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  • ...mes \frac{1}{6} \times \frac{1}{6} = \frac{2}{36}</math>. The sum of these two probabilities now gives the final answer: <math>\frac{1}{36} + \frac{2}{36}
    2 KB (248 words) - 14:51, 5 May 2021
  • Which of these four numbers <math> \sqrt{\pi^2},\,\sqrt[3]{.8},\,\sqrt[4]{.00016},\,\sqrt[3]{-1}\cdot \sqrt{(.09)^{-1}}< The sum of two numbers is <math> 10</math>; their product is <math> 20</math>. The sum of
    25 KB (3,872 words) - 14:21, 20 February 2020
  • ...math>¢ per text message sent, plus <math>10</math>¢ for each minute used over <math>30</math> hours. In January Juan sent <math>100</math> text messages ...ber of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws d
    13 KB (1,903 words) - 18:09, 19 April 2021
  • ...cmath>\tan (\theta) = \frac{3}{x}</cmath> YAY!!! We have two equations for two variables... that are relatively difficult to deal with. Well, we'll try to ...{6 - 3 \sqrt{3}} = 2 + \sqrt{3}</math>, <math>\theta = \frac{5 + 12n}{12} \pi</math>, where <math>n</math> is any integer. Converting to degrees, we have
    5 KB (782 words) - 14:29, 1 April 2024
  • ...went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and ...integers <math>a</math> and <math>b</math>, Ron reversed the digits of the two-digit number <math>a</math>. His erroneous product was 161. What is the c
    13 KB (1,978 words) - 16:28, 12 July 2020
  • ...d \mathrm{(C) \ } 6\pi\qquad \mathrm{(D) \ } 9\pi\qquad \mathrm{(E) \ } 12\pi </math> A line going through the centers of the two smaller circles also goes through the diameter. The length of this line wit
    2 KB (247 words) - 17:30, 5 January 2021
  • ...um of the numbers on every three consecutive vertices is a multiple of 3. Two acceptable arrangements are considered to be indistinguishable if one can b Suppose <math>x</math> is in the interval <math>[0,\pi/2]</math> and <math>\log_{24 \sin x} (24 \cos x) = \frac{3}{2}</math>. Fin
    10 KB (1,634 words) - 22:21, 28 December 2023
  • ...)}\ \pi \qquad \textbf{(D)}\ \frac{4\pi}{3} \qquad \textbf{(E)}\ \frac{5\pi}{3}</math> The curves of the track are semicircles, but since there are two of them, we can consider both of the at the same time by treating them as a
    2 KB (389 words) - 19:35, 7 August 2023
  • Suppose <math>x</math> is in the interval <math>[0, \pi/2]</math> and <math>\log_{24\sin x} (24\cos x)=\frac{3}{2}</math>. Find <ma There are now two ways to finish this problem.
    2 KB (330 words) - 20:47, 10 December 2023
  • ...7}}</math> are parallel, and its side length is the distance between these two lines. However, this is given to be the side length of the octagon, or <mat ...nt-and-a-line/ point to line distance formula], the distance between these two lines is <cmath>\frac{|c_{2}-c_{1}|}{\sqrt{a^{2}+b^{2}}}=\frac{2m\left(1+\s
    8 KB (1,344 words) - 18:39, 9 February 2023
  • ...the real parts of the blue dots is easily seen to be <math>8+16\cos\frac{\pi}{6}=8+8\sqrt{3}</math> and the negative of the sum of the imaginary parts o Note that <math>\sin(x) = \sin(x + \pi/2 - \pi/2) = \cos(x + \pi/2)</math>.
    5 KB (805 words) - 18:46, 27 January 2024
  • ...o went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and ...integers <math>a</math> and <math>b</math>, Ron reversed the digits of the two-digit number <math>a</math>. His erroneous product was <math>161</math>. Wh
    13 KB (2,090 words) - 18:05, 7 January 2021
  • ...l, and Al's pills cost a total of <math> \ </math><math>546</math> for the two weeks. How much does one green pill cost? ...math>. What is the distance between the <math>x</math>-intercepts of these two lines?
    15 KB (2,166 words) - 21:17, 16 February 2021
  • ...nd <math>1.5</math> points for each problem left unanswered. After looking over the <math>25</math> problems, Sarah has decided to attempt the first <math> Two points <math>B</math> and <math>C</math> are in a plane. Let <math>S</math>
    15 KB (2,297 words) - 12:57, 19 February 2020
  • ...(0,2).</math> What is the area of the intersection of the interiors of the two circles? ...\frac{\pi \sqrt{3}}{3} \qquad\textbf{(D) } 2(\pi -2) \qquad\textbf{(E) } \pi</math>
    898 bytes (142 words) - 20:42, 15 February 2024
  • The figure shown is the union of a circle and two semicircles of diameters <math>a</math> and <math>b</math>, all of whose ce The area of the whole circle is <math>A_{big} = \pi\cdot (a + b)^2</math>
    2 KB (307 words) - 18:58, 11 January 2014
  • ''Method 1:'' Dropping the altitude of our triangle splits it into two triangles. By HL congruence, these are congruent, so the "short side" is <m ...ac{ab\sin{C}}{2}</math>. Plugging in <math>a=b=s</math> and <math>C=\frac{\pi}{3}</math> (the angle at each vertex, in radians), we get the area to be <m
    1 KB (189 words) - 04:06, 18 June 2018
  • Solve for <math>x</math> for all answers in the domain <math>[0, 2\pi]</math>. We have a problem! The domain for values of <math>x</math> is <math>[0, 2\pi]</math>. However, no real value of <math>x</math> can become imaginary when
    8 KB (1,351 words) - 20:30, 10 July 2016
  • ...with <math>|z_0|=1.</math> What is the sum of all values <math>P(1)</math> over all the polynomials with these properties? ...these cases, <math>P(-1)=4-4+t-t+0=0</math>. The sum of <math>P(1)</math> over these cases is <math>\sum_{t=0}^{4} (4+4+t+t) = 40+20=60</math>.
    11 KB (1,979 words) - 17:25, 6 September 2021
  • The difference in the areas of two similar triangles is <math>18</math> square feet, and the ratio of the larg <math>\textbf{(A)}\ \frac{\pi m^2}{2}\qquad
    20 KB (3,108 words) - 14:14, 20 February 2020

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