that turns itself off. I'm using a PIC16F88, but because my battery has 3.6V and I need to drive a 5V LCD, I'm using the MAX682 to step this up. The problem is that according to the datasheet, the /SHDN pin of the MAX682 should be connected via a resistor to its input voltage. What I would suggest is using its output voltage as an input for /SHDN, like this (only relevant pins are shown): simulate this circuit – Schematic created using CircuitLab When the user wants to start the device up, he presses the button to activate the MAX682 and thus the PIC (R1 is required for the MAX682). The PIC is programmed so, that it directly puts high on P1. R2 and R3 form a voltage divider to make 3.6V (I didn't calculate them yet). R4 has then the same function as R1, and makes sure that the MAX682 keeps running. When the PIC wants to shut itself down, it pulls P1 to ground and the MAX682 shuts down. Would this work, or would the MAX682 have problems if the /SHDN pin isn't connected to IN? And if it would work, could I also remove R4 and connect the 'output' of the voltage divider to the point between SW1 and R1, to save a resistor? I don't think there is a problem with $\mathsf{\small \overline{\text{SHDN}}}$ not being connected to IN, the voltage level just sets the operating frequency based on the current going into the pin. If you want to get rid of the resistor R4, you will have to calculate the voltage divider resistors such that you get the desired current going into the $\mathsf{\small \overline{\text{SHDN}}}$ lead when the microcontroller is on. Note: there will be a brief time when the switch is activated and the PIC is on, meaning the current going into $\mathsf{\small \overline{\text{SHDN}}}$ will double affecting the oscillator frequency because the resistance is cut in half. I don't see an easy way around that. But make sure the calculation of the resistance is such the two frequencies for R and R/2 are both within the range specified in the datasheet (50KHz - 2MHz). I would add a fairly hefty capacitor (10 µF or more) to the line going from the MAX682 into the Vdd input of the PIC. This will even out any disturbances when the switch is release and the oscillator frequency changes. Also, don't forget 100 nF decoupling caps on all power inputs. • You are right, I was too lazy to add all capacitors to this circuit, but the MAX682 datasheet prescribes 47uF. Good point about the 'double input' time, thanks! – user17592 Oct 19, 2014 at 21:59 • On second thought, when we'd remove R4 as suggested, the current going into /SHDN wouldn't be doubled anymore, right? Should I add diodes between the switch and R1 and between the voltage divider and R1, to make sure no current can flow from the battery to the voltage divider or vice versa? – user17592 Oct 20, 2014 at 11:31 • @CamilStaps Re the voltage divider resistor values, that's why I said in my answer you would have to recalculate everything. I don't think it matters it comes out exactly the same. I think the diodes are a good idea. Oct 20, 2014 at 12:03 • For reference: I checked this now and it works fine. I used R1=100K, R2=39K, R3=300K (2x150K) which works fine - at least with the 2mA this circuit draws. I used two simple 1N4148's, and I didn't use R4 but applied the voltage divider's output to R1, as discussed. Thanks again! – user17592 Oct 20, 2014 at 17:42

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# Math Quiz Question for Class 1 Students, Kids Grade 1 Math Quiz Question for Class 1 Students, Kids Grade 1 GK: Worried about your kid’s study that are studding in Class 1 Or looking for the Math quiz question answers practices set for class 1 Kids/students. Here we will help you in your kids Math subjects study. Here we have updated number of Math Quiz question answers for Class 1 kids/Students which are almost in the subjects of various public schools. In this section you will find Class 1 Math Quiz Question answers or practice sets which include Number Counting, Addition, Subtraction, Grater than (>), Less Than (<) or Equals to (=) sign, Ascending and Descending order, Ordinal Numbers, dodging table, Missing Number etc. Scroll down the web post to get same Math Quiz for Class 1 Kids/Students Math Quiz Question for Class 1 Students, Kids Grade 1 GK Below of the post important links of GK Quiz for Class 1 Students are provided. Which is based on Computer, Science and English Subjects ## Math’s Multiple Choice Question for Grade 1 Students, Kids Key Point: If you are going to teach addition to your kids or students use a simple method that will easily understood by your kids or students. Applying below mention steps you can easily teach Whatever the number you have draw a vertical line in front of number i.e. if number is 5 then draw five vertical line i.e. ||||| and then draw the same line for second number.  At last count all the vertical line and that will be the answer Question: Subtraction Question Answer (Subtract the below given number) Key point: Apply the same method that we mention in addition section.  But in subtraction cut the lines whatever number you have from the below mention number. Question: Put the Grater than (>), Less Than (<) or Equals to (=) sign between below mention number Note: These questions will help the students to find out which number is larger and smaller as compare to other given number. Students will also identify which numbers are equal also Question: Write the following number in Ascending Order Example: Question: Write the following number in Descending Order Example: Question: Fill in the blanks with correct number Number Counting Quiz, Missing Number, After, Before, Between Number Math Quiz Question: Which number comes after the following mention numbers? Question: Which number comes before the following mention numbers? ### Important First Grade Math Quiz Question Question: What number comes between the following numbers? Question: Write the following number in word Example:  Mention Below PRACTICS SET Question: Write the Missing Numbers Question: Write the dodging table Dodging table will be random number table that will sharps the kids mind. Question: Write Ordinal Numbers #### Math Quiz for Grade 1 Students| Class 1 Math Quiz Question Practices Set 1: Number Counting Question: Write Reverse Counting from 10 to 1 Question: Write Reverse counting from 50 to 1 Question: Write Reverse counting from 100 to 50 Question: Write Reverse counting from 100 to 1 Practice Set 2: Learn Tables Learn the table of Two Lean the table of Three Learn the table of Four Learn the table of Five Practice of writing dodging table Practice of abacus number

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https://forum.smallgiantgames.com/t/wilbur-and-quintus-special-combo/124925

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# Wilbur and Quintus Special Combo? So I have recently shared to use a new team and I’ve decided to use both Wilbur and Quintus, until I realized that Wilbur’s ability shares the damage of all enemies between them. This is what I need to figure out So with Quintus he currently deals 245% damage to all enemies which is great but if I use this with Wilbur what will happen? As the damaged will be shared will it hit and split to 49% each X5 for each enemy? So kinda what I am trying to say is using Wilbur then Quintus will it reduce his overall damage due to the shared damage I hope this makes sense 1 Like Each hit of 245% will be split between all enemies. The damage will be the same across enemies before the added damage from wilbur’s def down. The damage won’t be reduced due to shared damage, it will be even out across all enemies. Imagine you first use Wilbur special and then Quintus special. Because of Quintus special (and if shared damage is not apllied) damage could be (I’m making up numbers): Enemy 1: 500 damage Enemy 2: 400 damage Enemy 3: 300 damage Enemy 4: 200 damage Enemy 5: 100 damage But since shared damage is active, it will be 500 / 5 = 100 damage each enemy 400 / 5 = 80 damage each enemy 300 / 5 = 60 damage each enemy 200 / 5 = 40 damage each enemy 100 / 5 = 20 damage each enemy Add all and you will have 100 + 80 + 60 + 40 + 20 = 300 damage each enemy So 1500 damage total, which is the same than adding all five initial damages without sharing. Would he be useful in this team eg a team that mainly focuses on attacking all or does he really make no difference Good explanation, but in case 2 with Wilbur’s special active, the total damage inflicted will be greater because of the -44% defense the enemies now have… so it’s a good combo I think. I also like to combine AoE hitters with Wilbur, or try to have dispel ready to remove the enemy’s shared damage. In the current rush attack raid tournament, I’m using Wilbur and Little John together in most attacks, a great combo also… especially with LJ’s mana slowing effect. 1 Like Quintus is a slow hero with high AOE damage and lowish defense and HP stats. Even at 4/80, 90% of the cases he goes down without casting. At 1/45 the chances to cast his special are close to zero… Wilbur may help in keeping him alive a little bit longer, but coordinating Quintus’ special within four turns of Wilbur’s, will be extremely difficult for that team… Same goes for Hu Tao… Slow heroes in wing positions rarely get to cast their special. 1 Like Ah yes to @Ian487’s point, I should clarify there is a big difference between offense and defense, I was thinking about offense more… that’s where I find Wilbur most useful anyway, and you have better control over who fires when of course. I agree on defense it’s going to be a little bit different, and yes it will be hard to charge the slow mana guys in the wing positions. Also you’d want Wilbur to be on their left to fire first, in case multiple heroes have their specials charged at the same time. Also, while I like reflect, the Boril’s effect will be diminished to some degree by Wilbur’s defense boost… maybe not the best synergy there. I think I would choose either Wilbur as a tank, or Boril, and not have both on the same team. Their positioning is just temp I am yet to use the temp so it can be changed is there anyone you would suggest over Boril Kiril could be good since you don’t have a healer in that lineup… except Kiril’s defense boost would overwrite the higher defense boost from Wilbur, which can be a downside but IMHO not a super huge one. If you don’t mind color stacking (which on defense, I only like to do normally with the flanks in the contrasting color behind the tank), then actually Boldtusk pairs nicely with Wilbur also.

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https://www.physicsforums.com/threads/link-between-quantummechanical-probabilistics-and-entropy.540018/

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# Link between quantummechanical probabilistics and entropy Gold Member ## Main Question or Discussion Point I am an amateur on physics. Lately I have been thinking about this: Is there a link between quantummechanical probabilistics and entropy? I can put it into words like this: "Entropy: The greatest possible chance that outcomes even out (are as similar as possible)." For instance: The chance that an off-axis polarized photon passes the filter. Sometimes it does, sometimes it doesn't, but take a large number of measurements, and the correlation between angle and probable pass-through are inexcapable. I don't know very much about thermodynamics, but I figured that pressure in a closed box with gas also 'evens out' due to entropy (the particles becomes evenly spread), so that the probability a particle has a specific momentum becomes as great as possible. Similar, the probability a photon passes the filter is directly proportional to the angle of the filter, so the proportion of particles that pass to those blocked is 'evenly spread'... (grosso modo, each photon 'behaves' similar, or at least, becomes more statistically probable to do so...) Does this make the tinyest bit sense? I hope you can forgive me my poor english. Last edited: ## Answers and Replies Related Quantum Physics News on Phys.org Staff Emeritus 2019 Award First, I don't see why we need a different definition of entropy than what is in the textbooks. Second, there is no tendency for outcomes to "even out". Every trial is independent of previois trials. Gold Member Every trial is independent of previois trials. First, I don't see why we need a different definition of entropy than what is in the textbooks. I was thinking there might be a correlation between outcomes of different measurements, like in quantumentanglement, a way of nature to compensate information that occurs in one part in the universe, in the other part of it, so that the independent appearance of outcomes is just an illusion. I am not sure if I state this correctly: Of all the states of a given system, the one with the highest entropy is the most likely one. I feel my knowledge falls short here :tongue: I will try to catch up a bit. Last edited:

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https://locke-movie.com/2022/10/15/how-is-density-related-to-vapor-pressure/

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# How is density related to vapor pressure? ## How is density related to vapor pressure? Higher density decreases vapor pressure. The denser the condensed phase, the stronger the intermolecular forces that hold the substance together, so the less easily the surface particles can vaporize. Hence, the vapor pressure above the liquid decreases for increasing liquid density. How do you calculate the density of water vapour? It can be used to calculate exact quantity of water vapor in the air from a relative humidity (RH = % local air humidity measured / local total air humidity possible ) Given an RH percentage, the density of water in the air is given by RH × SVD = Actual Vapor Density. ### What is the density of water vapor kg m3? 0.013 kg/m3 Hence the specific humidity corresponding to these atmospheric conditions is 0.0107 kg/kg, which says that the water vapor makes up about 1% of the moist air by weight. Hence the vapor density is 0.013 kg/m3. How are pressure density and temperature related? Density and pressure/temperature Density is directly proportional to pressure and indirectly proportional to temperature. As pressure increases, with temperature constant, density increases. Conversely when temperature increases, with pressure constant, density decreases. ## How do you find the density of water with temperature and pressure? The formula can be rewritten as: c = √(γ * p / ρ) , where γ is the adiabatic index, p is pressure, and ρ is the density of air. For most liquids, the relationship is usually not that simple, but in general, the speed of sound in the water rises when the density decreases over a wide range of temperatures. How is VPD calculated? To Get VPD, we need to subtract the actual vapour pressure of the air from the saturated vapour pressure (VPsat – VPair). And VOILA, you have VPD. Now it’s time to consult the VPD chart and your plants’ ideal growing temperature range to see if your VPD is within a correct range and your plant is transpiring healthily. ### What is the relationship between temperature and density of water? Temperature Affects Density When the water is heated, it expands, increasing in volume. This is represented by the increase in the size of the box from Fig. 2.2 A to 2.2 C. The warmer the water, the more space it takes up, and the lower its density. What is the relationship between temperature density and pressure? Density and pressure/temperature Density is directly proportional to pressure and indirectly proportional to temperature. As pressure increases, with temperature constant, density increases. ## How does density change with temperature and pressure? Density is directly proportional to pressure and indirectly proportional to temperature. As pressure increases, with temperature constant, density increases. Conversely when temperature increases, with pressure constant, density decreases. How does the density of water change with pressure? Density increases when pressure increases and decreases when pressure decreases. As pressure increases, the molecules of a substance come closer resulting in a higher density. ### Does vapour density depend on temperature? The temperature of a gas depends on volume, rates of diffusion and pressure. But vapour density is the density of a gas relative to that of hydrogen at the same temperature is known as the vapour density of the gas. Thus, vapour density is independent of temperature. Therefore, the correct answer is Option C. Does vapor pressure depend on temperature? The vapor pressure of a liquid varies with its temperature, as the following graph shows for water. The line on the graph shows the boiling temperature for water. As the temperature of a liquid or solid increases its vapor pressure also increases. Conversely, vapor pressure decreases as the temperature decreases. ## What is the VPD chart? A VPD chart is a visual representation of how relative humidity and temperature interact to provide an environment for your plants. Normally relative humidity is shown horizontally and temperature vertically. What is good VPD? A VPD range of 0.8–1.1 (kPa) is commonly known as ideal in the vegetative stage, while a VPD range of 1.0–1.5 (kPa) is commonly known as ideal in the flowering stage. ### How does pressure effect the density of water? – What happens to density if pressure increases? – Increases p~ P (Boyle’s Law) – What happens to density if temperature increases? – Decreases p~ 1/T (Charle’s Law) – What happens to pressure if temperature increases? – Increases P ~ T (Gay-Lussac’s Law) – Putting all 3 together, we have P ~ p×T What are the effects of temperature on the density of water? Temperature Affects Density. The density of water can also be affected by temperature. When the same amount of water is heated or cooled, its density changes. When the water is heated, it expands, increasing in volume . ## How can a temperature change affect the density of water? The density of water at 40C is maximum and it is in liquid state at this temperature. • Icebergs float on water but 90% volume of an iceberg remains underwater. • The “competition” between hydrogen bond formation and thermal motion of water molecules is the reason behind the maximum density of water at 40C. • Do different temperatures affect water density? Temperature Affects Density. The density of water can also be affected by temperature. When the same amount of water is heated or cooled, its density changes. When the water is heated, it expands, increasing in volume. This is represented by the increase in the size of the box from Fig. 2.2 A to 2.2 C.

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# Osmosis Lab ```OSMOSIS LAB Osmosis: the movement of water molecules from a region of lower solute concentration to a region of higher solute concentration. SOLUTION CONCENTRATIONS:  Isotonic: two solutions have the same concentration of solutes. (iso- same, toncondition, -ic pertaining to) Two solutions of different concentration:  The one with more solute is hypertonic to the solution with less solute. (hyper- more than)  The solution that has less solute is hypotonic to the one with more solute. (hypo- less than) Semi-permeable membrane IN WHAT DIRECTION WILL NET H2O MOVEMENT OCCUR? SET UP:  Six dialysis tubing bags are filled with (15-25mL) six solutions of differing sucrose concentrations and placed in beakers of distilled water.       0M 0.2M 0.4M 0.6M 0.8M 1.0M Sucrose solution Distilled water Reminder: Molarity (M) = mol/L ex. 1 mole of sucrose per liter of water = 1.0M  RQ: HOW DOES THE MOLARITY OF A SOLUTION EFFECT THE RATE OF OSMOSIS THROUGH A SEMI PERMEABLE MEMBRANE? Independent Variable:  Dependent Variable:  PREDICTIONS? Change Initial Final Contents in Dialysis Bag in Mass Mass (g) Mass (g) (g) a) 0M (distilled water) 26.0 b) 0.2M sucrose 26.2 c) 0.4M sucrose 26.1 d) 0.6M sucrose 26.4 e) 0.8M sucrose 26.3 f) 1.0M sucrose 26.4 RESULTS: Contents in Dialysis Bag Initial Final Mass Change in Mass (g) (g) Mass (g) a) 0M (distilled water) 26.0 26.3 0.3 b) 0.2M sucrose 26.2 27.0 0.8 c) 0.4M sucrose 26.1 28.1 2.0 d) 0.6M sucrose 26.4 29.3 2.9 e) 0.8M sucrose 26.3 30.2 3.9 f) 1.0M sucrose 26.4 31.2 4.8 Explain the relationship between the change in mass and the molarity of sucrose within the dialysis tubing bag. RELATIONSHIP? Change in Mass vs. Molarity 6.0 Change in mass (g) 5.0 4.0 3.0 2.0 1.0 0.0 0 0.2 0.4 0.6 0.8 1 1.2 Molarity (M) Predict what would happen to the mass of each bag in this experiment if all the bags were placed in a 0.4M solution instead of distilled water. ``` 39 Cards Pastoralists 20 Cards Marketing 46 Cards Ethnology 14 Cards

