prompt list | ground_truth string |
|---|---|
[
{
"content": "For $y=\\frac{x-4}{5x-10}$ and $x\\neq 2$, what is the value of $y$ that is not attainable? Express your answer as a common fraction.",
"role": "user"
}
] | \frac15 |
[
{
"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... | $58.95 |
[
{
"content": "Find all real numbers $a$ such that the roots of the polynomial\n$$x^3 - 6x^2 + 21x + a$$form an arithmetic progression and are not all real.",
"role": "user"
}
] | -26 |
[
{
"content": "Determine if there is a known bound for the VC-dimension of the set of binary classifiers \\(\\mathcal{H} = \\{\\boldsymbol{x}\\mapsto\\boldsymbol{1}\\hspace{-0.9ex}\\mathrm{1}(\\boldsymbol{h}^\\mathsf{T}\\boldsymbol{x}\\ge 0)\\mid \\boldsymbol{h} \\in \\mathcal{C} \\}\\), where \\(\\mathcal{C}\\... | d |
[
{
"content": "Evaluate the limit of the infinite product:\n\n$$\\prod_{k=5}^{\\infty}\\frac{(k-1)(k+1)(k-4)(k+4)}{(k-2)^2(k+2)^2}$$",
"role": "user"
}
] | \dfrac{1}{14} |
[
{
"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... | 17.79 radian |
[
{
"content": "Solve the system of congruences using the Chinese Remainder Theorem:\n\n\\[ 560x \\equiv 1 \\pmod{3} \\]\n\\[ 560x \\equiv 1 \\pmod{11} \\]\n\\[ 560x \\equiv 1 \\pmod{13} \\]\n\nFind the solution for \\(x\\) modulo 429.",
"role": "user"
}
] | 131 |
[
{
"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... | 5.780 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.05 |
[
{
"content": "Calculate the line integral \\(\\oint_{L} P(x,y)\\,dx + Q(x,y)\\,dy\\), where \\(L\\) is the closed contour defined by \\(y=\\sin(x)\\) from \\(x=0\\) to \\(x=\\pi\\) and \\(y=0\\) for the same interval. Given \\(P(x,y) = e^{x}y\\) and \\(Q(x,y) = e^{x}\\), verify the result using Green's theorem.... | 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... | 0.21 M |
[
{
"content": "Determine the number of equivalence classes for the relation \\( R \\) on \\( \\mathcal{P}(\\mathbb{Z}) \\) defined by: For all sets \\( A, B \\in \\mathcal{P}(\\mathbb{Z}) \\), \\((A, B) \\in R\\) if and only if \\(|A \\Delta B|\\) is even, where \\(\\Delta\\) represents the symmetric difference ... | 2 |
[
{
"content": "Consider a sequence of random variables $X_n$ where $X_n \\sim \\mathrm{Normal}\\left(\\frac{1}{n}, \\frac{1}{n}\\right)$. Does $X_n$ converge in distribution to a random variable $X$? If so, identify the distribution of $X$. Use the Weak Law of Large Numbers in your solution.",
"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... | -0.032 M/s |
[
{
"content": "Find the smallest positive solution for \\( x \\) using Euler's Totient Function method, where \\( \\phi(400) \\) is used in the equation \\( x \\equiv 254 \\times 353^{\\phi(400) - 1} \\pmod{400} \\).",
"role": "user"
}
] | 318 |
[
{
"content": "Let $H$ be a Hilbert space and $T$ be a linear operator on $H$. Suppose that \\( \\sum_{j=1}^\\infty\\langle T\\xi_j,\\eta_j\\rangle \\) converges for any choice of orthonormal bases \\(\\{\\xi_j\\}\\), \\(\\{\\eta_j\\}\\). Does this imply that $T$ is a Hilbert-Schmidt operator?",
"role": "use... | Yes |
[
{
"content": "Let \\( S = \\{(x, y) \\mid x^{2} - y^{2} = \\text{odd}, \\, x, y \\in \\mathbb{R} \\} \\) and \\( T = \\{(x, y) \\mid \\sin(2 \\pi x^{2}) - \\sin(2 \\pi y^{2}) = \\cos(2 \\pi x^{2}) - \\cos(2 \\pi y^{2}), \\, x, y \\in \\mathbb{R} \\} \\). Determine which of the following is true: (A) \\( S \\sub... | A |
[
{
"content": "Is it always possible to find an element in \\( \\mathbb{Q}[\\sqrt{2}] \\) whose square root is not in \\( \\mathbb{Q}[\\sqrt{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... | $7,999.92 |
[
{
"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... | 19.48% |
[
{
"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... | 611.67 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... | 13.5% |
[
{
"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... | The velocity of the skater with mass M is {\sqrt{\frac{2Wm}{M^2+mM}}} and the velocity of the skater with mass m is {\sqrt{\frac{2WM}{mM+m^2}}}. |
[
{
"content": "Determine the number of solutions to the equation \\( \\sin^5 x + \\cos^3 x = 1 \\) in the interval \\((0, 2\\pi]\\).",
