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... | 55 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... | 27.60 N |
[
{
"content": "Given the transition matrix \\( M = \\begin{pmatrix} 0.25 & 0.5 & 0.25 \\\\ 0.5 & 0.25 & 0.25 \\\\ 0.5 & 0.25 & 0.25 \\end{pmatrix} \\) of a Markov chain with states \\( S = \\{0, 1, 2\\} \\), calculate the expected number of steps to reach state 1 starting from state 2.",
"role": "user"
}
] | \dfrac{20}{7} |
[
{
"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... | 962,671 |
[
{
"content": "In the inner product space $P([0,1])$ of all real polynomials on $[0,1]$ with the inner product \\( \\langle f,g\\rangle=\\int_0^1f(x)g(x)dx \\), consider the subspace \\( V=\\text{span}\\{t^2\\} \\). Determine the polynomial \\( h(t) \\in V \\) such that \\( \\|(2t-1)-h(t)\\| \\le \\|(2t-1)-x(t)\... | 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... | 17.69 |
[
{
"content": "Consider a continuous bijection between manifolds of the same dimension. Must this map be a homeomorphism? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the infinite series: \\[ \\sum_{n=1}^\\infty \\frac{n^2 \\cdot (n+1)^2}{n!} \\]",
"role": "user"
}
] | 27e |
[
{
"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... | 70 milliliters of 32% solution and 100 milliliters of 66% solution |
[
{
"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... | ML^2/54 |
[
{
"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... | 163,265 |
[
{
"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... | $56.52 |
[
{
"content": "Construct a \\( \\varepsilon - \\delta \\) proof to show that \\( \\lim_{x \\to 27} 2x^{2/3} = 18 \\).",
"role": "user"
}
] | 18 |
[
{
"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... | 11.6 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... | 751 sec |
[
{
"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 |
[
{
"content": "Determine the maximum value of the parameter \\( a \\) such that the coefficient of \\( x^4 \\) in the expansion of \\( \\left(1-2x+ax^2\\right)^8 \\) is equal to \\(-1540\\).",
"role": "user"
}
] | -5 |
[
{
"content": "In triangle $ABC$ with sides $AB = \\sqrt{17}$, $BC = 5$, and $CA = 4\\sqrt{2}$, points $D, E, F$ lie on lines $AB, BC$, and $CA$, respectively, forming triangle $DEF$ inside $ABC$. If the minimum perimeter of triangle $DEF$ can be expressed as $\\left(\\frac{q}{p}\\right)\\sqrt{34}$, where $p$ an... | 37 |
[
{
"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... | 14.95% |
[
{
"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... | 0.0087m |
[
{
"content": "In a commutative ring, if the product $xy$ is a unit, must both $x$ and $y$ be units?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the triple integral \\( \\iiint x \\, dV \\) over the solid enclosed by the cylinder \\( x^2 + z^2 = 4 \\) and the planes \\( y = 0 \\) and \\( y + z = 4 \\). Verify if the bounds for the integration are correct.",
"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... | $298,550 |
[
{
"content": "What is the remainder when $40!$ is divided by $1763$?",
"role": "user"
}
] | 1311 |
[
{
"content": "Compute $\\cos 1050^\\circ$.",
"role": "user"
}
] | \frac{\sqrt{3}}{2} |
[
{
"content": "Given a positive bounded sequence where the average converges to zero, does the average of the square of the sequence also converge to zero? Specifically, if \\( \\frac{\\sum\\limits_{i=1}^n |x_i|}{n}\\rightarrow 0 \\) and \\( |x_i|\\leq C \\), does \\( \\frac{\\sum\\limits_{i=1}^n |x_i|^2}{n}\\ri... | 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... | 49.9% |
[
{
"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... | $427,705,627.70 |
[
{
"content": "Evaluate the limit \\( \\lim_{h \\to 0} \\frac{f(2+2h+h^2) - f(2)}{f(1+h-h^2) - f(1)} \\) given that \\( f(x) \\) is a differentiable function with \\( f'(1) = 4 \\) and \\( f'(2) = 6 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the image of the imaginary axis under the function \\( f(z) = \\frac{z+1}{z-1} \\), where \\( f: \\mathbb{C} \\to \\mathbb{C} \\).",
"role": "user"
}
] | |w| = 1 |
[
{