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Upcoming SlideShare × # 1. linear power supply 9,875 views Published on 10 Likes Statistics Notes • Full Name Comment goes here. Are you sure you want to Yes No • Be the first to comment Views Total views 9,875 On SlideShare 0 From Embeds 0 Number of Embeds 9 Actions Shares 0 444 0 Likes 10 Embeds 0 No embeds No notes for slide ### 1. linear power supply 1. 1. A presentation of eSyst.org 2. 2. LINEAR POWER SUPPLYBlock diagram and functions of a transformer, rectifier, filter, voltage regulator and voltage divider.Types of rectifier, filter and regulator circuits A presentation of eSyst.org 3. 3. Power SupplyAll electronic circuits need a power source to work.For electronic circuits made up of transistors and/or ICs, this power source must be a DC voltage of a specific value.A battery is a common DC voltage source for some types of electronic equipment especially portables like cell phones and iPods.Most non-portable equipment uses power supplies that operate from the AC power line but produce one or more DC outputs. A presentation of eSyst.org 4. 4. Power Supply Characteristics The input is the 120 volt 60 Hz AC power line. The power supply converts the AC into DC and provides one or more DC output voltages. Some modern electronic circuits need two or more different voltages. A good example of a modern power supply is the one inside a PC that furnishes 12, 5, 3.3 and 1.2 volts. A presentation of eSyst.org 5. 5. Components of a Power SupplyMain circuits in most power supplies. A presentation of eSyst.org 6. 6. Transformer A transformer is commonly used to step the input AC voltage level down or up. Most electronic circuits operate from voltages lower than the AC line voltage so the transformer normally steps the voltage down by its turns ratio to a desired lower level. For example, a transformer with a turns ratio of 10 to 1 would convert the 120 volt 60 Hz input sine wave into a 12 volt sine wave. A presentation of eSyst.org 7. 7. RectifierThe rectifier converts the AC sine wave into a pulsating DC wave.There are several forms of rectifiers used but all are made up of diodes.Rectifier types and operation will be covered later. A presentation of eSyst.org 8. 8. FilterThe rectifier produces a DC output but it is pulsating rather than a constant steady value over time like that from a battery.A filter is used to remove the pulsations and create a constant output.The most common filter is a large capacitor. A presentation of eSyst.org 9. 9. RegulatorThe regulator is a circuit that helps maintain a fixed or constant output voltage.Changes in the load or the AC line voltage will cause the output voltage to vary.Most electronic circuits cannot withstand the variations since they are designed to work properly with a fixed voltage.The regulator fixes the output voltage to the desired level then maintains that value despite any output or input variations. A presentation of eSyst.org 10. 10. How Rectifiers Work The simplest form of rectifier is the half wave rectifier shown. Only the transformer, rectifier diode, and load (RL) are shown without the filter and other components. The half wave rectifier produces one sine pulse for each cycle of the input sine wave. When the sine wave goes positive, the anode of the diode goes positive causing the diode to be forward biased. The diode conducts and acts like a closed switch letting the positive pulse of the sine wave to appear across the load resistor. A presentation of eSyst.org 11. 11. How Rectifiers Work (continued) When the sine wave goes negative, the diode anode will be negative so the diode will be reverse biased and no current will flow. No negative voltage will appear across the load. The load voltage will be zero during the time of the negative half cycle. See the waveforms that show the positive pulses across the load. These pulses need to be converted to a constant DC. A presentation of eSyst.org 12. 12. Bridge Rectifier Another widely used rectifier is the bridge rectifier. It uses four diodes. This is called a full wave rectifier as it produces an output pulse for each half cycle of the input sine wave. On the positive half cycle of the input sine wave, diodes D1 and D2 are forward biased so act as closed switches appearing in series with the load. On the negative half cycle, diode D1 and D2 are reverse biased and diodes D3 and D4 are forward biased so current flows through the load in the same direction. A presentation of eSyst.org 13. 13. How the Filter Works A large capacitor is connected across the load resistor. This capacitor filters the pulses into a more constant DC. When the diode conducts, the capacitor charges up to the peak of the sine wave. Then when the sine voltage drops, the charge on the capacitor remains. Since the capacitor is large it forms a long time constant with the load resistor. The capacitor slowly discharges into the load maintaining a more constant output. The next positive pulse comes along recharging the capacitor and the process continues. A presentation of eSyst.org 14. 14. The RegulatorMost regulators are ICs .These are feedback control circuits that actually monitor the output voltage to detect variations.If the output varies, for whatever reason, the regulator circuit automatically adjusts the output back to the set value.Regulators hold the output to the desired value.Since ripple represents changes in the output, the regulator also compensates for these variations producing a near constant DC output. A presentation of eSyst.org 15. 15. RC pi Filterii) RC pi Filter•C1 performs the same function that it didin the single capacitor filter. It is used toreduce the percentage of ripple to arelatively low value.•C2 offers infinite impedance (resistance)to the dc component of the outputvoltage. Thus, the dc voltage is passed tothe load, but reduced in value by theamount of the voltage drop across R2.However, R2 is generally small compared A presentation of eSyst.orgto the load resistance. Therefore, the drop 16. 16. RC pi Filter• C2 offers very low impedance to the ac ripple frequency. Thus, the ac ripple senses a voltage divider consisting of R2 and C2 between the output of the rectifier and ground. Therefore, most of the ripple voltage is dropped across R2.• The RC filter has some disadvantages, however. First, the voltage drop across R2 takes voltage away from the load. Second, power is wasted in R2, R1 and is dissipated in the form of unwanted heat.• The input capacitor (C1) has the greatest pulsating voltage applied to it and is the most susceptible to voltage surges. As a result, it is frequently subject to voltage breakdown and shorting. The shunt capacitor (C1 and C2) in the filter circuit is not subject to voltage surges because of the protection offered by the series filter resistor. A presentation of eSyst.org 17. 17. Definition of Ripple The amount of ripple factor of the full wave rectified signal is smaller than the half wave signal and provides a better filtered signal. The amount of ripple factor of the full wave rectified signal is smaller than the half wave signal and provides a better filtered signal. 18. 18. •As is known, in an inductor filter,INPUT (L-C RL but decreases in THE CHOKE ripple increases with FILTER)a capacitor filter.•The combination of L and C filter makes the ripple independent of RL a) Shows the filter circuit. b) The voltage variation. 19. 19. •The LC input filter is one of the most commonlyused filters. CLC or Pi Filter•The input capacitor C1 is selected to offer very lowreactance to the ripple frequency. Hence, major partof filtering is done by C1. Most of the remainingripple is removed by the combined action of L andC2.•L is a large value iron-core inductor (choke.) It hasa high value of inductance and, therefore, a highvalue of XL, which offers a high reactance to theripple frequency. At the same time, C2 offers a verylow reactance to the ac ripple. L and C2 form an acvoltage divider and, because the reactance of L ismuch higher than that of C2, most of the ripple 20. 20. • Aside from the voltage divider effect, the inductor improves filtering in another way. You should recall that an inductor resists changes in the magnitude of the current flowing through it. Consequently, when the inductor is placed in series with the load, the inductor tends to hold the current steady. This, in turn, helps to hold the voltage across the load constant.• Generally, this resistance is very low and the dc voltage drop across the coil is minimal. Thus, the LC filter overcomes the disadvantages of the RC filter.• The LC filter has two disadvantages. The first is cost. The LC filter is more expensive than the RC filter because its iron-core choke costs more than the resistor of the RC filter. The second disadvantage is size, since the iron-core choke is bulky and heavy. Thus, the LC filter may be unsuitable for some applications but is still one of the most widely used. A presentation of eSyst.org 21. 21. a)ZENER DIODE AS VOLTAGE REGULATOR•A zener shunt regulator is thatthe diode dissipation is toolarge in some application. 22. 22. b) SERIAL TRANSISTOR•The way to reduce the diode zener shunt power Q β = 50dissipation is called an amplifier zener regulator. Transistor Q1 is the seriesOperation control element.•Zener diode DZ provides the reference voltage •If the output voltage decreases, the increased base-emitter voltage causes transistor Q1 to conduct more. •Thereby raising the output voltage, maintaining the outputconstant. •If the output increases, the decreased base-emittervoltage causes transistor Q1 to conduct less, reducing theoutput voltage maintaining the output constant. A presentation of eSyst.org 23. 23.  A simple regulator consists of a sampling circuit, an error amplifier, a conduction element, and a voltage reference element. The sampling regulator circuit (voltage divider) monitors the output voltage by feeding sample voltage back to the error amplifier. The reference voltage element (zener diode) acts to maintain a constant reference voltage that used by the error amplifier. The error amplifier’s output is then fed to the current-control element (transistor), which used to control the load current. 24. 24. Negative-feedback•Transistor Q1 acts like an emitter follower. voltage regulator.Transistor Q1 provides voltage gain in anegative-feedback loop.•Suppose the load voltage tries to increase. Thefeedback voltage VF will increase. Since theemitter voltage Q1 is held constant by the Zenerdiode, more collector current flows through Q1and through R3.•This reduces the current throughQ1 and R3.The higher voltage at the base of Q2 increasesthe emitter voltage of Q2, and this almostcompletely offsets the original decrease in loadvoltage. A presentation of eSyst.org 25. 25. Voltage regulator•The positive voltage regulator LM78 “xx” andnegative voltage regulator LM79xx digits representthe output voltage such as 7805 (5V), 7806 (6 V),7909 (-9V) etc.•Can handle a maximum output current of 1.5A ifproperly heat-sink.•To remove unwanted input or output spikes/noise,capacitors can be attached to the regulator’s inputand output terminals, as shown on figure above. A presentation of eSyst.org 26. 26. SIMPLE POWER SUPPLY 27. 27. In Summary All electronic circuits and equipment need a power supply, usually one that supplies are very specific DC voltage. A battery is a near perfect DC supply but it is used mainly in portable applications. Most equipment uses an AC to DC power supply. In most AC to DC supplies, the 120 volt AC line is first filtered then stepped up or down to the desired voltage level then rectified into pulsating DC, then filtered to a constant DC. A regulator holds the output to a desired level. A DC-DC converter may also be used to generate another DC voltage. The two most common rectifiers are the single diode half wave rectifier and the four diode full wave bridge rectifier.

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Game Development Reference In-Depth Information velocity, and spin rate. Further, experiments show that the drag coefficient is also affected by spin. For example, consider a golf ball struck perfectly (right!) such that the ball spins about a horizontal axis perpendicular to its direction of travel while in flight. In this case the Magnus force will tend to lift the ball higher in the air, increasing its flight time and range. For a golf ball struck such that its initial velocity is 58 m/s with a take-off angle of 10 degrees, the increase in range due to Magnus lift is on the order of 59 meters; thus, it's clear that this effect is significant. In fact, over the long history of the game of golf, people have attempted to maximize this effect. In the late 1800s, when golf balls were still made with smooth surfaces, players observed that used balls with roughened sur‐ faces flew even better than smooth balls. This observation prompted manufacturers to start making balls with rough surfaces so as to maximize the Magnus lift effect. The dimples that you see on modern golf balls are the result of many decades of experience and research and are thought to be optimum. Typically a golf ball takes off from the club with an initial velocity on the order of 76 m/ s, with a backspin on the order of 60 revolutions per second (rps). For these initial conditions, the corresponding Magnus lift coefficient is within the range of 0.1 to 0.35. Depending on the spin rate, this lift coefficient can be as high as 0.45, and the lift force acting on the ball can be as much as 50% of the ball's weight. If the golf ball is struck with a less-than-perfect stroke (that's more like it), the Magnus lift force may work against you. For example, if your swing is such that the ball leaves the club head spinning about an axis that is not horizontal, then the ball's trajectory will curve, resulting in a slice or a draw. If you top the ball such that the upper surface of the ball is spinning away from you, then the ball will tend to curve downward much more rapidly, significantly reducing the range of your shot. As another example, consider a baseball pitched such that it's spinning with topspin about a horizontal axis perpendicular to its direction of travel. Here the Magnus force will tend to cause the ball to curve in a downward direction, making it drop more rapidly than it otherwise would without spin. If the pitcher spins the ball such that the axis of rotation is not horizontal, then the ball will curve out of the vertical plane. Another trick that pitchers use is to give the ball backspin, making it appear (to the batter) to actually rise. This rising fastball does not actually rise, but because of the Magnus lift force it falls much less rapidly than it would without spin. For a typical pitched speed and spin rate of 45 m/s and 30 rps, respectively, the lift force can be up to 33% of the ball's weight. For a typical curveball, the lift coefficient is within the range of 0.1 to 0.2, and for flyballs it can be up to 0.4. These are only two examples; however, you need not look far to find other examples of the Magnus force in action. Think about the behavior of cricket balls, soccer balls, tennis balls, or ping-pong balls when they spin in flight. Bullets fired from a gun with a rifling

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# 567 as a roman numeral Here you will see step by step solution to convert 567 number to roman numeral. How to write 567 as a roman numeral? 567 as a roman numeral written as DLXVII, please check the explanation that how to convert 567 in roman number. ## Answer: 567 in roman numeral = DLXVII ### How to convert 567 in roman number? To convert the 567 to roman number simply expand the 567 from hindu-arabic number to roman numerals, then replace the all numbers of expanded form with respective roman numerals. That's how simple it is to convert in roman numeral. #### Solution for 567 to roman numeral Given number is => 567 1. After expanding 567, here we got - = 500 + 50 + 10 + 5 + 1 + 1 2. Replace all numbers in expanded form with their roman numeral. = D + L + X + V + I + I 3. After simplify the roman numeral. = DLXVII Final conclusion is - 567 = DLXVII or DLXVII = 567 Hence, the 567 is in roman numeral form written as DLXVII or DLXVII roman number written as 567.

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# Proof of Program Correctness - Loop Invariants I've been reading a book on using loop invariants and induction to prove program correctness. Then I came across the following program which got me thinking... # Specification for Cube_Root(n) Pre-Condition: $n$ is a natural number. Post-Condition: Cube_Root returns a natural number $i$ that is the cube root of $n$ or it returns $-1$ if no such root exists Cube_Root(n) i = 0 while i < n if i * i * i = n return(i) else i = i + 1 return(-1) In the book, the proof proceeds by finding a loop invariant. So for example let us define the following as our loop invariant: Loop Invariant $P(i)$: $i$ is either the natural number cube root of $n$ or $i \geq n$. The proof is then supposed to proceed by induction on $i$. So we need to prove that $P(0)$ is true, assume that $P(i)$ is true for some $i$ and then establish that if $P(i)$ is true then $P(i+1)$ is true. $P(0)$ is trivial to prove true: if $n = 0$ then $i$ is a natural number and the the cube root of $n$ otherwise $n > 0$ (since $n$ is a natural number) and hence $i < n$. However, the problem arises when you try to infer $P(i+1)$ from $P(i)$. it doesn't look like you can because if $i$ is not the cube root of $n$, it doesn't tell you anything about whether $i+1$ is or is not the cube root of $n$. So my question(s) are: 1. Has it been proven that for any program there exists a loop invariant on which you can use induction to prove the program is correct? 2. The loop invariant chosen for Cube_Root is obviously true after the loop terminates which proves that the post-condition of the program is satisfied. Hence, that proves partial correctness of the program. However, we did not need to use induction to prove that. Is that an acceptable proof? If not, how do we use induction to prove Cube_Root correct? ## Generalities Regarding your first question, the correctness of every loop (without fancy control flow!) can always be proven using a loop invariant which states all the possible values of all variables. In your case (or rather in the modification below), this loop invariant would be $$(n,i,r) \in \{(0,0,-1),(0,0,0),(1,0,-1),(1,1,-1),(1,1,1),(2,0,-1),(2,1,-1),(2,2,-1),(2,3,-1), \ldots \}.$$ Of course, this invariant isn't particularly helpful, though it can certainly be used to prove the correctness of the loop. A more delicate issue is whether we can actually express the invariant in any formal sense - when the loop always terminates as in this case, the set of possible values of the variables is certainly computable. Regarding your second question, when you're using a loop invariant you always reason by induction - that's how you know that the loop invariant is actually maintained. Consider the following problem: x, y = 0, 1 for i in range(n): x, y = y, x + y return x I claim that this program computes the $n$th Fibonacci number $F_n$. Here is a "loop invariant" that can be used to prove it: if $i = n$ then $x = F_n$. Of course, this is not really a loop invariant since you can't prove that it's maintained by the loop; an actual loop invariant is $(x,y) = (F_i,F_{i+1})$. Your suggested loop invariant is like the first example above - it's simply not a loop invariant, and in particular it's not clear how you'd prove that if the loop terminates then it holds. It might seem "trivial", but this argument doesn't constitute a formal proof. In contrast, if you use an actual loop invariant, then you can use induction to prove that the loop invariant is maintained throughout the loop, and in particular is satisfied if the loop terminates. That's more formal, and can be turned into an actual formal proof (in the sense of program verification or axiomatic logic). Whether your type of proof is acceptable or not depends on the venue. If this is a question in a course in which you're supposed to learn how to write this kind of formal proofs, then your answer isn't acceptable. In an algorithms class, it might be acceptable since the proof is "obvious". Ask your professor if in doubt. ## Specifics We now turn to the problem at hand. The idea of a loop invariant is a condition which is true throughout the loop. As you mention, the condition that you describe is only true after the loop terminates (in the return statement). Ergo, it's not the correct condition. First, let's modify the program in the following way: instead of returning $i$, let's have a variable $r$ initialized with $-1$; when $i^3 = n$, assign $r = i$ and break out of the loop. Throughout the loop one of the following is always true, assuming $n > 1$ (for $n = 0,1$ the program fails; the condition in the main loop needs to be $i \leq n$ instead of $i < n$): 1. $i^3 < n$ and $r = -1$. 2. $i^3 = n$. In this case, $r = -1$ if the loop hasn't terminated, and $r = i$ otherwise. 3. $\sqrt[3]{n} \notin \mathbb{Z}$ and $i^3 > n$ and $r = -1$. The second condition isn't quite of the usual form, and that is because usually break statements are not allowed. You can correct this by modifying the code as follows (this code also corrects the bug mentioned above): r = -1 i = 0 while i <= n and r == -1: if i*i*i == n: r = i continue else: i = i + 1 return r Now the loop invariant becomes: 1. $i^3 < n$ and $r = -1$. 2. $i^3 = n$ and $r \in \{-1,i\}$. 3. $\sqrt[3]{n} \notin \mathbb{Z}$ and $i^3>n$ and $r = -1$. Now the loop termination condition makes it clear that if $i \leq n$ then necessarily $r \neq -1$, and so by the loop invariant, $r = i$. • Hi @YuvalFilmus, thank you for responding. I had suspected that this method of proof does not allow "break" statements. However, this is a valid design pattern used by many professional programmers. Jun 12, 2013 at 18:56 • Hi @YuvalFilmus, you are right that the code needs to be rewritten. However, I'm not sure that you are allowed to rewrite a piece of code before attempting to prove its correctness. More importantly for me is the second part of my question. Is it possible to use induction on i to prove the correctness? The book seems to imply that we have to use induction... Jun 12, 2013 at 19:10 • @EggHead I answered your actual questions. As for modifying the code, if you want to use the formalism of loop invariants then you cannot have break statements; break statements can always be implemented using an extra Boolean variable. In this case I used a shortcut, but if you want to be more formal, you can just add an extra Boolean variable $b$ which is init to True, forms part of the condition of the loop, and is set to False in case of a break statement (which then functions more like the continue statement). Jun 12, 2013 at 22:03

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1. ## The numbers First full test on pool. As many of you know bought the house on short sale and pool not open or running in years. A month ago it was black, now it is cloudy. I have been adding in bleach. Tried the pool calc but I got a number way off the charts. 4.5 ppm fc 3 ppm cc 300 ta 7.5 ph 190 ch 35 cya. It is a plaster pool water temp is 60 degress thanks 2. ## The numbers I take it these results are from one of our recommended test kits ? If they are then .... With the CC of 3 and cloudy water you need to follow the SLAM process. First lower your PH a bit with acid then start the SLAM. http://www.troublefreepool.com/conte...tain-shockingl Use pool math for your dosing of acid and bleach. http://www.troublefreepool.com/calc.html 😎 3. ## Re: The numbers Originally Posted by rlefig Tried the pool calc but I got a number way off the charts. What does that mean? 4. ## Re: The numbers jbizzle, just the TA seemed to be so high. When I put in that number the fields did not populate like on other calculations. 5. ## Re: The numbers What are you trying to adjust? I just entered all of your results into PoolMath and had no problems. 6. ## Re: The numbers yes you are correct, long day of moving big rocks. Just trying to clean up the cloudiness. Will look at slam again. I think i got ascared because TA was so much higher. 7. ## Re: The numbers Yes, your TA is high, but it won't hurt anything for now. You can get it down later. For now worry about the SLAM and cleaning up the water. I would bring your pH down to 7.2 and then get started. 8. ## Re: The numbers thanks, this patio is wearing on me. But it is getting there. I plan to lay another pallet or so of brick this weekend 9. ## Re: The numbers A couple thoughts: 1) The TA test is prone to errors due to static electricity. Wipe the tip of the bottle with a damp paper towel between drops. If it did have a problem with static electricity, the drops would be smaller, which would mean more drops to get the same change, which would give an artificially high TA reading. 2) TA in itself is not harmful. You bathe in the same water, drink it, wash dishes in it. It's not critical and it's relatively easy to fix once the pool is clear. So don't sweat it. 3) Are you still dragging the bottom for leaves and muck? If the pool was black, I suspect there would have been a lot of sludge. It will burn up chlorine at an amazing rate, which slows the SLAM process. 10. ## Re: The numbers Quick number test yesterday afternoon and this morning yesterday was fc = 19 ppm cc = 1 ppm This morning it is fc = 12.5 ppm cc = 0 Watewr is still cloudy and I still have vacuuming to do. But hopefully getting there thanks everybody for all your help, it is greatly appreciated 11. ## Re: The numbers Still slamming 12. ## Re: The numbers Good morning the water is still cloudy. I have still also been scooping some leaves from bottom. Have also been brushing a lot and vacuuming some. I guess I keep SLAM-ing. here is a recent round of readings. Can CYA go down if no water is replaced? And is this length of time to get a clear pool normal? It has been looking better, but not there yet. thanks 5/9 fc = 13 ppm cc = 0 5/10 fc = 14.5 ppm cc = 0 CYA = 20 ph = 7.5 5/11 FC = 11ppm CC = 0 PH 7.5 CYA = 25 CH = 300 5/12 FC = 12.5 ppm CC = 0 13. ## Re: The numbers Your pics show a lot of improvement and it sure sounds like you are doing all the right things. I think it's time for some POP (pool Owner Patience). Your situation is not at all uncommon. Stay the course. Keep your FC up there just as you have been doing. Watch your filter psi to clean/backwash when necessary. Your getting there and doing all things correctly as nearly as I can tell. 14. ## Re: The numbers Thanks, I cleaned the cartridges this weekend as my newly purchased pressure gauge from here did show an increase from the normal 6-7 PSI up to 9. Plus I had no cleaned it all from the "black stage". I will be patient. Laying another 3 pallets of brick this weekend for the pool patio 15. ## Re: The numbers At least you can see progress! In light of your brushing the pool and bricklaying, I suggest you buy your bleach somewhere like Target, that also sells Motrin and beer. 16. ## Re: The numbers That is a great suggestion, but in MA only Liquor Stores sell beer. I do get most of my bleach at Wal-Mart. 17. ## Re: The numbers Still slamming cc's are usually 0 or .5 I am still putting in LC to keep the FC at shock 18. ## Re: The numbers Looks like you still need some SLAM time. Stay with it. It'll come around. 😎 19. ## Re: The numbers Progress! Keep up the good work! 20. ## Re: The numbers Looking better. As a newb trying to learn, I was just curious as to how much bleach you have gone through. Page 1 of 2 12 Last #### Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts •

