prompt list | ground_truth string |
|---|---|
[
{
"content": "What is the value of $x + y + z$ when $6x + 5y - 2z = -4$ and $4x + 5y + 12z = 54$?",
"role": "user"
}
] | 5 |
[
{
"content": "Let $X_1, X_2, \\ldots, X_{100}$ be independent random variables each having the standard normal distribution. Calculate the approximate probability $P(80 < \\sum_{j=1}^{100} X_j^2 < 120)$. Express your answer as a single probability value.",
"role": "user"
}
] | 0.843 |
[
{
"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... | 1.36e+23 ions |
[
{
"content": "Using Stokes' theorem, evaluate the closed loop integral of the vector field \\( \\vec{F}(x,y,z) = \\langle yx-yz , 2x^2+z^2, y^3 \\cos(xz)\\rangle \\) over the boundary of the square defined by:\n\\[\n\\begin{cases}\n0 \\leq x \\leq 2\\\\\n0 \\leq y \\leq 2\\\\\nz=5\n\\end{cases}\n\\]",
"role... | 32 |
[
{
"content": "Determine the center of the Lie algebra $\\mathfrak{gl}_n(\\mathbb{F})$ when $\\mathbb{F}$ is a field with positive characteristic $p$ and $n$ is an integral multiple of $p$. Provide your answer in terms of $n$ and $p$.",
"role": "user"
}
] | \mathbb{F} I_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... | 3.79 m |
[
{
"content": "Let \\( f = \\chi_{\\{0\\}} \\) be the characteristic function of the set \\( \\{0\\} \\) on the measure space \\((X, \\Omega, \\mu)\\), where \\( X = [0,1] \\), \\( \\Omega \\) is the Borel subsets of \\([0,1]\\), and \\( \\mu(S) = \\infty \\) if \\( 0 \\in S \\), otherwise \\( \\mu \\) is the Le... | 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... | 39.50 months |
[
{
"content": "What is the largest value of $n$ less than 100,000 for which the expression $8(n-2)^5-n^2+14n-24$ is a multiple of 5?",
"role": "user"
}
] | 99997 |
[
{
"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... | investment, decreasing, no overall change |
[
{
"content": "Consider a directed graph $G(V,A)$ with arc capacities $c_i$ and a source/sink. Let $f$ be the max flow in $G$. If we modify the capacities such that $c_i^{'} = c_i$ for all arcs where $f_i = c_i$ and $c_i^{'} = c_i + 1$ for all arcs where $f_i < c_i$, is $f$ still a max flow in $G$ with the new c... | 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... | The amount distributed to preferred stockholders is $32,000, and the amount distributed to common stockholders is $60,000. |
[
{
"content": "In a triangle, four points \\( K, P, H, \\) and \\( M \\) are located on one side. Here, \\( K \\) is the midpoint of the side, \\( P \\) is the foot of the angle bisector from the opposite angle, \\( H \\) is the point of tangency of the incircle with the side, and \\( M \\) is the foot of the al... | \sqrt{ab} |
[
{
"content": "Determine whether the surface defined by the equation \\(xy - y \\log(z) + \\sin(xz) = 0\\) can be expressed in the form \\(z = f(x, y)\\) near the point \\((0, 2, 1)\\) using the implicit function theorem. Assume \\(f\\) is a smooth function. Is the invertibility of the matrix \\(M(x, y, z)\\), o... | Yes |
[
{
"content": "Determine the convergence of the complex series \\(\\sum_{n=1}^\\infty\\dfrac{n!}{n^n}z^n\\) using the Ratio test.",
"role": "user"
}
] | |z| < e |
[
{
"content": "Determine whether the infinite product \\( \\prod\\limits_{n=0}^{\\infty} (1+x^{2^{n}}) \\) converges.",
"role": "user"
}
] | |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... | 20.5% |
[
{
"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... | 15.37% |
[
{
"content": "Determine the possible cardinalities of the equivalence classes formed by the relation $x \\sim y \\iff d(x,y) \\in \\mathbb{Q}$ on the set of real numbers $\\mathbb{R}$. Provide a justification for your answer.",
"role": "user"
}
] | \aleph_0 |
[
{
"content": "Determine the order of growth for the binomial coefficient \\( {}^n C_k \\) when approximated by a polynomial. Consider the case where \\( n \\gg k \\) and provide the general order of growth for \\( {}^n C_k \\).",
"role": "user"
}
] | \Theta(n^k) |
[
{
"content": "For a finite group \\( G \\), determine if there exists a set \\( X \\) and a group action of \\( G \\) on \\( X \\) such that every subgroup of \\( G \\) is the stabilizer of some element \\( x \\) in \\( X \\).",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $5,100 |
