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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 of25 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 d13 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 have5 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 c13 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 wit2 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>. Fin10 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 a2 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+\s8 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>. Wh13 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 <m1 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 when8 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}\qquad20 KB (3,108 words) - 14:14, 20 February 2020
