prompt list | ground_truth string |
|---|---|
[
{
"content": "Let $f$ be a real-valued function defined on the interval $[1, \\infty)$ with $f(1) = 3$. For all $x \\geq 1$, the function satisfies the equation \\( 2 \\int_{2}^x f(t)\\,dt = xf(x) + x^3 \\). Determine the value of $f(2)$. \\( \\boxed{} \\)",
"role": "user"
}
] | -4 |
[
{
"content": "Find the value of \\(k\\) such that the equation \\((x^2 - 1)(x^2 - 4) = k\\) has four distinct equidistant real roots, where \\(k\\) is a real, non-zero number.",
"role": "user"
}
] | \dfrac{7}{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... | 0.072 N to the right |
[
{
"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... | -0.0443% |
[
{
"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... | 0.06775g |
[
{
"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... | 2.0 |
[
{
"content": "Determine the values of \\( a \\) such that the function \\( f(x) = (x^2 + 2ax + a^2 - 1)^{\\frac{1}{4}} \\) has a domain and range that together cover all real numbers.",
"role": "user"
}
] | (-\infty, -1] |
[
{
"content": "Given $n$ students seated in a line, each student chooses one element from the set $S=\\{1, \\omega, \\omega^2\\}$, where $\\omega$ is a root of $x^2 + x + 1 = 0$. If the product of any two consecutive students' choices is not 1, determine the number of possible arrangements for any value of $n$. ... | 3 \cdot 2^{n-1} |
[
{
"content": "Determine whether the following statement is true or false: If \\( f: \\mathbb{R} \\to \\mathbb{R} \\) is a bijective and Lebesgue measurable function, then its inverse \\( f^{-1}: \\mathbb{R} \\to \\mathbb{R} \\) is also Lebesgue measurable.",
"role": "user"
}
] | B |
[
{
"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... | $76,006.4 |
[
{
"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... | 60.6 micro-Tesla |
[
{
"content": "Is a finite subring $R$ of a division ring $D$ also a division ring?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the line integral \\( \\oint_C (x+ 2y)dx + (2z+ 2x)dy + (z+y)dz \\) using Stokes' theorem, where \\( C \\) is the intersection of the sphere \\( x^2 + y^2 + z^2 = 1 \\) and the plane \\( y = z \\). The curve \\( C \\) is oriented counterclockwise when viewed from above.",
"role": "use... | 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... | 20.8 L |
[
{
"content": "Calculate the mass of a bullet-shaped object formed by a cylinder with a curved top. The cylinder has a radius of \\(a\\) and is situated with its base on the \\((x, y)\\)-plane, with the origin at the center of the base. The curved top is described by the equation \\(z = 4a - \\frac{x^2}{a} + \\f... | 6\pi D a^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... | 1.4e-15 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... | $25.93 |
[
{
"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... | -2.21e-7 C/m^2 |
[
{
"content": "Determine the number \\( n \\) of colors for which it is possible to cover the plane with hexagons such that the centers of hexagons of the same color form the vertices of a grid of identical equilateral triangles. The grids for each color must have the same sizes and directions of sides and be ob... | 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... | 7450 |
[
{
"content": "Does every subset \\(V\\) of \\(\\mathbb{R}^n\\) with no two vectors having an angle greater than \\(\\frac{\\pi}{2}\\) between them necessarily lie within a hypercone? Specifically, is there a vector \\(u\\in \\mathbb{R}^n\\) such that the angle between \\(u\\) and any \\(v\\in V\\) is at most \\... | No |
[
{
"content": "Solve the equation $2^x + x = 11$ for $x$ without using graphing methods.",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the number of subgroups of the group $C_3 \\times C_3 \\times C_3$ that are isomorphic to $C_9$. Provide your answer as a single integer.",
"role": "user"
}
] | 0 |
[
{
"content": "Can a piece traverse an entire square board, visiting every cell exactly once, and end on the cell immediately to the right of the starting cell, given that it can move one cell up, one cell to the right, or one cell diagonally down-left?",
"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... | 264,600N |