[
{
"content": "Given a sequence $\\{a_n\\}$ where $a_n \\geq 0$ for all $n$ and the sequence is monotonically decreasing, determine if $n\\log(n)a_n \\rightarrow 0$ as $n\\rightarrow\\infty$ when $\\sum_{n=1}^\\infty a_n$ converges.",
"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... | 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... | $14,434 |
[
{
"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... | 4H/9 |
[
{
"content": "Determine the largest natural number \\( n \\) such that the group \\( \\mathbb{Z}_{180} \\times \\mathbb{Z}_{30} \\) is isomorphic to the direct product of \\( n \\) cyclic groups.",
"role": "user"
}
] | 6 |
[
{
"content": "Suppose $X$ and $Y$ are independent and identically distributed (i.i.d.) random variables, each following a normal distribution $N(0,1)$. Calculate the conditional probability $P(X > 0 \\mid X + Y > 0)$. Express your answer as a single probability value.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Provide an example of an irreducible polynomial \\(g\\) over \\(\\mathbb{Q}\\) such that the extension \\((\\mathbb{Q}[x]/(g))/\\mathbb{Q}\\) is not Galois.",
"role": "user"
}
] | x^3 - 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.00 |
[
{
"content": "Given the joint probability mass function \\( P(X=x, Y=y) = e^{-2}\\binom{x}{y} \\left(\\frac{3}{4}\\right)^{y}\\left(\\frac{1}{4}\\right)^{x-y}\\frac{2^{x}}{x!} \\) for \\( y=0,1,...,x \\) and \\( x = 0,1,2,... \\), find the expected value \\( E(Y) \\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.046 mg |
[
{
"content": "Let $G$ be a group of order 30 with a center $Z(G)$ of order 5. Determine the isomorphism class of the quotient group $G/Z(G)$. To which commonly known group is $G/Z(G)$ isomorphic?",
"role": "user"
}
] | S_3 |
[
{
"content": "108 singers participate in an art festival. Arrange them into performances with 4 singers in each performance such that among any 8 singers, any two singers perform together the same number of times. What is the minimum number of performances needed?",
"role": "user"
}
] | 2889 |
[
{
"content": "Calculate the sum of the squares of the distances from a point $P$ to the vertices of a regular 11-gon inscribed in a circle with radius 2, given that the distance from $P$ to the center of the circle is 3.",
"role": "user"
}
] | 143 |
[
{
"content": "What is the value of $\\frac{2013^3-2 \\cdot 2013^2 \\cdot 2014+3 \\cdot 2013 \\cdot 2014^2-2014^3+1}{2013 \\cdot 2014}$?",
"role": "user"
}
] | 2013 |
[
{
"content": "Evaluate the integral: \\[ \\int_0^{100} \\lfloor x \\rfloor x \\lceil x \\rceil \\, dx \\]",
"role": "user"
}
] | 24997500 |
[
{
"content": "Evaluate the line integral \\( \\int_{\\gamma} \\frac{\\mathrm{d}z}{z} \\) where \\( \\gamma \\) is a closed curve centered at the origin in the complex plane. Determine the value of the integral.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Let $A$ be an orthogonal matrix with $\\det(A) > 0$. Determine the range of possible values for $\\det(A+I)$.",
"role": "user"
}
] | [0, 2^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... | $87,052.80 |
[
{
"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... | 418.29 |
[
{
"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... | 7313.8 km |
[
{
"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... | 4.06% |
[
{
"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... | 14.3% |
[
{
"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... | 781683.84 |
[
{
"content": "Compute the residue field of the point \\((0,0)\\) on the affine scheme \\(X = \\operatorname{Spec}\\left(\\frac{\\mathbb{F}_p[x, y]}{(x^2 + y^2)}\\right)\\), where \\((0,0)\\) corresponds to the prime ideal \\((x, y)\\).",
"role": "user"
}
] | \mathbb{F}_p |
[
{
"content": "Calculate the line integral \\( \\int_\\ell xyz\\,ds \\), where \\( \\ell \\) is the circle formed by the intersection of the sphere \\( x^2+y^2+z^2=1 \\) and the plane \\( x+y=0 \\).",
"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... | 1. Locate the deleted transaction in the "Reconcile" view.
2. Reverse the transaction deletion, ensuring it's marked "Reconciled."
3. Utilize the Bank reconciliation tool to generate the reconciliation form and check for other opening balance discrepancies.
