prompt list | ground_truth string |
|---|---|
[
{
"content": "The arithmetic mean of an odd number of consecutive odd integers is $y$. Find the sum of the smallest and largest of the integers in terms of $y$.",
"role": "user"
}
] | 2y |
[
{
"content": "Determine whether the set of values \\(\\{\\sin n^m \\mid n \\in \\mathbb{N}\\}\\) is dense in the interval \\([-1,1]\\) for every natural number \\(m\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Find the radius of convergence for the infinite series \\( \\sum_{n=0}^{\\infty} (n+2^n)z^n \\) using the formula \\( R = \\lim_{n \\rightarrow \\infty} \\left| \\frac{a_n}{a_{n+1}} \\right| \\), where \\( a_n = n+2^n \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\infty} \\frac{dx}{(1+x^n)(1+x^2)} \\) for any \\( n \\neq 0 \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"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... | 2878 N |
[
{
"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... | 9.21e-24 J |
[
{
"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... | R = \frac{v_0^2\sin(2\theta_0)}{g} |
[
{
"content": "Let $A = K[x_1, x_2, \\ldots, x_n]$ be a polynomial ring over a field $K$. Consider the ideal $m = \\langle x_1 - a_1, x_2 - a_2, \\ldots, x_n - a_n \\rangle$ where $a_1, a_2, \\ldots, a_n \\in K$. Prove that the ideal $m$ is maximal in $A$. ",
"role": "user"
}
] | 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... | 2.86e-4 T |
[
{
"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... | 181.88 g/mol, Vanadium |
[
{
"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... | 178 per cm |
[
{
"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... | $17.01 |
[
{
"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... | 1.4e-4 V/m |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to 0} \\left(\\frac{2+\\cos x}{x^3\\sin x}-\\frac{3}{x^4}\\right) $$",
"role": "user"
}
] | \dfrac{1}{60} |
[
{
"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 kg |
[
{
"content": "Does there exist a complex number $z_0 \\notin \\{a_n\\}_{n \\geq 1}$ such that $f(z_0) = 0$, where $f(z) = \\prod\\limits_{n=1}^{\\infty} E_{p_n} (z/a_n)$ is an entire function defined by the Weierstrass Factorization Theorem?",
"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... | 90.9g |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f' \\) exists and satisfies the functional equation: \\[ f(x) = f\\left(\\frac{x}{2}\\right) + \\frac{x}{2} \\cdot f'(x), \\forall x \\in \\mathbb{R}. \\]",
"role": "user"
}
] | f(x) = ax + b |
[
{
"content": "Given a polynomial \\( P(x) = a_{2n} x^{2n} + a_{2n-1} x^{2n-1} + \\ldots + a_1 x + a_0 \\) where each coefficient \\( a_i \\) belongs to the interval \\([100,101]\\), determine the smallest natural number \\( n \\) such that this polynomial can have a real root.",
"role": "user"
}
] | 100 |
[
{
"content": "Given the recursive sequence $a_n$ with initial values $a_1 = 2$ and $a_2 = \\frac{3}{2}$, where $a_{n+2} = a_n - na_{n+1} + \\frac{1}{(n+2)!}$, find the explicit formula for $a_n$. Verify that $a_n = \\frac{n+1}{n!}$ using a method other than mathematical induction.",
"role": "user"
}
] | \dfrac{n+1}{n!} |
[
{
"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... | 24 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... | 215.5 J/mol K |
[
{
"content": "Let \\(\\mathbb{R}^3\\) be equipped with the inner product \\(\\langle \\cdot, \\cdot \\rangle\\) defined by \\(\\langle \\mathbf{u}, \\mathbf{v} \\rangle = 2u_1v_1 + 5u_2v_2 + 3u_3v_3\\) for any vectors \\(\\mathbf{u} = (u_1, u_2, u_3)\\) and \\(\\mathbf{v} = (v_1, v_2, v_3)\\). Determine which o... | C |
[
{
"content": "Find the degree of the field extension \\( \\mathbb{Q}(\\sqrt{2}+\\sqrt[3]{2}) \\) over \\( \\mathbb{Q}(\\sqrt{2}) \\).",
"role": "user"
}
] | 3 |
[
{
"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... | $148,398.97 |
[
{
"content": "Find the smallest number \\( k \\) such that \\( \\frac{l_a+l_b}{a+b} < k \\) for all triangles with sides \\( a \\) and \\( b \\) and bisectors \\( l_a \\) and \\( l_b \\) to them, respectively.",
