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... | $2.916 |
[
{
"content": "Determine if there exists an odd prime integer \\( q \\) such that \\( p = \\frac{q^3+1}{2} \\) is also a prime number.",
"role": "user"
}
] | No |
[
{
"content": "Determine the number of prime numbers $p$ such that there exists an integer $n$ for which both $n^3 + 3$ and $n^5 + 5$ are divisible by $p$.",
"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... | 4.58e23 atoms |
[
{
"content": "Determine the maximum number of points in general position in a finite projective plane of order $n$, where $n$ is an odd integer.",
"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... | 1.54 s |
[
{
"content": "Given a set \\( S = \\{1, 2, \\ldots, 2005\\} \\), find the maximum size of a subset \\( A = \\{a_1, a_2, \\ldots, a_k\\} \\subset S \\) such that for any distinct elements \\( a_i \\) and \\( a_j \\) in \\( A \\), the sum \\( a_i + a_j \\) is not a multiple of 125. What is the maximum possible va... | 998 |
[
{
"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... | 26.3 g |
[
{
"content": "Does the tensor product \\(\\otimes\\) endow the 2-category \\(\\operatorname{Mod}_\\mathcal{C}\\) of \\(k\\)-linear \\((\\mathcal{C}, \\mathcal{C})\\)-bimodule categories with the structure of a monoidal 2-category?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\pi} e^{\\cos t}\\,dt$$",
"role": "user"
}
] | \pi I_0(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... | 9.8m |
[
{
"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... | 59N |
[
{
"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... | $149,474 |
[
{
"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... | 3.63e-4 |
[
{
"content": "Calculate the line integral of the vector field \\( \\mathbf{F} = [x^2 + y^2, x^2 - y]^T \\) around the circle defined by \\( x^2 + y^2 = 1 \\).",
"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... | 41.7 mL |
[
{
"content": "Determine whether the following statement is true or false: If the perimeter of a triangle is twice the perimeter of the triangle formed by the feet of the altitudes, then the triangle is equilateral.",
"role": "user"
}
] | True |
[
{
"content": "Determine whether the cubic equation \\(x^3 + 10x^2 - 100x + 1729 = 0\\) has at least one complex root \\(\\alpha\\) such that \\(|\\alpha| > 12\\).",
"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... | 4.973 g |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\frac{\\sqrt{n}^{\\sqrt{n}}}{2^n}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\int_{0}^{2} \\frac{x^n}{1 + e^{nx}} \\, dx \\) using the Dominated Convergence Theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the equation \\(16( 1- x + 2\\sqrt{1 - x^2} + 1-x) = x^4 -16x^2 +64\\).",
"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... | 3.25% |
[
{
"content": "A plane parallel to the xz-plane passes through the point (1,1,1). A straight line in this plane touches the graph of the function \\( f(x,y) = -x^2 - y^2 + 4 \\) at the point (1,1,f(1,1)). Determine the slope of this straight line.",
"role": "user"
}
] | -2 |
[
{
"content": "In a graph G with diameter 2 and maximum degree \\( \\Delta < n-1 \\), if a chordless 7-cycle exists, is there a vertex \\( v \\in V(G) \\) such that the neighborhood \\( N(v) \\) contains at least three vertices of the 7-cycle?",
"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... | 976.7kJkg^-1K^-1 |
[
{
"content": "Let $E$ be the region in $\\\\mathbb{R}^3$ between the paraboloid $z = x^2 + y^2$ and the plane $z = 2$. Given the vector field $\\\\vec{F} = \\\\langle 2x, 2y, 0 \\\\rangle$, compute the flux integral $\\\\iint_S \\\\vec{F} \\\\cdot \\\\mathrm{d}\\\\vec{r}$ over the surface $S$ using the divergen... | 8\pi |
[
{
"content": "Given a positive integer $a$ and $n$ variables $a_1, a_2, \\ldots, a_n$ ranging independently over the interval $[0, a]$, determine the maximum value of the expression:\n\\[ \\sum_{k=1}^n (a-a_1)(a-a_2)\\cdots(a-a_{k-1})a_k(a-a_{k+1})\\cdots(a-a_n). \\]",