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My Math Forum Working out the demand function ?!?!? Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance February 1st, 2017, 11:30 AM #1 Newbie   Joined: Feb 2017 From: Eastbourne Posts: 1 Thanks: 0 Working out the demand function ?!?!? So I'm having a few difficulties here.... I am currently reading Mathematics for Economics and Finance by Martin Anthony & Norman Biggs. The very first example on page 2 of chapter 1 and I am already stuck.. The example is as follows : Suppose that demand set D consists of the points (q,p) on the straight line 6q+8p = 125. Then for a given value of p we can determine the corresponding q; we simply rearrange the equation of the line in the form q=(125-8p)/6 Now I think I can grasp most of the equation, however, the part I am confused with is the 125. Where has that come from ? February 1st, 2017, 09:01 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,981 Thanks: 1027 $6q + 8p = 125$ $6q = 125 - 8p$ $q = \dfrac{125-8p}{6}$ Tags demand, function, working Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post blimper Algebra 4 August 25th, 2016 04:48 PM Pumaftw Economics 0 September 15th, 2015 04:13 AM tsl182forever8 Calculus 1 March 2nd, 2012 02:47 PM tsl182forever8 Calculus 1 March 2nd, 2012 11:48 AM Mathematica Applied Math 0 March 1st, 2012 07:58 AM Contact - Home - Forums - Cryptocurrency Forum - Top

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# How do I use Subgraph to sample the $n$ vertices of a graph with the greatest connectivity? Let $G$ be an arbitrary graph with some number of vertices $||V||$ and some number of edges $||E||$. We can use Subgraph to generate, well, a subgraph of G with the vertices we desire. However, how can I use the patt option for Subgraph (or any method) to grab the set of n vertices with the greatest degree in $G$? In other words, if we make a list Sort[VertexDegree[G]], how can we select vertices for the subgraph starting from the right-hand-side of the output list then working our way to the left? • By using Sort you will lose the whole meaning of VertexDegree: the $i^{th}$ value returned by VertexDegree corresponds to the $i^{th}$ vertex. VertexDegree will only tell you the number of connections each vertex have. – Öskå Apr 17, 2014 at 9:57 • @Öskå I just meant to use Sort to illustrate what I was trying to do do. I'd like to use something like Select I suppose? Apr 17, 2014 at 9:59 • You want to extract each Subgraph and Sort them in terms of what Sort@VertexDegree@G would yield? – Öskå Apr 17, 2014 at 10:02 • @Öskå Oh, I meant that I would like to generate subgraph consisting of the vertices with the greatest possible connectivity in the larger graph we're pulling the subgraph from. Apr 17, 2014 at 10:17 First let's take a RandomGraph: SeedRandom@1; g = RandomGraph[BarabasiAlbertGraphDistribution[10, 2], VertexLabels -> "Name", list = Reverse@SortBy[ (*{vi, vertexdegree@i}*) {{1, 7}, {2, 6}, {6, 5}, {4, 4}, {10, 2}, {9, 2}, {8, 2}, {7, 2}, {5, 2}, {3, 2}} meaning that the vertex 1 has 7 neighbours, 2 has 6 and so on. Then you can define the following function: highlightSubgraph[list_] := HighlightGraph[g, Style[Subgraph[g, # <-> _], Hue[#/VertexCount@g]], VertexLabelStyle -> {# -> {Red, Bold, 16}}, PlotLabel -> {#, #2}] & @@@ list; and plot every Subgraph: highlightSubgraph@list or plot only the first $n^{th}$: highlightSubgraph@list[[1;;3]] If you want to use a threshold you can of course highlightSubgraph@Select[list, Last@# > n &] If you only want the Subgraph the following will do: Subgraph[g, # <-> _, PlotLabel -> {#, #2}] & @@@ list[[1 ;; 3]] • Wait, why do the subgraphs have more than the three vertices? I'm looking for the subgraph (connected or not) composed of only the vertices from the output of list[[1;;3]]? Apr 17, 2014 at 11:02 • Say we have a graph with five vertices connected in linear order (v1 <--> v2 <--> v3 <--> v4 <--> v5). We then select vertices {v1, v2, v4} (in a more complex example, these would be the vertices with highest order). Finally, we make the subgraph: {v1 <--> v2, v4 unconnected}. Does this make sense? We just want to grab the 'n' highest order vertices, and then grab all the edges these higher order vertices share with one-another, and draw a "subgraph" with just these grabbed vertices and edges. Apr 17, 2014 at 12:00 • So.., you want to make a Graph out of the shared vertices/edges of the first $n^{th}$ verticies? – Öskå Apr 17, 2014 at 12:21 • One of the issue is that in the Graph I took I have no shared vertices between the 3 vertices with the greatest connectivity. See here. – Öskå Apr 17, 2014 at 13:11 • Can we just delete any unconnected vertices, or if possible, keep grabbing vertices in the order of their connectivity in the larger graph until we have a subgraph of the desired size? The latter suggestion sounds maybe too hard, so I'd be fine with just deleting unconnected vertices. Apr 17, 2014 at 13:19 This question is not really about graphs, but about how to select n elements from list A so that the corresponding numbers in list B are the largest. The best way is Ordering, not Sort or SortBy. Suppose your graph is g. Then the indices of the n largest elements of VertexDegree[g] are indices = Ordering[VertexDegree[g], -n] Then just take vertices = VertexList[g][[ indices ]];, and finally Subgraph[g, vertices].

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# Math Required in Medical Field? • Math I'm in high school right now and have always dreamed of being a surgeon, so naturally, I read up on an assortment of medical information as well as the pre-requisites of becoming a surgeon. A common pattern I'm finding, is that the medical field requires a good deal of math. However, when I research medical/surgical topics themselves, I see little mathematical based science involved, just anatomical knowledge and surgical technique. So where's the math??? I enjoy math based sciences like physics, for instance, and while physics may not have much involvement, all the pre-req stuff stresses math and physical science based backgrounds. Obviously I know very little about surgical medicine, but could someone please tell me, where is the real math/science based area of medicine, and when does it come into play. Thanks! Related STEM Career Guidance News on Phys.org chiro Hey claytonh4. As an educated guess based on the kinds of things that a lot of the natural scientists like biologists, ecologists, chemists, and so on take, I think you'll find a lot of the actual mathematics is actually related to statistics and related material as opposed to something like say differential equations. One reason for the use of statistics is that it's the study of things under uncertainty and in an experimental or scientific context, nothing is actually certain so people resort to statistics (unfortunately sometimes in horrible ways) to make their point to support some particular hypothesis or idea to give it more credibility. It comes into play primarily when people need to evaluate something especially in reference to a study, a suggestion, or a report of some kind. If you are a surgeon for example and you read something with statistical information that is bound up in some kind of proposition or claim, the statistical analysis will, if you understand it correctly, give you some kind of context of understanding what the data is saying if it is represented correctly. Remember that as a doctor, you will have to work under uncertainty and you will be making decisions so it's important that you make the best possible decisions you can under uncertainty. The statistics is not in any way a replacement for that, but an aid that can be used to enhance this, but not substitute in any way your final responsibility to make a decision (and you can imagine the kinds of decisions you will have to make as a surgeon). Other than this, I can't comment but I can say that if you want to be a surgeon, you need to get in the habit of becoming a more independent learner because you will need this kind of dedication for many many years after medical school and even once you have you fellowship if you get that far. You have a much better chance if you start this earlier because by the time university and all of that comes, you'll already be in the habit of doing this which will put you at an advantage, and it will rub off on people on selection boards that see the initiative and independent attributes of your behaviour. I wish you the best of luck. Hey claytonh4. As an educated guess based on the kinds of things that a lot of the natural scientists like biologists, ecologists, chemists, and so on take, I think you'll find a lot of the actual mathematics is actually related to statistics and related material as opposed to something like say differential equations. One reason for the use of statistics is that it's the study of things under uncertainty and in an experimental or scientific context, nothing is actually certain so people resort to statistics (unfortunately sometimes in horrible ways) to make their point to support some particular hypothesis or idea to give it more credibility. It comes into play primarily when people need to evaluate something especially in reference to a study, a suggestion, or a report of some kind. If you are a surgeon for example and you read something with statistical information that is bound up in some kind of proposition or claim, the statistical analysis will, if you understand it correctly, give you some kind of context of understanding what the data is saying if it is represented correctly. Remember that as a doctor, you will have to work under uncertainty and you will be making decisions so it's important that you make the best possible decisions you can under uncertainty. The statistics is not in any way a replacement for that, but an aid that can be used to enhance this, but not substitute in any way your final responsibility to make a decision (and you can imagine the kinds of decisions you will have to make as a surgeon). Other than this, I can't comment but I can say that if you want to be a surgeon, you need to get in the habit of becoming a more independent learner because you will need this kind of dedication for many many years after medical school and even once you have you fellowship if you get that far. You have a much better chance if you start this earlier because by the time university and all of that comes, you'll already be in the habit of doing this which will put you at an advantage, and it will rub off on people on selection boards that see the initiative and independent attributes of your behaviour. I wish you the best of luck. I'd definitely consider myself a more independent person, so that helps. Thanks for the reply!

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fpt and WinFPT Reference Manual - Command-line Commands CHECK UNITS Syntax: [DO NOT] CHECK UNITS fpt Version This command is implemented experimentally in version 3.6-b of fpt and later. Function fpt automatically determines the physical units of all scalar real and complex variables. It reports any inconsistencies in units detected during the analysis. A table of the different units identified and the relationships between them may be generated by the SHOW UNITS command. The report generated by CHECK UNITS is limited to the inconsistencies detected. fpt infers units from the use of variables in algebraic expressions. It first analyses the use of every REAL or COMPLEX variable to determine which uses are independent of one another and are therefore not required to have the same units. The independent usages are termed "lives". Please see the command SHOW LIVES for a description of this analysis. The physical units and dimensions are then analysed as follows: • If two variable lives are connected by assignment, addition, subtraction or relational operators they must have the same units. • If two variable lives are connected by multiplication, division or exponentiation operators, a relationship is inferred between the units associated with the lives. • The arguments and reslts of many intrinsic functions have predeterined units. For example, the argument to SIND has units of degrees of arc and the result is dimensionless. • Pattern matching is used to identify equivalence between units. If two different units are found to equivalent to the same algebraic combination of other unts, the two units are recognised as equivalent. All inconsistencies between units could be resolved by the assumption that all units are dimensionless. fpt therefore assumes that no real or complex variables represent dimensionless quantities unless they have been declared to be dimensionless by the user, in a UNITS command, or they have been used in intrinsic functions in such a way that they must be dimensionless. Notation: The notation for the reported units is as follows: 1. If the units are determined from the use of intrinsic functions they are reported as the unit name, for example, dimensionless, degrees_arc or seconds. 2. If the units have been specified by UNITS statements in fsp files or in the code, they are reported by the name specified in the UNITS statement. 3. Units for which no description is available are reported as, for example, units(gamma,5), where gamma is the name of the variable, and 5 is the life number. If the variable has only a single life, the life number is omitted, as in units(gamma). If a variable name is ambiguous because the name is used in two or more routines, the name is written, for example, as /coeffs/gamma or as dragsub\gamma where /coeffs/ is the name of the COMMON block containing gamma or dragsub is the name of the sub-program in which it occurs. Format of the Report Inconsistencies in units are detected during the analysis of algebraic expressions. When an inconsistency is detected, fpt reports an audit trail of the successive units substitutions made in analysing the expression. An inconsistency implies either the use of an undeclared dimensionless quantity, or an error in the code. The audit trail should assist in identifying the problem. Where to Use this Command Operating system command line Yes Configuration file, config.fsp Yes Specification (fsp) files, *.fsp Yes Interactively, to FPT> prompt Yes Interactive command files Yes Embedded in the Fortran code Yes Default No check is made by default. Example A section of a report is shown below: ------------------------------------------------------------- WARNING Number 3253 Severity 1 (Worst 1) Count 48 File: e:\projects\fpt\fpttests\uh60a\original_source\bench.f C4Q=1.0-C1Q-C2Q-C3Q ^ Inconsistency detected in units and dimensions -------------------------------------------------------------- Units of the objects -------------------- C1Q Units(C2Q) C2Q Units(C2Q) C3Q Units(EZWNTQ) Successive substitutions in analysing units ------------------------------------------- Initial units of sub-expression: <Undetermined> - Units(C2Q) - Units(C2Q) - Units(EZWNTQ) Units(C2Q) + Units(C2Q) + Units(EZWNTQ) Units(C2Q) + Units(EZWNTQ) These units are inconsistent

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Purchase Solution # Comparing Populations Using Statistical Inference Not what you're looking for? Sammy, the owner of a fast food chain called Sammy's Subs, wants to know whether the levels of daily sales are different between his shop in Edina and the one in Richfield. He records sales in each shop for a month, in the Sammy's Subs Sales Data Excel file. Use the data in this file to determine whether sales levels are different between the two stores at the .05 level of significance. State the null hypothesis, and explain how you determined whether to reject it. Please see attachment. ##### Solution Summary This solution compares populations using statistical inference. ##### Free BrainMass Quizzes Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept. ##### Measures of Central Tendency This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research. ##### Terms and Definitions for Statistics This quiz covers basic terms and definitions of statistics. ##### Measures of Central Tendency Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

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# Doubt about computability of integrals over open sets. In Spivak's Calculus on Manifolds after showing that partitions of unity exists, Spivak defines integrals of functions over open sets as follows. He says: "An open cover $\mathcal{O}$ of an open set $A\subset \mathbb{R}^n$ is called admissible if each $U\in \mathcal{O}$ is contained in $A$. If $\Phi$ is a partition of unity subordinate to $\mathcal{O}$, $f : A\to \mathbb{R}$ is bounded in some open set around each point of $A$, and the set of discontinuities of $f$ has measure zero, then for each $\varphi \in \Phi$, $\int_A \varphi |f|$ exists. We define $f$ to be integrable if $\sum_{\varphi \in \Phi}\int_A \varphi |f|$ converges. This implies the convergence of $\sum_{\varphi \in \Phi}|\int_A \varphi f|$ and hence absolute convergence of $\sum_{\varphi \in \Phi}\int_A \varphi f$ which we define to be $\int_A f$." Now, this indeed shows to be a great theoretical tool, because it made the proof of many theorems really nice, like the change of variables theorem. And this makes sense pretty fine intuitively. However, in this way we are defining the integral as the sum of a series. Proving convergence is something we do all the time in analysis, but finding the sum can be tricky as I know. The methods I know for finding for example that $\sum_{n=1}^\infty 1/n^2=\pi^2/6$ involves techniques of integration by residues on $\mathbb{C}$ and so on. In that case, is it feasible to compute integrals with this definition? Or this definition just serves for theory and there are other ways then to compute this kind of integral over open sets? Thanks very much in advance! • It is generally not feasible to compute integrals using this definition. Theorems like Stokes' Theorem are used instead. – Potato Oct 31 '13 at 19:14

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# Rook Leetcode解決方案的可用捕獲 ## 問題陳述 ### 例 ```board = [[".",".",".",".",".",".",".","."], [".",".",".","p",".",".",".","."], [".",".",".","R",".",".",".","p"], [".",".",".",".",".",".",".","."], [".",".",".",".",".",".",".","."], [".",".",".","p",".",".",".","."], [".",".",".",".",".",".",".","."], [".",".",".",".",".",".",".","."]]``` `3` ```board = [[".",".",".",".",".",".",".","."], [".","p","p","p","p","p",".","."], [".","p","p","B","p","p",".","."], [".","p","B","R","B","p",".","."], [".","p","p","B","p","p",".","."], [".","p","p","p","p","p",".","."], [".",".",".",".",".",".",".","."], [".",".",".",".",".",".",".","."]]``` `0` ## 途徑 ### 算法 1. 遍歷整個矩陣以找到字符“ R”，並將其行和列號保存在 分別。 2. 初始化 CNT 存儲可以捕獲的典當數量 3. 檢查頂部方向，範圍： i∈（0，r – 1）: • if 板[i] [c] =='p'： • 增量 CNT, cnt ++ • 打破 • if 板[i] [c] =='B'： • 打破 4. 對左，右和下方向進行相同的操作 5. 返回 CNT ### Rook Leetcode解決方案可用捕獲的實現 #### C ++程序 ```#include <bits/stdc++.h> using namespace std; int numRookCaptures(vector<vector<char>>& board) { if(board.empty()) return 0; int n = board.size() , m = board[0].size() , cnt = 0 , r , c; for(int i = 0 ; i < n ; i++) for(int j = 0 ; j < m ; j++) { if(board[i][j] == 'R') { r = i; c = j; break; } } for(int i = r - 1 ; i >= 0 ; i--) { if(board[i][c] == 'p') { cnt++; break; } if(board[i][c] == 'B') break; } for(int i = r + 1 ; i < n ; i++) { if(board[i][c] == 'p') { cnt++; break; } if(board[i][c] == 'B') break; } for(int j = c - 1 ; j >= 0 ; j--) { if(board[r][j] == 'p') { cnt++; break; } if(board[r][j] == 'B') break; } for(int j = c + 1 ; j < m ; j++) { if(board[r][j] == 'p') { cnt++; break; } if(board[r][j] == 'B') break; } return cnt; } int main() { vector <vector <char> > board = {{'.','.','.','.','.','.','.','.'}, {'.','.','.','p','.','.','.','.'}, {'.','.','.','R','.','.','.','p'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','p','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}}; cout << numRookCaptures(board) << endl; return 0; }``` #### Java程序 ```class number_of_rook_captures { public static void main(String args[]) { char[][] board = {{'.','.','.','.','.','.','.','.'}, {'.','.','.','p','.','.','.','.'}, {'.','.','.','R','.','.','.','p'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','p','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}, {'.','.','.','.','.','.','.','.'}}; System.out.println(numRookCaptures(board)); } public static int numRookCaptures(char [][] board) { if(board.length == 0) return 0; int n = board.length , m = board[0].length , cnt = 0 , r = -1 , c = -1; for(int i = 0 ; i < n ; i++) for(int j = 0 ; j < m ; j++) { if(board[i][j] == 'R') { r = i; c = j; break; } } for(int i = r - 1 ; i >= 0 ; i--) { if(board[i][c] == 'p') { cnt++; break; } if(board[i][c] == 'B') break; } for(int i = r + 1 ; i < n ; i++) { if(board[i][c] == 'p') { cnt++; break; } if(board[i][c] == 'B') break; } for(int j = c - 1 ; j >= 0 ; j--) { if(board[r][j] == 'p') { cnt++; break; } if(board[r][j] == 'B') break; } for(int j = c + 1 ; j < m ; j++) { if(board[r][j] == 'p') { cnt++; break; } if(board[r][j] == 'B') break; } return cnt; } }``` `3` ### Rook Leetcode解決方案可用捕獲的複雜性分析 #### 時間複雜度 O（1），因為我們迭代了恆定的次數。 #### 空間複雜度 O（1），因為無論輸入內容如何，我們僅使用恆定的存儲空間。