[
{
"content": "Determine if the integral \\( \\int_0^\\infty \\frac{\\log(x)}{(1+x^2)^2} \\, dx \\) can be solved without using complex analysis methods.",
"role": "user"
}
] | -\dfrac{\pi}{4} |
[
{
"content": "Find all pairs of prime numbers \\((p, q)\\) such that:\n\\[p + p^2 + \\cdots + p^{10} - q = 2017.\\]\nGiven that \\((p, q) = (2, 29)\\) is a solution, determine if there are any other solutions.",
"role": "user"
}
] | (2, 29) |
[
{
"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... | 4.53e+04 N/C |
[
{
"content": "For how many positive integers \\( m \\leq 25 \\) does there exist a positive integer \\( n \\) such that the number of positive divisors of \\( S_n = \\sum_{k=1}^n k^3 \\) is equal to \\( m \\)?",
"role": "user"
}
] | 6 |
[
{
"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... | 20 < H < 60 |
[
{
"content": "Determine the smallest positive integer \\( a \\) such that the inequality \\[ \\frac{1}{n+1} + \\frac{1}{n+2} + \\cdots + \\frac{1}{2n+1} < a - 2007 \\cdot \\frac{1}{3} \\] holds for all positive integers \\( n \\).",
"role": "user"
}
] | 670 |
[
{
"content": "Determine whether the limit \\( \\lim_{n \\to \\infty} \\int_{0}^{1} \\sin^2\\left(\\frac{1}{ny^2}\\right)\\mathrm{d}y \\) exists.",
"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... | 2.36 |
[
{
"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... | 98.9 m/s |
[
{
"content": "Does there exist a nontrivial ultrafilter $a$ such that there is no sequence of sets $K_0, K_1, K_2, \\ldots \\in a$ for which $K_0 \\cap K_1 \\cap K_2 \\cap \\ldots = \\emptyset$?",
"role": "user"
}
] | No |
[
{
"content": "Determine the points where the function \\( f(z) = e^{x^2-y^2} [\\cos(2xy) - i\\sin(2xy)] \\) is differentiable. Use the Cauchy-Riemann equations to find these points.",
"role": "user"
}
] | 0 |
[
{
"content": "Compute \\( \\sup_{f \\in \\mathcal{F}} |f(0)| \\), where \\( \\mathcal{F} = \\{ f \\text{ holomorphic in } \\mathbb{D} \\text{ with } f(\\mathbb{D}) \\subset \\mathbb{D}, f\\left(\\frac{1}{2}\\right) = f'\\left(\\frac{1}{2}\\right) = 0 \\} \\) and \\( \\mathbb{D} \\) is the unit disc.",
"role... | \dfrac{1}{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... | 1205.6 g |
[
{
"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... | 305 seconds |
[
{
"content": "Determine the value of $x$ at which the Bessel equation $x^2y'' + xy' + (x^2 - n^2)y = 0$ has a regular singularity.",
"role": "user"
}
] | 0 |
[
{
"content": "In triangle $ABC$, where $AB = AC$ and $I$ is the in-center, it is given that $BC = AB + AI$. Determine the measure of angle $\\angle BAC$. \\( \\text{Express your answer in degrees.} \\)",
"role": "user"
}
] | 90 |
[
{
"content": "If $f(a) = \\frac{1}{1-a}$, find the product $f^{-1}(a) \\times a \\times f(a)$. (Assume $a \\neq 0$ and $a \\neq 1$.)",
"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... | The cost of oil shipped in the pipeline is $10,660.82 million, and the amount in work-in-process ending inventory as of May 31 is $979.18 million. |
[
{
"content": "Provide an example of an $n \\times n$ matrix $A$ such that $A^T A = -I$, where $I$ is the identity matrix. Use a well-known type of matrix for your example.",
"role": "user"
}
] | iI |
[
{
"content": "What is the least upper bound for the Hausdorff dimension of the graph of a real-valued, continuous function on an interval? Is this least upper bound attained by some function?",
"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... | 6452 J |
[
{
"content": "Given the function \\( f(X)=\\exp\\left(\\frac{-\\gamma^2}{a^2X+b^2}\\right) \\) where \\( X \\sim \\mathrm{Binomial}(n,p) \\), use the central limit theorem to find an approximate expression for the value of \\( \\gamma^2 \\) that maximizes the variance of \\( f(X) \\).",
"role": "user"
}
] | a^2 np + b^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... | 21.03% |
[
{
"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... | 1.17V |
[
{
"content": "Determine whether there exists a topological space \\( X \\) such that \\( X \\) is connected, the boundary \\( \\partial X \\) is connected, but the interior \\( \\text{int}(X) \\) is not connected.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the derivative of the function $g \\circ f^{-1}$ at $x = 2$, where $f(x) = x^{3} + x$ and $g(x) = x^{3} - x$. Express 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... | $21.60 per room cleaned |
