prompt list | ground_truth string |
|---|---|
[
{
"content": "Consider quadratic trinomials \\( f_{1}(x), f_{2}(x), \\ldots, f_{100}(x) \\) with equal coefficients for \\( x^{2} \\) and equal coefficients for \\( x \\), but different constant terms. Each trinomial has two roots. For each trinomial \\( f_{i}(x) \\), one root is chosen and denoted as \\( x_{i}... | 0 |
[
{
"content": "Find the value of \\( a \\) such that the vector \\( \\begin{pmatrix} a \\\\ -1 \\\\ -2 \\end{pmatrix} \\) is an eigenvector of the matrix \\( \\begin{pmatrix} a & 6 & 3 \\\\ -1 & a & 1 \\\\ 1 & 2 & -1 \\end{pmatrix} \\).",
"role": "user"
}
] | -\dfrac{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... | 5.98 |
[
{
"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... | Iodine in presence of a base |
[
{
"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. Debit Service Revenue $34,600
Debit Rent Revenue $13,100
Credit Income Summary $47,700
(To close revenue accounts)
2. Debit Income Summary $31,500
Credit Salaries and Wages Expense $18,100
Credit Supplies Expense $2,000
Credit Rent Expense $10,800
Credit Insurance Expense $1,500
Credit Depreciation Expense $1,200
(T... |
[
{
"content": "Determine the Big-O notation for the function \\((n^n + n2^n + 5^n)(n! + 2^n)\\).",
"role": "user"
}
] | O(n^n \cdot n!) |
[
{
"content": "Given positive integers $n$ and sequences of positive numbers $a_1, a_2, \\ldots, a_n$ and $b_1, b_2, \\ldots, b_n$ such that \\(\\sum_{i=1}^{n}a^2_{i} = \\sum_{i=1}^{n}b^2_{i} = 1,\\) find the maximum value of the minimum ratio \\(\\min_{1\\le i\\le n}\\left(\\frac{a_{i}}{b_{i}}\\right).\\)",
... | 1 |
[
{
"content": "Let $(X,Y)$ be a random variable with the joint probability density function (PDF): \\[ f(x,y) = \\begin{cases} e^{-x-y} & \\text{if } x,y \\ge 0 \\\\ 0 & \\text{otherwise} \\end{cases} \\] Calculate the conditional expectation $E(X+Y|X<Y)$. Express your answer in terms of integrals if necessary."... | 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... | 91.65 J/K |
[
{
"content": "Determine the coefficient of $x^n$ in the expansion of the expression $\\frac{(1-x)^n}{1+x}$.",
"role": "user"
}
] | (-2)^n |
[
{
"content": "If $R$ is a field and $f(x) \\in R[X]$ is an irreducible polynomial, is $(f(x))$ a principal ideal in $R[X]$?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $A,$ $B,$ $C,$ and $D$ be points on a circle. For each pair of points, we draw the line passing through the midpoint of those two points that is perpendicular to the line formed by the other two points. For example, we draw the line passing through the midpoint of $\\overline{AB}$ that is pe... | 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... | 2.86e-23 N |
[
{
"content": "Suppose random variables $Z_i$ are distributed according to $p(z)$ and $X_i$ are distributed according to $p(x|z)$. Does the sequence $\\frac{\\sum_{i=1}^n X_i}{n}$ converge to the expected value $E(X)$?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the volume of the solid formed by revolving the triangular region bounded by the lines $y = |x|$ and $y = 1$ around the line $x = -2$.",