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Determining Price. At the beginning of this unit, we examined demand: Presentation on theme: "Determining Price. At the beginning of this unit, we examined demand:"— Presentation transcript: Determining Price At the beginning of this unit, we examined demand: Price per Gadget # Gadgets Demanded \$10600 \$9720 \$8850 \$7990 \$61140 \$51300 \$41470 \$31650 \$21840 \$12040 Then we examined supply: Price per Gadget # Gadgets Supplied \$101550 \$91500 \$81450 \$71400 \$61350 \$51300 \$41250 \$31200 \$21150 \$11100 In order to determine price, supply and demand must be examined together: Price per Gadget # Gadgets Demanded # Gadgets Supplied \$106001550 \$97201500 \$88501450 \$79901400 \$611401350 \$51300 \$414701250 \$316501200 \$218401150 \$120401100 Three Possible Results Surplus – Because the price is too high, quantity supplied exceeds quantity demanded at a given price. Shortage – Because the price is too low quantity supplied is less than quantity demanded at a given price. Equilibrium – Quantity supplied equals quantity demanded at a given price. (See \$5 in the previous example.) – This is the desired result. – Equilibrium price is also known as market price. Surplus price Quantity Demanded Quantity Supplied Surplus DS Shortage price Quantity Supplied Quantity Demanded Shortage DS Adjustments While the equilibrium is where the price should be, it does not always work that way. When there is a surplus, suppliers need to attract more buyers. – They do this by lowering the price during the next trading period. – At the same time, they decrease the quantity supplied. – This results in a move toward equilibrium. Adjustments, cont. When there is a shortage, suppliers try to meet the needs of more buyers. – They do this by increasing the quantity supplied during the next trading period. – At the same time, they increase the price. – This results in a move toward equilibrium. Equilibrium Competition is necessary for equilibrium to be reached. – Without competition, a supplier may raise the price without worrying about a surplus, since buyers have nowhere else to go. – In a command economy, shortages may result because prices are set too low – there is no way for equilibrium to be reached. Price-Related Policies Sometimes consumers or suppliers are not actually happy with the market price, so they ask the government to step in. There are two main types of price-related policies: – Price ceilings – Price floors Both of these involve trade-offs which are not always considered. Price Ceilings Purpose: to keep prices low so that a product is affordable for a greater number of people. – This is essentially what many people would like to see happen with health care. A price ceiling is set below the market price (which is considered too high), or it will have no effect. Result (unintended): shortage – It is affordable for more people, but fewer people actually get it. Example: rent control – People who had cheap apartments were happy, but others had difficulty finding housing. Price Ceilings D S Market price (considered to be too high) Price ceiling Shortage Price floors Purpose: to keep prices high so that suppliers can make more money. A price floor is set above the market price (which is considered too low), or it will have no effect. Result (unintended): surplus – Suppliers would receive a higher price, but would actually sell less. Example: minimum wage – If minimum wage were increased, fewer people would have those jobs, but they would be making more money. Price Floors D S Market price (considered to be too low) Price floor Surplus Download ppt "Determining Price. At the beginning of this unit, we examined demand:" Similar presentations

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How do you divide 11-3/8-in. (or any other mathematically difficult number) into equal parts without dividing fractions? Simple. Angle your tape across the workpiece until it reads an easily-divisible dimension and make your marks with the tape angled. For example, say you want to divide an 11-3/8-in. board into three equal parts. Angle the tape until it reads 12-in., and then make marks at “4” and “8”. Plus: More measuring tips and tricks. # From the image above it seems that you do not require a big tutorial to help you to build this candle holder. All you need is a wood panel, a hook and some nails/screws and do exactly what you see in the picture. Attach the hook to the wood panel using two screws and then, attach the panel to the wall using more nails or screws. That’s it. I hope this gets the job done. Finally, properly preparing your wood surface is super important. It will make a huge difference when it comes times to stain, paint, or finish your wood. There are a lot of tips for wood surface preparation, but sanding the wood is one of the most important steps. And I find it really helpful to do the bulk of my sanding before I start ripping (cutting) and building with my wood since it’s still in whole pieces. You can check out my simple tips for how to sand wood in my how to stain wood tutorial, which is also good to reference if you need to learn how to stain too! With an orbital sander and good sandpaper you can smooth wood evenly and easily with first-class results. When flush-sanding solid edge-banding, draw a squiggly line across the joint before sanding. The edge-banding will be slightly proud of the plywood veneer, so the pencil marks provide a visual aid to make sure that you’re sanding flat, and that you don’t sand through the plywood’s veneer. As you go, you can also test for a smooth, level transition by gently scraping your fingernails against the transition. If it’s smooth, your fingers will not catch on the seam between the two pieces ```Examples of Bronze Age wood-carving include tree trunks worked into coffins from northern Germany and Denmark and wooden folding-chairs. The site of Fellbach-Schmieden in Germany has provided fine examples of wooden animal statues from the Iron Age. Wooden idols from the La Tène period are known from a sanctuary at the source of the Seine in France. ``` Using shelving in your room or kitchen is a great way to arrange and de-clutter space… I know, such ground-breaking term it is. Do not write me off yet, I just want to show you how you can build some clean floating corner shelving that appears to have no brackets. You can create them at no cost, and the hardest part of the plan is figuring out what you are going to put on these shelves when you are finished. Clamping up four mitered corners is tricky. You can buy specialty clamps for this, but I make my own. Here’s how to do it. Start with a long 1×4, as it’s easier (and safer) to clamp for making the angled cuts than a short piece. Mark out the blocks, and then drill a 1-in. diameter hole in the center of each one. The hole prevents the blocks from getting glued to your project. Cut 45-degree angles tangent to the hole, and then cut the blocks free from the long board. We’ll walk you through how to make one for your home shop. Finally, properly preparing your wood surface is super important. It will make a huge difference when it comes times to stain, paint, or finish your wood. There are a lot of tips for wood surface preparation, but sanding the wood is one of the most important steps. And I find it really helpful to do the bulk of my sanding before I start ripping (cutting) and building with my wood since it’s still in whole pieces. You can check out my simple tips for how to sand wood in my how to stain wood tutorial, which is also good to reference if you need to learn how to stain too! This is definitely going to be one of the easiest woodworking projects you’ll be reading about today. So why not just get started? The tutorial link is given below. Just do exactly what they are saying in the tutorial and you will end up making a beautiful wooden doormat just like the one in the image above. They are using pine wood to build this doormat. You can choose any wood material that best suits your budget. It is one of the easiest woodwork projects we are going to discuss today. Although it looks very easy to make, I still could not find any good tutorial on the internet that explains how to build this one. So I am here sharing an article link that gets the closest. The article explains how to make different kinds of DIY candle holders and what items you may need for the project. Founded in 1977, Harbor Freight Tools is the leading discount tool retailer in the U.S. selling great quality tools at "ridiculously low prices" in our 1000+ stores nationwide and on its website www.harborfreight.com. Harbor Freight Tools stocks over 7,000 items in categories including automotive, air and power tools, shop equipment and hand tools. With a commitment to quality and a lifetime guarantee on all hand tools, Harbor Freight Tools is a favorite of automotive and truck repair shops, government agencies, schools, manufacturers, contractors and tool enthusiasts who want top-quality and great selection and value. The results speak for themselves - with over 40 million customers and thousands of people switching to Harbor Freight Tools every day. ```Each entry must feature some kind of inlay. This can be wood, glass, metal, etc. Epoxy pours are not allowed per /u/kevin0611's request. An epoxy pour does not count as an inlay for the sake of this contest. (Example would be cutting a pattern on CNC or by hand then filling with a colored epoxy to give the illusion that it's inlay.) Bowties, marquetry, and banding are good examples of allowed inlay in this contest. ``` From the image above it seems that you do not require a big tutorial to help you to build this candle holder. All you need is a wood panel, a hook and some nails/screws and do exactly what you see in the picture. Attach the hook to the wood panel using two screws and then, attach the panel to the wall using more nails or screws. That’s it. I hope this gets the job done. DoItYourself.com®, founded in 1995, is the leading independent home improvement and repair website. We welcome your comments and suggestions. All information is provided "AS IS." Website operating problems contact [email protected] Questions of a Do It Yourself nature should be submitted to our "DoItYourself.com Community Forums". Copyright© 1995-2018 MH Sub I, LLC dba Internet Brands. All rights reserved. You may freely link to this site, and use it for non-commercial use subject to our terms of use. View our Privacy Policy here. Figure out a simple setup for your woodworking space. You don’t need a fancy and expensive workshop or garage to start woodworking. In fact, we’ve never had a workshop or garage (though I do dream of having one haha). In our current town home, we always setup a temporary workshop table in our backyard with a pair of sawhorses and a plywood board from the home improvement store. Can you believe that this amazing wine rack the image below has been built using old wood pallets? Perhaps you can. Isn’t it wonderful that your old wood pallets can be reused to build something so beautiful and useful? I am not a drinker but I liked the idea so much that I just couldn’t resist making myself one. Although later I gifted it to my parents, who totally loved it. I’m 91 years old, but I still enjoy spending time in the wood shop. I like to make wooden toys and give them to my great-grandkids and charity groups. One trick I’ve learned over the years is to use emery boards—the kind for filing fingernails— to sand small parts. Emery boards come in different sizes, and some are more abrasive than others, so I keep an assortment on hand. — Joe Aboussleman ### For many of us, the moment we learned that a 2×4 board is actually 1.5 inches x 3.5 inches was simply mind-blowing. The reason for this apparent contradiction is that the board has been planed down to eliminate irregularities. At one point, many years ago, 2x4s actually were 2 inches x 4 inches, but their rough surfaces made them difficult to stock and handle. The old terms, such as 2×4 or 4×4, are still used, and are known as the “nominal” size of the board. These nominal sizes are used because they are easier to say and they stick to tradition. Now, thanks to a lawsuit, most big box stores list the nominal and actual sizes of lumber. Another important factor to be considered is the durability of the wood, especially in regards to moisture. If the finished project will be exposed to moisture (e.g. outdoor projects) or high humidity or condensation (e.g. in kitchens or bathrooms), then the wood needs to be especially durable in order to prevent rot. Because of their oily qualities, many tropical hardwoods such as teak and mahogany are popular for such applications.[9] See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products Among early finds of wooden tools are the worked sticks from Kalambo Falls, Clacton-on-Sea and Lehringen. The spears from Schöningen (Germany) provide some of the first examples of wooden hunting gear. Flint tools were used for carving. Since Neolithic times, carved wooden vessels are known, for example, from the Linear Pottery culture wells at Kückhofen and Eythra. KHIEM NGUYEN (Age 28, Austin, TX): Inspired by midcentury modern and Japanese design, Nguyen is a true craftsman. His passion for crafting began with photography and led to him becoming an open major in art school so he could "get (his) hands into everything." After college, Nguyen and his fiancée moved to Austin, where they began A & K Woodworking & Design, specializing in furniture and wood crafts. Aside from the privacy it offers, a latticework porch trellis is a perfect way to add major curb appeal to your home for \$100 or less. The trellis shown here is made of cedar, but any decay-resistant wood like redwood, cypress or treated pine would also be a good option. Constructed with lap joints for a flat surface and an oval cutout for elegance, it’s a far upgrade from traditional premade garden lattice. As long as you have experience working a router, this project’s complexity lies mostly in the time it takes to cut and assemble. Get the instructions complete with detailed illustrations here. Simply soak a washcloth in water and ring it out a bit so it’s not sopping wet. Put the damp washcloth on the affected area. The water will wick through the wood, and that’s fine. Now, with your iron on its highest setting, place it on the damp washcloth over the affected area, and make small movements back and forth and in circles. Press down firmly and continue until your wash cloth is dry. It won’t take long to evaporate. At this point, the wood fibers are absorbing the water and should expand back to where they were originally. Continue this process and repeat by adding more water until the dents rise up to be flush with the rest of the material. While trying to trace an exact copy of the throat plate for my table saw, I came up with this nifty technique using an ordinary pencil. I just shaved my pencil into a half-pencil by carefully grinding it on my belt sander. The flat edge enables my modified pencil to ride straight up along the edge of the template. It also works great for marking and then shaping inlays for my woodworking projects. — Tim Reese. How to cut circles with a band saw. Having swing in your own home, yard or garden can be so de-stressing and be relaxing a thing to enjoy, that doesn’t matter you have a big yard or patio, or vacant porch. Kids will surely fall in love with this swing porch and love playing on a breezy day. Even, adults also do relax and enjoy a quite morning coffee, or just being embraced by the sun in the swing. Making a garden arched footbridge out of some wood boards can be fun, hard working plan and also it’s quite rewarding. We are providing the project tutorial for how to build an arched footbridge without rails or having rails. If you take your hands of work and have some basic woodworking skills you can easily build this type of bridge. While this garden bridge is too small to walk over but it can make a really stunning addition to your lush yard or garden. Some tools required to build a picture frame are a table saw, miter saw, measuring tape, wood glue etc. A table saw with a backing board and miter gauge can be used to get the right angle and lengths of picture frame every time. You can use builders square to arrange the final cut pieces before nailing, screwing or gluing. Check out the video tutorial below for more details. Making a garden arched footbridge out of some wood boards can be fun, hard working plan and also it’s quite rewarding. We are providing the project tutorial for how to build an arched footbridge without rails or having rails. If you take your hands of work and have some basic woodworking skills you can easily build this type of bridge. While this garden bridge is too small to walk over but it can make a really stunning addition to your lush yard or garden. You can also make one for elders and put it in your garden or terrace or anywhere in the house. Elders can use it to relax and kids can use it to play or sleep. Although this is a really beautiful piece of woodwork, it is not that easy to make. Only someone with good woodworking skill can think of making this swing set. Also, I couldn’t find a good tutorial that illustrates the process of building a wooden boat-shaped swing set. Most Probably, I will write one when I build mine.But if you really want this swing set like right now, I would suggest you hire a good woodworker, who can build something similar. Or just search the internet and maybe you get lucky enough to find a tutorial for this. Good luck either way. ### I am sharing here a link to the detailed tutorial written by Pete at diypete.com, who shares the step by step process for making a wonderful barrel coffee table from scratch. He also tells you what items you’ll need for this project and where to find them. For example, you can buy an old whiskey barrel online or from a local whiskey store for a few bucks, if you haven’t already got one. How do you divide 11-3/8-in. (or any other mathematically difficult number) into equal parts without dividing fractions? Simple. Angle your tape across the workpiece until it reads an easily-divisible dimension and make your marks with the tape angled. For example, say you want to divide an 11-3/8-in. board into three equal parts. Angle the tape until it reads 12-in., and then make marks at “4” and “8”. Plus: More measuring tips and tricks. ```You can also make one for elders and put it in your garden or terrace or anywhere in the house. Elders can use it to relax and kids can use it to play or sleep. Although this is a really beautiful piece of woodwork, it is not that easy to make. Only someone with good woodworking skill can think of making this swing set. Also, I couldn’t find a good tutorial that illustrates the process of building a wooden boat-shaped swing set. Most Probably, I will write one when I build mine.But if you really want this swing set like right now, I would suggest you hire a good woodworker, who can build something similar. Or just search the internet and maybe you get lucky enough to find a tutorial for this. Good luck either way. ``` Working on one side at a time, glue and nail the side to the back. Apply glue and drive three 1-5/8-in. nails into each shelf, attach the other side and nail those shelves into place to secure them. Clamps are helpful to hold the unit together while you’re driving nails. Center the top piece, leaving a 2-in. overhang on both sides, and glue and nail it into place. Paint or stain the unit and then drill pilot holes into the top face of each side of the unit and screw in the hooks to hold your ironing board. Mount the shelf on drywall using screw-in wall anchors. ##### Cut the 6-1/2-in. x 3-in. lid from the leftover board, and slice the remaining piece into 1/4-in.-thick pieces for the sides and end of the box. Glue them around the plywood floor. Cut a rabbet on three sides of the lid so it fits snugly on the box and drill a 5/8-in. hole for a finger pull. Then just add a finish and you’ve got a beautiful, useful gift. If you don’t have time to make a gift this year, consider offering to do something for the person. You could offer to sharpen their knives! Here’s how. You can also make one for elders and put it in your garden or terrace or anywhere in the house. Elders can use it to relax and kids can use it to play or sleep. Although this is a really beautiful piece of woodwork, it is not that easy to make. Only someone with good woodworking skill can think of making this swing set. Also, I couldn’t find a good tutorial that illustrates the process of building a wooden boat-shaped swing set. Most Probably, I will write one when I build mine.But if you really want this swing set like right now, I would suggest you hire a good woodworker, who can build something similar. Or just search the internet and maybe you get lucky enough to find a tutorial for this. Good luck either way. With strength, sturdiness, and durability, maple is a common material for furniture for the bedroom and even china cabinets. Maple is moisture-resistant and frequently displays stand-out swirls in the wood grain, an aesthetically pleasing differentiator from other hardwoods. While most commonly a lighter color, maple also can take stains and paint well.[13] Making a garden arched footbridge out of some wood boards can be fun, hard working plan and also it’s quite rewarding. We are providing the project tutorial for how to build an arched footbridge without rails or having rails. If you take your hands of work and have some basic woodworking skills you can easily build this type of bridge. While this garden bridge is too small to walk over but it can make a really stunning addition to your lush yard or garden. Afrormosia Alder Andiroba Anigre Ash Apple Aspen Avodire Balsa Beech Bilinga Birch African Blackwood Australian Blackwood Boxwood Bubinga Camphor Cedrela Cherry Chestnut Cocobolo Cumaru Ebony Elm Eucalyptus Hazel Hickory Hornbeam Idigbo Imbuia Ipê Iroko Jarra Jelutong Lignum vitae Linden (lime, basswood) Merbau Mahogany (American, African) Maple Meranti Oak Padauk Pear Plum Poplar Purpleheart Ovankol Ramin Red Quebracho Rosewood Rubberwood Sapele Teak Totara Utile Walnut Wenge Willow Zebrano “I do a lot of finish-sanding freehand, without a sandpaper block, so I can smooth edges and get into nooks and crannies. But the finer grits are usually bonded to thinner paper and, at least for me, the paper is too thin and ends up tearing long before the grit wears out. So I apply duct tape to the back of the sandpaper. The sandpaper is still flexible enough to sand a tight radius and it’s far more durable. You can use this super-strong sandpaper like a shoeshine rag.” — Chuck Merchant ​The plan tutorial includes images, diagrams, step-by-step instructions, and even a video to help you along the way. You can also go with some more bookcase design ideas. Browse the internet for more and we are also proving a link below to some more ideas to this plan. Select and build one of these free bookcase DIYs and you will have everything available easily that you need to get started creating a bookshelf for any room in your house. Using shelving in your room or kitchen is a great way to arrange and de-clutter space… I know, such ground-breaking term it is. Do not write me off yet, I just want to show you how you can build some clean floating corner shelving that appears to have no brackets. You can create them at no cost, and the hardest part of the plan is figuring out what you are going to put on these shelves when you are finished. KHIEM NGUYEN (Age 28, Austin, TX): Inspired by midcentury modern and Japanese design, Nguyen is a true craftsman. His passion for crafting began with photography and led to him becoming an open major in art school so he could "get (his) hands into everything." After college, Nguyen and his fiancée moved to Austin, where they began A & K Woodworking & Design, specializing in furniture and wood crafts. Using shelving in your room or kitchen is a great way to arrange and de-clutter space… I know, such ground-breaking term it is. Do not write me off yet, I just want to show you how you can build some clean floating corner shelving that appears to have no brackets. You can create them at no cost, and the hardest part of the plan is figuring out what you are going to put on these shelves when you are finished. Cutting sandpaper is a quick way to dull your scissors or utility knife blade. Instead, I fastened a hacksaw blade to the edge of my workbench. I slipped a washer behind the blade at each of the mounting holes so a sheet of sandpaper to easily slides in behind the blade. I fold the paper where I want to cut, just as a reference. — Kim Boley. Try some of these storage solutions! Finding affordable lumber has always been a mainstay for woodworkers, and when you tie our dwindling natural resources into the conversation the time is right to look at milling your own lumber. This seven-part weekly video series takes you through how to find lumber, how to operate a sawmill, details on types of sawing methods, stickering and drying and ultimately advice on using a mill as part of a business. Learn what you need to know to understand Milling Your Own Lumber. Building a Wooden Office Desk Organizer is an easy task for a professional woodworker, but not so much for normal people like you and me. But that doesn’t mean you cannot do this. Two years ago, I had almost no woodworking experience, but now I make most of my household and office wooden items by myself. This saves me a lot of money. And believe me when I say this; you can also manage to make wonderful wood items with a little practice and some woodworking experience. Finally, as I shared in my post last week on how I learned woodworking, I learned how to use power tools by watching YouTube videos and then just trying them out for myself. I highly recommend this method to learn how to use your power tools. There are lots of videos on specific models of tools too. So, watch a few how-to videos and very importantly, review the tool manual and safety guide for your own tools. Then, go ahead and try the tool out yourself and start using it! ```From the source tutorial, you can get illustrates to the instruction about the plan. Everything is fairly described as diagrams, images, the list of supplies and tools need etc. The process to this plan is very easy to understand and follow for if you are having some basic woodworking knowledge. Make sure to collect all the supplies you need before you start with the project. You may even ask any question directly in the comment section of the tutorial post and also comment the images of your final product if you have completed it. Either way, I hope that you will manage to build this one nicely.​ ``` A few days back, I was searching for some cool DIY plans. So, I got to work and ended up coming up with some easy to follow project and an awesome new ice chest cooler to have out on the deck! It was going to be perfect for summer hangouts and barbecues. It was a fun and practical plan to work on and I know you will have fun tackling select a design from this plan and start building your own. Enjoy learning how you can build a rustic cooler also sing the video tutorial and source tutorial plan! To corral shelf-dwelling books or DVDs that like to wander, cut 3/4-in.-thick hardwood pieces into 6-in. x 6-in. squares. Use a band saw or jigsaw to cut a slot along one edge (with the grain) that’s a smidgen wider than the shelf thickness. Stop the notch 3/4 in. from the other edge. Finish the bookend and slide it on the shelf. Want to build the shelves, too? We’ve got complete plans for great-looking shelves here. Clamping mitered edges can be a real hassle because they never seems to line up correctly. The easiest way that I’ve found to get around this process is to use painter’s tape as clamps. First set the pieces so that the outer edges are facing up and tape them edge-to-edge. The flip the pieces over so the beveled edges are facing up and glue them together. Complete the process by taping the last two edges together and let sit until completed. The tape removes easily and the glue won’t attach to the tape, making sanding and finishing very simple. Try this tip with this clever project! See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products See Products Along with stone, clay and animal parts, wood was one of the first materials worked by early humans. Microwear analysis of the Mousterian stone tools used by the Neanderthals show that many were used to work wood. The development of civilization was closely tied to the development of increasingly greater degrees of skill in working these materials. # Some types of wood filler can be hard to get off your hands after they dry, especially if you use your fingers to push it into small cracks and holes. When that happens, I reach for fine grit sandpaper and sand it off my fingers. It’s great for removing dried-on polyurethane glue and canned foam from your hands, too. — Chris James. We’ve got great solutions for removing super glue, too. Cut the 6-1/2-in. x 3-in. lid from the leftover board, and slice the remaining piece into 1/4-in.-thick pieces for the sides and end of the box. Glue them around the plywood floor. Cut a rabbet on three sides of the lid so it fits snugly on the box and drill a 5/8-in. hole for a finger pull. Then just add a finish and you’ve got a beautiful, useful gift. If you don’t have time to make a gift this year, consider offering to do something for the person. You could offer to sharpen their knives! Here’s how. The best thing about this wine rack is that it is very easy to build. All you need is the basic understanding of woodworking and a few tools to get started. You can modify your wine rack any way you want or build in a design or color different from this one. The basic steps to build a wooden wine rack are the same for all variants. I have included here the video tutorial that I followed in order to build myself a pallet wide rack. Slice, dice and serve in style on this easy, attractive board. We’ll show you a simple way to dry-fit the parts, scribe the arc and then glue the whole thing together. We used a 4-ft. steel ruler to scribe the arcs, but a yardstick or any thin board would also work. Find complete how-to instructions on this woodworking crafts project here. Also, be sure to use water-resistant wood glue and keep your board out of the dishwasher or it might fall apart. And one more thing: Keep the boards as even as possible during glue-up to minimize sanding later. For great tips on gluing wood, check out this collection.