[
{
"content": "Let $U$ be an orthonormal set in a Hilbert space $H$, and let $x \\in H$ be such that $\\| x \\| = 2$. Consider the set\n\\[ E = \\{ u \\in U : |\\langle x, u \\rangle| \\geq \\frac{1}{4} \\} \\]\nWhat is the maximal possible number of elements in $E$?",
"role": "user"
}
] | 64 |
[
{
"content": "Determine the values of the positive integer $d$ for which the moment-generating function $M_{Z^d}(t)$ of $Z^d$ is finite for all $t > 0$, where $Z$ is a standard normal random variable.",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the limit: $$\\lim_{n \\to \\infty} \\left(\\dfrac{n}{(n+1)^2}+\\dfrac{n}{(n+2)^2}+\\cdots+\\dfrac{n}{(n+n)^2}\\right).$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Approximate \\( \\text{erf}(1) \\) using the series expansion \\( \\frac{2}{\\sqrt{\\pi}} \\sum_{k=0}^{\\infty} \\frac{(-1)^{k}1^{2k+1}}{(2k+1)k!} \\) to within \\( 10^{-7} \\).",
"role": "user"
}
] | 0.8427008 |
[
{
"content": "Let \\( x, y, z \\) be real numbers such that \\( 3x, 4y, 5z \\) form a geometric sequence, and \\(\\frac{1}{x}, \\frac{1}{y}, \\frac{1}{z}\\) form an arithmetic sequence. Find the value of \\( \\frac{x}{z} + \\frac{z}{x} \\).",
"role": "user"
}
] | \dfrac{34}{15} |
[
{
"content": "Given positive real numbers $a, b, c$ such that $a + b + c = 1$, determine the maximum value of the expression $$P = a^2 + b^2 + c^2 + 2\\sqrt{3abc}.$$",
"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... | 6.541e3 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... | 20.01% |
[
{
"content": "Suppose that \\(\\{x_1, x_2, \\cdots x_n\\}\\) are \\(n\\) independently uniformly distributed real numbers from 0 to \\(k\\). What is the probability that their sum is less than \\(k\\)?",
"role": "user"
}
] | \dfrac{1}{n!} |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} \\left(\\frac{1}{x}\\frac{b^x-1}{b+1}\\right)^{\\frac{1}{x}}$$ where $b$ is a constant and $0 < b < 1$. ",
"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... | 121.749s |
[
{
"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... | 1.42 |
[
{
"content": "Determine whether there exists a topological space \\((X, \\tau)\\) that is totally separated, meaning for any distinct points \\(x\\) and \\(y\\) in \\(X\\), there exists a clopen set containing \\(x\\) but not \\(y\\), yet the collection of clopen sets does not form a basis for the topology \\(\... | 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": "Compute \\( \\lim_{n\\to \\infty} \\int_1^\\infty \\frac{1 + (-1)^n \\exp(-nx^2)}{x^2} \\, dx \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let \\( X \\) and \\( Y \\) be independent random variables, each following a geometric distribution with parameter \\( p \\). Compute \\( E(X \\mid X+Y=k) \\) for all \\( k = 2, 3, \\ldots \\).",
"role": "user"
}
] | \dfrac{k}{2} |
[
{
"content": "Find the coefficient $a_{-1}$ in the Laurent series expansion of the function \\( f(z) = z^3 \\cos\\left(\\frac{1}{z}\\right) e^{\\frac{1}{z^2}} \\).",
"role": "user"
}
] | \dfrac{1}{24} |
[
{
"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... | 0.02363 mm |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{+\\infty} \\text{sinc}(x) \\, dx \\).",
"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... | ~( (~A nand ~B) nand (~A nand ~C) nand (A nand B nand C) nand (~A nand D) ) |
[
{
"content": "Determine whether it is true for sufficiently large integers $x$ and $y$ that $p(x+y) < p(x)p(y)$, where $p(n)$ denotes the number of integer partitions of $n$. Provide a justification for your answer.",
"role": "user"
}
] | True |
[
{
"content": "Find the pointwise limit of the sequence \\(f_n(x) = \\frac{x^n}{n}\\) on the interval \\([0,1]\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given a matrix $A^{n \\times m}$ and a vector $b \\in F^n$, consider the homogeneous system $H = \\{h \\in F^m \\mid Ah = 0\\}$ and the non-homogeneous system $L = \\{l \\in F^m \\mid Al = b\\}$. If $L \\neq \\emptyset$, determine the relationship between the cardinalities $|L|$ and $|H|$.",