"role": "user"
}
] | 4\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... | 1.56e4 N/C |
[
{
"content": "Let $A$ and $B$ be subsets of a set $M$ and let $S_0=\\{A,B\\}$. For $i\\geq 0$, define $S_{i+1}$ inductively to be the collection of subsets $X$ of $M$ that are of the form $C\\cup D, C\\cap D,$ or $M-C$ (the complement of $C$ in $M$), where $C,D \\in S_i$. Let $S=\\cup^\\infty_{i=0} S_i$. What i... | 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... | 21.667 ft/s |
[
{
"content": "Evaluate the integral: \\[ \\int_0^{\\frac{\\pi}{2}} \\frac{\\sin^3(t)}{\\sin^3(t)+\\cos^3(t)} \\, dt \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Calculate the Fourier coefficient \\( c_1 \\) for the function \\( f(x) = x \\cos(x) \\) defined on the interval \\( [-\\pi, \\pi] \\). The Fourier coefficients are given by:\n\\[ c_n = \\frac{1}{2 \\pi} \\int_{-\\pi}^{\\pi} f(x) e^{-inx} dx \\]\nGiven that \\( c_0 = 0 \\) because the function is ... | \dfrac{i}{4} |
[
{
"content": "Given that \\(T_1\\) is a lower \\(\\alpha \\times 100\\%\\) confidence limit and \\(T_2\\) is an upper \\(\\alpha \\times 100\\%\\) confidence limit for the parameter \\(\\theta\\), such that \\(P(T_1 < T_2) = 1\\), determine the \\((2\\alpha - 1) \\times 100\\%\\) confidence interval for \\(\\th... | [T_1, T_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... | The identity of the reactants or the mass of acid and antacid used to make the standard solutions and the volume of antacid that was added. |
[
{
"content": "Calculate the limit: $$\\lim_{x\\to\\infty}x\\left(\\int_0^x te^{-2t}\\,dt-\\dfrac{1}{4}\\right)$$",
"role": "user"
}
] | 0 |
[
{
"content": "Let $ABC$ be a triangle. There exists a positive real number $k$, such that if the altitudes of triangle $ABC$ are extended past $A$, $B$, and $C$, to $A'$, $B'$, and $C'$, as shown, such that $AA' = kBC$, $BB' = kAC$, and $CC' = kAB$, then triangle $A'B'C'$ is equilateral.\n\n[asy]\nunitsize(0.6... | \frac{1}{\sqrt{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... | 0.0867 m |
[
{
"content": "Determine the value of $N \\geq 9$ for which it is possible that on a board with $N$ distinct non-negative numbers less than one, for any eight distinct numbers, there exists a ninth number such that the sum of these nine numbers is an integer.",
"role": "user"
}
] | 9 |
[
{
"content": "Given the quadratic polynomial \\( f(x) = ax^2 - ax + 1 \\), find the maximum value of \\( a \\) such that \\( |f(x)| \\leq 1 \\) for all \\( x \\in [0, 1] \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Find the integer value of $c$ that satisfies the following system of Diophantine equations: \\( c = 143x + 1 \\), \\( c = 323y + 315 \\), and \\( c = 667z + 167 \\), where $x$, $y$, and $z$ are integers.",
"role": "user"
}
] | 1000000 |
[
{
"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... | Hart Company
Balance sheet (partial) on December 31, 2009.