"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... | 2.42e-12 m |
[
{
"content": "Determine if there exists a positive integer \\( n > 0 \\) such that \\( f(n) = 0 \\), where \\( f(n) = n - \\sum_{k=1}^{m} \\lfloor r_k n \\rfloor \\) and \\( r_1, r_2, \\ldots, r_m \\) are positive rational numbers with \\( r_1 + r_2 + \\cdots + r_m = 1 \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following statement is true or false: If $F$ is a finite field and $K$ is a finite field extension of $F$ of degree 2, then the minimal polynomial of any element $a \\in K \\setminus F$ over $F$ splits completely over $K$. Provide a justification for your answer.",
"role"... | True |
[
{
"content": "Determine whether there exists a connected compact set $X$ in the complex plane $\\mathbb{C}$ such that $X$ is not locally connected at any point.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a positive real number $a$ and a continuous function $f: [0,1] \\to \\mathbb{R}$, which is not identically zero, such that $f(1) = 0$ and the integral \\( \\int_0^1 \\cosh(ax) f(x) \\, dx = 0 \\) holds true. Here, \\( \\cosh(x) \\) denotes the hyperbolic cosine funct... | Yes |
[
{
"content": "Determine if the set \\( \\{1, 2, 3, 5, 7, 11, 2310\\} \\) under the relation \"divides\" forms a lattice in which every element, except the least and greatest elements, has four complements.",
"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... | q1=q2 |
[
{
"content": "Is the expression \\( \\pi \\cdot a^{\\frac{m}{n}} \\) always irrational for every choice of natural numbers \\( m, n, \\) and \\( a \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty}\\frac{x_n}{\\prod_{i=1}^{n-1} x_i} \\) where \\( x_n = x_{n-1}^2 - 2 \\) and \\( x_1 = 5 \\).",
"role": "user"
}
] | \sqrt{21} |
[
{
"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... | $21215.86 |
[
{
"content": "Find the largest natural number \\( n \\) such that from the numbers \\( 1, 2, \\ldots, n \\), any selection of 51 distinct numbers includes at least one pair whose sum is 101.",
"role": "user"
}
] | 100 |
[
{
"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... | $139,242 |
[
{
"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... | 51% |
[
{
"content": "Determine if there exists a largest nested prime number, and if so, find it.",
"role": "user"
}
] | 739397 |
[
{
"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... | 5.57 m |
[
{
"content": "Let \\( f(x) = \\frac{1-2x^2}{1+x^2} \\) for \\( x \\in \\mathbb{R} \\). Find the Chebyshev norm \\( ||f||_\\infty \\).",
"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... | 0.0022 g^2 L^-2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.14*10^(-5) N/C downwards |
[
{
"content": "Find the function \\( f(x) \\) such that the differential equation \\( y'' - 2(\\tan x)y' - y = e^x \\sec x \\) can be rewritten in the form \\( \\frac{d^2}{dx^2}(f(x)y) = e^x \\).",
"role": "user"
}
] | \cos x |
[
{
"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... | 82.38% |
[
{
"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... | 80.74 nm |
[
{
"content": "Compute the integral \\( \\int_{\\mathbb{R}} \\left(\\int_{\\mathbb{R}} f(x,y)\\,dx \\right)dy \\) where the function \\( f: \\mathbb{R}^2 \\rightarrow \\mathbb{R} \\) is defined as follows:\n\n\\[\nf(x,y) = \\begin{cases} \n1, & \\text{for } x \\ge 0, \\ x \\le y < x+1 \\\\\n-1, & \\text{for } x ... | 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... | 0.02255 mol/L |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty}\\frac{\\displaystyle\\sum_{n=1}^{N}a_{n}}{\\ln(n)} \\), given that \\( a_1 + a_2 + a_3 + \\ldots + a_n = \\int_{1}^{e}\\ln^{k}(x)dx \\) for \\( n \\ge 2 \\) where \\( a_n = \\int_{0}^{1}x^{n}e^{x}dx \\).",
"role": "user"
}
] | e |
[
{
"content": "Evaluate the integral \\( \\int_{\\mathbb{R}^3} \\langle x,b \\rangle^3 e^{-\\frac{1}{4}\\lvert x \\rvert^2} \\, dx \\) where \\( x,b \\in \\mathbb{R}^3 \\).",
"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... | 17,201,000 |
[
{
"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... | 3.04 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... | $8,075 |
[
{
