prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.65E34 |
[
{
"content": "If $5^x=100$, what is the value of $5^{x+2}$?",
"role": "user"
}
] | 2500 |
[
{
"content": "Consider the function \\(f:\\mathbb{R^3} \\to \\mathbb{R}\\) defined by \\(f(x, y, z)=\\left(x^{2}+y^{2}+z^{2}+R^{2}-r^{2}\\right)^2-4 R^{2}\\left(x^{2}+y^{2}\\right)\\). Let \\(Z=\\{ (x,y,z) \\in \\mathbb{R^3} \\mid f(x,y,z)=0\\}\\). For \\(R=3\\) and \\(r=2\\), find the surface area of \\(Z\\)."... | 24\pi^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.5 mN |
[
{
"content": "Determine the value of $x$ in the following 6x6 matrix, representing survival and fecundity of different life stages of an animal, such that the dominant eigenvalue $\\lambda$ is 1:\n\n\\[\n\\begin{pmatrix} \n0 & 0 & 0 & 0 & 3 & 4\\\\ \n0.5 & 0 & 0 & 0 & 0 & 0 \\\\\n0 & 0.6 & 0 & 0 & 0 & 0\\\\\n0 ... | -\dfrac{34}{155} |
[
{
"content": "Determine whether the following two statements are equivalent for a function $g(x)$ defined on $(a,+\\infty)$:\n\n1. $\\lim_{x \\to +\\infty} g(x) = m$\n2. $\\lim_{x \\to 0 \\atop x>0} g\\left(\\frac{1}{x}\\right) = m$",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8957 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {E = \frac{z\rho}{\epsilon_0}, -d \leq z \leq d; E = \frac{d\rho}{\epsilon_0}, |z| \geq d} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 28 g |
[
{
"content": "Two cards are chosen at random from a standard 52-card deck. What is the probability that they are either both hearts or both diamonds?",
"role": "user"
}
] | \frac{2}{17} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.7 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.96 A |
[
{
"content": "What is the second smallest four-digit number in Pascal's triangle?",
"role": "user"
}
] | 1001 |
[
{
"content": "Given an unlimited supply of coins with values $1^2$, $2^2$, $3^2$, $4^2$,..., $17^2$, determine the number of ways to exchange a given amount $X$ using these coins. For instance, if $X = 24$, there are 16 ways to make change.",
"role": "user"
}
] | 16 |
[
{
"content": "Determine whether the following statement is true or false: \\( \\int_0^t X_1(s-) \\, dX_2^c(s) = \\int_0^t X_1(s) \\, dX_2^c(s) \\) because the integration on the jumps of the integrand \\( X_1 \\) is zero.",
"role": "user"
}
] | True |
[
{
"content": "Solve the equation: \\[ \\log_3\\left(\\frac{1}{\\sqrt{\\log_3(x)}}\\right) = \\log_9\\left(\\log_9\\left(\\frac{x}{3}\\right)\\right) \\]",
"role": "user"
}
] | 9 |
[
{
"content": "Does there exist a sequence \\((x_n)\\) belonging to \\(\\ell_1 \\cap \\ell_2\\) which converges in one space but not the other?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.62e8 m/s |
[
{
"content": "Given the sequence defined by $U_{n+1} = 1 - \\sqrt{1 - U_n}$ with $0 < U_1 < 1$, find the value of $\\lim_{n \\to \\infty} \\frac{U_{n+1}}{U_n}$. Provide your answer as a single number.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 34.7 Bq |
[
{
"content": "Determine whether there exists a metric $d$ on $\\mathbb{R}$ such that the function $f: (\\mathbb{R}, d) \\to (\\mathbb{R}, d)$ defined by $f(x) = -x$ is not continuous.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $22,784 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.70 cm/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 76 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 67% |
[
{
"content": "Find the last two digits of the number $9^{9^{9^{\\cdots^{9}}}}$ where there are nine 9s in the power tower, using modular arithmetic.",
"role": "user"
}
] | 89 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 23 m/s |
[
{
"content": "If $(x+2)(x-3)=14$, find the sum of the possible values of $x$.",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.13 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | <img>/cimages/multimages/16/electron-dot1735335046360865114.png</img> |