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16103 16,103 (sixteen thousand one hundred three) is an odd five-digits prime number following 16102 and preceding 16104. In scientific notation, it is written as 1.6103 × 104. The sum of its digits is 11. It has a total of 1 prime factor and 2 positive divisors. There are 16,102 positive integers (up to 16103) that are relatively prime to 16103. Basic properties • Is Prime? Yes • Number parity Odd • Number length 5 • Sum of Digits 11 • Digital Root 2 Name Short name 16 thousand 103 sixteen thousand one hundred three Notation Scientific notation 1.6103 × 104 16.103 × 103 Prime Factorization of 16103 Prime Factorization 16103 Prime number Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 16103 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 9.68676 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0 The prime factorization of 16,103 is 16103. Since it has a total of 1 prime factor, 16,103 is a prime number. Divisors of 16103 2 divisors Even divisors 0 2 1 1 Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 16104 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 8052 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 126.898 Returns the nth root of the product of n divisors H(n) 1.99988 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors The number 16,103 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 16,103) is 16,104, the average is 8,052. Other Arithmetic Functions (n = 16103) 1 φ(n) n Euler Totient Carmichael Lambda Prime Pi φ(n) 16102 Total number of positive integers not greater than n that are coprime to n λ(n) 16102 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1871 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares There are 16,102 positive integers (less than 16,103) that are coprime with 16,103. And there are approximately 1,871 prime numbers less than or equal to 16,103. Divisibility of 16103 m n mod m 2 3 4 5 6 7 8 9 1 2 3 3 5 3 7 2 16,103 is not divisible by any number less than or equal to 9. Classification of 16103 • Arithmetic • Prime • Deficient Expressible via specific sums • Polite • Non-hypotenuse • Prime Power • Square Free Base conversion (16103) Base System Value 2 Binary 11111011100111 3 Ternary 211002102 4 Quaternary 3323213 5 Quinary 1003403 6 Senary 202315 8 Octal 37347 10 Decimal 16103 12 Duodecimal 939b 20 Vigesimal 2053 36 Base36 cfb Basic calculations (n = 16103) Multiplication n×i n×2 32206 48309 64412 80515 Division ni n⁄2 8051.5 5367.67 4025.75 3220.6 Exponentiation ni n2 259306609 4175614324727 67239917471078881 1082764391036783220743 Nth Root i√n 2√n 126.898 25.2524 11.2649 6.94035 16103 as geometric shapes Circle Diameter 32206 101178 8.14636e+08 Sphere Volume 1.74908e+13 3.25854e+09 101178 Square Length = n Perimeter 64412 2.59307e+08 22773.1 Cube Length = n Surface area 1.55584e+09 4.17561e+12 27891.2 Equilateral Triangle Length = n Perimeter 48309 1.12283e+08 13945.6 Triangular Pyramid Length = n Surface area 4.49132e+08 4.92101e+11 13148 Cryptographic Hash Functions md5 8f5c01673292dca6425ee6f028fc2ffa 4bb43b2234f239c49b4c96aec3154f4f0cedb439 1fcabbbe1175761ca95cf7156ec7c5c0553714e850ec7bd151afd6f0403d7da3 9454b493a6e3e2e10cca437ff96c8574b2084ba5bb57629f3e1d6c04054b763d83b50845877ac5fae82b012d02c9e710f84e4d628ecf5fcfe7932ab0d790fd79 5dc01985c7248f84cf7e136459e51dbc6f581df9

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# A General Approach to Variance Estimation under Imputation for Missing Survey Data Save this PDF as: Size: px Start display at page: Download "A General Approach to Variance Estimation under Imputation for Missing Survey Data" ## Transcription 1 A General Approach to Variance Estimation under Imputation for Missing Survey Data J.N.K. Rao Carleton University Ottawa, Canada Joint work with J.K. Kim at Iowa State University. 2 Workshop on Survey Sampling in honor of Jean-Claude Deville, Neuchâtel, Switzerland, June 24-26, 2009 2 Outline Item Nonresponse Deterministic imputation: Population model approach Imputed estimator Linearization variance estimator Examples: Domain estimation, Composite imputation Stochastic imputation: variance estimation Examples: Multiple imputation, binary response Simulation results Doubly robust approach Extensions 3 Survey Data Design features: clustering, stratification, unequal probability of selection Source of error: 1. Sampling errors 2. Non-sampling errors: Nonresponse (missing data) Noncoverage Measurement errors 4 Types of nonresponse Unit (or total) nonresponse: refusal, not-at-home Remedy: weight adjustment within classes Item nonresponse: sensitive item, answer not known, inconsistent answer Remedy: imputation (fill in missing data) 5 Advantages of imputation Complete data file: standard complete data methods Different analyses consistent with each other Reduce nonresponse bias Auxiliary x observed can be used to get good imputed values Same survey weight for all items 6 Commonly used imputation methods Marginal imputation methods: 1. Business surveys: Ratio, Regression, Nearest neighbor (NN) 2. Socio-economic surveys: Random donor (within classes), Stochastic ratio or regression, Fractional imputation (FI), Multiple imputation (MI) 7 Complete response set-up Population total: θ N = N i=1 y i NHT estimator: ˆθ n = i s d i y i where d i = π 1 i : design weight π i = inclusion probability = Pr (i s) Variance estimator: ˆV n = i s Ω ij y i y j j s Ω ij depends on joint inclusion probabilities π ij > 0 8 Deterministic imputation Population model approach (Deville and Särndal, 1994): E ζ (y i x i ) = m (x i, β 0 ) a i = 1 if y i observed when i s = 0 otherwise for i U = {1, 2,, N} MAR: Distribution of a i depends only on x i Imputed value: ŷ i = m(x i, ˆβ) ˆβ: unique solution of EE Û (β) = d i a i {y i m (x i, β)} h (x i, β) = 0 i s 9 Model specification Further model specification: Var ζ (y i x i ) = σ 2 q (x i, β 0 ) h (x i, β) = ṁ (x i, β) /q (x i, β) h i Examples: commonly used imputations 1. Ratio imputation: h i = 1 E ζ (y i x i ) = β 0 x i, Var ζ (y i x i ) = σ 2 x i 2. Linear regression imputation: h i = x i E ζ (y i x i ) = x i β 0, Var ζ (y i x i ) = σ 2 3. Logistic regression imputation (y i = 0 or 1): h i = x i log {m i / (1 m i )} = x i β 0, Var ζ (y i x i ) = m i (1 m i ) where m i = E ζ (y i x i ) 10 Imputed estimator Imputed estimator of total θ N : ˆθ Id = } d i {a i y i + (1 a i ) m(x i, ˆβ) i s i s d i ỹ i Examples 1. Ratio imputation: m(x i, ˆβ) = x i ˆβ where ˆβ = ( i s d ) 1 ia i x i i s d ia i y i 2. Linear regression imputation: m(x i, ˆβ) = x i ˆβ where ˆβ = ( i s d ) ia i x i x i 1 i s d ia i x i y i 3. Logistic regression imputation: ˆβ is the solution to i s d i {y i m (x i, β)} x i = 0 Imputed estimator of domain total θ z = N i=1 z iy i : ˆθ I,z = i s d i z i ỹ i where z i = 1 if i D; z i = 0 otherwise. 11 Variance estimation Treating imputed values as if observed: Underestimation if ỹ i used in ˆV n for y i Methods that account for imputation: Adjusted jackknife: Rao and Shao (1992) Linearization (Pop. model): Deville and Särndal (1994) Fractional imputation method: Fuller and Kim (2005) Bootstrap: Shao and Sitter (1996) Reverse approach: Shao and Steel (1999) 12 Variance estimation (Cont d) Linearization method: Theorem 1 (Kim and Rao, 2009): Under regularity conditions, n 1/2 N 1 (ˆθId θ Id ) = o p (1) where θ Id = i s w i η i { η i = m (x i ; β 0 ) + a i 1 + c } h i {yi m (x i ; β 0 )}, { N } 1 N c = a i ṁ (x i ; β 0 ) h i (1 a i ) ṁ (x i ; β 0 ). i=1 Reference distribution: Joint distribution of population model and sampling mechanism, conditional on realized (x i, a i ) in the population. i=1 13 Variance estimation (Cont d) Reverse approach: 1. ˆV 1d = Ω ij ˆη i ˆη j i s j s 2. where ˆη i = η i ( ˆβ). ˆV 2d = i s ( ) 2 ( )} d i a i 1 + ĉ ĥ i {y i m x i ; ˆβ ˆV 2d valid even if V ζ (y i x i ) is misspecified. 3. Variance estimator of ˆθ Id ( θ Id ): ˆV d = ˆV 1d + ˆV 2d ˆV d approximately design-model unbiased. If the overall sampling rate negligible: ˆV d = ˆV1d 14 Variance estimation (Cont d) Domain estimation: 1. ˆθ I,z : design-model unbiased for θ z 2. Use ˆV 1d = Ω ij ˆη iz ˆη jz i s j s where ˆη iz = z i m(x i ; ˆβ) + a i {z i + ĉ zh i } { } y i m(x i ; ˆβ), ĉ z = { } 1 d i a i ṁ(x i ; ˆβ)ĥ i d i z i (1 a i ) ṁ(x i ; ˆβ) i s i s 15 Composite imputation x, y, z: z always observed Imputation model: s = s RR s RM s MR s MM θ N = N i=1 y i s RM : x observed and y missing s MM : x and y missing E ζ (y i x i, z i ) = β y x x i E ζ (x i z i ) = β x z x i Imputed estimator: ˆθ Id = ( ) d i y i + d i ˆβy x x i + i s +R i s RM i s MM d i ( ˆβy x ˆβx z z i ) 16 Composite imputation (Cont d) ˆβ y x and ˆβ x z solutions of estimation equations: ( ) ( ) Û 1 βy x = yi β y x x i = 0 i S RR d i Û 2 ( βx z ) = i S R+ d i ( xi β x z z i ) = 0 Taylor linearization of the imputed estimator: ˆθ Id ( ˆβ) = ˆθ Id (β) ( ˆθ Id β ) ( Û β where Û = (Û1, Û 2 ) and β = ( βy x, β x z ). ) 1 Û (β) 17 Stochastic imputation y i = imputed value of y i such that Imputed estimator of θ N : E I (y i ) = m(x i, ˆβ) ˆm i ˆθ I = i s d i {a i y i + (1 a i ) y i } Variance estimator of ˆθ I : E I (ˆθI ) = ˆθ Id ˆV I = ˆV d + ˆV where ˆV = i s d 2 i (1 a i ) (y i ˆm i ) 2 18 Multiple imputation: Rubin y (1) i,..., y (M) i = imputed values of y i (M 2) ˆθ (k) I Imputed estimator = i s Rubin s variance estimator: { } d i a i y i + (1 a i ) y (k) ˆθ MI = M 1 M k=1 ˆθ (k) I ˆV R = W M + M + 1 M B M where W M is the average of M naive variance estimators and B M = (M 1) 1 M k=1 (ˆθ(k) I ˆθ ) 2 MI i 19 Multiple imputation (Cont d) ˆV R theoretically justified when ) ) V (ˆθId = V (ˆθn + V (ˆθId ˆθ ) n (A) (Congenialty assumption) ˆVR seriously biased if assumption (A) violated. (A) not satisfied for domain estimation when domains not specified at the imputation stage. Our proposal: ˆV MI = ˆV d + M 1 B M ˆVMI valid for ˆθ Id as well as ˆθ I,z without (A). 20 Binary response Model: y i x i Bernoulli {m i = m (x i, β 0 )} logit (m i ) = x i β; q (x i, β 0 ) = m i (1 m i ) q i ( ˆm i = m x i, ˆβ ) where ˆβ is the solution to d i a i {y i m (x i, β)} x i = 0 i s Stochastic hot deck imputation { yi 1 with prob ˆmi = 0 with prob 1 ˆm i ˆη i = ˆm i + a i (1 + ĉ x i ) (y i ˆm i ) ĉ = { i s d ia i ˆq i x i x i } 1 i s d i (1 a i ) ˆq i x i. 21 Binary response (Cont d) Fractional imputation (FI): Eliminate imputation variance V by FI M = 2 fractions: impute { yi 1 with fractional weight ˆmi = 0 with fractional weight 1 ˆm i Data file reports real values 1 and 0 with associated fractions ˆm i and 1 ˆm i. ˆθ FI = ˆθ Id : V eliminated Estimation of domain total and mean: ˆθ FI,z, ( i s d iz i ) 1 ˆθ FI,z 22 Binary response (Cont d) Multiple imputation (MI): { 1. Generate β N ( ˆβ, i s a ) } i ˆq i x i x i 1 2. Generate yi Bernoulli (mi ) with m i = m (x i, β ) 3. Repeat steps 1 and 2 independently M times. 23 Simulation Study : Binary response Finite population of size N = 10, 000 from x i N (3, 1) y i x i Bernoulli (m i ), where logit (m i ) = 0.5x i 2 z i Bernoulli (0.4) (z i : Domain indicator) SRS of size n = 100 x i and z i : always observed. y i subject to missing. Missing response mechanism a i Bernoulli (π i ) ; logit (π i ) = φ 0 + φ 1 (x i 3) + φ 2 x i 3 (a) φ 1 = 0, φ 2 = 0; (b) φ 1 = 1, φ 2 = 0; (c) φ 1 = 0, φ 2 = 1 φ 0 is determined to achieve 70% response rate. Two variance estimates of multiple imputation are computed. 24 Simulation Study (Cont d) Table: Relative bias (RB) of the Rubin s variance estimator (R) and proposed variance estimator (KR) for multiple imputation Parameter Response RB (%) Mechanism R KR Case Population Case Mean Case Case Domain Case Mean Case Conclusion: 1. KR has small RB in all cases 2. R leads to large RB in the case of domain mean: 28% to 34% 25 Doubly robust method Case 1: p i known (p i = probability of response) Let β be the solution to Û (β) = ( ) 1 d i a i 1 {y i m (x i, β)} h (x i, β) = 0 p i i s Imputed estimator: θ Id = i s d i {a i y i + (1 a i ) m(x i, β) } If 1 is an element of h i, then θ Id = { ( ai d i y i + 1 a ) } i m(x i, β) p i p i i s 26 Doubly robust method (Cont d) Properties of θ Id : 1. Under the assumed response model, E R ( θ Id ) = ˆθ n regardless of the choice of m(x i, β). 2. Under the imputation model, E ζ ( θ Id ˆθ n ) = 0. (1) and (2) imply that θ Id is doubly robust. 27 Doubly robust method (Cont d) Case 2: p i unknown (p i = p i (α)) Linearization variance estimator: Haziza and Rao (2006): linear regression imputation Deville (1999), Demnati and Rao (2004) approach: general case 28 Extensions Calibration estimators Davison and Sardy (2007): deterministic linear regression imputation, stratified SRS Pseudo-empirical likelihood intervals Other parameters ### A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models Grace Y. Yi 13, JNK Rao 2 and Haocheng Li 1 1. 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Canberra February June 2015 c Statistical Group and College of Engineering and Computer Science Canberra February June (Many figures from C. M. Bishop, "Pattern Recognition and ") 1of 829 c Part VIII Linear Classification 2 Logistic ### Sovereign Defaults. Iskander Karibzhanov. October 14, 2014 Sovereign Defaults Iskander Karibzhanov October 14, 214 1 Motivation Two recent papers advance frontiers of sovereign default modeling. First, Aguiar and Gopinath (26) highlight the importance of fluctuations ### An extension of the factoring likelihood approach for non-monotone missing data An extension of the factoring likelihood approach for non-monotone missing data Jae Kwang Kim Dong Wan Shin January 14, 2010 ABSTRACT We address the problem of parameter estimation in multivariate distributions ### Bayesian Statistics in One Hour. Patrick Lam Bayesian Statistics in One Hour Patrick Lam Outline Introduction Bayesian Models Applications Missing Data Hierarchical Models Outline Introduction Bayesian Models Applications Missing Data Hierarchical ### Ordinal Regression. Chapter Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe ### arxiv:1206.6666v1 [stat.ap] 28 Jun 2012 The Annals of Applied Statistics 2012, Vol. 6, No. 2, 772 794 DOI: 10.1214/11-AOAS521 In the Public Domain arxiv:1206.6666v1 [stat.ap] 28 Jun 2012 ANALYZING ESTABLISHMENT NONRESPONSE USING AN INTERPRETABLE ### Course 4 Examination Questions And Illustrative Solutions. November 2000 Course 4 Examination Questions And Illustrative Solutions Novemer 000 1. You fit an invertile first-order moving average model to a time series. The lag-one sample autocorrelation coefficient is 0.35. ### Deflator Selection and Generalized Linear Modelling in Market-based Accounting Research Deflator Selection and Generalized Linear Modelling in Market-based Accounting Research Changbao Wu and Bixia Xu 1 Abstract The scale factor refers to an unknown size variable which affects some or all