Stockholders' equity:
Common Stock (75,000 $48 par value shares authorized):
... 50,000 Shares issued $2,400,000
... Paid-in Captial in Excess of par value 720,000
Preferred stock - 12,000 6%, cumulative, $120 par value share authorized
... 8,000 Share... |
[
{
"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... | 5/3 |
[
{
"content": "Is the subspace of $M_{n}(\\mathbb{C})$ consisting of all matrices of rank $k$ connected, where $n$ is a positive integer and $0\\leq k\\leq n$ is an integer?",
"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... | 48.67 |
[
{
"content": "A finite set of points \\( M \\) on the plane satisfies the condition that for any two points \\( A \\) and \\( B \\) in \\( M \\), there exists a third point \\( C \\) such that \\( \\triangle ABC \\) is an equilateral triangle. Determine the maximum number of points in the set \\( M \\).",
"... | 3 |
[
{
"content": "Given that $Y$ is uniformly distributed over $(0,6)$ and $X|Y=y$ follows an exponential distribution with rate $1/(3y)$ for $x \\geq 0$, calculate the mean of $X$. Express the mean as $E[X] = \\int_{0}^{\\infty} x f_X(x)\\ dx$, where $f_X(x)$ is the marginal distribution of $X$.",
"role": "use... | 9 |
[
{
"content": "Determine which of the following sets form an ideal in the ring of all continuous real-valued functions on \\(\\mathbb{R}\\), denoted as \\(C(\\mathbb{R})\\):\n\nA. The set of all \\(C^{\\infty}\\) functions with compact support.\nB. The set of all continuous functions with compact support.\nC. Th... | B |
[
{
"content": "Determine the range of values of \\( k \\) for which the function \\( f(x) = \\frac{x^2 - 1}{(x-2)(x+k)} \\) takes all real values, where \\( x \\) is a real number.",
"role": "user"
}
] | (-1, 1) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.90 |
[
{
"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... | 0.13 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... | 60.94 m |
[
{
"content": "Let $A$ be an $n \\times n$ real matrix such that all its conjugates (matrices similar to $A$ over $\\mathbb{R}$) have zero diagonal entries. Determine whether it is necessarily true that $A=0$. Provide a justification for your answer.",
"role": "user"
}
] | A = 0 |
[
{
"content": "Calculate the flux of the vector field \\( \\mathbf{v} = (x^2, y^2, z^2) \\) over the surface defined by \\( \\mathbf{r} = (u^2, v^2, uv) \\), where \\( 0 \\leq u \\leq 1 \\) and \\( 0 \\leq v \\leq 2 \\). Assume the normal vector satisfies \\( \\mathbf{n} \\cdot \\mathbf{e_z} > 0 \\).",
"role... | -\dfrac{4}{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... | 5.83e-11 m |
[
{
"content": "Determine the number of real solutions for the equation \\( g(x) = x^4 - 5\\sin 3x + \\arctan (x-2) \\) for \\( x > 2 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $X$ and $Y$ be two independent, identically distributed random variables, each taking values in $\\{0,1\\}$ according to the uniform distribution. Given that the mutual information between $X$ and an arbitrary random variable $B$ is $I(X:B) = 0$, the mutual information between $Y$ and $B$ is $... | true |
[
{
"content": "Estimate the value of \\( \\int^{1}_{-1} \\left(\\frac{\\sin{x}}{x}\\right)^{300} dx \\) to one significant figure.",
"role": "user"
}
] | 0.3 |
[
{
"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... | 125 |
[
{
"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... | 5550 |
[
{
"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... | 384.27 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $163,000 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\int_{-\\infty}^\\infty e^{-(5x^2-6xy+5y^2)} \\, dx \\, dy \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Determine the operator to which $T_t: \\varphi(x) = \\varphi(x+t)$ on $L^2(\\mathbb{R})$ converges as $t \\to \\infty$, and specify the topology of this convergence.",
"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... | 6.45 m/s at an angle of 38.3 degrees |
[
{
"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... | debit Accumulated depreciation 112,500
debit Loss on disposal 1,500
debit Cash 71,000
credit Machine 185,000 |
[
{
"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... | 3.1 pC |
[
{
"content": "Consider the short exact sequence of divisible abelian groups: \\(0 \\rightarrow A \\rightarrow B \\rightarrow C \\rightarrow 0\\). Determine whether this sequence splits.",
"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... | 65000 V |
[
{
