prompt list | ground_truth string |
|---|---|
[
{
"content": "Evaluate the integral \\( \\int_0^{\\pi} \\frac{1}{5+3\\cos\\theta}\\,\\mathrm{d}\\theta \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | Zero Balance:
a) Capital/Withdrawals
d) Revenue/Capital
Non-Zero Balance:
c) Assets/Withdrawals
b) Capital/Expenses |
[
{
"content": "Determine the condition for repeated roots in the fourth-order polynomial equation: \\( x^4 + ax^3 + bx^2 + cx + d = 0 \\).",
"role": "user"
}
] | \Delta = 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... | 5.986e-8 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $21,918 |
[
{
"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... | 3.13 atm |
[
{
"content": "Compute \\( \\lim\\limits_{(x,y)\\to (0,0)}{\\sin(xy)-xy\\over x^2y} \\) using Taylor's theorem.",
"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... | Cl_2 + 2H_2O -> 2HClO + 2H^+ + 2e^- |
[
{
"content": "Determine if there exists a constant $K > 0$ such that \\( \\int_U g^{1/p}f^{1/q} \\le K\\int_U f^{1/q}g^{1/p} \\) for all integrable functions $f, g \\ge 0$, where $U \\subset \\mathbb{R}^n$ is open and $p, q > 1$ satisfy \\( \\frac{1}{p} + \\frac{1}{q} = 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... | CH |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|z|=\\frac{1}{2}} \\frac{1}{z(z-1)} \\, dz \\) using the residue theorem.",
"role": "user"
}
] | -2\pi i |
[
{
"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... | 9.8j |
[
{
"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... | 33320 Pa |
[
{
"content": "Consider the equations:\n\\[ 2Z - p = Xq \\]\n\\[ 2Z - q = Yp \\]\nwhere \\( X, Y, Z \\in \\mathbb{N} \\) and \\( p, q \\in \\mathbb{P} - \\{2\\} \\). Determine if there exist solutions where \\( Z \\) is not a prime number.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the minimum achievable accuracy for an algorithm $\\psi$ that approximates an elementary function $f$ within a floating-point system characterized by $e$ bits for the exponent and $m$ bits for the mantissa, given that the domain $D(f) = [1,2)$ and the range $f(D(f)) = [1,2)$. Provide you... | 2^{-(m+1)} |
[
{
"content": "Determine the number of solutions to the equation \\(x^{2} - 2x \\cdot \\sin(x \\cdot y) + 1 = 0\\) that lie within the circle defined by \\(x^{2} + y^{2} \\leq 100\\).",
"role": "user"
}
] | 6 |
[
{
"content": "Determine whether every closed subspace of a Fréchet space is reflexive. Answer with true or false.",
"role": "user"
}
] | False |
[
{
"content": "A point has rectangular coordinates $(10, -18, 35)$ and spherical coordinates $(\\rho, \\theta, \\phi).$ Find $\\tan \\theta.$",
"role": "user"
}
] | -\frac{9}{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... | 8.42% |
[
{
"content": "Evaluate the contour integral \\( \\oint_C \\frac{z^2+1}{e^{\\frac{z}{10}}-1}\\,dz \\) where \\(C\\) is the unit circle traced counterclockwise.",
"role": "user"
}
] | 20\pi i |
[
{
"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... | 79.84 mL of benzoic acid and 20.16 mL of sodium benzoate |
[
{
"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... | Non-cash investing and financing activities:
Issuance of common stock for building: $107,000
Purchase of truck by long-term note: $28,000
Retirement of short-term notes by issuing common stock: $19,000
Total: $154,000 |
[
{
"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... | 121 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... | 1.4e+21 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... | 39N |
[
{
"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... | 4.88% |
[
{
"content": "Find the last two digits of \\(12^{12^{12^{12}}}\\) using Euler's theorem.",
"role": "user"
}
] | 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... | CH3-CH(CH3)-CH(CH2-CH3)-CH2-CH2-CH2-CH2-CH2-CH3 |
[
{