[
{
"content": "Solve for $x$, where $x > 0$ and $0 = -9x^2 - 3x + 2.$ Express your answer as a simplified common fraction.",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Determine whether the following statement is true or false:\n\nLet $g: \\mathbb{R} \\to \\mathbb{R}$ be a homeomorphism such that $g(0)=0$ and $ | g^{-1}-Id | \\nless M$ for any $ M>0$. Then there exists a sequence $\\{ b_{n} \\}$ of real numbers such that:\n\n1. $| b_{n+1}| > |b_{n} |$ for all $n... | True |
[
{
"content": "Suppose $g$ is the density of the standard normal distribution $N(0,1)$, and $f: \\mathbb{R} \\to \\mathbb{R}$ is an arbitrary function. If the convolution $[f \\ast g](x) = \\int_{-\\infty}^{\\infty} f(x-t)g(t)dt = 0$ for all $x$ on a closed interval $[a,b]$ where $-\\infty < a < b < +\\infty$, i... | Yes |
[
{
"content": "A sequence of squares and circles is constructed as follows: A square \\( S_1 \\) with unit area is given. A circle \\( C_1 \\) is inscribed in \\( S_1 \\). A square \\( S_2 \\) is inscribed in \\( C_1 \\), and so on. In general, a circle \\( C_n \\) is inscribed in the square \\( S_n \\), and the... | \dfrac{\pi}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $1,054.032 |
[
{
"content": "Given a reproducing kernel Hilbert space (RKHS) \\( \\mathcal{H} \\) with a radial basis kernel, and a function \\( f \\in \\mathcal{H} \\) such that \\( \\|f\\|_{\\mathcal{H}} \\leq C \\), determine if the inequality \\( |f(X)| \\leq C \\) holds for any input \\( X \\).",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5000 g/mol |
[
{
"content": "A regular tetrahedron has two spheres, one inscribed within it and the other circumscribed around it. Between each face of the tetrahedron and the circumscribed sphere, there are four smaller spheres centered on each face. Given a point \\( P \\) within the circumscribed sphere, the probability th... | C |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Stolton: $23,500
Bright: $28,500 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.91 kg |
[
{
"content": "Given the complex numbers $z$ and $w$ that satisfy the conditions $|2z - w| = 25$, $|z + 2w| = 5$, and $|z + w| = 2$, determine the value of $|z|$.",
"role": "user"
}
] | 9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (a), (b), (c), (d) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $1,223 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 88.9 mL |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1640.84 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.82% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 49 mL |
[
{
"content": "Given the joint distribution of two random variables \\(X\\) and \\(Y\\): \\[ f(x, y) = \\frac{3}{2}x + \\frac{y}{2} \\] for \\(x, y \\in [0, 1]\\) and 0 otherwise, calculate the probability \\( P(XY < \\frac{1}{2}) \\).",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\pi} \\cos(x) \\log(\\sin^2(x) + 1) \\, dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "An urn contains $4$ green balls and $6$ blue balls. A second urn contains $16$ green balls and $N$ blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is $0.58$. Find $N$.",
"role": "user"
}
] | 144 |
[
{
"content": "Evaluate the limit: $$\\lim_{k \\to \\infty} \\int_0^1 e^{- (k^2x^2/2)} \\, dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Given the equation $x+y+z=3$, determine the minimum value of $A = (x^2 + 1)(y^2 +1)(z^2 +1)$. Provide your answer as a single number.",
"role": "user"
}
] | \dfrac{125}{16} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.2133 ms^{-2} |
[
{
"content": "Determine the conditions on the numbers \\(a, b,\\) and \\(c\\) such that the linear operator \\(T: \\mathbb{R}^{4} \\to \\mathbb{R}^{4}\\), defined by \\(T(x_{1},x_{2},x_{3},x_{4})=(0,ax_{1},bx_{2},cx_{3})\\), is diagonalizable.",
