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• LaTeX:Pictures
  ...o be in the EPS (Encapsulated PostScript) format. If you followed all the steps correctly, you should get a file that looks a lot like what you'll see [htt ...ft corner of the portion of the image file you want to include. The second two coordinates are the upper right values of (x,y). Try changing the values in
  9 KB (1,454 words) - 16:52, 19 February 2024
• LaTeX:Packages
  ...ou can include in any of your LaTeX documents is simple. Just follow these steps: <li>You have two options for where to save the file to be able to include it in LaTeX source
  10 KB (1,581 words) - 12:57, 22 June 2024
• 2006 AIME II Problems/Problem 5
  ...<math>1/6</math>, and the sum of the numbers on opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is <math>47/2 Since the two dice are identical, <math>B(1)=A(1)</math> and <math>B(6)=A(6)</math> so
  5 KB (712 words) - 12:10, 5 November 2023
• 2002 AMC 12B Problems/Problem 8
  Then, the rest of the steps in Solution 1 can be followed. ...irst of the bottom three cells is a Monday, it is clear that the following two days are Tuesday and Wednesday. This means that the new bottom three cells
  2 KB (329 words) - 15:48, 14 October 2023
• 2002 AMC 10A Problems/Problem 22
  ...ps we cycle down a perfect square, and in <math>(10-1)\times 2 = 18</math> steps, we are left with <math>1</math> tile, hence our answer is <math>\boxed{\te
  3 KB (430 words) - 23:13, 13 September 2023
• 2008 AMC 10B Problems
  ...diagonal are to be added. What will be the positive difference between the two diagonal sums? ...- 2ax + b = 0</math> has two real solutions. What is the average of these two solutions?
  12 KB (1,838 words) - 16:52, 7 October 2022
• 2008 AMC 12B Problems
  ...diagonal are to be added. What will be the positive difference between the two diagonal sums? ...math> the pedometer reads <math>50000</math>. Pete takes <math>1800</math> steps per mile. Which of the following is closest to the number of miles Pete wal
  14 KB (2,199 words) - 13:43, 28 August 2020
• Asymptote: Macintosh
  '''The first two installations were tested on Mac OS 10.15.7 "Catalina," but should work for If you wish to not use "asytex", you can rename it via following the steps above, except, instead of copy and pasting the code above, change the "asyt
  5 KB (732 words) - 00:47, 13 December 2023
• 1999 AHSME Problems/Problem 22
  ...easily find out that the only way how to get these graphs to intersect in two points is the one depicted below: ...larly, the minimum of the other graph is <math>(c,d)</math>. Therefore the two remaining vertices of the area between the graphs are <math>(a,b)</math> an
  3 KB (538 words) - 12:02, 17 October 2020
• 2009 AMC 12A Problems/Problem 24
  Testing the first two (or three) positive integers instead of 2009, <math>k</math> seems to alway ...stuck 😐. There is no pretty formula for taking the <math>\log</math> of two things added together. So we rack our brains, sigh in frustration... and gi
  10 KB (1,595 words) - 22:13, 20 September 2021
• 2009 AIME II Problems/Problem 6
  ...from the set of the first <math>14</math> natural numbers so that at least two of the five numbers are consecutive. Find the remainder when <math>m</math> ...ubset in <math>{14\choose 5}</math> ways. We will now count those where no two numbers are consecutive. We will show a bijection between this set, and the
  5 KB (921 words) - 00:15, 11 December 2022
• 2009 AIME II Problems/Problem 7
  Using the steps of the previous solution we get <math>c = \sum_{i=1}^{2009} {2i\choose i} \ Using the initial steps from Solution 1, <math>S=\sum_{i=1}^{2009} \dfrac{{2i\choose i}}{2^{2i}}</m
  8 KB (1,312 words) - 16:23, 30 March 2024
• 2010 AMC 12A Problems/Problem 18
  ...wo. For <math>(1,0)</math> and <math>(1,-1)</math> we can just multiply by two. So we count paths from <math>(-4,4)</math> to each of these points, and th ...ases, notice that the path the ant takes can be expressed as a sequence of steps, such as:
  5 KB (910 words) - 01:40, 2 February 2021
• Mock AIME 2 2010 Problems
  ...e remainder, or pick one lemming and purge it. Find the smallest number of steps necessary to remove all <math>2010</math> lemmings. ...hooses one of the other four to shoot. The probability that there are some two people shooting each other can be expressed in the form <math>\frac{a}{b}</
  7 KB (1,150 words) - 09:10, 8 October 2018
• Mock AIME 2 2010 Answer Key
  ...e remainder, or pick one lemming and purge it. Find the smallest number of steps necessary to remove all 2010 lemmings. ...s process can be repeated every for every 15 lemmings, so since it takes 6 steps to clear 15 lemmings, it will take us <math>2010\cdot\frac{6}{15}=\boxed{80
  36 KB (6,214 words) - 20:22, 13 July 2023
• 2010 USAMO Problems/Problem 2
  with height <math>h_{k-2}</math> or less, the two students are permitted to ...kward motion is allowed. With this definition of forward motion, the first two students with heights <math>h_1</math> and <math>h_2</math> are always stat
  5 KB (823 words) - 19:20, 3 October 2017
• Python reference
  ...the file object that the open function returns. The function itself takes two parameters. The first is a string with the name of the file. ...list. So it will go through all of the list and return the number every 2 steps, which is what the 2 means. This will return the list [1,3,5].
  28 KB (4,762 words) - 21:20, 12 June 2023
• 2011 AMC 10B Problems/Problem 23
  ...s also <math>11^5</math>. In other words, each number is <math>10^n</math> steps from the right side of the row. The hundreds digit is <math>0</math>. We ca ...the hundreds digit of <math>2011^{2011}</math>, but you never cite way the two hundreds digits are the same.
  9 KB (1,288 words) - 20:47, 13 June 2024
• ...'g'' converge to zero or infinity, and whether the limits are one-sided or two-sided. * Note: Steps are missing.
  4 KB (764 words) - 23:10, 2 January 2012
• 2011 AMC 10B Problems/Problem 20
  ...as <math>B</math>. The line <math>\ell_{BC}</math> divides the plane into two half-planes; let <math>S_{BC}</math> be the half-plane containing <math>B</ We follow the steps shown above until we draw pentagon <math>BIHFE</math>. We know that rhombus
  7 KB (1,155 words) - 21:05, 19 June 2024

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