"content": "Find the minimum number of odd entries in a $3 \\times 3$ matrix with integer entries and a determinant of $1$. Provide your answer as a single integer.",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the integral: \\[ \\int_{1/4}^4 \\frac{1}{x}\\sin\\left(x-\\frac{1}{x}\\right)\\,dx \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the degree of the field extension \\( \\mathbb{Q}(\\sqrt{1+\\sqrt{3}}) \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | 4 |
[
{
"content": "In the sequence \\(\\{a_n\\}\\), where \\(a_n = a \\cdot 2^n + b \\cdot n - 80\\) and \\(a, b \\in \\mathbf{N}_{+}\\), it is known that the sum of the first \\(n\\) terms, \\(S_n\\), attains its minimum value if and only if \\(n = 6\\), and \\(a_{36}\\) is divisible by 7. Find the value of \\(\\le... | 8010 |
[
{
"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... | 0.5757 mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3087 |
[
{
"content": "Determine the number of k-tuples of sets \\(<S_1, S_2, \\ldots, S_k>\\) such that each set \\(S_i\\) is a subset of \\(\\{1, 2, \\ldots, n\\}\\) and the following conditions hold: \\(S_1 \\subseteq S_2 \\supseteq S_3 \\subseteq S_4 \\supseteq S_5 \\subseteq S_6 \\supseteq \\ldots\\).",
"role":... | F_{k+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... | 0.77 m/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... | 20 J |
[
{
"content": "Find the smallest positive integer $n$ such that an $n \\times n$ grid can be colored with red, yellow, and blue, with each color appearing the same number of times, and satisfying the condition that if a row contains a yellow cell, it must also contain a blue cell and cannot contain a red cell.",... | 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... | 48.96 AU |
[
{
"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... | N = A - Z |
[
{
"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... | 2.05e7 m/s |
[
{
"content": "Evaluate the integral \\( I = \\int_{0}^{1} \\frac{\\sqrt{1-x^4}}{1+x^4} \\, dx \\) and show that it equals \\( \\frac{\\pi}{4} \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Find the smallest positive integer \\( n \\) such that in a game played on a board with 2018 squares in a row, Tom can ensure a win by choosing appropriate numbers in a finite number of moves. Initially, Jerry places a coin on one of the squares. In each subsequent step, Tom states a positive inte... | 1009 |
[
{
"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... | (m)*9.8*(height difference) |
[
{
"content": "Assuming a Poisson distribution with an unknown rate parameter \\(\\lambda\\) for software failures, where two failures occurred in one week, determine the waiting time without any additional failures needed to declare with 95% confidence that a workaround is successful. A successful workaround wi... | 1.5 |
[
{
"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... | 0 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... | 0.00248 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... | <img>/cimages/multimages/16/111111123450356316018302708635781128111855868575.png</img> |
[
{
"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... | 6.7e+9 J |
[
{
"content": "Let $R$ be a valuation ring with maximal ideal $\\mathfrak{m}$, residue field $k$, and field of fractions $K$. Assume the valuation on $K$ satisfies $v(K)=\\mathbb{Q}$. For each $\\lambda \\in \\mathbb{Q}$, define:\n\\[ \\mathfrak{m}_{\\lambda}:=\\{ x\\in K\\:|\\:v(x)\\geq \\lambda \\} \\]\n\\[ \\... | 1 |
[
{
"content": "Determine whether the components $Z_i$ of a standard Gaussian distributed random vector $Z=(Z_1,Z_2,\\ldots,Z_n)^T$ in $\\Bbb R^n$ are independent random variables.",
"role": "user"
}
] | Yes |
[
{
"content": "Provide an example of a function $f(x)$ such that the integral \\( \\int_{1}^{\\infty} f(x^2) \\, dx \\) converges, but the integral \\( \\int_{1}^{\\infty} f(x) \\, dx \\) diverges.",