"role": "user"
}
] | \dfrac{4}{3} |
[
{
"content": "Is the unitary group compact in the strong operator topology (SOT) for a finite-dimensional Hilbert space?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left( \\frac{\\cos x}{\\cos 2x} \\right)^{\\frac{1}{x^2}}. \\]",
"role": "user"
}
] | e^{\frac{3}{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... | too low |
[
{
"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... | 570 J |
[
{
"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... | [H2] = [I2] = 0.0591M, [HI] = 0.6713 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... | 50 minutes |
[
{
"content": "Find the value of $u+v$ for the point $(u,v)$ on the ellipse $4x^2+a^2y^2=4a^2$, where $4<a^2<8$, that is farthest from the point $(0,-2)$. What is $u+v$?",
"role": "user"
}
] | 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... | 5.1 m/s^2 |
[
{
"content": "Determine whether the set of numbers whose sum of digits is prime has zero natural density. Specifically, evaluate if \\( \\lim_{n \\to +\\infty} \\frac{A(n)}{n} = 0 \\), where \\( A(n) \\) is the number of elements in the set that are less than or equal to \\( n \\).",
"role": "user"
}
] | 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... | 8.849 L |
[
{
"content": "In triangle \\( \\triangle ABC \\), cevians \\( AD, BE, \\) and \\( CF \\) intersect at point \\( P \\). Given that \\( AP = PD = 6 \\), \\( BP = 9 \\), \\( PE = 3 \\), and \\( CF = 20 \\), find the area of triangle \\( \\triangle ABC \\).",
"role": "user"
}
] | 108 |
[
{
"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... | 1.155e-3 m^2 |
[
{
"content": "Determine the number of ways to traverse an 8-cycle graph in 10 moves, starting from a given vertex and ending at the vertex directly opposite to it.",
"role": "user"
}
] | 240 |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\infty} \\frac{1}{(1+x^2)(1+x^{\\alpha})} \\, dx \\) for any \\( \\alpha > 0 \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Determine the number of $2 \\times 2$ matrices over $\\mathbb{C}$ that satisfy the equation $A^2 = I$, where $I$ is the identity matrix.",
"role": "user"
}
] | \infty |
[
{
"content": "Given two positive integers $a$ and $b$, where $a$ has 20,041 '1's and $b$ has 20,051 '1's in their binary representations, determine the smallest possible number of '1's in the binary representation of $a + b$. Provide your answer as a single integer.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $K \\subseteq M \\subseteq L$ be three fields such that $L=K(\\alpha)$ with $\\alpha\\in \\overline{K}$. Determine whether $M$ is also a simple extension of $K$. Provide a justification for your answer.",
"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... | 5.956e-3 m/s^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... | (3.5 m, 5.77 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... | Cr(NO_3)_3(aq) + Al(s) -> Al(NO_3)_3(aq) + Cr(s) |
[
{
"content": "Given the joint probability density function of \\(X = (X_1, X_2)\\):\n\\[\nf(x_1, x_2) = \\begin{cases} \\frac{e^{-\\frac{x_2^2}{2}}}{x_2\\sqrt{2\\pi}}, & \\text{if } 0 < |x_1| \\le x_2 < \\infty, \\\\ 0, & \\text{otherwise} \\end{cases}\n\\]\nFind the variance of \\(X_1\\).",
"role": "user"
... | \dfrac{1}{3} |
[
{
"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... | $204,000 |
[
{
"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... | 629 |
[
{
"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... | 31 |
[
{
"content": "Consider the sequence \\((x_n)_{n\\geq 0}\\) of positive integers defined recursively as follows: \\(x_0 = 0\\), \\(x_1 = a\\), and \\(x_n = x_{n-2} + bx_{n-1}\\) for \\(n \\geq 2\\), where \\(a\\) and \\(b\\) are fixed positive integers. Determine \\(\\gcd(x_n, x_{n+1})\\) for all \\(n\\).",
... | a |
[
{
"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... | 1.88e17 N/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... | 18.35 m/s |