"role": "user"
}
] | a^n |
[
{
"content": "Calculate the work done by the force field \\( F(x, y, z) = \\langle 3x^2+yz+y, xz+x+z^2, xy+2yz+2z \\rangle \\) on a particle moving along the path \\( C \\), which consists of the line segment from \\((2, 3, 0)\\) to \\((5, 7, 9)\\) followed by the line segment from \\((5, 7, 9)\\) to \\((1, 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... | Na2S, K2S or (NH4)2S |
[
{
"content": "Given the equation \\( f(x)=e^{\\frac{x^2}{2}}+\\int_0^x tf(t)dt \\), find the value of \\( f(\\sqrt{2}) \\).",
"role": "user"
}
] | 2e |
[
{
"content": "Compute the norm of the inverse operator \\((iI + \\frac{1}{2}U)^{-1}\\), where \\(U\\) is the bilateral shift operator on \\(\\ell^2(\\mathbb{Z})\\) defined by \\(U\\delta_k = \\delta_{k+1}\\) for \\(k \\in \\mathbb{Z}\\), and \\(I\\) is the identity operator on \\(\\ell^2(\\mathbb{Z})\\).",
... | 2 |
[
{
"content": "Let \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) be a differentiable function such that \\( \\lim_{x\\to\\infty} f(x) \\) exists and is finite. If \\( \\lim_{x\\to\\infty} xf'(x) \\) exists, find this limit.",
"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... | The uncertainty in the velocity of electron is 5.79e+04 m/s and the uncertainty in the velocity of proton is 31.6 m/s |
[
{
"content": "Let $X$ be a metric space and $B \\subseteq X$ be a subset. If $y \\in B$ is a limit point of $B$, does it follow that $y$ is a limit point of $X$? 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... | Quantity|FC|VC|TC|AFC|AVC|ATC|MC
---|---|---|---|---|---|---|---
0|150|0|150|-|-|-|-
1|150|50|200|150|50|200|50
2|150|60|210|75|30|105|10
3|150|90|240|50|30|80|30 |
[
{
"content": "In a free group with two generators $a$ and $b$, you start with a word of length 1 at time $0$. Every second, you multiply the current word by one of the elements $a$, $b$, $a^{-1}$, or $b^{-1}$, each chosen with probability $\\frac{1}{4}$. What is the probability that the reduced word $a$ ever ap... | \dfrac{1}{3} |
[
{
"content": "Given a continuous random variable $X$ with cumulative distribution function $F_{X}$, calculate the expected value $E[F_{X}(X)]$. Provide your answer as a single expression.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $3,356,644.06 |
[
{
"content": "Calculate the directional derivative of the function \\( f(x, y, z) = x^2 + y^2 - z^2 \\) at the point \\((3, 4, 5)\\) along the curve formed by the intersection of the surfaces \\( 2x^2 + 2y^2 - z^2 = 25 \\) and \\( x^2 + y^2 = z^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... | 16.05 m/s |
[
{
"content": "Let $X_1, X_2, \\ldots$ be a sequence of independent random variables. For $k = 1, 2, \\ldots$, suppose $P(X_{2k-1} = 1) = P(X_{2k-1} = -1) = \\frac{1}{2}$, and the probability density function of $X_{2k}$ is $f(x) = \\frac{1}{\\sqrt{2}} e^{-\\sqrt{2}|x|}$ for $-\\infty < x < \\infty$. Determine $... | C |
[
{
"content": "Let $V$ be a $K$-vector space with basis $B = (v_1, v_2, v_3, v_4)$ and let $f \\in \\text{End}(V)$ be a linear transformation defined by $f(v_i) = v_{i+1}$ for $i = 1, 2, 3$ and $f(v_4) = v_1$. Calculate the characteristic polynomial $P_f(t)$ of the endomorphism $f$. \\( \\text{Note: } M^B_B(f) \... | t^4 - 1 |
[
{
"content": "Consider a collection $(X_a)_{a\\in[0,1]}$ of i.i.d. random variables following the uniform distribution on [0,1]. For every real number $a \\in [0,1]$, there is a random variable $X_a$. Determine the probability of the event that at least one of the variables $X_a$ equals $1/2$. What is this prob... | 0 |
[
{
"content": "Find the order of the element \\((2, 3, 1)\\) in the group \\((\\mathbf{Z}/105\\mathbf{Z})^\\times\\) using the Chinese Remainder Theorem.",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the number of similarity classes of 6x6 matrices over \\(\\mathbb{C}\\) with the minimal polynomial \\((x-1)(x-2)^2\\) and the characteristic polynomial \\((x-1)^2(x-2)^4\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the number of pairs of natural numbers \\((p, q)\\) such that \\(p^2q^2 - 4(p+q) = a^2\\) for some natural number \\(a\\).",