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1 / 2 # slope - PowerPoint PPT Presentation slope. slope. measure of the steepness of a line written as a ratio of vertical rise to horizontal run between any two points on a line. slope ( m ) =. Rise: Difference of y-values. Find the slope of the line passing through (2,1) and (5,3). I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described. ## PowerPoint Slideshow about 'slope' - nicki Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - Presentation Transcript slope measure of the steepness of a line written as a ratio of vertical rise to horizontal run between any two points on a line slope (m) = Rise: Difference of y-values Find the slope of the line passing through (2,1) and (5,3). Let (x1,y1) = (2,1) and (x2,y2) = (5,3). Run: Difference of x-values Substitute values. Slope is positive y 0 x an sbl original ‘06 slope measure of the ______________ of a line written as a _________of ___________ _____ to ____________ _____ between any ______ points on a line slope (__) = Rise: Difference of y-values Find the slope of the line passing through (2,1) and (5,3). Let (x1,y1) = (2,1) and (x2,y2) = (5,3). Run: Difference of x-values Substitute values. Slope is positive y 0 x an sbl original ‘06

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  pythagtriplem8 Structured version   Unicode version Theorem pythagtriplem8 13190 Description: Lemma for pythagtrip 13201. Show that is a natural number (Contributed by Scott Fenton, 17-Apr-2014.) (Revised by Mario Carneiro, 19-Apr-2014.) Assertion Ref Expression pythagtriplem8 Proof of Theorem pythagtriplem8 StepHypRef Expression 1 pythagtriplem6 13188 . 2 2 nnz 10296 . . . . . 6 3 nnz 10296 . . . . . 6 4 zsubcl 10312 . . . . . 6 52, 3, 4syl2anr 465 . . . . 5 653adant1 975 . . . 4 7 nnz 10296 . . . . 5 873ad2ant1 978 . . . 4 9 nnne0 10025 . . . . . . 7 109neneqd 2615 . . . . . 6 1110intnand 883 . . . . 5 12113ad2ant1 978 . . . 4 13 gcdn0cl 13007 . . . 4 146, 8, 12, 13syl21anc 1183 . . 3

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CFD Online Discussion Forums (http://www.cfd-online.com/Forums/) -   OpenFOAM Running, Solving & CFD (http://www.cfd-online.com/Forums/openfoam-solving/) -   -   Don't understand solver's behaviour (http://www.cfd-online.com/Forums/openfoam-solving/113178-dont-understand-solvers-behaviour.html) galap February 14, 2013 05:44 Don't understand solver's behaviour Hello guys, today I'm facing a problem, which I can't explain. I have done a dummy calculation for a variable f. f is set everywhere to 1 (boundary/internal). Nevertheless OpenFOAM calculates values differing from 1. Can anyone explain that behaviour to me? Thank you very much in advance. I have a normal transport equation for variable f: Code: ```    f_(         IOobject         (             "f",             mesh.time().timeName(),             mesh,             IOobject::MUST_READ,             IOobject::AUTO_WRITE         ),         mesh     ),``` dimensions [0 0 0 0 0 0 0]; Boundary and internal values all set to 1. Code: ```  multivariateSurfaceInterpolationScheme<scalar>::fielTable fields;     fields.add(f);     tmp<fv::convectionScheme<scalar> > convection     (         fv::convectionScheme<scalar>::New         (             mesh_,             fields,             phi,             mesh_.divScheme("div(phi,f)")         )     );``` So again keep in mind, for testing purpose I set all values to 1. Now I'm trying to solve the following equations: Code: ```Info << "fmin/max  = " << min(f_).value() << ", " << max(f_).value() << endl;; tmp<fvScalarMatrix> fEqn (     fvm::ddt(rho, f_)     +  convection->fvmDiv(phi, f_)     -  fvm::laplacian(turbulence_->alphaEff(), f_) ); fEqn().relax(); solve(fEqn == rho* fSource);``` fSource is set to 0. Code: `Info << "fmin/max  = " << min(f_).value() << ", " << max(f_).value() << endl;;` The Output is: f min/max = 1, 1 f min/max = 0.90082369, 1.1320949 Schemes: laplacian(alphaEff,f) Gauss linear corrected; div(phi,f) Gauss upwind; RASModel kEpsilon; galap February 14, 2013 06:05 solver used: solver PBiCG; preconditioner DILU; tolerance 1e-7; relTol 0.01; All times are GMT -4. The time now is 21:00.

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WOLFRAM SYSTEM MODELER # IdealTransformer Ideal transformer core with or without magnetization # Wolfram Language In[1]:= `SystemModel["Modelica.Electrical.Analog.Ideal.IdealTransformer"]` Out[1]:= # Information This information is part of the Modelica Standard Library maintained by the Modelica Association. The ideal transformer is a two-port circuit element; in case of Boolean parameter `considerMagnetization = false` it is characterized by the following equations: ```i2 = -i1*n; v2 = v1/n; ``` where `n` is a real number called the turns ratio. Due to this equations, also DC voltages and currents are transformed - which is not the case for technical transformers. In case of Boolean parameter `considerMagnetization = true` it is characterized by the following equations: ```im1 = i1 + i2/n "Magnetizing current w.r.t. primary side"; psim1= Lm1*im1 "Magnetic flux w.r.t. primary side"; v1 = der(psim1) "Primary voltage"; v2 = v1/n "Secondary voltage"; ``` where `Lm` denotes the magnetizing inductance. Due to this equations, the DC offset of secondary voltages and currents decrement according to the time constant defined by the connected circuit. Taking primary `L1sigma` and secondary `L2ssigma` leakage inductances into account, compared with the basic transformer the following parameter conversion can be applied (which leads to identical results): ```L1 = L1sigma + M*n "Primary inductance at secondary no-load"; L2 = L2sigma + M/n "Secondary inductance at primary no-load"; M = Lm1/n "Mutual inductance"; ``` For the backward conversion, one has to decide about the partitioning of the leakage to primary and secondary side. # Parameters (3) n Value: Type: Real Description: Turns ratio primary:secondary voltage Value: false Type: Boolean Description: Choice of considering magnetization Value: Type: Inductance (H) Description: Magnetization inductance w.r.t. primary side # Connectors (4) p1 Type: PositivePin Description: Positive electrical pin of port 1 Type: NegativePin Description: Negative electrical pin of port 1 Type: PositivePin Description: Positive electrical pin of port 2 Type: NegativePin Description: Negative electrical pin of port 2 # Used in Examples (1) CompareTransformers Modelica.Electrical.Analog.Examples Transformer circuit to show the magnetization facilities # Used in Components (1) IdealTransformer Modelica.Electrical.Polyphase.Ideal Polyphase ideal transformer # Revisions • June 3, 2009 magnetisation current added by Anton Haumer • 1998 initially implemented by Christoph Clauss

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# Employee Turnover Rate ## What is Employee Turnover Rate? Employee Turnover Rate is the percentage of employees who voluntarily or involuntarily leave an organization (typically calculated annually). You should consider voluntary and involuntary categories separately, in addition to looking at overall Employee Turnover Rate. Alternate names: Turnover ### How to calculate Employee Turnover Rate ƒ Count(Employees who have left) / (Sum(beginning + ending number of employees) / 2) ### Example Company total at beginning of the year = 100 Number of employees that left = 6 Company total at end of year = 94 6 / ((100 + 94) / 2) = 6.4% annual employee turnover

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# How to convert kW to BTU/hr How to convert kilowatts (kW) to British Thermal Units per hour (BTU/hr). One kilowatt is equal to 3412.142 BTU per hour: 1 kW = 3412.142 BTU/hr ### Kilowatts to BTU/hr conversion formula The power in BTUIT per hour P(BTU/hr) is equal to 3412.142 times the power in kilowatts P(kW): P(BTU/hr) = 3412.142 ⋅ P(kW) ### Example Convert 5kW to BTU/hr: P(BTU/hr) = 3412.142 ⋅ 5kW = 17060.71 BTU/hr How to convert BTU/hr to kW ►

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Mathematics # Bill measures the circumference of a circular fish pond to be 28 ft. What is the diameter of the fish pond, rounded to the nearest foot? Use 3.14 to approximate pi. #### Jayda 3 years ago C=pid c=28 28=pid pi=3..14 28=3.14d divide both sides by 3.14 8.917...=d rounded 9=d diameter=9ft

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# Torsion Constant for Square Cross-section Written by Jerry Ratzlaff on . Posted in Classical Mechanics ### Torsion Constant for Square Cross-section formula $$\large{ J = 2.25 \; a^4 }$$ Where: $$\large{ J }$$  (Greek symbol alpha) = torsion constant $$\large{ a }$$ = half the edge length of a square

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You are Here: Home >< Maths # Stuck on this M2 question watch 1. I feel like it's easy but I just can't do it for some reason. What am I missing? I've tried: If s = 15, but you can't sub t in so how do you find out A? If s = 0, t = 0, and you can't find A here. 2. (Original post by 2014_GCSE) I feel like it's easy but I just can't do it for some reason. What am I missing? I've tried: If s = 15, but you can't sub t in so how do you find out A? If s = 0, t = 0, and you can't find A here. What else do you know when t=0? 3. (Original post by morgan8002) What else do you know when t=0? initial velocity = 20 Do I differentiate the equation and put it equal to 20? 4. (Original post by 2014_GCSE) initial velocity = 20 Do I differentiate the equation and put it equal to 20? yeah 5. (Original post by morgan8002) yeah Thanks for helping me here but urhh I'm still having trouble haha so S = A - Ae^-kt V = kAe^kt 20 = kAe^k(0) 20 = kA What have I done wrong...? 6. (Original post by 2014_GCSE) Thanks for helping me here but urhh I'm still having trouble haha so S = A - Ae^-kt V = kAe^kt 20 = kAe^k(0) 20 = kA What have I done wrong...? Sorry. I looked at the question quickly and didn't take into account the extra k when differentiating. Sketch a graph of s against t. What happens as ? This is another common way of getting around the problem and removing the ks. 7. (Original post by morgan8002) Sorry. I looked at the question quickly and didn't take into account the extra k when differentiating. Sketch a graph of s against t. What happens as ? This is another common way of getting around the problem and removing the ks. S gets bigger and moves towards the asymptote of A? 8. (Original post by 2014_GCSE) S gets bigger and moves towards the asymptote of A? Yes. The question says that the particle stops at s=15m, so this is the value of A. ### Related university courses TSR Support Team We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. This forum is supported by: Updated: September 8, 2015 Today on TSR ### Top unis in Clearing Tons of places at all these high-ranking unis Poll Useful resources ### Maths Forum posting guidelines Not sure where to post? Read the updated guidelines here ### How to use LaTex Writing equations the easy way ### Study habits of A* students Top tips from students who have already aced their exams

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top of page # What is 1 Ohm ? The dimension of an electric resistance is the “Ohm”. It is abbreviated with the Greek letter Omega Ω Georg Simon Ohm 16 March 1789 – 6 July 1854 •     German physicist and mathematician •     Ohm’s Law  R = U  / I  published 1827 in “The Galvanic Circuit Investigated Mathematically” •     The unit of resistance was named “Ohm” in his honour Mr Ohm wanted to develop a mathematical relation in order to calculate the “intensity of flowing electricity” (= electric current) as a function of the material and the dimensions of the wire. What he found is one of the very basic laws of electrical engineering. It seems almost trivial to us but it wasn't at all at the time: The higher the voltage U and the smaller the resistance R, the larger is the electric current I I = U/R   or   U = R·I    or    R = U/I The dimension:  [ R ] = Ohm = Ω = V/A Ohm stipulated that the relation U/I  i.e. the resistance was an independent constant. Insofar he was not quite right as we know today that most resistances are not constant but most often depend on the temperature or many other things. The diagram shows how a currentthat is flowing from A to B develops a voltage U  across the resistance R . For our particular application in piezo-electrics we talk about extremely high resistances. As we have seen before a piezo element is a good insulator with an internal resistance from pole to pole (from electrode to electrode) in the order of 10¹²  Ohms or more. In a “normal electronics” environment we would simply neglect such high resistances but in a “piezo electric environment” we need to care about. Normally we count in logarithmic terms like 10⁷, 10⁸, 10⁹  etc. We remember that 10⁹   would mean a one with 9 zeros. Sometimes the decimal multipliers  Mega- ; Giga- ; Tera- are used for 10⁶, 10⁹, 10¹²  respectively. bottom of page

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+0 # geometry question 0 55 3 Solve for the value of x in simplest radical form. Remember to write square roots as SQRT. Mar 2, 2021 ### 3+0 Answers #1 +31281 +2 Wow....what a skewed-not-to-scale looking drawing..... if that angle is really 45 then the lower right angle is also 45o the hypotenuse of the 3-4 triangle is 5 sin45 = opposite/hypotenuse = x / 5 sqrt 2/ 2 = x/5 x = 5 sqrt(2) / 2     or  5/2  sqrt 2 Mar 2, 2021 #2 +118069 +1 LOL!!!!......the  second near-to-impossible figure.....here's  the first : CPhill  Mar 2, 2021 #3 +31281 +2 Yah...no kidding !   Kinda Escher-like  !     Makes my mind all pretzel-up ! Mar 2, 2021

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top of page Search How to Slice an Elliptical Pizza? Updated: Aug 2 One day, a famous pizzeria in Chicago is booked by mathematicians for a special day (PI DAY) celebration. As being a Mathematics major, the store owner decides to serve elliptical pizzas to his guests on this day. In this regard, he makes sure that the pizzas served have the shape of an ellipse expressed mathematically as (we assume x and y have arbitrary units) He bakes the pizzas and serves them uncut. He leaves it to his special guests to figure out how to slice each pizza so that everybody will have a fair share, noting that each pizza will be shared by 8 people. In few minutes, they all figure out how to slice the elliptical pizzas so that each slice would have the same size. Can you also figure it out? If so, can you also find a general solution for any pizza served in an elliptical shape and expressed mathematically as where a and b are any positive real numbers.

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Temperature and Heat The heat of fusion is the amount of heat needed to convert 1 g of a solid at its melting point into a liquid. Equation Q = mHf 3.9 Equation Q = mHv 3.10 Change of State No, we don’t mean moving from New York to Texas. State and phase are words used interchangeably in physics to describe whether a material is a solid, liquid, gas or plasma – more on plasmas later. When heat is added to a material, at some point the material changes its state. Warming ice to 0°C causes it to change to water, a solid to liquid phase change. Continuing to add heat causes the water’s temperature to rise, ultimately reaching 100°C and the liquid begins to evaporate or become a gas. Left: Condensation; Image from Wikipedia And just as a person might move back from Texas to New York, materials can change their states in the opposite direction when they cool. Water condenses from a gas to a liquid – you see that all the time when droplets of water form on a cold bottle of water just brought out of a refrigerator into the afternoon sunlight. To make water colder you can fill an ice cube tray with water, put it in the freezer, and the liquid will solidify as heat is removed. We are familiar with these state changes, and with physics you can calculate how much energy is required to change states. And you will also learn unexpected things like why boiling water can freeze almost instantly into ice. H2O; Image from WikipediaSubstances change state because of the way their atoms and molecules react to heat. Consider water, which is a simple molecule made of one atom of oxygen (red in diagram) and two atoms of hydrogen (white). Molecules in a liquid (left) are closely bonded, whereas molecules making up ice (right) are interconnected in a more open but rigid structure of six-sided ice crystals. Each hydrogen atom is connected to two oxygen atoms, and a strong regular structure results. Heating ice causes its temperature to rise and its molecules to vibrate, in a sense pulling the electrons away from the oxygens. But the strength of the bonds is great so the molecule stays connected to other molecules. When the temperature reaches 0°C enough energy has been introduced into the ice to break the bonds connecting molecule to molecule, and the individual molecules become free to move. The solid ice begins to break apart, forming water. If energy continues to be added to the ice-water mixture the temperature does not change  - its stays at 0°C  - until all the ice is melted. All of the added energy goes to breaking the tight bonds of ice. Additional heating of water causes its temperature to increase because the water molecules move more rapidly, until the temperature reaches 100°C. What happens then? At 100°C the water begins to boil, which means that the water molecules are breaking apart and steam (hot water vapor) is created. Ice, liquid water and steam all have the same chemical formula of H2O, but the H2O has very different properties in its different phases. Energy to Change States It takes exactly 80 calories of heat to turn 1 g of ice into 1 g of liquid water.  This is called the heat of fusion of water. A liquid releases the same amount of heat when it solidifies.  Note that while a solid melts to become a liquid, or a liquid freezes to become solid, there is no increase in temperature because all of the energy goes into the phase change.  Different materials require differing amounts of heat to melt. If you want to melt 100 g of ice you would need 80 calories of heat for each gram or 8,000 calories for the entire amount of ice. Why is this type of information important? Well, if you were operating a factory and had to melt solid iron to pour into molds to make plows, for example, you would probably want to calculate how much energy was required so you could estimate the cost. Iron is easier to melt than ice, requiring only 65 calories for each gram.  To melt 1,000 g of iron already at its melting temperature would require 65 calories/g x 1,000 g = 65,000 calories of energy. Of course, first you would have to heat the iron to its melting point of 1,535°C before it would melt – and that would take additional energy! Lets go back to water and trace its energy use as it changes from ice to liquid to steam. The animation summaries the critical temperatures and heat required for 1 gram throughout all the phases. Here is a table that summarizes all this: A: The specific heat of ice is 0.5 so to heat the ice from its starting temperature, say -50°C to its melting temperature of 0°C requires 0.5 cal/degree x 50 degrees = 25 calories per gram of ice. B: As we saw earlier, to melt ice requires 80 calories/g, with the temperature of the water-ice mixtures staying constant at 0°C until all the ice has melted. C: To heat each gram of water from 0°C to 100°C requires 1 calorie of energy for each degree of warming or a total of 100 calories/g for the 100°C increase. D: Once the water reaches 100° the temperature remains constant as it starts to boil – or vaporize – and this requires 540 calories for each gram. This is much more than melting ice or heating water, because now the bonds between each water molecule are being broken, rather than just being stretched and reorganized. E: After all the water has become a gas – steam – the addition of more heat will raise the temperature of the gas, that is, make the gas molecules move faster. To cool a gas to liquid and then to an ice requires removing energy from the water for each step. For example, to cool water from 100°C to 0°C requires the water to lose 100 calories for each gram. The heat removed usually goes into the surrounding air. Another example: a wet T-shirt chills the wearer because 540 calories of body heat are removed to evaporate each gram of water from the shirt. On a hot day this is a cheap way to keep cool, but is generally not approved for classroom application. To calculate the energy needed to melt a solid already at its melting temperature use this equation: Heat needed = mass in grams x heat of fusion Q = mH f Where Hf is the heat of fusion of the solid. To calculate the energy needed to vaporize a liquid already at its evaporation temperature use this equation: Heat needed = mass in grams x heat of vaporization Q = mH v Where Hv is the heat of vaporization of the liquid. Crystalline and Amorphous Solids Water ice is a crystalline solid. All of the molecules are linked together with the same type of bonds. Once the ice’s temperature reaches 0°C all of the bonds begin to break and melting occurs. Some other solids don’t have regular crystal structure and do have chemical bonds of different types, so that melting occurs over a range of temperatures as each type of bond breaks. Such substances are called amorphous solids. Two of the most familiar examples are butter and glass. We all know that butter gradually softens when warmed and as the heat increases it finally completely melts to a sticky liquid. Although we don’t often get to see glass melt it behaves in the same manner. In both cases the melting occurs over a range of temperatures rather than at one temperature as with a crystalline solid. Left: Butter sculpture of astronaut Neil Armstrong. Neil is displayed in a chilled space to avoid disastrous phase change. Image from Flickr.