4. After resolving the discrepancy, report the deleted transa... |
[
{
"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... | T-shaped |
[
{
"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... | 108 g |
[
{
"content": "Find a function $g(x)$ such that $g'(x_*) = 0$ and $g''(x_*) = 0$, but $x_*$ is not a local minimum.",
"role": "user"
}
] | x^3 |
[
{
"content": "Determine whether the following statement is true or false: For any linear operators $\\rho$ and $\\sigma$ on a Hilbert space, $\\operatorname{Tr}(\\rho\\sigma) \\geqslant 0$ for all $\\sigma \\geqslant 0$ implies that $\\rho$ is positive-semidefinite.",
"role": "user"
}
] | True |
[
{
"content": "Determine all finite sets \\( A \\) such that \\( A \\times \\mathcal{P}(A) = \\mathcal{P}(A) \\times A \\), where \\( \\mathcal{P}(A) \\) denotes the power set of \\( A \\).",
"role": "user"
}
] | \emptyset |
[
{
"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... | Cell division |
[
{
"content": "Determine the radius of convergence of the power series \\(\\sum_{n \\geq 0}a_n z^{n!}\\) given that the radius of convergence of \\(\\sum_{n \\geq 0}a_n z^{n}\\) is \\(L\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let $Q(x)$ be a smooth symmetric matrix with constant signature $(p,q,k)$, where $x$ belongs to $\\mathbb{R}^n$ and $p+q+k=m$. Locally around a point $x_0$, does there exist an invertible matrix $P(x)$ of size $m$ such that:\n\\[\nP^T(x) Q(x) P(x) = \\begin{pmatrix} Id_p &0&0\\\\0&-Id_q&0\\\\ 0&0&... | Yes |
[
{
"content": "Suppose $\\overline{a_1a_2...a_{2009}}$ is a 2009-digit integer such that for each $i = 1,2,...,2007$, the 2-digit integer $\\overline{a_ia_{i+1}}$ contains 3 distinct prime factors. Determine the value of $a_{2008}$. (Note: $\\overline{xyz...}$ denotes an integer whose digits are $x, y, z,...$.)"... | 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... | 9.22e-14 M |
[
{
"content": "Determine the values of \\(a\\) for which the series \\(\\sum_{n=0}^{\\infty}\\frac{n!2^n}{e^{an}n^n}\\) is convergent.",
"role": "user"
}
] | a > \ln 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... | 270 mL |
[
{
"content": "Determine the number of distinct ways to visit 6 cities, visiting each city exactly twice, without visiting the same city consecutively.",
"role": "user"
}
] | 2631600 |
[
{
"content": "Consider the topology \\(\\tau = \\{ G \\subseteq \\mathbb{R}: G^c\\text{ is compact in }(\\mathbb{R}, \\tau_u) \\} \\cup \\{\\mathbb{R}, \\varnothing\\} \\text{ on } \\mathbb{R}\\), where \\(\\tau_u\\) is the usual topology on \\(\\mathbb{R}\\). Determine whether \\((\\mathbb{R}, \\tau)\\) is: (A... | B |
[
{
"content": "Let $\\Omega \\subset \\mathbb{R}^n$ be a bounded domain with a smooth boundary. Suppose $u \\in C^{2}(\\Omega) \\cap C(\\overline{\\Omega})$ satisfies the equation $\\Delta u = u^5$ in $\\Omega$ and the boundary condition $u = 0$ on $\\partial \\Omega$. Can we conclude that $u$ is identically zer... | Yes |
[
{
"content": "Given two positive real numbers $m$ and $n$, where $m > n$, determine which is greater: $(m!)^n$ or $(n!)^m$?",
"role": "user"
}
] | (m!)^n |
[
{
"content": "For how many different digits $n$ is the two-digit number $\\underline{6}\\underline{n}$ divisible by $n$? (The expression $\\underline{6}\\underline{n}$ should be interpreted as a two-digit integer with tens digit 6 and units digit $n$, not as 6 times $n$.)",
"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... | 1. **Back pain relief:** Massages can reduce inflammation and increase blood flow, alleviating back pain.
2. **Stress and depression relief:** Massages reduce stress hormones, promoting relaxation.
3. **Improved sleep:** By reducing stress hormones, massages can improve sleep patterns.