[
{
"content": "Determine the range of the real number \\( a \\) such that the inequality \\( \\sin 2 \\theta-(2 \\sqrt{2}+\\sqrt{2} a) \\cdot \\sin \\left(\\theta+\\frac{\\pi}{4}\\right)-\\frac{2 \\sqrt{2}}{\\cos \\left(\\theta-\\frac{\\pi}{4}\\right)}>-3-2 a \\) holds for all \\( \\theta \\in\\left[ 0, \\frac{\... | (3, +\infty) |
[
{
"content": "Determine the range of values for \\(a\\) such that the roots of the equation \\(x^2 - 2x - a^2 + 1 = 0\\) are between the roots of the equation \\(x^2 - 2(a + 1)x + a(a - 1) = 0\\). Express this range as \\((p, q)\\). Then, calculate the value of \\(q + \\frac{1}{p^2}\\).",
"role": "user"
}... | 17 |
[
{
"content": "In square $ABCD$, point $E$ is located on side $BC$ and point $F$ is located on side $DE$ such that $DF = BF$ and $EF = EB$. Given that $\\angle BFE = 2\\angle BDF$, find the measure of angle $DFA$.",
"role": "user"
}
] | 75^\circ |
[
{
"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... | 21 kWh |
[
{
"content": "Evaluate the integral \\( I = \\int_{-1}^2 \\{|x-1| - \\lfloor x \\rfloor \\} \\, dx \\), where \\( \\{\\cdot\\} \\) denotes the fractional part function, defined as \\( \\{x\\} = x - \\lfloor x \\rfloor \\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Consider the sequence of functions \\(\\{y_{m}(x)\\}\\) on \\([a,b]\\). Assume that \\(|y_{m}(x)|\\leq M_{m}\\) for all \\(x\\in [a,b]\\) and all \\(m\\in \\mathbb{Z}^{+}\\). Suppose \\(\\sum_{m=1}^{+\\infty}M_{m}<+\\infty\\). Does \\(y_{m}(x)\\) uniformly converge to zero on \\([a,b]\\)?",
"r... | Yes |
[
{
"content": "Minimize the function $2x + y$ subject to the constraint $x^2 + y^2 = 1$. Use the Karush-Kuhn-Tucker (KKT) conditions to find the solution.",
"role": "user"
}
] | -\sqrt{5} |
[
{
"content": "Let $\\mathcal{C}$ be the hyperbola $y^2 - x^2 = 1$. Given a point $P_0$ on the $x$-axis, we construct a sequence of points $(P_n)$ on the $x$-axis in the following manner: let $\\ell_n$ be the line with slope 1 passing passing through $P_n$, then $P_{n+1}$ is the orthogonal projection of the poi... | 2^{2008} -2 |
[
{
"content": "A triangle is inscribed in a circle with a unit radius. Determine the possible distance between the centers of two excircles of the triangle.",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the minimum number of black boxes required to pinpoint the location of the origin of a signal that caused spaceships to explode. Assume the signal spreads through space at a constant velocity uniformly in every direction, and each black box contains the spatial coordinates of the ship an... | 4 |
[
{
"content": "Given two perpendicular tangents to a variable circle, which are also tangent to a fixed circle $C_1$ with a radius of 2 units. The locus of the center of the variable circle is a curve $C_2$. Find the product of the maximum and minimum distances between the curves $C_1$ and $C_2$. \\( \\text{Expr... | 4 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1000} \\frac{e^{-10x}\\sin x}{x} \\text{d}x \\) to within \\( \\pm 10^{-5} \\).",
"role": "user"
}
] | 0.09967 |
[
{
"content": "Find the norm of the functional \\( f(x) = \\sum_{j=1}^{\\infty} \\xi_j \\frac{1}{\\sqrt{j(j+1)}} \\) defined by \\( f: l^2 \\rightarrow \\mathbb{R} \\) for all \\( x = (\\xi) \\in l^2 \\).",
"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... | 4.3e5 N/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... | 160 L |
[
{
"content": "Determine the greatest lower bound for the real roots of the polynomial function \\( f(x) = x^4 - 3x^2 + 2x - 4 \\).",
"role": "user"
}
] | -2.18 |
[
{
"content": "Can a complete Riemannian metric be defined on every differential manifold $M$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the improper integral: $$ \\int_{0}^{1} \\left(1+\\frac{1}{x} \\right) e^{-1/x}dx $$",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Calculate the integer \\( \\lambda \\) such that the group homomorphism \\( \\mathbb{Z} \\cong \\pi_{n+1}(S^{n+1}) \\rightarrow \\pi_n(SO_{n+1}) \\rightarrow \\pi_n(S^n) \\cong \\mathbb{Z} \\) is multiplication by \\( \\lambda \\). The map is induced by the matrix multiplication map \\( \\alpha: S... | 2 |
