prompt list | ground_truth string |
|---|---|
[
{
"content": "Let $X$ be a Polish space and $(\\mu_n)_{n \\geq 1}$ be a sequence of Borel probability measures on $X$. Assume that for every continuous bounded function $f : X \\to \\mathbb{R}$, the limit $L(f) := \\lim_{n \\to \\infty} \\int_X f \\, d \\mu_n$ exists. Does there exist a Borel probability measur... | 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... | -$81,840.02 |
[
{
"content": "Suppose \\(X\\sim N(\\mu,\\sigma^2)\\) and \\(X_1,\\cdots,X_n\\) are samples from \\(X\\). If it is known that \\(\\bar{X}_n-\\mu=o_p(n^{-\\beta})\\), find the minimum possible value of \\(\\beta\\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Alice picks a number from the set \\( \\{1, 2, \\ldots, 1000000\\} \\). Bob can ask yes/no questions to determine Alice's number, but Alice is allowed to lie once. What is the minimum number of questions Bob must ask to guarantee he correctly identifies the number?",
"role": "user"
}
] | 25 |
[
{
"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... | 41218 N |
[
{
"content": "Consider a bounded sequence $(b_n)$ such that any of its convergent subsequences converge to a limit $b$. Does the sequence $(b_n)$ necessarily converge to $b$? 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... | 8.85% monthly investment |
[
{
"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... | 74 million |
[
{
"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... | 3.25e-9 |
[
{
"content": "Let $A$ be a self-adjoint operator on a functional Hilbert space $\\mathscr{H}$. Define the norm $N(A)$ as follows:\n\\[ N(A) := \\sup\\{ |\\langle A\\widehat{k}_{\\lambda}, \\widehat{k}_{\\lambda} \\rangle| : \\lambda \\in \\Omega \\}, \\]\nwhere $\\widehat{k}_{\\lambda}$ is the normalized reprod... | No |
[
{
"content": "Find the Jacobian matrix of the expression $x^T A x$, where $A$ is a symmetric matrix in $\\mathbb{R}^{n \\times n}$ and $x$ is a vector in $\\mathbb{R}^n$. Provide your answer in terms of $A$ and $x$.",
"role": "user"
}
] | 2x^T A |
[
{
"content": "Let $M$ be a smooth manifold and $N$ a submanifold of $M$. Consider vector fields $X_1, \\\\ldots, X_k \\in \\Gamma(TM)$ on $M$ that restrict to vector fields on $N$. For a smooth function $f \\in C^\\infty(M)$, we obtain two smooth functions on $N$: one by restricting the derivative $X_1 \\ldots ... | Yes |
[
{
"content": "Determine whether the following statement is true or false:\n\nSuppose $N$ and $L$ are submodules of $M$ with $N \\subseteq L$. If $M/L \\cong M/N$, then $L = N$. Consider both the general case and the specific case where $L = \\ker \\varphi$ for some $\\varphi \\in \\text{Hom}(M,P)$. Provide a ju... | False |
[
{
"content": "Determine whether the number of distinct values of $c$ for which the polynomial $f(z) - c$ has multiple roots is finite for any polynomial $f(z)$ with complex coefficients.",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the coefficients $a_n$ for $n<0$ in the Laurent expansion of $\\cot(\\pi z)$ on the annulus $1<|z|<2$, where $\\cot(\\pi z)=\\sum_{n=-\\infty}^{\\infty} a_n z^n$. Specifically, find $a_{-1}$.",
"role": "user"
}
] | \dfrac{3}{\pi} |
[
{
"content": "Determine whether there exists a noncommutative abelian ring with nontrivial idempotents.",
"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... | 855 J |
[
{
"content": "Find the smallest integer $n$ such that $n$ is divisible by a perfect square, $n+1$ is divisible by a perfect cube, and $n+2$ is divisible by a perfect fourth power.",
"role": "user"
}
] | 350 |
[
{
"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... | 589 W |
[
{
"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... | 479.3 J/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... | 1.41 |
[
{
"content": "Calculate the work done by the vector field \\( \\overrightarrow{F} = \\left(\\frac{-y}{x^2+y^2},\\frac{x}{x^2+y^2}\\right) \\) along a straight line from the point \\((0,1)\\) to the point \\((1,0)\\). Note that the potential function \\( \\phi = \\arctan\\left(\\frac{x}{y}\\right) \\) is undefin... | -\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... | 0.006N |