"role": "user"
}
] | a = b = c = 0 |
[
{
"content": "Determine whether it is possible to transform the RSA problem (FACT) into a SAT problem in polynomial time, with a polynomial number of variables and clauses in the logical formula, given that the size of the task is the number of bits $n$. Provide a justification for your answer.",
"role": "u... | Yes |
[
{
"content": "Find all injective functions \\( f: \\mathbb{N} \\rightarrow \\mathbb{N} \\) such that for all natural numbers \\( m, n \\), the equation \\( f(f(m) + f(n)) = f(f(m)) + f(n) \\) holds.",
"role": "user"
}
] | f(n) = n + c |
[
{
"content": "Are there infinitely many primes of the form \\(2^{2^n}-1\\) where \\(n\\) is a natural number?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $28,959.49 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 52.6 torr |
[
{
"content": "Suppose $f:(a,b) \\rightarrow \\mathbb{R}$ is differentiable on $(a,b)$ and $c \\in (a,b)$ satisfies $f(c) = f'(c) = \\dots = f^{n-1}(c) = 0$ and $f^{(n)}(c) < 0$. If $n$ is odd, does $f$ have a local maximum at $c$? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "Let $A$ be an algebra of finite type over $\\mathbb{Z}$, meaning $A$ is a finitely generated ring. If $\\mathfrak{m}$ is a maximal ideal of $A$, is $A/\\mathfrak{m}$ necessarily a finite field?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 100 units |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 118.6 x 10^6 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.6 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.78e-3 m^3 |
[
{
"content": "Let \\( f(x) \\) be a continuously differentiable function defined on the interval \\( [a, b] \\) with \\( f(a) = 0 \\) and \\( f'(a+) = 0 \\). If \\( f(x) \\) is positive for all \\( x \\in (a, b) \\), determine if there exists a \\( \\delta > 0 \\) such that \\( f(x) \\leq f'(x) \\) for all \\( ... | Yes |
[
{
"content": "In a sequence $a_1, a_2, \\dots$ of real numbers, it is observed that $a_p=\\sqrt{2}$, $a_q=\\sqrt{3}$, and $a_r=\\sqrt{5}$, where $1\\leq p<q<r$ are positive integers. Determine which of the following statements is true:\n\n(A) $a_p$, $a_q$, $a_r$ can be terms of an arithmetic progression.\n\n(B)... | D |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | enterogastric reflex |
[
{
"content": "In a triangular prism formed by the planes $P_1: 2x + y + z = 2$, $P_2: x + y - z = 3$, and $P_3: x + 2z = 2$, the normal vectors of the planes are co-planar. Determine the area of the base of the prism.",
"role": "user"
}
] | \dfrac{9\sqrt{14}}{28} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.05*10^7 m/s |
[
{
"content": "Given that $p + q + r = 0$, find the value of \\( \\left(\\frac{Y}{X}\\right)^2 + 8\\left(\\frac{p^2 - qr}{2X}\\right) \\), where $X = p^2 + q^2 + r^2$ and $Y = pq + qr + pr$. \\(p, q, r\\) are real numbers.",
"role": "user"
}
] | \dfrac{9}{4} |
[
{
"content": "Find the limit of the expression \\( A = \\lim_{n \\to \\infty} \\frac{1}{n}\\left((m+1)(m+2) \\cdots (m+n)\\right)^{\\frac{1}{n}} \\).",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Determine whether there exists a polynomial $p(x, y) \\in \\mathbb{R}[x, y]$ such that $p(\\sin 1, \\cos 1) = 0$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the volume of the half-cone defined by the inequalities \\( \\sqrt{x^{2}+y^{2}}<z<1 \\) and \\( x>0 \\).",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "Let $f(x)$ and $g(x)$ be two increasing and differentiable functions from $\\Bbb{R}$ to $\\Bbb{R}$. If $f'(x) > g'(x)$ for all $x$, does there exist an interval $[a, \\infty)$ for some real number $a$ such that $f(x) > g(x)$?",
"role": "user"
}
] | No |
[
{
"content": "Given the joint probability density function (pdf) \\(f(x,y) = xy e^{-x-y}\\) for \\((x > 0, y > 0)\\), calculate the probability \\(P[X \\geq 2Y]\\).",
