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  • ...the three sleepers were determined randomly, the probability that exactly two of the sleepers are from the same country is <math>\frac{m}{n}</math>, wher ...2</math> of the remaining <math>8</math> socks at random, and on Wednesday two of the remaining <math>6</math> socks at random. The probability that Wedn
    10 KB (1,615 words) - 21:48, 13 January 2024
  • ...= z,</math> and the imaginary part of <math>z</math> is <math>\sin{\frac{m\pi}{n}}</math>, for relatively prime positive integers <math>m</math> and <mat ...he plane divides the cube into two solids. The volume of the larger of the two solids can be written in the form <math>\tfrac{p}{q},</math> where <math>p<
    10 KB (1,617 words) - 14:49, 2 June 2023
  • ...ath> and <math>\sqrt{11}</math> from point <math>B</math>, so they are the two points where a circle centered at <math>A</math> with radius <math>\sqrt{11 There are two equilateral triangles with <math>\overline{AD_1}</math> as a side; let <mat
    13 KB (2,052 words) - 18:02, 5 February 2024
  • ...ves but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are tru ...with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?
    12 KB (1,771 words) - 09:41, 13 June 2024
  • ...math>, <math>\cdots</math>, <math>9\}</math> is called ''golden'' if every two consecutive numbers in the permutation are relatively prime. How many ''gol ...ing (possibly the same string) chosen at random. He continues on by tying two randomly selected untied ends together until there are no more untied ends,
    7 KB (1,309 words) - 11:13, 8 April 2012
  • if, for any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math> regular polygons <math>P_n</math> with <math>n</math> sides: given any two vertices <math>A</math> and
    4 KB (773 words) - 08:14, 19 July 2016
  • ...{a_n}</math> are all <math>n</math>th roots of unity. If <math>\omega=e^{2\pi i/n}</math>, then the sum of <math>32</math>nd powers of these roots will b ...mials of degree <math>n</math> over the field <math>\mathbb{F}_2</math> of two elements, and on the left, we have the factorisation of this generating fun
    8 KB (1,348 words) - 09:44, 25 June 2022
  • A geometric series is one where the ratio between each two consecutive terms is constant (ex. <math> 3, 6, 12, 24,\cdots </math>). The Given two <math> 2 </math>'s, "plus" can be changed to "times" without changing the r
    10 KB (1,477 words) - 16:02, 27 May 2012
  • ...e <math> M </math> minus the volume fo cone <math> N </math> is <math> 140\pi </math>, find the length of <math> \overline{BC} </math>. ...ath> S_n=\sum_{i=1}^{n-1}i\cdot S_{n-i} </math>. For example, if the first two elements are <math> 2 </math> and <math> 3 </math>, respectively, the third
    6 KB (910 words) - 17:32, 27 May 2012
  • ...s the square root of himself, or the square root of <math> i </math>. What two answers should he give? ...math> i=\cos\left(\frac{\pi}{2}\right)+i\sin\left(\frac{\pi}{2}\right)=e^{\pi i/2} </math>.
    1 KB (170 words) - 20:12, 27 May 2012
  • Two high school classes took the same test. One class of <math> 20 </math> stud Two equal circles in the same plane cannot have the following number of common
    23 KB (3,556 words) - 15:35, 30 December 2023
  • \textbf{(B)}\ \frac{440}{\pi} \qquad \textbf{(C)}\ \frac{880}{\pi} \qquad
    21 KB (3,123 words) - 14:24, 20 February 2020
  • The ratio of the areas of two concentric circles is <math>1: 3</math>. If the radius of the smaller is <m Two numbers whose sum is <math>6</math> and the absolute value of whose differe
    22 KB (3,509 words) - 21:29, 31 December 2023
  • ..., we can easily alternate them, but if <math>n</math> is odd, we must have two adjacent sides be the same length, and that length must be the larger side
    5 KB (871 words) - 18:59, 10 May 2023
  • ...xtbf{(C)}\ 12\pi+\sqrt{3}\qquad\textbf{(D)}\ 10\pi+9\qquad\textbf{(E)}\ 13\pi</math> ...<math>\dfrac{1}{2}</math>, we get <math>2\sqrt{3}</math>. Since there are two 30-60-90 triangles in the equilateral triangle, we multiply the area of the
    4 KB (675 words) - 03:58, 23 January 2023
  • Two distinct circles <math>K_1</math> and <math>K_2</math> are drawn in the pla ...lar to a line through a point on or off the line), find a construction for two points <math>C</math> and <math>D</math> on <math>K_1</math> such that <mat
    3 KB (500 words) - 19:00, 23 October 2019
  • ...(6) = 96\pi</math>. The volume of the wedge is half this which is <math>48\pi \approx \boxed{\textbf{(C)}\ 151}</math>.
    1 KB (198 words) - 20:54, 29 October 2023
  • In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During the the first year investment showed a <math>20\%</math> gain. Over the two-year period, what was the change
    14 KB (2,035 words) - 15:23, 26 January 2024
  • A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inche ...ass. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she r
    13 KB (1,835 words) - 08:51, 8 March 2024
  • ...D)}\hspace{.05in}\frac{\pi-1}{\pi}\qquad\textbf{(E)}\hspace{.05in}\frac{3}\pi </math> ...two areas, we find the answer is <math> \boxed{\textbf{(A)}\ \frac{4-\pi}{\pi}} </math>.
    2 KB (310 words) - 16:18, 10 November 2023

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