conversations listlengths 2 2 | system stringclasses 1
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"value": "Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between 0 and 1 will $20_{}^{}!$ be the resulting product?"
},
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"from": "assistant",
"value": "<|begin_... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[
{
"from": "user",
"value": "Let $ \\mathcal{H}$ be an infinite-dimensional Hilbert space, let $ d>0$ , and suppose that $ S$ is a set of points (not necessarily countable) in $ \\mathcal{H}$ such that the distance between any two distinct points in $ S$ is equal to $ d$ . Show that there is a poin... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[
{
"from": "user",
"value": "Find the remainder when $9 \\times 99 \\times 999 \\times \\cdots \\times \\underbrace{99\\cdots9}_{\\text{999 9's}}$ is divided by $1000$ ."
},
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"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, so I have this problem here: I need to find the remainder... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[
{
"from": "user",
"value": "Compute the mean molecular speed v in the heavy gas radon (Rn) in m/s"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, I need to calculate the mean molecular speed of radon gas. Hmm, first, I remember there's a formula for the root mean square speed,... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[
{
"from": "user",
"value": "Two capacitors with capacitance values $C_{1}=2000 \\pm 10 \\mathrm{pF}$ and $C_{2}=3000 \\pm 15 \\mathrm{pF}$ are connected in series. The voltage applied across this combination is $V=5.00 \\pm 0.02 \\mathrm{~V}$. What is the percentage error in the calculation of the energy st... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[
{
"from": "user",
"value": "One base of a trapezoid is $100$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $2: 3$ . Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel... | Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... |
[{"from":"user","value":"Let's say a language $L \\subseteq \\{0,1\\}^*$ is in $\\textbf{P}_{ange(...TRUNCATED) | "Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) |
[{"from":"user","value":"In a mathematics test number of participants is $N < 40$ . The passmark is(...TRUNCATED) | "Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) |
[{"from":"user","value":"Kathy has $5$ red cards and $5$ green cards. She shuffles the $10$ cards an(...TRUNCATED) | "Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) |
[{"from":"user","value":"Square $AIME$ has sides of length $10$ units. Isosceles triangle $GEM$ has(...TRUNCATED) | "Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) |
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