"role": "user"
}
] | 4 |
[
{
"content": "Let $f(x)$ and $g(x)$ be differentiable functions on $\\mathbb{R}^+$ satisfying the equations:\n\n$$xf'(x) - g(x) = 0$$\n$$xg'(x) - f(x) = 0$$\n\nGiven that $f(2) + g(2) = 8$, find the value of $f'(1) \\cdot g'(1)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 4 |
[
{
"content": "Compute the homology groups $H_n(X,A)$ for a connected sum of two tori $X$ with a center circle $A$. Specifically, verify the value of $H_2(X,A)$ and explain any discrepancies with the expected result.",
"role": "user"
}
] | \mathbb{Z} \oplus \mathbb{Z} |
[
{
"content": "Determine whether it is true that if $F_{1}$ is a subfield of $F_{2}$, then $GL(N,F_{1})$ is a subset of $GL(N,F_{2})$. Specifically, consider the case where $F_{1} = \\mathbb{Q}(\\omega)$ and $F_{2} = \\mathbb{C}$, with $\\omega$ being a complex root of unity.",
"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... | C(y) = 0.04y + (1/2)(ln(y+1))^2 + 6.06 |
[
{
"content": "Evaluate the series \\( \\sum_{n=1}^\\infty\\frac{n}{(n+1)!} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Date: July 1, 2022
Particulars: Equipment
Debit:
Credit:
Amount: $15,400
Date: July 1, 2022
Particulars: Prepaid Insurance
Debit:
Credit:
Amount: $2,650
Date: July 1, 2022
Particulars: Equipment
Debit:
Credit:
Amount: $6,400
Date: July 1, 2022
Particulars: Equipment
Debit:
Credit:
Amount: $2,850 |
[
{
"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... | 6.9e+5 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... | {
"Assets": {
"Current Assets": {
"Cash": 8200,
"Debt investments (short-term)": 1620,
"Notes receivable - due before December 31, 2018": 360,
"Accounts receivable": 5620,
"Inventory": 16570,
"Total Current Assets": 32370
},
"Non-Current Assets": {
"Buildings": 21980,
"Accumulated depreciation - buildings": -13310,
"Net Buildings": 8670,
"Notes receivable - due after December 31, 2018": 5400,
"Patents": 11190,
"Total Non-Current Assets": 25260
},
"Total Assets": 57630
}
} |
[
{
"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... | 6596 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... | 2e18 molecules/L |
[
{
"content": "Given that $X$ and $Y$ are independent and identically distributed standard normal random variables, i.e., $X, Y \\sim \\mathcal{N}(0,1)$, determine the probability $Pr(X > 0, X + Y < 0)$. Provide your answer as a single probability value.",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"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... | -3.55 kJ |
[
{
"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... | $105,600 |
[
{
"content": "Which of the following conditions ensures that $f(X)$, the image of a continuous map $f: X \\rightarrow Y$ between metric spaces, is a complete subset of $Y$?\\n\\nA. $X$ is compact.\\nB. $Y$ is compact.\\nC. $X$ is complete.\\nD. $Y$ is complete.",
"role": "user"
}
] | A |
[
{
"content": "Find the equation of the directrix of a parabola with a focus at (-1, -1) and a tangent at the point (7, 13) given by the equation 3x - y - 8 = 0.",
"role": "user"
}
] | x + 8y + 19 = 0 |
[
{
"content": "Determine the type of curve described by the equation \\( \\int_{0}^{y}\\frac{f(v)dv}{\\sqrt{y-v}}=4\\sqrt{y} \\), where the curve \\( y=y(x) \\) passes through the point \\( (\\sqrt{3},1) \\) and \\( f(y)=\\sqrt{1+\\frac{1}{y^{'2}}} \\). Choose from the following options:\n1. Straight line\n2. Ci... | 1 |
[
{
"content": "On a piece of paper, there are 10 points: 8 blue points and 2 red points. Each red point is connected to all the blue points, but not to each other. All the blue points are connected to each other. Each connection is made by a single segment. Determine the number of different ways to travel from o... | 109600 |
[
{