"role": "user"
}
] | \dfrac{1}{x} |
[
{
"content": "Calculate the work done by the engine pistons when the pressure vector field is given by \\( \\mathbf{P} = (y - x^2) \\mathbf{i} + (z - y^2) \\mathbf{j} + (x - z^2) \\mathbf{k} \\) and the path \\( C \\) is the helix \\( \\mathbf{V}(t) = t\\mathbf{i} + t^2\\mathbf{j} + t^3\\mathbf{k} \\) from \\((... | \dfrac{29}{60} |
[
{
"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... | $412,362.17 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1065.16 kW |
[
{
"content": "A transport company operates 40 trams and 80 buses. Each day, independently, each tram breaks down with a probability of 0.01, and each bus breaks down with a probability of 0.02. Let $X$ be the number of trams that break down in a day, and $Y$ be the number of buses that break down on the same da... | 0.6336 |
[
{
"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... | At 15,000 machine hours:
Utilities: $4,500
Indirect Labor: $73,000
Supplies: $3,000
Maintenance: $19,500
Depreciation: $90,000
Total: $190,000
At 25,000 machine hours:
Utilities: $7,500
Indirect Labor: $87,000
Supplies: $5,000
Maintenance: $20,500
Depreciation: $90,000
Total: $210,000 |
[
{
"content": "Let $f$ be a function defined on the positive integers such that for any positive integers $a$, $b$, and $n$ with $a + b = 2^n$, it holds that $f(a) + f(b) = n^2$. Determine the value of $f(2021)$. \\( \\)",
"role": "user"
}
] | \dfrac{203}{2} |
[
{
"content": "Determine whether the minimal polynomial of a square matrix over a field \\( F \\) can be of the form \\( P(x) = (x-\\lambda)^2 \\) for some \\( \\lambda \\in F \\).",
"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... | 1st Year entries:
Deferred tax asset 3,000
Benefit due to loss carry forward 3,000
Benefit due to loss carry forward 1,050
Allowance to reduce DTA to expected realizable value 1,050
2nd Year entries:
Income tax expense 60,000
Income tax payable 60,000
Adjustment entries required:
Deferred tax asset 4,000
Income ta... |
[
{
"content": "Calculate the radius of convergence for the power series \\( \\sum_{n = 0}^{\\infty}{2^{-n^{2}}n!}x^n \\) using the Limit Superior of the coefficient sequence \\( c_n = 2^{-n^{2}}n! \\).",
"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... | 26 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... | $1,643,619 |
[
{
"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... | scientific theory |
[
{
"content": "Determine the values of \\( p \\) for which the series \\( \\frac{3}{1} + \\frac{4}{2^p} + \\frac{5}{3^p} + \\frac{6}{4^p} + \\cdots \\) converges.",
"role": "user"
}
] | p > 2 |
[
{
"content": "Determine the order of the pole at \\(z = \\pi i\\) for the function \\(f(z) = \\frac{2e^{iz}}{e^{2iz}+2e^{iz}+1}\\). Justify your answer using a theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "In an isosceles trapezoid \\(ABCD\\) with diagonals intersecting at point \\(P\\), determine if the center of the circumcircle of the trapezoid lies on the circumcircle of triangle \\(ABP\\). Answer with 'True' or 'False'.",
"role": "user"
}
] | False |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\rightarrow \\infty } \\lim_{n\\rightarrow \\infty} \\sum_{r=1}^{n} \\frac{\\left [ r^2(\\sin x)^x \\right ]}{n^3} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\to\\infty} \\exp\\left(\\frac{\\log\\left(\\sqrt{x^2+1}-x\\right)}{\\log (x)}\\right) \\) without using L'Hopital's rule.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Let $F:(0,\\infty) \\to [0,\\infty)$ be a continuous function such that $F(1)=0$, $F$ is strictly increasing on $[1,\\infty)$, and strictly decreasing on $(0,1]$. Suppose $F$ is strictly convex on $[1-\\epsilon,1+\\epsilon]$ for some $\\epsilon>0$. Does there exist a $\\delta>0$ such that $F$ is 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... | 5.75 |