"content": "Suppose $a$, $b$, $p$, and $q$ are natural numbers such that $a < 300$, $\\gcd(p, q) = 1$, and $a \\neq 300b^2$. Determine if it is possible for \\( k = \\frac{900q^2 + ap^2}{3q^2 + b^2 p^2} \\) to be an integer when $a$ and $b$ are fixed.",
"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... | 4.5e5 volts |
[
{
"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... | -5962020 cal |
[
{
"content": "On a blackboard, the numbers $1, \\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\ldots, \\frac{1}{2018}$ are written. You can repeatedly choose any two numbers, $x$ and $y$, erase them, and replace them with the number $x + y + xy$. Continue this process until only one number remains. What is the poss... | 2018 |
[
{
"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... | 6.8506 |
[
{
"content": "Compute the intersection number of the divisors \\(\\iota^*\\mathcal{O}(3,2)\\) and \\(\\iota^*\\mathcal{O}(1,4)\\) on the smooth subvariety \\(\\iota:X=V_+(f)\\subset\\mathbb{P}^2\\times\\mathbb{P}^1\\), where \\(f\\in H^0(\\mathcal{O}(1,2))\\).",
"role": "user"
}
] | 20 |
[
{
"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... | 0.0572 mm |
[
{
"content": "Determine whether the following statement is true or false: For any topological space $(X,T)$, if $E$ is a subset of $X$ with an empty boundary, then $E$ is closed.",
"role": "user"
}
] | 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... | 35 J |
[
{
"content": "Evaluate the line integral \\( \\int_C (x^2 \\, dx + y^2 \\, dy + z^2 \\, dz) \\), where \\( C \\) is the curve consisting of line segments from \\((0,1,0)\\) to \\((1,0,1)\\) and then from \\((1,0,1)\\) to \\((2,1,3)\\).",
"role": "user"
}
] | \dfrac{35}{3} |
[
{
"content": "For discrete probability distributions \\( P \\) and \\( Q \\) defined on the same probability space, \\( \\mathcal{X} \\), the relative entropy from \\( Q \\) to \\( P \\) is defined as\n\\[\nD_{\\mathrm{KL}}(P \\| Q)=\\sum_{x \\in \\mathcal{X}} P(x) \\log \\left(\\frac{P(x)}{Q(x)}\\right)\n\\]\n... | 1 - p |
[
{
"content": "Let $a_n = \\frac{m}{n}$ for $m$ such that \\( \\frac{(m-1)!}{n^{m-1}} \\le 1 < \\frac{m!}{n^m} \\). Find \\( \\lim_{n \\to \\infty} a_n \\).",
"role": "user"
}
] | e |
[
{
"content": "Provide an example of a continuous function \\( f: \\mathbb{R} \\to [0, \\infty) \\) that is unbounded, but such that \\( f^2 \\) is uniformly continuous on \\( \\mathbb{R} \\).",
"role": "user"
}
] | f(x) = \sqrt{|x|} |
[
{
"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... | 1,463,965,949.52 |
[
{
"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... | 13.1V |
[
{
"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 concentration gradient across the membrane, the surface area of the membrane, and temperature. |
[
{
"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... | 3.31m |
[
{
"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... | 157.43 W |
[
{
"content": "Let \\(a\\), \\(b\\), and \\(c\\) be positive integers forming an arithmetic sequence with \\(a < b < c\\). Define the function \\(f(x) = ax^2 + bx + c\\). Two distinct real numbers \\(r\\) and \\(s\\) satisfy \\(f(r) = s\\) and \\(f(s) = r\\). Given that \\(rs = 2017\\), determine the smallest po... | 9 |
[
{
"content": "Find the value of \\(x\\) at which the function \\(f(x) = (x+\\sqrt{x})(10-x+\\sqrt{10-x})\\) attains its maximum in the domain of real numbers.",
"role": "user"
}
] | 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... | 1.16 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $122,000 |
[
{
"content": "For a given fixed integer $N$, determine the largest integer $n$ such that the symmetric group $\\Sigma_n$ can be embedded as a subgroup of the orthogonal group $O(N)$ acting on $\\mathbb{R}^N$. Provide your answer as the maximal $n$.",
"role": "user"
}
] | N + 1 |
[
{
"content": "Determine the rank of the $n \\times n$ matrix $A$ where the entry $a_{i,j} = \\frac{1}{i+j}$ for all $1 \\leq i, j \\leq n$. Provide your answer as a single integer.",
"role": "user"
}
] | n |
[
{
"content": "For any \\(\\varepsilon > 0\\), does there exist a countable \\(\\varepsilon\\)-net for the family of all Lebesgue measurable sets of the interval \\([0,1]\\) with respect to the metric \\(d(A_1,A_2) = \\int |1_{A_1} - 1_{A_2}|\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Given the system of equations:\n\n$$x + y\\sqrt{x} = \\frac{95}{8}$$\n$$y + x\\sqrt{y} = \\frac{93}{8}$$\n\nwhere $x, y \\in \\mathbb{R}$, find the value of $\\sqrt{xy}$.",