"role": "user"
}
] | \dfrac{7}{27} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Basic: $77,962.90
Luxury: $67,048.09 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.77% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 260 s^-1 |
[
{
"content": "Let $X$ be a standard normal random variable and $a > 0$ be a constant. Find \\( \\lim_{x \\to \\infty} \\mathbb{P}\\left(X > x + \\frac{a}{x} \\mid X > x\\right) \\).",
"role": "user"
}
] | e^{-a} |
[
{
"content": "Determine the values of $p$ for which the sequence $\\{f_n\\}$, defined by \\[ f_n(x) = \\begin{cases} 1 - nx, & \\text{if } 0 \\leq x \\leq \\frac{1}{n}, \\\\ 0, & \\text{otherwise}, \\end{cases} \\] is a Cauchy sequence in the space $(C[0,1], \\lVert\\cdot\\rVert_p)$ for $1 \\leq p \\leq \\infty... | [1, \infty) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | C_{13}H_{18}O_2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1-ethoxyhexane |
[
{
"content": "Compute the limit \\( \\lim_{n\\rightarrow\\infty}\\frac{a_n}{n} \\) where \\( a_n \\) is the solution to \\( \\tan(x) = n \\) within the interval \\((n-2)\\pi + \\frac{\\pi}{2}, (n-1)\\pi + \\frac{\\pi}{2}\\) for \\( n \\geq 2 \\).",
"role": "user"
}
] | \pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $8,212.17 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{\\sin x}{1+x^8} \\, dx \\) using complex analysis.",
"role": "user"
}
] | 0 |
[
{
"content": "For any positive integer $m$, determine if it is possible to pair up a class of $2m$ students each day such that no student is left unmatched and no two students are paired together more than once until every student has been paired with every other student exactly once.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1/12Ma^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3,810 units |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9591 km |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 27000 |
[
{
"content": "Determine the fundamental group of the space \\( X \\) defined as the union \\( X = X_1 \\cup X_2 \\cup X_3 \\), where \\( X_1 \\), \\( X_2 \\), and \\( X_3 \\) are the following subsets of \\( \\mathbb{R}^3 \\):\n\\[ X_1 = \\left\\{ (x, y, z) : x^2 + (y - 1)^2 + z^2 = 1 \\right\\} \\]\n\\[ X_2 = ... | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 14000 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 14112 Pa |
[
{
"content": "Let $x_n$ be a convergent sequence $x_n \\to x$ in a topological space $X$ and $F:X\\longrightarrow \\mathbb R$ be any function (not necessarily continuous). If there exists a subsequence $x_{n_k}$ such that \\(F(x) \\leq \\liminf_k F(x_{n_k})\\), can we conclude that \\(F(x) \\leq \\liminf_n F(x_... | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.8% |
[
{
"content": "Calculate the limit \\( \\lim_{r\\to0}\\int_{\\sigma_{r}}\\frac{e^{iz}}{z}\\, dz \\) where \\(\\sigma_{r}:[0,\\pi]\\to\\mathbb{C}\\) is defined as \\(\\sigma_{r}(t)=re^{it}\\).",
"role": "user"
}
] | i\pi |
[
{
"content": "Solve the congruence $x^3 \\equiv 27 \\pmod{41}$.",
"role": "user"
}
] | 3 |
[
{
"content": "Two trains are 80 kilometers apart and are traveling toward each other on the same track, each at a speed of 25 kilometers per hour. A bee starts at the first train and flies back and forth between the two trains until they are 100 meters apart. The bee completes 36 rounds, landing 18 times on eac... | 270 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Arguments for raising the SUTA tax rate ceiling include:
1. Increased funding for government programs during economic downturns.
2. Maximizing tax collections, even with employer merit rating.
3. Providing states with more funds for unemployment programs, reducing reliance on federal funding. |
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