4. **Strengthened muscles and bon... |
[
{
"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... | Land $69,360
Building $55,760
Equipment $10,880
Notes Payable $136,000 |
[
{
"content": "Consider the parabola defined by the equation \\(y^2 = 8x\\) with focus \\(S_1\\). The circle \\(x^2 + y^2 - 2x - 4y = 0\\) intersects this parabola at points \\(P\\) and \\(Q\\), forming a chord \\(PQ\\). Determine the area of triangle \\(PQS_1\\), where \\(S_1\\) is the focus of the parabola.",
... | 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... | 36,897 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... | 8m/s |
[
{
"content": "Determine the number of different ring homomorphisms from \\(\\mathbb{Z}[i]\\) to \\(\\mathbb{Z}/(85)\\).",
"role": "user"
}
] | 4 |
[
{
"content": "Given that \\(3f(x) = 3x^4 + x^3 + 3x^2\\), evaluate \\(\\lim\\limits_{a \\to \\infty} \\int\\limits_{2a}^{8a} \\frac{1}{(f^{-1}(x))^2 + (f^{-1}(x))^4} \\, dx = \\ln(n)\\). Find the value of \\(n\\).",
"role": "user"
}
] | 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... | Short futures contracts or put options |
[
{
"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... | increase by 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... | water |
[
{
"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... | 3.3 mol |
[
{
"content": "Consider the solution set of the equation \\(x^{10} = 1\\), which corresponds to a set of points \\(M\\) in the complex plane. Determine the number of distinct right triangles that can be formed with vertices among the points in \\(M\\).",
"role": "user"
}
] | 40 |
[
{
"content": "Determine if the differential equation \\((a^2-x^2) y''-2xy'+12y=0\\) is a Legendre's differential equation. If it is, find the value of \\(n\\).",
"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... | The absolute minimum acceleration is 29.54 ft/s^2 and the absolute maximum acceleration is 49.18 ft/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.409e-6 Joule m^-2 s^-1 |
[
{
"content": "Find the partial derivative of the function \\( f = \\text{tr}((ABC)(ABC)^T) \\) with respect to the matrix \\( B \\).",
"role": "user"
}
] | 2 A^\top A B C C^\top |
[
{
"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
87
138
186
330 |
[
{
"content": "Segments \\(AD\\), \\(BD\\), and \\(CD\\) are pairwise perpendicular. Given that the area of triangle \\(ABC\\) is \\(S\\) and the area of triangle \\(ABD\\) is \\(Q\\), find the area of the orthogonal projection of triangle \\(ABD\\) onto the plane \\(ABC\\).",
"role": "user"
}
] | \dfrac{Q^2}{S} |
[
{
"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 it follow that there exists a Borel pro... | 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... | 40.24 |
[
{
"content": "Given the equations \\(x+y=2010\\) and \\((\\sqrt[3]{x}+\\sqrt[3]{y})(\\sqrt[3]{x}+11)(\\sqrt[3]{y}+11)=2942\\), find the value of \\(\\sqrt[3]{x}+\\sqrt[3]{y}\\).",
"role": "user"
}
] | 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... | Each firm produces 10.1 units and charge $10,100 |
[
{
"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... | 0.35% |
[
{
"content": "Given the polynomial \\( P(x) \\) such that \\( P(x^4) = ax^8 + (b+1)x^5 + (ab)x^4 + (a-1)x^2 + 2b-2 \\), find the remainder when \\( P(x^3 - 3) \\) is divided by \\( x+1 \\).",
"role": "user"
}
] | 16 |
[
{
"content": "Determine the radius of convergence for the series \\( \\sum_{n=1}^\\infty \\frac{z^{n^2}}{n!} \\), where \\( z \\in \\mathbb{C} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Consider the sequence space of real-valued sequences that eventually become zero, denoted as \\(c_{00}(\\mathbb{R})\\). Let \\(X_1=(c_{00}(\\mathbb{R}),\\lVert\\cdot\\rVert_1)\\) and \\(X_2=(c_{00}(\\mathbb{R}),\\lVert\\cdot\\rVert_2)\\) be normed spaces with the usual \\(\\ell_p\\) norms. Determi... | 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... | Phenomenology |
[
{
"content": "Evaluate the integral \\( \\frac{1}{\\sqrt{4\\pi kt}}\\int\\limits_{\\mathbb{R}}e^{-\\sigma^2/(4kt)}(\\sigma^2 +2\\sigma x+x^2)d\\sigma \\) and show that it equals \\( 2kt+x^2 \\).",
"role": "user"
}
] | 2kt + 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... | 4.5% |
[
{
"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... | 8.59% |
[
{
"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... | 14.0 kV/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... | -38.97 m/s^2 |
[
{
"content": "Let $A_p$ and $B_p$ be sequences of symmetric positive-definite $p \\times p$ matrices such that their spectral norms satisfy $\\|A_p - B_p\\|_2 \\leq \\frac{1}{p}$. Assuming the spectra of $A_p$ and $B_p$ are contained in a compact interval $(0, \\infty)$ for all $p$, and $\\operatorname{tr}(B_p)... | Yes |
[
{
"content": "Consider a diffusion process defined by the stochastic differential equation \\(dX_t = g(X_t,t) \\, dt + \\sigma \\, dW_t\\), which induces a path measure \\(Q\\) over the interval \\([0,T]\\). Let \\(f\\) be a bounded function. Determine whether the expectation \\[ \\left\\langle \\int^T_0 \\frac... | 0 |
[
{
"content": "Given that $g(2) = -3$ and $g'(x) = (x^3 - 2x)g(x)$ for all $x$, find the value of $g''(2)$. Express your answer as a single number.",
"role": "user"
}
] | -78 |
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