"content": "Compute $a^2 + b^2 + c^2,$ given that $a,$ $b,$ and $c$ are the roots of \\[2x^3 - x^2 + 4x + 10 = 0.\\]",
"role": "user"
}
] | -\frac{15}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... | 23777.38 |
[
{
"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... | 0.291 atm |
[
{
"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... | 3.85e+9 C |
[
{
"content": "Maximize the expression \\( A = \\sqrt{1+x^2} + \\sqrt{1+y^2} + \\sqrt{1+z^2} + 2(\\sqrt{x} + \\sqrt{y} + \\sqrt{z}) \\) given that \\( x, y, z \\) are positive numbers satisfying \\( x+y+z \\le 3 \\). Find the maximum value of \\( A \\).",
"role": "user"
}
] | 6 + 3\sqrt{2} |
[
{
"content": "Let $X_1, X_2, \\ldots$ be an i.i.d. sequence of random variables with a distribution that has a continuous density function on $[0,1]$. Determine whether the following limit holds almost surely:\n\n$$\\lim_{n\\to \\infty}\\frac{\\sum_{1\\le i<j \\le n}{\\bf{1}}_{(-1/n,1/n)}{(X_i-X_j)}}{n}=1$$",
... | 0 |
[
{
"content": "Determine the number of cyclic subgroups of order 12 in the group \\( \\mathbb{Z}/2\\mathbb{Z} \\times \\mathbb{Z}/3\\mathbb{Z} \\times \\mathbb{Z}/3\\mathbb{Z} \\times \\mathbb{Z}/4\\mathbb{Z} \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Evaluate the infinite series \\( \\sum_{k=0}^\\infty \\frac{k(vt)^k e^{-vt}}{k!} \\) and verify that the result is equal to \\( vt \\), where \\( v \\) is a constant.",
"role": "user"
}
] | vt |
[
{
"content": "Determine the set of all values of \\(a\\) such that the equation \\((a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2 = 0\\) has real and distinct roots. Choose from the following options:\n\n(a) \\(\\left(0,\\frac{1}{2}\\right)\\)\n(b) \\(\\left(-\\frac{1}{2},0\\right)\\cup \\left(0,\\frac{1}{2}\\right)\\)\n(c)... | B |
[
{
"content": "Determine whether there exists a bijective map \\( f: \\mathbb{Z} \\rightarrow \\mathbb{Z}^2 \\) that can be extended to a continuous map from \\( \\mathbb{R} \\) to \\( \\mathbb{R}^2 \\).",
"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... | 17.81 |
[
{
"content": "Find the number of solutions in natural numbers to the equation \\(x_{1} + x_{2} + x_{3} + x_{4} + y_{1} + y_{2} = 6\\), where \\(0 \\leq x_{i} \\leq 2\\) and \\(y_{i}\\) is divisible by 3, by calculating the coefficient of \\(x^{6}\\) in the generating function:\n\\[f(x) = (1 + x + x^{2})^{4} \\l... | 45 |
[
{
"content": "Consider the function \\( f(z)=(1+i)z+1 \\). It is known that \\( f^n(z) \\) is a rotation and a homothetic transformation with center \\( z_0=i \\). Determine the value of \\( n \\) for which \\( f^n(z) \\) is a reflection about the point \\( z_0 \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Find the norm of the operator \\( A:L_2[0,2] \\rightarrow L_2[0,2] \\) defined by \\((Ax)(t) = t \\, \\operatorname{sgn}(t-1) x(t)\\). Determine if the operator is bounded, and if so, find the operator norm.",
"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... | 0.9505 N |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to \\infty} x^2\\left(\\arctan(x)-\\frac{\\pi}{2}\\right)+x$$ as $x$ approaches infinity.",
"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... | 15.02 |
[
{
"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... | 0.056 |
[
{
"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... | 690 nm |
[
{
"content": "Let $W$ be a finite-dimensional vector space over $\\mathbb{R}$. Let $S:W\\to W$ be a linear transformation with minimal polynomial $x^6(x+2)^2$. Determine the minimal polynomial of $S^3$.",
"role": "user"
}
] | x^2 (x + 8)^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... | 0.92 |
[
{
"content": "Find the value of \\( \\sqrt{2+\\sqrt{5}-\\sqrt{6-3\\sqrt{5}+\\sqrt{14-6\\sqrt{5}}}} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Consider an open and connected subset of the plane that intersects the unit circle. Does this subset necessarily contain points within a small distance of the circle's center?",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to 0} \\frac{e^{-1/x^2}}{x} \\) without using L'Hôpital's rule.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the expected value of the cumulative distribution function (CDF) of a standard normal random variable $X$ at a point $Y$, where $Y$ is a normal random variable with mean $0$ and variance $\\sigma^2$. That is, find $E[F(Y)]$, where $F(z) = \\Pr(X < z)$ is the CDF of $X$. Assume $X \\sim N(... | \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... | $192 |