[
{
"content": "Let $[x]$ denote the largest integer not greater than the real number $x$. Define \\( A = \\left[\\frac{7}{8}\\right] + \\left[\\frac{7^{2}}{8}\\right] + \\cdots + \\left[\\frac{7^{2016}}{8}\\right] \\). Find the remainder when \\( A \\) is divided by 50.",
"role": "user"
}
] | 42 |
[
{
"content": "Let $X_i \\sim \\text{Bernoulli}\\left(\\frac{\\theta}{n}\\right)$ and $Y_i \\sim \\text{Poisson}\\left(\\frac{\\theta}{n}\\right)$ be independent and identically distributed random variables, where $n \\ge \\theta \\ge 0$. Define $T_n = \\sum_{i=1}^{n^2} X_i$ and $S_n = \\sum_{i=1}^{n^2} Y_i$. De... | 1 |
[
{
"content": "Let \\( f:[0,1] \\to \\mathbb{R} \\) be a continuous function satisfying the equation \\( \\int_{0}^{1} f(x) \\, dx = \\frac{1}{3} + \\int_{0}^{1} \\left(f\\left(x^{2}\\right)\\right)^{2} \\, dx \\). Determine the value of \\( f\\left(\\frac{1}{4}\\right) \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "For a prime number $p > 3$, consider the fraction:\n\\[\n1 + \\frac{1}{2} + \\frac{1}{3} + \\ldots + \\frac{1}{p-1}.\n\\]\nIs the numerator of this fraction divisible by $p^3$?",
"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... | 10426 slits/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... | 2.02 times |
[
{
"content": "Participation in the local soccer league is $10\\%$ higher this year than it was last year. Also, from last year to this year, the number of males increased by $5\\%$ and the number of females increased by $20\\%$. There were $20$ males participating in the league last year. What fraction of the l... | \frac{4}{11} |
[
{
"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... | 1907.39 |
[
{
"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... | 21.6 kg |
[
{
"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... | 40.20 g/mol |
[
{
"content": "In a topological vector space $(A, \\tau)$, consider a subset $B$ of $A$ that is metrizable and complete with a translation-invariant metric. If the metric topology on $B$ coincides with the induced subspace topology, is $B$ necessarily closed in $\\tau$?",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\(\\lambda_k\\), \\(k = 1, \\dots, N\\) be distinct real numbers. Consider the function \\(g(x) = \\sum_{k =1}^N \\beta_k e^{i\\lambda_k x}\\), where \\(\\beta_k\\) are complex numbers not all zero. Does there exist a constant \\(c > 0\\) and a sequence \\(x_n \\to \\infty\\) such that \\(|g(... | Yes |
[
{
"content": "There are 8 pens along a wall in the pound. The pound has to allocate 4 pens to dogs, 3 to cats, and one to roosters. In how many ways can the pound make the allocation?",
"role": "user"
}
] | 280 |
[
{
"content": "Is it true that among the set of special linear matrices $M$ (i.e., matrices with $\\det(M)=1$), the matrices with minimal norm $\\Vert A\\Vert = \\sqrt{\\operatorname{Tr}(A^TA)}$ are the special orthogonal matrices (i.e., matrices with $A^TA=I_n$)?",
"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... | 11.36% |
[
{
"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... | June 1:
Inventory $1,755
Accounts Payable $1,755
June 3:
Accounts Receivable $1,550
Sales $1,550
Cost of Goods Sold $850
Inventory $850
June 6:
Accounts Payable $55
Inventory $55
June 9:
Accounts Payable $1,700
Purchase Discounts $51
Cash $1,649
June 15:
Cash ... |
[
{
"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... | mass H2CO3 = 0.019 g, mass HCO3- = 0.13 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... | 20.040 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... | 1.56e-8 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... | Three methods mentioned can be used to separate and recover components of the mixture: Method 1 involves adding water and diethyl ether for extraction and isolation. Method 2 makes use of cold water insolubility of benzoic acid and strain the mixture using filter paper. Method 3 involves separation based on their polar... |