[
{
"content": "Find the expected value of the determinant of a symmetric matrix with three entries that are uniformly distributed random variables between -60 and 60.",
"role": "user"
}
] | -1200 |
[
{
"content": "Evaluate the definite integral: \\[ \\int_{0}^{\\frac{\\pi}{2}} \\frac{1}{1+\\tan^{\\sqrt{2}}(x)} \\, \\mathrm{d}x \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"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... | (8.4115+2.947m{eq}_2{/eq}) kg/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... | 1.8% |
[
{
"content": "Calculate the limit: $$\\lim_{n\\to\\infty} \\sqrt[n]{\\frac{\\prod_{k=1}^{n}(2n+k)}{n^n}}.$$",
"role": "user"
}
] | \dfrac{27}{4e} |
[
{
"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... | Breakeven point (units) = fixed costs / (sales price per unit - variable cost per unit) OR
Breakeven point (sales) = fixed costs / contribution margin |
[
{
"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... | 0.016811 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... | 107.7 nm |
[
{
"content": "Determine the number of surjective functions from the set \\( N_{10} = \\{1, 2, \\ldots, 10\\} \\) to the set \\( N_4 = \\{1, 2, 3, 4\\} \\) such that each element in \\( N_4 \\) has exactly 2 pre-images. Provide your answer as a single number.",
"role": "user"
}
] | 0 |
[
{
"content": "Does the convergence of \\(\\lim_{n\\to \\infty} \\frac{a_{n+1}}{a_n}\\) imply the convergence of \\(\\lim_{n\\to \\infty} a_n^{1/n}\\)? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the radius of convergence for the power series \\( \\sum_{n=1}^{\\infty}2^n x^{n^2} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral \\( \\iiint_V \\sqrt{x^2+y^2+z^2}\\, dV \\), where \\( V: x^2 + y^2 + z^2 \\leq 2z \\).",
"role": "user"
}
] | \dfrac{8\pi}{5} |
[
{
"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... | $4,207.27 |
[
{
"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... | 5924 |
[
{
"content": "Derive the asymptotic distribution of \\( \\sqrt{n} (\\hat{\\theta}_{MLE} - \\theta) \\) as \\( n \\to \\infty \\), where \\( \\hat{\\theta}_{MLE} = \\frac{n}{\\sum_{i=1}^n{X_i}} \\) is the maximum likelihood estimator for the parameter \\( \\theta \\) of an exponential distribution. Show that it ... | N(0, \theta^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... | 6.94 kg*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... | 900 N/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... | 5.4e5 m |
[
{
"content": "Express $0.\\overline{1}+0.\\overline{02}+0.\\overline{003}$ as a common fraction.",
"role": "user"
}
] | \frac{164}{1221} |
[
{
"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... | 140 |
[
{
"content": "Evaluate the integral: $$\\int_0^{200}\\lfloor x\\rfloor x\\lceil x\\rceil \\, dx$$",
"role": "user"
}
] | 399990000 |
[
{
"content": "Let $S$ be a spherical belt on the unit sphere in $\\mathbb{R}^d$. If $n$ points are sampled uniformly at random from $S$, find the probability that the first $d$ points are linearly independent, given that all $n$ points are linearly independent.",
"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... | 47.03 m/s |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\frac{\\Gamma\\left(\\frac{n+1}{3}\\right)}{\\Gamma\\left(\\frac{n+2}{3}\\right)}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the inequality \\( f(n)^{f(n)} \\leq f(n^n) \\) holds for all increasing functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\).",
"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... | 25\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... | -92 kJ |
[
{
"content": "Evaluate the integral: $$\\int_1^3 \\sqrt{x^4+1} \\, dx$$",
"role": "user"
}
] | 8.980 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.