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# Probability of getting 4 of a kind in a 5 card hand 4. Poker probability in deck poker. Q: What is the probability getting Straight Flush, Four of a Kind, House etc. when given five Cards? .. In 5 - card stud, the stronger hands are less frequent than the weaker hands ; i.e., no pair is most. Since it's not stated which 4 cards, whatever you get when you pick the first card can A poker hand consists of 5 cards. It will come from a. If all hands are equally likely, the probability of a single pair is obtained by dividing by 5). FOUR OF A KIND This is five cards in a sequence (e.g., 4, 5 with aces allowed to be either 1 or 13 (low or high). ### Roulette game: Probability of getting 4 of a kind in a 5 card hand FREE ORIGIN PC Ghost rider games to play free two Cooking games play free online without downloading Poker game java Chard Museum Best sign up games in the world Probability with xisf.org How many choices for the other card? Detailed answers to any questions you might. The number of combinations of things taken at a time is:. A TRIPLE This hand has the pattern AAABC where A, B. Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. People thought about probability and gambling Goalie (hockey) before the invention of poker.

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This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN. This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN. Joint probabilities of demands on a water distribution network: A non-parametric approach / Ridolfi, Elena; Ina, Vertommen; Magini, Roberto. - 1558:(2013), pp. 1681-1684. (Intervento presentato al convegno 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) tenutosi a GREECE nel SEP 21-27, 2013) [10.1063/1.4825853]. Joint probabilities of demands on a water distribution network: A non-parametric approach Abstract This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN. Scheda breve Scheda completa 2013 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN. water supply; joint probabilities; contingency tables; demand scenarios 04 Pubblicazione in atti di convegno::04b Atto di convegno in volume Joint probabilities of demands on a water distribution network: A non-parametric approach / Ridolfi, Elena; Ina, Vertommen; Magini, Roberto. - 1558:(2013), pp. 1681-1684. (Intervento presentato al convegno 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) tenutosi a GREECE nel SEP 21-27, 2013) [10.1063/1.4825853]. File allegati a questo prodotto Non ci sono file associati a questo prodotto. I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione. Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/551877` Attenzione Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo • ND • 4 • 4

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# Existence of a root in $k[x_1, \ldots, x_n]$ Prove the following: If $k$ is an algebraically closed field and $f(x_1, \ldots, x_n) \in k[x_1,\ldots, x_n]$ is non-zero, then there exists $(a_1, \ldots, a_n)\in k^n$ s.t $f(a_1, \ldots, a_n) = 0$. I am supposed to prove this without the use of any large theorem and just from elementary principles. I thought I had a proof for it, but realized that it did not cover all cases. I then tried an inductive argument, but it wasn't working as well as I had hoped. • Maybe this could help: $k[x_1,\ldots,x_n]=k[x_1,\ldots, x_{n-1}][x_n]$. – Sigur Jan 16 '13 at 23:20 • The basic idea is that you let $n-1$ of the variables be arbitrary, then solve for the remaining variable. The hitch is that when you assign values to the $n-1$ variables, the polynommial could vanish identically. But you win in that case, too. – Gerry Myerson Jan 16 '13 at 23:21 • @Gerry And what about the possibility that the polynomial is identically constant $\ne 0$ under all specializations? E.g. $f = 1$ is a counterexample. – Math Gems Jan 17 '13 at 3:31 • @MathGems This is the problem I was having with my argument. I assigned n-1 variables to be arbitrary, but realized the constant case was a hitch – Math2012pc Jan 17 '13 at 4:05 • @MathGems, welcome back, haven't seen you here for a while. Yes, non-zero constants would seem to be a bit of a worry. If $f$ is not constant, then presumably you can find some variable $x_k$ and some number $c$ such that if you set $x_k$ to $c$ you still get a non-constant polynomial, and then proceed by induction. But I admit that's a handwave, not a proof. I knew there was a reason I felt more comfortable leaving a comment than an answer! – Gerry Myerson Jan 17 '13 at 4:50 The correct hypothesis is $f$ non-constant (non-zero is not sufficient as pointed out in the comment by MathGems, and it is also useless because otherwise there is nothing to prove). Let us prove the following statement by induction on $n$: If $f\in k[x_1,\dots, x_n]\setminus k$, there exists $a=(a_1, \dots, a_n), b=(b_1, \dots, b_n)\in k^n$ such that $f(a)=0$ and $f(b)\ne 0$. The statement is clear when $n=1$. Suppose $n\ge 2$ and the statement true in $\le n-1$ variables. We can suppose $f\notin k[x_1,\cdots, x_{n-1}]$ (otherwise we are done). Write $$f=g_d(x_1,\dots, x_{n-1})x_n^d+\cdots + g_1(x_1, \dots, x_{n-1})x_n+ g_0(x_1, \dots, x_{n-1}), \quad d\ge 1, \ g_d\ne 0.$$ Let $b'\in k^{n-1}$ be such that $g_d(b')\ne 0$. Then the polynomial $f(b',x_n)\in k[x_n]\setminus k$ has a zero $a_n$ and a non-zero $b_n$. So $a:=(b',a_n)$, $b:=(b', b_n)$ satisfy the desired properties.

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# Mathematical relationship between molarity and normality ### Relationship between normality and molarity | Chemistry tutorials What is the mathematical equation to calculate the normality/molarity of standard bottle of . /a/serii.info Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic The relation between mole fraction and molality. The best morality is to have common sense. The common sense means we should be normal person who respect women and avoid criticism. A normp as Z' sal. It is the mass of solute dissolved in mL of the solution. This method is commonly used in medicine and pharmacy. When a solute is present in trace quantities, it is convenient to express concentration in parts per million ppm and is defined as: As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. Such a small concentration is also expressed as 5. Strength or Concentration Grams per litre: It is defined as the amount of the solute in gram present in the one litre of the solution. The mole fraction of any component of a solution is defined as the ratio of the number of moles of that component present in the solution to the total number of moles of all components of the solution. ### Mole Fraction, Molality & Molarity and relation between them It is to be noted that the sum of mole fraction of solute and mole fraction of liquid is 1. Mole fraction is independent of temperature Molarity Molar Concentration: Molarity M is defined as a number of moles of solute dissolved in one litre or one cubic decimetre of the solution. Unit of molarity is mol L-1 0r mol dm-3 or M. • Molarity, Molality, or Normality? (A Quick Review) • Relation Between Molarity and Normality • Chemistry tutorials Number of moles of a substance can be found using the formula Molarity changes with temperature because volume changes with temperature. Molality m is defined as a number of moles of solute expressed in kg dissolved in one kg of solvent, Molality has no unit. Molality is a better way of expressing concentration than molarity because there is no term of volume of solvent is involved. The volume of the solvent depends on the temperature of the solvent. ## Concentration of Solution Thus there is no effect of the change of temperature on the molality. Molality is related with solubility as Normality: Normality N is defined as gram-equivalent of solute dissolved in one litre or one cubic decimetre of the solution, Unit of molarity is N. Molarity is also called the molar concentration. This is because this gives the concentration of a compound as moles per litre. Sometimes, this unit is given as M. Since the measurement is taken for a litre, molarity is measured regarding solutions liquids. A solution is composed of solutes and a solvent. The solutes are dissolved in the solvent. The mixture of solutes and the solvent is called a solution. The molarity of a particular solution is the amount of that solute in moles present in one litre of the solution. Therefore, molarity is calculated by dividing the number of moles from the volume of the solution. Molarity Equation The equation for the molarity is given as below. 5.4 Molarity and Normality Molarity of a solution depends on the changes of volume, temperature of the solution, addition of more solutes and any other factors that affect the solubility of a solute in a solution. When the volume of solvent is increased, the molarity decreases according to above equation. The temperature has a direct effect on the volume of a solution. When the temperature is increased, the volume of the solution is increased. When more solutes are added to the solution, the number of moles of the solute is increased, which will increase the molarity of the solution. What is Normality Normality of a solution is the gram equivalent weight of a solute in one litre of solution. Therefore, it is also called the equivalent concentration of a solution. But when a different reaction occurs, the same compound may have a different normality.

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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!) A167709 Numbers y such that 19*y^2 + 81 is a square. 12 0, 1, 15, 24, 220, 351, 560, 5124, 8175, 74801, 119340, 190399, 1742145, 2779476, 25432120, 40575249, 64735100, 592324176, 945013665, 8646845999, 13795465320, 22009743601, 201388477695, 321301866624, 2939902207540, 4690417633551 (list; graph; refs; listen; history; text; internal format) OFFSET 0,3 REFERENCES A. H. Beiler, "Recreations in the theory of numbers": Ex. 38, page 298 (Dover Publications, Inc., New York, 1966). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,340,0,0,0,0,-1). FORMULA G.f.: (z + 15*z^2 + 24*z^3 + 220*z^4 + 351*z^5 + 560*z^6 + 5124*z^7 + 8175*z^8 + 74801*z^9 - 340*z^5*(z + 15*z^2 + 24*z^3 + 220*z^4) ) / (1 - 340*z^5 + z^10). a(n+10) = 340*a(n+5) - a(n). a(n+5) = 170*a(n) + 39*sqrt(19*a(n)^2 + 81). For n == 0 (mod 5): a(n) = ( 9*sqrt(19) )/38*(170 + 39*sqrt(19))^(n) + (-9*sqrt(19))/38*(170 - 39*sqrt(19))^(n); the subsequence is 0, 351, 119340, 40575249, 13795465320, 4690417633551, 1594728199942020, 542202897562653249, 184347390443102162640, ... For n == 1 (mod 5): a(n) = (10*sqrt(19) + 19)/38*(170 + 39*sqrt(19))^(n) + (-10*sqrt(19) + 19)/38*(170 - 39*sqrt(19))^(n); the subsequence is 1, 560, 190399, 64735100, 22009743601, 7483248089240, 2544282340597999, 865048512555230420, 294113949986437744801, ... For n == 2 (mod 5): a(n) = (66*sqrt(19) + 285)/38*(170 + 39*sqrt(19))^(n) + (-66*sqrt(19) + 285)/38*(170 - 39*sqrt(19))^(n); the subsequence is 15, 5124, 1742145, 592324176, 201388477695, 68471490092124, 23280105242844465, 7915167311077025976, 2691133605660945987375, ... For n == 3 (mod 5): a(n) = (105*sqrt(19) + 456)/38*(170 + 39*sqrt(19))^(n) + (-105*sqrt(19) + 456)/38*(170 - 39*sqrt(19))^(n); the subsequence is 24, 8175, 2779476, 945013665, 321301866624, 109241689638495, 37141853175221676, 12628120837885731345, 4293523943027973435624, ... For n == 4 (mod 5): a(n) = (959*sqrt(19) + 4180)/38*(170 + 39*sqrt(19))^(n) + (-959*sqrt(19) + 4180)/38*(170 - 39*sqrt(19))^(n); the subsequence is 220, 74801, 25432120, 8646845999, 2939902207540, 999558103717601, 339846815361776800, 115546917664900394399, 39285612159250772318860, ... EXAMPLE a(0) = 0 because 19*0 + 81 = 9^2, a(1)=1 because 19*1 + 81 = 10^2. MAPLE a(0):=0:a(1):=1:a(2):=15:a(3):=24:a(4):=220:a(5):=351:a(6):=560: a(7):=5124: a(8):=8175:a(9):=74801:for n from 0 to 40 do a(n+10):=340*a(n+5)-a(n):od:seq(a(n), n=0..40); MATHEMATICA a[0]=0; a[1]=a[-1]=1; a[2]=a[-2]=15; a[n_] := a[n] = 170*a[n-5]+39*Sqrt[19*a[n-5]^2+81]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 19 2013 *) LinearRecurrence[{0, 0, 0, 0, 340, 0, 0, 0, 0, -1}, {0, 1, 15, 24,   220, 351, 560, 5124, 8175, 74801}, 100] (* G. C. Greubel, Jun 20 2016 *) CROSSREFS Cf. A167708, A167774, A167775, A167778, A167779, A167780. Sequence in context: A247315 A154150 A324484 * A167353 A219880 A216379 Adjacent sequences:  A167706 A167707 A167708 * A167710 A167711 A167712 KEYWORD easy,nonn AUTHOR Richard Choulet, Nov 10 2009 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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Cody # Problem 314. Find the sum of the elements in the "second" diagonal Solution 522806 Submitted on 6 Nov 2014 by Christophe 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 %% x = magic(6); y_correct = 111; assert(isequal(sum_of_sec_diag(x),y_correct)) 2   Pass %% x = magic(10); y_correct = 505; assert(isequal(sum_of_sec_diag(x),y_correct)) 3   Pass %% x = magic(11); y_correct = 671; assert(isequal(sum_of_sec_diag(x),y_correct)) 4   Pass %% x=[1 2 3; 4 4 6; 2 8 9]; y_correct = 9; assert(isequal(sum_of_sec_diag(x),y_correct))

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Runtime Complexity TRS: The TRS R consists of the following rules: half(0) → 0 half(s(0)) → 0 half(s(s(x))) → s(half(x)) inc(0) → 0 inc(s(x)) → s(inc(x)) zero(0) → true zero(s(x)) → false p(0) → 0 p(s(x)) → x bits(x) → bitIter(x, 0) bitIter(x, y) → if(zero(x), x, inc(y)) if(true, x, y) → p(y) if(false, x, y) → bitIter(half(x), y) Rewrite Strategy: INNERMOST Renamed function symbols to avoid clashes with predefined symbol. Runtime Complexity TRS: The TRS R consists of the following rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Rewrite Strategy: INNERMOST Infered types. Rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Types: half' :: 0':s' → 0':s' 0' :: 0':s' s' :: 0':s' → 0':s' inc' :: 0':s' → 0':s' zero' :: 0':s' → true':false' true' :: true':false' false' :: true':false' p' :: 0':s' → 0':s' bits' :: 0':s' → 0':s' bitIter' :: 0':s' → 0':s' → 0':s' if' :: true':false' → 0':s' → 0':s' → 0':s' _hole_0':s'1 :: 0':s' _hole_true':false'2 :: true':false' _gen_0':s'3 :: Nat → 0':s' Heuristically decided to analyse the following defined symbols: half', inc', bitIter' They will be analysed ascendingly in the following order: half' < bitIter' inc' < bitIter' Rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Types: half' :: 0':s' → 0':s' 0' :: 0':s' s' :: 0':s' → 0':s' inc' :: 0':s' → 0':s' zero' :: 0':s' → true':false' true' :: true':false' false' :: true':false' p' :: 0':s' → 0':s' bits' :: 0':s' → 0':s' bitIter' :: 0':s' → 0':s' → 0':s' if' :: true':false' → 0':s' → 0':s' → 0':s' _hole_0':s'1 :: 0':s' _hole_true':false'2 :: true':false' _gen_0':s'3 :: Nat → 0':s' Generator Equations: _gen_0':s'3(0) ⇔ 0' _gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x)) The following defined symbols remain to be analysed: half', inc', bitIter' They will be analysed ascendingly in the following order: half' < bitIter' inc' < bitIter' Proved the following rewrite lemma: half'(_gen_0':s'3(*(2, _n5))) → _gen_0':s'3(_n5), rt ∈ Ω(1 + n5) Induction Base: half'(_gen_0':s'3(*(2, 0))) →RΩ(1) 0' Induction Step: half'(_gen_0':s'3(*(2, +(_\$n6, 1)))) →RΩ(1) s'(half'(_gen_0':s'3(*(2, _\$n6)))) →IH s'(_gen_0':s'3(_\$n6)) We have rt ∈ Ω(n) and sz ∈ O(n). Thus, we have ircR ∈ Ω(n). Rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Types: half' :: 0':s' → 0':s' 0' :: 0':s' s' :: 0':s' → 0':s' inc' :: 0':s' → 0':s' zero' :: 0':s' → true':false' true' :: true':false' false' :: true':false' p' :: 0':s' → 0':s' bits' :: 0':s' → 0':s' bitIter' :: 0':s' → 0':s' → 0':s' if' :: true':false' → 0':s' → 0':s' → 0':s' _hole_0':s'1 :: 0':s' _hole_true':false'2 :: true':false' _gen_0':s'3 :: Nat → 0':s' Lemmas: half'(_gen_0':s'3(*(2, _n5))) → _gen_0':s'3(_n5), rt ∈ Ω(1 + n5) Generator Equations: _gen_0':s'3(0) ⇔ 0' _gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x)) The following defined symbols remain to be analysed: inc', bitIter' They will be analysed ascendingly in the following order: inc' < bitIter' Proved the following rewrite lemma: inc'(_gen_0':s'3(_n509)) → _gen_0':s'3(_n509), rt ∈ Ω(1 + n509) Induction Base: inc'(_gen_0':s'3(0)) →RΩ(1) 0' Induction Step: inc'(_gen_0':s'3(+(_\$n510, 1))) →RΩ(1) s'(inc'(_gen_0':s'3(_\$n510))) →IH s'(_gen_0':s'3(_\$n510)) We have rt ∈ Ω(n) and sz ∈ O(n). Thus, we have ircR ∈ Ω(n). Rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Types: half' :: 0':s' → 0':s' 0' :: 0':s' s' :: 0':s' → 0':s' inc' :: 0':s' → 0':s' zero' :: 0':s' → true':false' true' :: true':false' false' :: true':false' p' :: 0':s' → 0':s' bits' :: 0':s' → 0':s' bitIter' :: 0':s' → 0':s' → 0':s' if' :: true':false' → 0':s' → 0':s' → 0':s' _hole_0':s'1 :: 0':s' _hole_true':false'2 :: true':false' _gen_0':s'3 :: Nat → 0':s' Lemmas: half'(_gen_0':s'3(*(2, _n5))) → _gen_0':s'3(_n5), rt ∈ Ω(1 + n5) inc'(_gen_0':s'3(_n509)) → _gen_0':s'3(_n509), rt ∈ Ω(1 + n509) Generator Equations: _gen_0':s'3(0) ⇔ 0' _gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x)) The following defined symbols remain to be analysed: bitIter' Could not prove a rewrite lemma for the defined symbol bitIter'. Rules: half'(0') → 0' half'(s'(0')) → 0' half'(s'(s'(x))) → s'(half'(x)) inc'(0') → 0' inc'(s'(x)) → s'(inc'(x)) zero'(0') → true' zero'(s'(x)) → false' p'(0') → 0' p'(s'(x)) → x bits'(x) → bitIter'(x, 0') bitIter'(x, y) → if'(zero'(x), x, inc'(y)) if'(true', x, y) → p'(y) if'(false', x, y) → bitIter'(half'(x), y) Types: half' :: 0':s' → 0':s' 0' :: 0':s' s' :: 0':s' → 0':s' inc' :: 0':s' → 0':s' zero' :: 0':s' → true':false' true' :: true':false' false' :: true':false' p' :: 0':s' → 0':s' bits' :: 0':s' → 0':s' bitIter' :: 0':s' → 0':s' → 0':s' if' :: true':false' → 0':s' → 0':s' → 0':s' _hole_0':s'1 :: 0':s' _hole_true':false'2 :: true':false' _gen_0':s'3 :: Nat → 0':s' Lemmas: half'(_gen_0':s'3(*(2, _n5))) → _gen_0':s'3(_n5), rt ∈ Ω(1 + n5) inc'(_gen_0':s'3(_n509)) → _gen_0':s'3(_n509), rt ∈ Ω(1 + n509) Generator Equations: _gen_0':s'3(0) ⇔ 0' _gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x)) No more defined symbols left to analyse. The lowerbound Ω(n) was proven with the following lemma: half'(_gen_0':s'3(*(2, _n5))) → _gen_0':s'3(_n5), rt ∈ Ω(1 + n5)