[
{
"content": "In a Gaussian random walk, where $x_n$ is the sum of $n$ normal random variables, calculate the probability $P(x_1 > 0, x_2 > 0)$. Assume that the events $x_1 > 0$ and $x_2 > 0$ are not independent.",
"role": "user"
}
] | \dfrac{3}{8} |
[
{
"content": "Find the number of elements in the conjugacy class of the permutation \\( \\partial = (1\\ 10)(2\\ 6\\ 3\\ 7\\ 6\\ 8\\ 12)(4)(9\\ 11) \\) in the symmetric group \\( S_{12} \\).",
"role": "user"
}
] | 4989600 |
[
{
"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/sqrt(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... | 1.254e6 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... | 1.98M |
[
{
"content": "Let $n \\geq 2$ be an integer and let $a_1, \\ldots, a_n \\in \\mathbb{Z}$ with $\\gcd(a_1, \\ldots, a_n) = 1$. Determine whether the equation \\[ \\begin{vmatrix} a_1 & \\cdots & a_n \\\\ x_{11} & \\cdots & x_{1n} \\\\ x_{21} & \\cdots & x_{2n} \\\\ \\vdots & \\ddots & \\vdots \\\\ x_{n-1,1} & \\... | Yes |
[
{
"content": "In a locally compact Hausdorff space $X$, given a Radon measure $\\mu$ and a function $f$ that is continuous everywhere except on a set $N$ with $\\mu(N) = 0$, determine whether there exists an everywhere continuous function $g$ such that $f = g$ on the complement of $N$ in $X$. Provide a justific... | No |
[
{
"content": "Determine whether the statement is true or false: If a real or complex-valued function $f$ is injective, then it must be analytic.",
"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... | a, b, c, d, e |
[
{
"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... | 1.63e13 J |
[
{
"content": "Let $O$ be the origin, and let $OABC$ be a rectangle, where $A$ and $C$ lie on the parabola $y = x^2.$ Then vertex $B$ must lie on a fixed parabola. Enter the equation of the fixed parabola in the form \"$y = px^2 + qx + r$\".",
"role": "user"
}
] | y = x^2 + 2 |
[
{
"content": "A number is called a visible factor number if it is divisible by each of its non-zero digits. For example, 102 is divisible by 1 and 2, so it is a visible factor number. How many visible factor numbers are there from 100 through 150, inclusive?",
"role": "user"
}
] | 19 |
[
{
"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... | 0.0191 |
[
{
"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... | 46.98% |
[
{
"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... | 249.19 ohm |
[
{
"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... | 0.053 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... | 0.5 * arccos((v_0^2+gh)/(2v_0^2)-1) |
[
{
"content": "Evaluate the sum \\( \\displaystyle \\sum_{k=0}^{n}{n+2 \\choose k+2}(-1)^k \\).",
"role": "user"
}
] | n + 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... | variable interval |
[
{
"content": "Find the area of the figure bounded by the curve \\((x^2+y^2)^3=x^4+y^4\\) using polar coordinates.",
"role": "user"
}
] | \dfrac{3\pi}{4} |
[
{
"content": "Determine the cardinality of a basis for the vector space of the real numbers over the field of rational numbers.",
"role": "user"
}
] | 2^{\aleph_0} |
[
{
"content": "Find the boundary of the manifold $D^2 \\times S^1$, where $D^2$ is the closed unit disk and $S^1$ is the circle.",
"role": "user"
}
] | S^1 \times S^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... | 7500 |
[
{
"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... | $8.91 |
[
{
"content": "Suppose $m$ and $n$ are positive integers such that the greatest common divisor of $m$ and $n$ is divisible by exactly 5 distinct primes, and the least common multiple of $m$ and $n$ is divisible by exactly 20 distinct primes. If $m$ has more distinct prime factors than $n$, what is the maximum nu... | 12 |
[
{
"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... | intimate terrorism |
[
{
"content": "Find the limit of the sequence \\( \\frac{n}{\\sqrt[n]{n!}} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | e |
