aops_id int64 2 3.62M | text stringlengths 66 38.8k | text_vector listlengths 2.56k 2.56k | last_modified stringdate 2025-08-27 00:00:00 2025-08-28 00:00:00 |
|---|---|---|---|
1,000,044 | Justin has a 55% chance of winning any given point in a ping-pong game. To the nearest 0.1%, what is the probability that he wins exactly 7 out of the first 10 points? So if he has a 55% chance of winning, he conversely has a 45% chance of losing. The problem calls for him winning 7 times and losing 3, so his win perce... | [
-0.000028682397896773182,
-0.0019284101435914636,
0.04229530319571495,
-0.008460083976387978,
0.00020720176689792424,
0.024417396634817123,
0.08298446238040924,
-0.002606229390949011,
0.0017844049725681543,
0.007450968958437443,
0.03830680996179581,
-0.02406933344900608,
-0.00147451821248978... | 2025-08-27 |
100,009 | Evaluate
\[
\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\sqrt{\sin x}+\sqrt{\cos x}+3(\sqrt{\sin x}-\sqrt{\cos x})\cos 2x}{\sqrt{\sin 2x}}\;dx.
\] You may be right. I made this problem by the differentiation of $\sin x \sqrt{\cos x}+\cos x\sqrt{\sin x}$ as shyong showed. | [
-0.00015488899953197688,
0.029078107327222824,
0.02750416286289692,
-0.016059471294283867,
-0.00042895026854239404,
0.0008880043751560152,
0.03721340000629425,
0.007023415062576532,
0.011194401420652866,
0.008629193529486656,
0.02136939764022827,
-0.007670710328966379,
0.005455693695694208,
... | 2025-08-27 |
100,010 | Billy Bob has a pet snail called Larry. The wall is 37 feet tall. Larry can climb 3 feet in one day, but at night he slips down 2 feet. Larry starts the climb on Sunday, June 2, 2006. On what day (day of the week and date) will Larry finish the climb? [quote="mtms5467"][hide]So basically Larry climbs 1ft/day. The day/d... | [
-0.00011699845344992355,
-0.06170457974076271,
0.039657700806856155,
-0.04013722017407417,
-0.0001758466096362099,
0.04066888242959976,
0.031141497194767,
0.054923806339502335,
0.005147380288690329,
0.014685465022921562,
-0.01185104064643383,
-0.027735494077205658,
-0.0017331704730167985,
... | 2025-08-27 |
1,000,136 | "Deriving the Quadratic Formula\n\nProblem:\nDerive the quadratic formula.\n\nSolution:\nStart with (...TRUNCATED) | [-0.0002122835285263136,-0.04541593790054321,0.0046520717442035675,0.04031360149383545,-0.0005049610(...TRUNCATED) | 2025-08-27 |
1,000,141 | "[b]Coin Problems[/b]\r\n\r\n[i]Tony has 11 more nickels than quarters. If the total value of his co(...TRUNCATED) | [-0.00006175064481794834,0.007315790746361017,0.026415608823299408,0.034050799906253815,0.0002337306(...TRUNCATED) | 2025-08-27 |
100,015 | "A 6-letter car plaque is to be made using the letters \\(A,\\dots,Z\\) such that the letters are in(...TRUNCATED) | [-0.000032167423341888934,-0.05821501463651657,0.010568084195256233,0.049778323620557785,-0.00017727(...TRUNCATED) | 2025-08-27 |
100,019 | "Billy Bob has a huge garden. He picks a few flowers from it. There is one red flower, one blue flow(...TRUNCATED) | [0.00030263312510214746,-0.06200506165623665,0.004736138507723808,0.005954334978014231,0.00155126536(...TRUNCATED) | 2025-08-27 |
100,023 | "Simplify\n\\[\n(1+x)(1+x^{2})(1+x^{4})(1+x^{8})\\cdots\n\\]\nfor \\(|x|<1\\). [hide]When you multip(...TRUNCATED) | [-0.0000482597533846274,-0.008691142313182354,0.030783245339989662,0.05414757505059242,-0.0001775505(...TRUNCATED) | 2025-08-27 |
1,000,249 | "Two players (You and Ben) are each arrested and placed in separate jail cells with no communication(...TRUNCATED) | [-0.000031315295927925035,-0.0027431652415543795,0.03295576944947243,-0.02672015316784382,3.97694066(...TRUNCATED) | 2025-08-27 |
100,026 | "Let r and s be the roots of\n\\[\nx^{2}-(a+d)x+(ad-bc)=0.\n\\]\nProve that \\(r^{3}\\) and \\(s^{3}(...TRUNCATED) | [0.0000723194534657523,-0.012164993211627007,0.017007797956466675,0.005845030304044485,0.00057241902(...TRUNCATED) | 2025-08-27 |
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