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Search a number 2132383 = 11217623 BaseRepresentation bin1000001000100110011111 311000100002011 420020212133 51021214013 6113412051 724060601 oct10104637 94010064 102132383 111227100 1286a027 13598786 143d7171 152c1c3d hex20899f 2132383 has 6 divisors (see below), whose sum is σ = 2343992. Its totient is φ = 1938420. The previous prime is 2132381. The next prime is 2132387. The reversal of 2132383 is 3832312. It is a happy number. It is not a de Polignac number, because 2132383 - 21 = 2132381 is a prime. It is a Duffinian number. It is a congruent number. It is not an unprimeable number, because it can be changed into a prime (2132381) by changing a digit. It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 8691 + ... + 8932. 22132383 is an apocalyptic number. 2132383 is a deficient number, since it is larger than the sum of its proper divisors (211609). 2132383 is a wasteful number, since it uses less digits than its factorization. 2132383 is an evil number, because the sum of its binary digits is even. The sum of its prime factors is 17645 (or 17634 counting only the distinct ones). The product of its digits is 864, while the sum is 22. The square root of 2132383 is about 1460.2681260645. The cubic root of 2132383 is about 128.7127997594. Adding to 2132383 its reverse (3832312), we get a palindrome (5964695). The spelling of 2132383 in words is "two million, one hundred thirty-two thousand, three hundred eighty-three". Divisors: 1 11 121 17623 193853 2132383

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# Nurse logic Topics: Oxygen, Nursing, Respiratory system Pages: 7 (1352 words) Published: October 30, 2014 The nurse assesses Josh's vital signs. His respirations are rapid and shallow. 1. What is the best technique for the nurse to use to assess Josh's respirations accurately? A. Observe chest expansion for 15 seconds and multiply by 4 B. Encourage Josh to breath as deeply and slowly as possible C. Watch for nasal flaring and count the air exchanges with each movement D. Place a hand on Josh's chest and count the hand motion D. Place a hand on Josh's chest and count the hand motion - Rationale: This technique allows the nurse to observe and count the chest movement, even when respirations are shallow.  Josh's respirtory rate is 36. 2. How should the nurse describe Josh's respiratory pattern? A. Eupnea C. Trachypnea D. Orthopnea C. Trachypnea - Rationale: A rapid respiratory rate, which is consistent with Josh's rate of 36. Normal respiratory rate for a school-aged child is 16-30 breaths per minute.  Because of Josh's dyspnea, the nurse is concerned that he may need to receive oxygen. 3. To determine the need for the application of a nasal cannula, which assessment is most important for the nurse to perform? A. Measure oxygen saturation B. Auscultate breathing sounds C. Measure capillary refill D. Observe chest excursion A. Measure oxygen saturation - Rationale: Oxygen saturation provides important data about the percentage of hemoglobin that is saturated with oxygen - a valuable reflection of the client's overall oxygenation.  4. In assessing Josh's breathing sounds, the nurse should ask him to perform which action? A. Hold his breath for fifteen seconds B. Repeat the phrase, "ninety-nine" C. Cough deeply after each breath D. Breath deeply through the mouth D. Breath deeply through the mouth - Rationale: Josh should be instructed to breathe slowly and deeply through a slightly opened mouth to allow best auscultation of breathing sound.  5. To measure capillary refill, the nurse must first perform which action? B. Compress Josh's nailbed C. Obtain a healthcare provider's prescription D. Elevate the extremity to be assessed B. Compress Josh's nailbed - Rationale: To measure capillary refill, the nurse should first compress the client's nailbed, and then observe the return of normal color to the nailbed.  The nurse plans to measure Josh's oxygen saturation with a spring-tension finger clip. While the nurse is explaining this procedure, Josh asks if it will hurt. 6. Which response is best for the nurse to provide? A. "Yes, but the pain will only last a very short time." B. "No, you will not even know the clip is on your finger." C. "The clip feels like squeezing your finger with your other hand." D. "You seem to be worried about experiencing pain." C. "The clip feels like squeezing your finger with your other hand." - Rationale: This is an honest response to Josh's question regarding pain and one that places the sensation he will feel in a context he can understand.  The nurse measure Josh's oxygen saturation at 88% and capillary refill at 1 second. Breathing sounds are absent in the base and coarse bilaterally throughout the rest of the lung fields. The nurse applies a nasal cannula and administers oxygen at 2 liters per minute. 7. When applying a nasal cannula, it is most important for the nurse to provide which instructions? A. Make sure the cannula tubing stays snugly around the ears and under the chin B. Remove the clients toy pistol from the room C. Make sure the humidifier always contains some water D. Keep some type of padding around the ear and over the cheeckbones B.Remove the clients toy pistol from the room- Rationale: Oxygen supports combustion and is essential to ensure client safety during oxygen administration  8. Which nursing diagnosis is most relevant to Josh's current status? A. Excess fluid volume B. Impaired spontaneous ventilation C. Impaired gas exchange...

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Question # Claim: Most adults would erase all of their personal information online if they could. A software... Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 550 randomly selected adults showed that 65​% of them would erase all of their personal information online if they could. Find the value of the test statistic. We have for given example, Population proportion value is =0.5 Estimate for sample proportion = 0.65 Z test statistic formula for proportion #### Earn Coins Coins can be redeemed for fabulous gifts.

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• # User Defined Function To Sum And Round To Two Decimal Places Macro Purpose: • To round a Sum formula to two decimal places Examples of where this function shines: • When you are feeling really lazy, and don't want to type =Round(Sum(A1:A3),2), you can just type =Sumr(A1:A3) Macro Weakness(es): • Will calculate slower than the nested Round and Sum combination. Performance degridation most likely won't be noticed if it is only used a few times, but if hundreds of formulas are used, it may slow the calculation down noticeably. • Only accepts range arguments, not values. • Only accept one contiguous range (not multiple ranges). Versions Tested: This function has been tested with Excel 2003. It should not have any issues running from any of the Office applications from 97 or higher, but to date this has not been tested. VBA Code Required: • Place the following code in a standard module Code: ```Function SumR(rng As Range) As Double 'Author : Ken Puls (www.excelguru.ca) 'With thanks to Remco Boom for the "\1" method 'Macro Purpose: Rounds the Sum'd range to 2 decimals SumR = ((100 * Application.WorksheetFunction.Sum(rng.Cells) + 0.01) \ 1) / 100 End Function``` How to use the code: • Once the code is in a standard module, use it as a regular formula in a worksheet cell, as shown below <img src="/images/VBA06-01.jpg"> How it works: • The uses Excel's native SUM formula to sum up the range, multiplies it by 100 and adds .01. At this point it then rounds it off to no decimal places, and divides it by 100 to get the result. • The \1 operator rounds the amount to zero decimal places. The .01 addition in the middle of the formula corrects an issue with the rounding of this function, as it rounds 0.5 down to zero. The End Result: • The sum of the range is returned, rounded to 2 decimal places. An Alternative: • The SumRDown function, shown below, will always round the value down to 2 decimal places. Code: ```Function SumRDown(rng As Range) As Double 'Author : Ken Puls (www.excelguru.ca) 'Macro Purpose: Rounds the Sum'd range down to 2 decimals SumRDown = Int(100 * Application.WorksheetFunction.Sum(rng.Cells)) / 100 End Function``` <img src="/images/VBA06-02.jpg"> I'm afraid that you must be logged in to comment or leave a testimonial. I wish it could be otherwise, but I'm trying to keep my site spam free for everyone's benefit. If you don't yet have an account it's completely free to sign up, and a very quick process. Simply click here to Register. Not only can you post a comment here, but it gives you full access to posts questions in our forum as well! If you already have an account, and just haven't logged in yet, what are you waiting for? Login Now! 1. Rick Rothstein - I have another (somewhat shorter) alternate for your SumR function.. Code: ```Function SumR(rng As Range) As Double SumR = Evaluate("SUM(ROUND(" & rng.Address & ",2))") End Function``` 1. Rick Rothstein - I see my function code did not layout correctly. I'll try again... Code: ```Function SumR(rng As Range) As Double SumR = Evaluate("SUM(ROUND(" & rng.Address & ",2))") End Function``` 1. Bob Phillips - I would suggest the precision is an optional parameter Code: ```Function SumR(rng As Range, Optional ByVal precision As Long = 2) As Double SumR = Evaluate("SUM(ROUND(" & rng.Address & "," & precision & "))") End Function``` 1. Rick Rothstein - That is a good suggestion Bob, especially given how easy it is to incorporate into my function. In my defense, I was responding to the post code which only wanted to round to 2 decimal places, so unthinkingly I just did the same thing. 1. Bob Phillips - No defence needed Rick, just thought that as you had taken the trouble to suggest the alternative, I might as well suggest an enhancement to make it a tad more useful - couldn't resist .t Good to see you here BTW. It is not the busiest site, but you will be a good addition. • ### Recent Forum Posts #### Formula help Pictures don't really help us to help you. Please attach a workbook and ideally indicate what result you are expecting as it's not clear to me at all... JoePublic Today, 08:13 AM #### Help doing some calculations within pivot table Wow this is awesome, thank you all for your help!... accountingguy Today, 02:40 AM #### Help doing some calculations within pivot table ricklinty, • a nice tutorial for adding measures in the Data Model! • the only thing I might have done differently is use your prior created measures ... p45cal Yesterday, 01:20 PM #### Help doing some calculations within pivot table alansidman Yesterday, 07:56 AM #### Formula help Hello, I am going to attach the sheets for reference! This is sheet 1 This is sheet 2 ... KhodrK1590 Yesterday, 06:23 AM

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Manhattan GMAT Challenge Problem of the Week- 22 April 2013 by on April 22nd, 2013 Here is a new Challenge Problem! If you want to win prizes, try entering our Challenge Problem Showdown. The more people that enter our challenge, the better the prizes! Question The value of investment Q increased by q percent from the beginning of a particular year through June 30 of that year, and then experienced no net change from June 30 to the end of the year. The value of investment increased by p percent from the beginning of that year to June 30, and the new value increased again by p percent from June 30 to the end of the year. If the percent increase in value from the beginning to the end of the year was the same for both investments, which of the following expressions gives the value of p in terms of q? A. B. C. D. E. We can pick our own smart number or use an algebraic approach; both methods are shown below. Smart Numbers Let the initial value of the investment be \$100 (a value that works nicely with percent changes). Note that both investments can start off at \$100; nothing in the problem prevents this and choosing the same starting point for the two investments will make the math easier. It’s better to select a value for p and use that to calculate q, because investment P undergoes two consecutive percent changes while investment Q undergoes just one. Say p = 20. In that case, investment P increases by 20% during the first half of the year. Twenty percent of the initial value of \$100 is \$20, so investment P goes from \$100 to \$120. Then, the new value of investment P increases by a further 20% during the remainder of the year. This time, 20% of \$120 is \$24, so investment P goes from \$120 to \$144. Now, figure out investment Q, which also starts at \$100.  If the percent increase over the year for investment Q is the same as for investment P, then investment Q will also be worth \$144 at the end of the year. That’s a percent increase of 44%, so q = 44. Plug q = 44 into the answer choices, and look for the desired result of p = 20: (A) (B) (C) (D) (E) Algebraic Solution If the overall percent increase was the same for both investments, then the initial investments must have been multiplied by the same overall factor in the end. (For instance, if both investments went up by a net total of 30 percent, then both initial values would be multiplied by 1.30 to produce the final values.) Investment P undergoes two consecutive changes of p percent, so the initial value of that investment is multiplied by a factor of . Investment Q increases by q percent and then undergoes no further changes, so the initial value of that investment is multiplied by a factor of . Since both factors must be the same in the end, set them equal to each other and solve for p: Multiply by 100 on the left and  (the same as 100) on the right:

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# AP Board 5th Class Maths Solutions 7th Lesson Data Handling Andhra Pradesh AP Board 5th Class Maths Solutions 7th Lesson Data Handling Textbook Exercise Questions and Answers. ## AP State Syllabus 5th Class Maths Solutions Chapter 7 Data Handling One day Class-V teacher Mrs. Lakshmi collected the data about their favourite flower from the students. One student noted the data on the black board as follows. Rose, Rose, Marigold, Jasmine, Rose, Marigold, Rose, Lily, Rose, Jasmine, Rose, Marigold, Jasmine. Rose, Jasmine, Marigold, Jasmine, Rose, Rose, Jasmine, Rose. Marigold, Rose, Marigold, Marigold, Rose, Marigold, Rose, Lily, Rose. Complete the table by using the above data: Question 1. What flower is liked by most of the students? Rose flower is liked by most of the students. Question 2. How many children liked rose flower? 14 children liked rose flower. Question 3. Which flower is liked by less in number of students? Lilly flower is liked by less in number of students. II. Observe the following pictograph and fill the columns. = 5 members Question 1. Question 2. Which game was played by most of the players ? Kho-Kho was played by most of the players. Question 3. Which game was played by only 10 members? Tennicoit was played by only 10 members. III. Pochaiah, Solman, Lingaiah, Kareem and Veeresam are fishermen in Tallarevu village. The number of the fish caught by them is given in the table. Draw a pictograph for the given datAnswer: = 10 i.e., picture of one fish represents 10 fish. a) How many fish Pochaiah caught more than Lingaiah ? Fish caught by Pochaiah = 90 Fish caught by Lingaiah = 80 Difference = 10 ∴ Pochaiah caught 10 more fishes than Lingaiah. b) Is the number of fish caught by Lingaiah is equal to the total number of fish caught of Kareem and Veeresam? Yes, the number of fish caught by Lingaiah is equal to the total number of fish caught 5 by Kareem and Veeresam. c) How many fish pictures can you draw for Veeresam? Why ? 5 fish pictures can be draw for veeresam each fish picture = 10 fishes. d) Number offish pictures equal to 100 fishes are _________ 100 fishes = 10 fish pictures. IV. Class 5 students prepared data on players of different games in their school as shown below. We can represent the data in both horizontal and vertical bars. a) How many players are there in the ground? Totally 100 + 100 = 200 players are there in the ground. b) The difference between number of players played kho-kho and tennicoit is equal to which game? No. of players played kho-kho = 40 No. of players played tennicoit = 10 Difference = 40 – 10 = 30 The difference between these players is equal to cricket game. c) Which game has 40 players ? Kho-Kho has 40 players. d) “How many times” of number of tennicoit players is equal to number of kabbadi players? 4 times of number of tennicoit players is equal to number of kabbadi players. V. Rajani wants to compare her height with her four friends. She measured their heights and made a note like this. Rajani – 120 cm Rafi – 160 cm Ramesh – 140 cm Rosy – 140 cm Rani – 160 cm Help her to draw bar diagram. a) Who is the shortest person? Rajani is the shortest person. b) How much more heights is Rafi to Rajani? Height of Rafi = 160 cm Height of Rajani = 120 cm Difference = 40 cm 40 cm more height is Rafi to Rajani. c) Who is equal in height to Rajani? No one is equal to Rajani’s height. d) How much more height is Rajani than Rosy? 20 cm more height is Rajani than Rosy. VI. One day Rani collected the data of temperatures of 5 Major Cities from news papers. Prepare a bar diagram to the data and prepare 4 questions. Prepare a bar graph. 1. In which city temperature is less noted? 2. Name the cities which are equal in temperature. 4. How much move temperature is kurnool to Vijayawada? Exercise 1: Question 1. Parvathi collected the data of pet animals from her friends and recorded it in a table. She displayed the table in the class room. Question 1. Which animal is petted more in number? Hen is petted more in number Question 2. Which animal is petted less in number? Cat is petted less in number Question 3. How many students have goat as a pet animal? 10 members have goat as a pet animal. Question 4. How many students have dog as a pet animal? 6 members have dog as a pet animal. Question 2. The following table shows the number of tiles in different colours. Make a pictograph using the data and prepare some questions. Questions : 1. Which coloured blocks are more ? 2. What is the difference between white and blue coloured blocks ? 3. Which coloured blocks are less ? Question 3. Ravi maintains a provisional store in Parvatipuram. He recorded the quantities of goods and items in his shop daily. One day he records the quantities of rice, wheat, red gram and sugar as shown below. Now prepare a bar diagram to the given data and followed by some questions.

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# Deductive Reasoning How to determine whether the given reasoning is a deductive reasoning: definition, 3 examples, and their solutions. ## Definition ### Definition Deductive reasoning is a reasoning that starts from [given & known statements] to get a [specific conclusion], usually by using [logic]. ## Example 1 ### Solution The first statement is a conditional statement. p: It's raining. q: He's staying home. Assume that this statement is true. The second statement is p. Assume that this statement is also true. The third statement is q. If the top two statements are true, then q is true. p → q and p [given statements] are both true. Then, by the law of detachment, which is [logic], q [specific statement] is true. So these statements show deductive reasoning. So [deductive reasoning] is the answer. ## Example 2 ### Solution x + 2 = 3 [given statement] is true. Writing -2 on both sides doesn't change the equal sign: x + 2 - 2 = 3 - 2. This is [logic]. Then x = 1 is true. [specific statement] Linear Equation: One Variable So these equations show deductive reasoning. So [deductive reasoning] is the answer. ## Example 3 ### Solution The first two [given statements] are true: he went there yesterday, he goes there today. Then it says the last statement is true: he will go there tomorrow. These statements show a pattern, yesterday → today → tomorrow: not logic. So the given statements do not show deductive reasoning. (They show inductive reasoning.) So [not deductive reasoning] is the answer.

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