"role": "user"
}
] | \dfrac{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... | 4.4 mm |
[
{
"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... | 3.48 |
[
{
"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... | 48.59 degrees in clockwise with positive x axis or 48.59 degrees in anti clockwise with negative x axis |
[
{
"content": "Suppose $M$ is a $C^k$-manifold embedded into a Hilbert space $H$, and $g$ is the induced Riemannian metric on $M$. Let $g_H(x,y) = \\sqrt{\\langle (x-y),(x-y)\\rangle_H}$ be the Euclidean distance in $H$. Is it necessarily true that for all $x, y \\in M$, $g_H(x,y) \\leq g(x,y)$?",
"role": "u... | 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... | 2090 kJ/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3 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... | Demand for imports and exports, productivity, and trade barriers |
[
{
"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... | max q 100q - (100 + 10q), s.t.: q >= 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... | Joules per gram degrees Celsius |
[
{
"content": "In the symmetric group $S_7$, consider the permutation $(123)(456)$. Calculate the size of the stabilizer $|Stab_{S_7}(123)(456)|$ when $S_7$ acts on itself by conjugation.",
"role": "user"
}
] | 18 |
[
{
"content": "Let \\( \\omega \\) be a primitive third root of unity. Determine the number of distinct possible images of \\( \\omega \\) under all field homomorphisms from \\( \\mathbb{Q}(\\omega) \\) to \\( \\mathbb{C} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Calculate the value of the expression \\( \\frac{1}{n^2} \\sum_{i = 0}^{n} \\ln\\binom{n}{i} \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "When the repeating decimal $0.\\overline{12}$ is expressed as a common fraction in lowest terms, what is the sum of its numerator and denominator?",
"role": "user"
}
] | 37 |
[
{
"content": "Determine if the operator $S$ defined by $S(x_1, x_2, . . .) = (x_2, x_3, x_4, . . .)$ is a bounded linear operator on the complex space $l^2$. If it is bounded, find its operator norm.",
"role": "user"
}
] | 1 |
[
{
"content": "A cube with side length 3 is divided into 27 unit cubes. These small cubes are each randomly assigned a number between 1 and 27, with each number being assigned exactly once. The game is played as follows: at each step, the cube numbered 27 can be exchanged with one of its neighbors. Determine if ... | no |
[
{
"content": "Given that \\( A + B + C = 180^\\circ \\) and \\(\\frac{\\sin A + \\sin B + \\sin C}{\\cos A + \\cos B + \\cos C} = 1\\), find the value of \\(\\frac{\\cos 2A + \\cos 2B + \\cos 2C}{\\cos A + \\cos B + \\cos C}\\).",
"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... | 4.6 D |
[
{
"content": "Concentric circles \\(\\Omega_1\\) and \\(\\Omega_2\\) have radii 1 and 100, respectively, with center \\(O\\). Points \\(A\\) and \\(B\\) are chosen independently at random on the circumferences of \\(\\Omega_1\\) and \\(\\Omega_2\\), respectively. Let \\(\\ell\\) be the tangent line to \\(\\Omeg... | 10004 |
[
{
"content": "Let $f(x) = ax^2 + bx + c$ be a quadratic function such that $a + b + c = 3$ and $f(x+y) = f(x) + f(y) + xy$ for all real numbers $x$ and $y$. Calculate the value of $\\sum_{n=1}^{10} f(n)$. \\( \\text{Express your answer as a single number.} \\)",
"role": "user"
}
] | 330 |
[
{
"content": "Let $f:\\mathbb{R}\\to \\mathbb{R}$ be a continuous function such that $f(x+y)+f(x-y)=2f(x)+2f(y)$ for all $x,y\\in\\mathbb{R}$. Determine the function $f(x)$.",
"role": "user"
}
] | f(x) = ax^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... | 4.615 ft/s |
[
{
"content": "In a Frechet space with a countable family of semi-norms \\(\\{P_i\\}\\), consider a series \\(\\sum_k x_k\\). If \\(\\sum_k P_i(x_k) < \\infty\\) for every semi-norm \\(P_i\\), does the series \\(\\sum_k x_k\\) converge in the Frechet topology?",
"role": "user"
}
] | Yes |
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