"... | |L| = |H| |
[
{
"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... | 5.29 rad/s |
[
{
"content": "What is the minimum number of non-adjacent swaps required to sort a list of distinct integers in ascending order?",
"role": "user"
}
] | 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... | -1.54m |
[
{
"content": "Determine the order of the pole for the complex function \\( \\frac{z}{\\sin\\pi z^{2}} \\) at the following points: \\( z=0 \\), \\( z=\\pm\\sqrt{n} \\), and \\( z=\\pm i\\sqrt{n} \\), where \\( n \\in \\mathbb{Z}^{+} \\).",
"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... | $2,500 |
[
{
"content": "Consider a square defined by \\( \\{(x,y): 0\\le x,y \\le 1\\} \\) divided into \\( n^2 \\) small squares by the lines \\( x = i/n \\) and \\( y = j/n \\). For \\( 1\\le i \\le n \\), let \\( x_i = i/n \\) and define \\( d_i = \\min_{0\\le j\\le n} \\left| \\sqrt{1 - x_i^2 } - j/n\\right| \\). Det... | \dfrac{1}{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... | The beginning equity is $72,000 and the ending equity is $138,000 |
[
{
"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... | 1328 kg/m^3 |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\pi/2} \\frac{\\sqrt{\\sin x}}{\\sqrt{\\sin x} + \\sqrt{\\cos x}} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Compute the boundary map $d_0$ for the Cech cohomology with twisted coefficients on the circle, given the open cover $U_0, U_1, U_2$ and restriction morphisms $\\rho^i_{ij}:U_i \\to U_{ij}$ with $\\rho^2_{02} = -1$ and $\\rho^i_{ij} = 1$ for all other $i,j$. Express the map in terms of $(a,b,c) \\... | 0 |
[
{
"content": "Find the maximum value of \\( a \\) such that for any \\( m \\) and \\( x \\) with \\( 0 \\leqslant m \\leqslant a \\) and \\( 0 \\leqslant x \\leqslant \\pi \\), the inequality \\( |\\sin x - \\sin (x + m)| \\leqslant 1 \\) holds.",
"role": "user"
}
] | \dfrac{\pi}{3} |
[
{
"content": "Determine the dimension of the vector space $\\mathfrak{m}/\\mathfrak{m}^2$ for the curve $\\mathcal{C}=\\{ (x,y): x^3+y^3-1=0 \\} \\subset \\mathbb{C}^2$, where $\\mathfrak{m} = \\langle x-a,y-b\\rangle/\\langle x^3 + y^3 -1\\rangle$ and $p=(a,b) \\in \\mathcal{C}$. Provide your answer as a singl... | 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... | 31.9 g/mol |
[
{
"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... | Special agent |
[
{
"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... | 10.803% |
[
{
"content": "Determine the asymptotic distribution of the statistic \\(8nB = - 8n\\operatorname{ln}(\\sqrt{0.2\\hat{p}} + \\sqrt{0.8(1-\\hat{p})} )\\), where \\(\\hat{p} = (1/n)\\sum_i X_i = \\bar{X}_n\\) is the estimator of \\(p\\) from a random sample \\(X_1, ..., X_n\\) taken from a Bernoulli\\((p)\\) distr... | \chi^2_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... | 1*10^-9 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... | 68.72 |
[
{
"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... | $1,267,150 |
[
{
"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... | 96 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... | [CO]=[H2O]=0.01126 M, [CO2]=[H2]=0.113738 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... | 2037 |
[
{
"content": "Determine the number of solutions to the congruence equation \\(x_1 + 2x_2 + 3x_3 + 4x_4 + 5x_5 + 6x_6 + 7x_7 + 8x_8 + 9x_9 + 10x_{10} \\equiv 0 \\pmod{11}\\), where \\(x_1, x_2, \\ldots, x_9 \\in \\{0, 1, 2, \\ldots, 9\\}\\) and \\(x_{10} \\in \\{0, 1, 2, \\ldots, 10\\}\\).",
"role": "user"
... | 1000000000 |
[
{
"content": "Consider the six by six grid of unit squares below. How many rectangles of area 3 square units can be formed using only the line segments of the grid as the sides of the rectangles?\n\n[asy]unitsize(0.1inch);\ndraw((0,0)--(6,0)--(6,6)--(0,6)--cycle);\ndraw((1,0)--(1,6));\ndraw((2,0)--(2,6));\ndraw... | 48 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{1}{\\sqrt{n}} \\left( \\frac{1}{\\sqrt{1}} + \\frac{1}{\\sqrt{2}} + \\cdots + \\frac{1}{\\sqrt{n}} \\right) \\] without using integrals.",
"role": "user"
}
] | 2 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.