[
{
"content": "Determine the big O notation for the function \\(f(n, k)\\) defined as follows, given that \\(n < k\\):\n\n\\[f(n, k)=\\sum_{i=1}^{n-1}(n-i)(k-i)\\log(k-i)\\]",
"role": "user"
}
] | O(n^2 k \log k) |
[
{
"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... | 0.142 |
[
{
"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... | 136.8 g |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0} \\frac{1}{x} \\cdot \\int_{0}^{x}(1+\\sin(t))^\\frac{1}{t}dt$$",
"role": "user"
}
] | e |
[
{
"content": "Determine whether the following statement is true or false: Given functions $f, g$, and $g'$ in $L^1(\\mathbb{R})$, is it true that $(f \\ast g)' = f \\ast g'$?",
"role": "user"
}
] | True |
[
{
"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... | credentials |
[
{
"content": "Calculate the line integral \\( I = \\int_{C} \\mathbf{v} \\cdot d\\mathbf{r} \\) where \\( \\mathbf{v}(x,y) = y\\mathbf{i} - x\\mathbf{j} \\) and \\( C \\) is the semicircle of radius 2 centered at the origin, from \\((0,2)\\) to \\((0,-2)\\) along the negative x-axis (left half-plane). Use the p... | -4\pi |
[
{
"content": "Determine the maximum number of distinct real roots that the equation \\( \\sum_{i=1}^{n}a_{i}b_{i}^{x} + c = 0 \\) can have, where \\( a_{i}, b_{i}, c \\) are real constants, \\( b_{i} > 0 \\), \\( b_{i} \\neq b_{j} \\) for \\( i \\neq j \\), and \\( c \\neq 0 \\).",
"role": "user"
}
] | 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... | 23.96 km/min |
[
{
"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... | -4.553 rad/s^2 |
[
{
"content": "Find all pairs of natural numbers \\((x, y)\\) that satisfy the equation:\n\\[ (x^2 + 1)^y - (x^2 - 1)^y = 2x^y \\]",
"role": "user"
}
] | (1, 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... | vR/(R^2+x^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... | 98 N |
[
{
"content": "Determine whether the group homomorphism \\( F: \\text{SL}_n(\\mathbb{Z}) \\to \\text{SL}_n(\\mathbb{Z}/m\\mathbb{Z}) \\), induced by the reduction map \\( \\mathbb{Z} \\twoheadrightarrow \\mathbb{Z}/m\\mathbb{Z} \\), is surjective for \\( n, m > 1 \\).",
"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... | 11.86 L |
[
{
"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... | 0.756 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... | 49.4 mL |
[
{
"content": "Given two permutations of the set \\( \\{1, 2, \\ldots, N\\} \\) where \\( 3 \\leq N \\leq 1000 \\), find the number of permutations \\( X_1, X_2, \\ldots, X_N \\) such that when arranged in a 3xN matrix with the two given permutations, each column contains unique elements.\n\nFor example, for \\(... | 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... | 45.386 Btu |
[
{
"content": "Determine the necessary and sufficient condition for which \\( \\left(2+\\frac{x}{y}+\\frac{y}{x}\\right)^x > (1+x)^{1+x} \\) given that \\( 0 < y < x < 1 \\).",
"role": "user"
}
] | 0 < y < x < 1 |
[
{
"content": "Calculate the volume enclosed by the surface \\( z = \\frac{100}{1+(x^2+4y^2)^2} \\) and the \\((x,y)\\)-plane \\( z = 0 \\).",
"role": "user"
}
] | 25\pi^2 |
[
{
"content": "Does there exist a countable separating family for the space of measures \\(\\mathcal{M}_1\\) on a Polish space \\((E, \\mathcal{A})\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of non-isomorphic semidirect products between the groups \\( \\mathbb{Z}_2 \\) and \\( SL(2,3) \\).",
"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... | Bravo Unlimited Balance Sheet
ASSETS
Current Assets
Cash 88,450
Accounts Receivable 231,860
Supplies 17,255
Total Current Assets 337,565
Non-Current Assets
Equipment 395,285
Accumulated Depreciation (224,260)