[
{
"content": "Suppose that $x$, $y$, $x-y$, and $x+y$ are all positive prime numbers. Find the sum of these four numbers.",
"role": "user"
}
] | 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... | 44.31 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... | 138 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... | 46N, 25 degrees north of east |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y)\\to (0,0)} xy \\frac{(x+y)}{x^2-xy+y^2}$$",
"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... | 2.24e+07 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... | Cash in Bank: 107
Interest Income: 107
Service Charges: 34
Interest Income: 34
Accounts Payable: 284
Interest Income: 284 |
[
{
"content": "Find the last three digits of the product of all odd numbers from 1 to 1997.",
"role": "user"
}
] | 375 |
[
{
"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... | 0.95 g/L |
[
{
"content": "Let $S$ be the set of all continuous real functions $f(x)$ on the interval $[0,1]$ such that \\(\\lim_{x\\rightarrow 0}f(x)/x^k=0\\) for \\(k=1,2,...\\). Prove or disprove: 0 is the only common root of the elements of $S$. Provide a justification for your answer.",
"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... | 2241 g |
[
{
"content": "Use a triple integral to find the volume of the solid enclosed by the cylinder \\(x^2+y^2=9\\) and the planes \\(y+z=5\\) and \\(z=1\\).",
"role": "user"
}
] | 36\pi |
[
{
"content": "Given a parameterized curve \\(\\gamma :I\\rightarrow \\mathbb{R}^{3}\\) by arc length with curvature \\(\\| k \\| = 2\\) and torsion \\(\\| t \\| = 3\\), find the norm of the derivative of the normal vector \\(\\| {N}' \\|\\). Use the Frenet-Serret formulas to express \\(\\| {N}' \\|\\) in terms ... | \sqrt{13} |
[
{
"content": "A bead is placed on a vertex of a cube, and it can slide along the edges to adjacent vertices. In a sequence of 6 moves, the bead must return to its starting vertex. How many different sequences of moves are possible?",
"role": "user"
}
] | 183 |
[
{
"content": "Find the greatest common divisor of \\(5^{2023!} + 1\\) and \\(4046\\).",
"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... | 0.074 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... | 407.3 kJ/kg |
[
{
"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... | 2.26mV |
[
{
"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 mg |
[
{
"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... | 0.16 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... | 377 m/s^2 |
[
{
"content": "Calculate the Lebesgue integral \\( \\int_{\\mathbb{R}} f(x) \\, \\mu(dx) \\), where \\( \\mu \\) is a Borel measure on \\( \\mathbb{R} \\) defined by \\( \\mu(x)=\\begin{cases} 2x+1 & x \\leq 2 \\\\ 2x^2 & x > 2\\ \\end{cases} \\) and \\( f(x)=\\begin{cases} 1 & x\\in \\mathbb{Z}\\cap [-1,3] \\\\... | \dfrac{112}{3} |
[
{
"content": "Find the radius of curvature of the curve given by the equation \\(x^3 + y^3 = 12xy\\) at the point \\((0, 0)\\).",
"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... | $2,350.53 |
[
{
"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... | 37.73 m^2 |
[
{
"content": "Determine whether the function \\( f(x) = e^{\\frac{x+1}{x}} \\) has a unique fixed point in \\( \\mathbb{R} \\).",
"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... | FV_n = n*PV = PV(1+i)^n where n is in terms of every two years |
[
{
"content": "Find the angle of intersection between the logarithmic spiral given by the equation \\( r = Ce^{k\\theta} \\) and any line passing through the origin.",
"role": "user"
}
] | \arctan\left(\frac{1}{k}\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... | $865,920 |
[
{
"content": "Determine whether there exists a non-constant analytic function \\( f: \\Bbb{C} \\to \\Bbb{C} \\) such that \\( f(n) = 3 \\) for all integers \\( n \\).",
"role": "user"
}
] | Yes |
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