"content": "Find the greatest common divisor (GCD) of the polynomials $y^2 - 10y + 24 + 6x - 9x^2$ and $2y^4 - 18x^2y^2 - 48xy^2 - 32y^2$. Provide your answer as a polynomial.",
"role": "user"
}
] | y - 3x - 4 |
[
{
"content": "Determine whether the following statement is true or false: All critical points of a function must be either extrema or saddle points. In other words, if \\( f'(x) = 0 \\) or \\( f'(x) = D.N.E \\), there are only two possibilities: \\( f(x) \\) is an extrema or \\( f(x) \\) is a saddle point. Ther... | B |
[
{
"content": "Let \\( x_{1}, y_{1}, x_{2}, y_{2} \\) be real numbers satisfying the equations \\( x_{1}^{2}+5 x_{2}^{2}=10 \\), \\( x_{2} y_{1}-x_{1} y_{2}=5 \\), and \\( x_{1} y_{1}+5 x_{2} y_{2}=\\sqrt{105} \\). Find the value of \\( y_{1}^{2}+5 y_{2}^{2} \\).",
"role": "user"
}
] | 23 |
[
{
"content": "Determine the total number of positive real values of $x$ such that $x$, $\\lfloor x \\rfloor$, and $\\{x\\}$ are in harmonic progression, where $\\lfloor . \\rfloor$ denotes the greatest integer function and $\\{ . \\}$ denotes the fractional part.",
"role": "user"
}
] | 1 |
[
{
"content": "In an Artinian ring $R$, prove or disprove that any nilpotent ideal $J$ such that $R/J$ has no nil ideals must be equal to the nilradical $N(R)$. Provide a justification for your answer.",
"role": "user"
}
] | J = N(R) |
[
{
"content": "Given the function \\(g:\\mathbb{R}^3 \\to \\mathbb{R}^3\\) defined by \\(g(x, y, z) = (3x + 4z, 2x - 3z, x + 3y)\\) and the region \\(S = \\{(x, y, z) \\in \\mathbb{R}^3 : 0 \\leq x \\leq 1, 0 \\leq y \\leq 1, 0 \\leq z \\leq 1\\}\\), find the value of \\(\\alpha\\) such that the following integr... | 255 |
[
{
"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... | MC = w/MPL |
[
{
"content": "Determine the number of real roots of the equation \\(2013x^{2012} - 2012x^{2011} - 16x + 8 = 0\\) within the interval \\([0, 8^{\\frac{1}{2011}}]\\). Choose the correct option:\n\n- Exactly one real root.\n- No real root.\n- At least one and at most two real roots.\n- At least two real roots.",
... | D |
[
{
"content": "The monthly demand for the Instant Pie Maker is given by \\(D(x,y)= \\frac{1}{125}xe^{xy/1000} \\text{ units}\\) where \\(x\\) dollars are spent on infomercials and \\(y\\) dollars are spent on in-person demonstrations. If \\(t\\) months from now \\(x=20+t^{2/3}\\) dollars are spent on infomercial... | 0.027 |
[
{
"content": "Find the values of $n$ for which the determinant of the matrix defined by $a_{i,j} = (2i+3j)^3$ is zero.",
"role": "user"
}
] | n \geq 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... | + + |
[
{
"content": "For all complex numbers $z$, let \\[f(z) = \\left\\{\n\\begin{array}{cl}\nz^{2}&\\text{ if }z\\text{ is not real}, \\\\\n-z^2 &\\text{ if }z\\text{ is real}.\n\\end{array}\n\\right.\\]Find $f(f(f(f(1+i))))$.",
"role": "user"
}
] | -256 |
[
{
"content": "Let $f_n \\in L^p(B)$ be a sequence where $B$ is a ball in $\\mathbb{R}^n$. Assume that $\\|f_n\\|_{L^p_w(B)} \\rightarrow 0$ as $n\\rightarrow \\infty$, where $\\|f\\|_{L^p_w(B)}$ is the weak $L^p$-norm of $f$ in $B$. Does $\\int_B f_n \\phi \\rightarrow 0$ as $n\\rightarrow \\infty$ for any $\\p... | Yes |
[
{
"content": "Is there a calculable function that can transform a single uniformly distributed random value in the range \\(0 \\leq x < 1\\) into a normally distributed value with mean 0 and standard deviation 1? If an exact function does not exist, is there an approximation?",
"role": "user"
}
] | \Phi^{-1}(x) |
[
{
"content": "Given an analytic function $f: \\{z:|z|<1\\} \\to \\{z:|z|<1\\}$ with $f(0)=0$, and a specific $0<r<1$ such that $f(\\{z:|z|<r\\}) = \\{z:|z|<r\\}$, determine if $f(z)=cz$ for some $|c|=1$. If not, find the simplest possible form of $f$. Provide your answer with justification.",
"role": "user"... | f(z) = cz |
[
{
"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... | 6.67% |
[
{