Total Current Assets 171,025
TOTAL ASSETS 508,590
LIABILITIES AND STOCKHOLDERS' EQUITY
... |
[
{
"content": "Let $n > 1$ be an integer that is divisible by exactly two distinct primes, $p$ and $q$. If $G$ is a group with exactly $n$ elements of order $n$, determine the maximum possible number of cyclic subgroups of order $n$ in $G$. Provide your answer as a single integer.",
"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... | 3264 KWs |
[
{
"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... | 6.17 * 10^-3 J |
[
{
"content": "Determine the value of $c$ such that the equation \\[ v(x) = 1 + 2 \\int_0^1 xy v(y) \\, dy \\] has a solution of the form $v(x) = 1 + cx$. \\( \\text{Find } c. \\)",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the line integral \\( \\int_{\\gamma} x^2y \\, dx - xy^2 \\, dy \\), where \\( \\gamma \\) is the positively oriented boundary of the square with vertices \\((0,0)\\), \\((1,0)\\), \\((1,1)\\), and \\((0,1)\\), using Green's theorem.",
"role": "user"
}
] | -\dfrac{2}{3} |
[
{
"content": "Given that \\( a \\neq p \\), \\( b \\neq q \\), \\( c \\neq r \\), and the determinant \\( \\left|\\begin{array}{ccc} p & b & c \\\\ a & q & c \\\\ a & b & r \\end{array}\\right| = 0 \\), find the value of \\( \\frac{p}{p-a} + \\frac{q}{q-b} + \\frac{r}{r-c} \\).\\[\\text{(a) } -1 \\quad \\text{(... | 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... | I decided to make spaghetti myself, considering its opportunity cost of 25 minutes of my time was lower than the $5 difference in price compared to buying Chipotle. |
[
{
"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... | Chlorofluorocarbons (CFCs) |
[
{
"content": "Let $G$ be an abelian group of order 72. Determine the number of subgroups of order 8 that $G$ can have.",
"role": "user"
}
] | 1 |
[
{
"content": "Identify the error in the following solution that attempts to find the radius of convergence of the series \\(\\sum_{n = 1}^{\\infty} \\frac{1}{n^{n}} \\cdot r^{2^{n}}\\) using the Cauchy-Hadamard Theorem:\n\n\\[R = \\frac{1}{\\limsup_{n\\to\\infty} |a_{n}|^{1/2^{n}}} = \\frac{1}{\\lim_{n\\to\\inf... | 1 |
[
{
"content": "Determine whether the following statement is true or false: There are infinitely many continuous functions $f$ such that \\( \\int_0^1 f(x)(1-f(x)) \\, dx = \\frac{1}{4} \\).",
"role": "user"
}
] | False |
[
{
"content": "Given that $X_1$ and $X_2$ follow a normal distribution $N(\\mu, \\Sigma)$ with mean $\\mu = \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}$ and covariance $\\Sigma = \\begin{bmatrix} 4 & -4 \\\\ -4 & 8 \\end{bmatrix}$, find $\\mathbb{E}[X_1 \\mid (X_1 + X_2)^2]$. Assume $X_1$ and $X_2$ are jointly norm... | 2 |
[
{
"content": "Determine the number of solutions in natural numbers for the equation \\((a+1)(b+1)(c+1)=2abc\\).",
"role": "user"
}
] | 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... | (69.4j - 92.6i) km/hr |
[
{
"content": "The figure shows a square of side $y$ units divided into a square of side $x$ units and four congruent rectangles. What is the perimeter, in units, of one of the four congruent rectangles? Express your answer in terms of $y$. [asy]\nsize(4cm);\ndefaultpen(linewidth(1pt)+fontsize(12pt));\ndraw((0,0... | 2y |
[
{
"content": "Determine whether there exists a continuous function \\( g: [0,1] \\to S^1 \\) that is onto but not one-to-one.",
"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... | $124,100 |
[
{
"content": "If a sequence \\( \\{p_n\\} \\) of real numbers diverges to infinity, does it imply that the limit superior of \\( \\{p_n\\} \\), denoted as \\( \\limsup p_n \\), is also infinity? Justify your answer.",
"role": "user"
}
] | \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... | 33m/s |
[
{
"content": "Let \\( N \\) denote the set of natural numbers. Let \\( \\phi: N \\rightarrow N \\) be a bijective function and assume that there exists a finite limit \\( \\lim_{n\\rightarrow\\infty}\\frac{\\phi(n)}{n}=L. \\) Determine the possible values of \\( L \\).",
"role": "user"
}
] | 1 |
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