[
{
"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... | 0.055 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... | 4.48e17 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... | 17.3 m/s |
[
{
"content": "Find the smallest positive integer $x$ which is greater than $1$ and relatively prime to $120$ (recall that relatively prime means that the GCD of $x$ and $120$ is $1$)",
"role": "user"
}
] | 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... | -2.0e-4 V |
[
{
"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... | -39.41 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... | 3.72 m/s^2 |
[
{
"content": "If $T \\in \\mathcal{B}(X,Y)$ is not compact, can the restriction of $T$ to an infinite-dimensional subspace of $X$ be compact?",
"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... | 1.56 m/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... | Spending variances
Flexible Budget
Activity variances
Static Budget
Activity level (in units)
800
800
750
Variable costs :
Indirect material
6850
190
Favourable
7040
440
Unfavourable
6600
... |
[
{
"content": "Calculate the result of the convolution \\( \\delta_{im} \\epsilon_{ijk} \\) using Einstein summation notation, considering that two indices coincide.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the image of the polynomial ring $F[x]$ under the formal polynomial differentiation map $D$, where $F$ is a field of characteristic zero and $D$ is defined by \\( D(a_0+a_1x+a_2x^2+\\ldots+a_nx^n) = a_1+2a_2x+3a_3x^2+\\ldots+na_nx^{n-1} \\).",
"role": "user"
}
] | F[x] |
[
{
"content": "Evaluate the integral \\( \\int_{\\gamma} \\frac{e^{iz}}{z^2} \\, dz \\) where \\( \\gamma(t) = e^{it} \\) for \\( 0 \\le t \\le 2\\pi \\).",
"role": "user"
}
] | -2\pi |
[
{
"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... | $588,100 |
[
{
"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... | depression |
[
{
"content": "Suppose that $\\{X_n\\}$ is a sequence of nonnegative bounded random variables and $\\{a_n\\}$ is a sequence of positive constants such that \\( \\limsup_{n\\to\\infty}\\sum_{i=1}^n a_iX_i <\\infty \\) almost surely. Determine if it is true that \\( \\frac{1}{n}\\sum_{i=1}^n a_i\\mathsf{E}X_i\\to ... | True |
[
{
"content": "Calculate the value of \\( t \\) at which the velocity of the Bezier curve defined by the control points \\( P_0 = (0, 0) \\), \\( P_1 = (0.4, 0) \\), \\( P_2 = (0.2, 1) \\), and \\( P_3 = (1, 1) \\) is maximized. The Bezier curve is given by the equations:\n\\[ X(t) = 1.6t^3 - 1.8t^2 + 1.2t \\]\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... | -42 x 10^5 V |
[
{
"content": "Find the coefficient $b_1$ in the expression \\( \\sin n\\theta = \\sum_{r=0}^{n} b_r \\sin^r\\theta \\), where \\( n \\) is an odd integer.",
"role": "user"
}
] | n |
[
{
"content": "Determine whether there exists a set of $n$ integers $x_1, x_2, \\ldots, x_n$ such that the numbers $x_1^2 - 1, x_2^2 - 1, \\ldots, x_n^2 - 1$ are pairwise coprime.",
"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... | $1,069.56 |
[
{
"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... | 6.59 m |
[
{
"content": "Compute the limit: $$\\lim_{(x,y) \\to (0,0)} \\frac{y^3 \\sqrt{|x|}}{|x|+y^4}.$$",
"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... | 35.29 |
[
{
"content": "Let $z$ and $w$ be complex numbers such that $|2z - w| = 25$, $|z + 2w| = 5$, and $|z + w| = 2$. Find $|z|$. Express your answer as a single number.",
"role": "user"
}
] | 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... | 30100 |
[
{
"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... | 64 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... | Ca_3N_2 + 6H_2O -> 3Ca(OH)_2 + 2NH_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... | 6.96% |
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