"content": "Suppose $(x_n)$ and $(y_n)$ are two sequences such that (1) $(x_n)$ is bounded and (2) $|x_n - y_n| < \\frac{1}{n}$. If $(y_{n_i})$ is a convergent subsequence of $(y_n)$, is it guaranteed that $(x_{n_i})$ also converges?",
"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... | 611.23 Hz |
[
{
"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... | 13900 |
[
{
"content": "Evaluate the integral \\( \\int _0 ^ \\infty \\frac {dx} {x^3 (e^\\frac{\\pi}{x} -1)} \\) without using Taylor expansion.",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Evaluate the infinite series: $$\\sum_{k=1}^\\infty\\frac{k(k+1)(k+2)}{3!}\\left(\\frac{1}{3}\\right)^k$$",
"role": "user"
}
] | \dfrac{27}{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... | 20.4791 years |
[
{
"content": "Find the minimum value of \\((5+x)(5+y)\\) given that \\(x^2 + xy + y^2 = 3\\) and \\(x, y \\in \\mathbb{R}\\).",
"role": "user"
}
] | 16 |
[
{
"content": "Compute the Cheeger constant of the unit disc in \\(\\mathbb{R}^2\\), defined as \\(\\inf_E\\frac{S(E)}{\\min(V(A),V(B))}\\), where \\(E\\) is a 1-dimensional submanifold dividing the disc into disjoint subsets \\(A\\) and \\(B\\), \\(S(E)\\) denotes the 1-dimensional volume (length) of \\(E\\), a... | \dfrac{4}{\pi} |
[
{
"content": "Let $V \\subset [0,\\infty)^n$ be a closed set. Consider the set $W$ of minimal elements of $V$ under the partial ordering $\\leq'$ defined as $(x_1,...,x_n) \\leq' (y_1,...,y_n) \\iff x_k \\leq y_k, \\forall k$. That is, $$ W = \\big\\{ x \\in V \\ \\big| \\ \\nexists y\\in V, y<'x\\big\\}. $$ De... | 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... | 2311.48 |
[
{
"content": "Four points A, B, C, and D lie on a circle in that order. The extensions of AB and DC meet at point E, and the extensions of AD and BC meet at point F. Tangents EP and FQ are drawn from points E and F to the circle, touching the circle at points P and Q, respectively. If EP = 60 and FQ = 63, find ... | 87 |
[
{
"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... | Sales: $173,000, $187,100, $201,200, $215,300
Variable Expenses:
Sales Commissions: $10,380, $11,226, $12,072, $12,918
Advertising: $8,650, $9,355, $10,060, $10,765
Traveling: $6,920, $7,484, $8,048, $8,612
Delivery Charges: $1,730, $1,871, $2,012, $2,153
Total Variable Budget: $27,680, $29,936, $32,192, $34,448
Fixed Expenses:
Sales Salaries: $34,669, $34,669, $34,669, $34,669
Depreciation Charged: $6,947, $6,947, $6,947, $6,947
Insurance: $1,240, $1,240, $1,240, $1,240
Total Fixed Budget: $42,856, $42,856, $42,856, $42,856
Total Sales Budget: $70,536, $72,792, $75,048, $77,304 |
[
{
"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... | 168.5 degrees |
[
{
"content": "Find the value of \\(b\\) such that the polynomial \\(x^{4} + x^{3} - x^{2} + ax + b\\) is the square of another polynomial.",
"role": "user"
}
] | \dfrac{25}{64} |
[
{
"content": "Consider points \\(O(0, 0)\\), \\(P(a, a^2)\\), and \\(Q(b, b^2)\\) which lie on the parabola \\(y = x^2\\). Define \\(S_1\\) as the area bounded by the line segment \\(PQ\\) and the parabola, and \\(S_2\\) as the area of triangle \\(OPQ\\). Determine the minimum value of the ratio \\(\\frac{S_1}{... | \dfrac{4}{3} |
[
{
"content": "Compute the shortest distance between the surface $H = \\{(x,y,z) \\in \\mathbb{R}^{3}: x^2+y^2 - z^2 + 4 = 0\\}$ and the point $Q = (1,3,0)$. Express your answer as a single number.",
"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... | 20.6 pF |
[
{
"content": "Determine the greatest value of $k$ such that for all $x \\leq k$, the function $f(x)$ satisfies $f(x) \\geq -\\frac{3}{4}$, where $f(x)$ is defined by the following conditions:\n- The domain of $f(x)$ is $\\mathbb{R}$.\n- For all $x \\in \\mathbb{R}$, $f(x+1)=2f(x)$.\n- For $x \\in (0,1]$, $f(x)=... | \dfrac{9}{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... | 28.0 |
[
{
"content": "Provide an example of a non-abelian group whose quotient by its center is a non-cyclic abelian group.",
"role": "user"
}
] | D_4 |
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