"content": "Let \\( \\mathbb{X} \\) be the set of all bijective functions from the set \\( S = \\{1, 2, \\ldots, n\\} \\) to itself. For each \\( f \\in \\mathbb{X} \\), define\n\\[ T_f(j) = \\begin{cases} 1, & \\text{if} \\ f^{(2)}(j) = j, \\\\ 0, & \\text{otherwise} \\end{cases} \\]\nDetermine \\( \\sum_{f ... | 2n! |
[
{
"content": "Given a non-negative measurable function $f$, let $E = \\{ x : f(x) > 0 \\}$. If $m(E) = 0$, where $m(E)$ denotes the measure of $E$, does it follow that $f = 0$ almost everywhere? Answer 'yes' or 'no'.",
"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... | 5.43e-10 m |
[
{
"content": "Solve the equation \\(|(g^{-1}(x))^{-1}| = 1 + (g^{-1}(x))^{-1}\\), where \\(g(x)\\) is a function.",
"role": "user"
}
] | g(-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... | 95297 |
[
{
"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... | 16.52 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... | 1. Land: $480,000
Trust-Principal: $480,000
2. Cash-Income: $76,000
Trust-Income: $76,000
3. Insurance expense-Income: $5,600
Cash-Income: $5,600
4. Property taxes expense-Income: $7,600
Cash-Income: $7,600
5. Land improvements: $5,600
Cash-Income: $5,600
6. Due from trust-Principal: $5,600
Due to tru... |
[
{
"content": "In a bank with 10 operators, each operator's service time follows an exponential distribution. The average rate at which the $i$-th operator serves clients is $i$ clients per hour. All operators start serving simultaneously at time $0$ in a single-server queue system. Bob is the 20th customer in l... | \dfrac{7}{55} |
[
{
"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 capital structure weights are 45.11% common equity, 6.77% preferred stock and 48.12% debt. |
[
{
"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... | 8.0954 kJ/K |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Bone Marrow Therapy and Core Blood Stem Cells Therapy |
[
{
"content": "Each of the digits 3, 4, 6, 7, 8, and 9 is used once and only once to form a six-digit integer. What is the largest six-digit multiple of 4 that can be formed?",
"role": "user"
}
] | 987,\!436 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty}{(\\sqrt[5]{5} * \\sqrt[25]{5} * ... * \\sqrt[5^n]{5})}$$",
"role": "user"
}
] | \sqrt[4]{5} |
[
{
"content": "Find the values of \\( m \\) such that the inequality \\( \\left(\\frac{9}{25}\\right)^x - m\\left(\\frac{3}{5}\\right)^x + 1 > 0 \\) holds for all \\( x < 0 \\).",
"role": "user"
}
] | (-\infty, 2] |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\sum_{k=1}^n \\frac{2k+1}{k^2(k+1)^2} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the limit \\( \\lim_{x\\to 0}{f(x)-f(\\ln(1+x))\\over x^3} \\) given that \\( f(x) \\) is \\( C^1 \\) in some neighborhood about \\( x=0 \\), \\( f'(0)=0 \\), and \\( f''(0)=1 \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Suppose $X_1, X_2, \\ldots, X_n$ are independent and identically distributed (i.i.d.) random variables, and for some real coefficients $a_1, a_2, \\ldots, a_n$, the linear combination $\\sum_{i=1}^n a_i X_i$ follows a standard normal distribution, $\\mathcal{N}(0, 1)$. Is it necessary that each $X... | 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... | 24.8 mL |
[
{
"content": "Determine whether a countable linearly independent set in a separable Hilbert space necessarily forms a Schauder basis for the space. Answer with 'Yes' or 'No' and justify your response.",
"role": "user"
}
] | No |
[
{
"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... | SO_2 + 3H_2 -> H_2S + 2H_2O |
[
{
"content": "Let point \\( P \\) be a moving point on the circle \\( C: (x+2)^2 + y^2 = 4 \\), and it is not at the origin. The coordinates of the fixed point \\( A \\) are \\( (2, 0) \\). The perpendicular bisector of the line segment \\( AP \\) intersects the line \\( CP \\) at point \\( Q \\). Given that \\... | 3 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\pi}^\\pi \\sin(2\\cos\\theta)\\cos((2m+1)\\theta)\\,d\\theta \\) using complex analysis methods, where \\( m \\in \\mathbb{N} \\).",
"role": "user"
}
] | 2\pi (-1)^m J_{2m+1}(2) |
[
{
"content": "Given a real function $f(x)$, which is continuous on an interval $(a, b)$ and has nondifferentiable points within this interval, determine if there always exists a nonzero infinitely differentiable function $g(x)$ such that the product $f(x)g(x)$ is differentiable on the entire interval $(a, b)$. ... | No |
[
{
"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... | 9.18% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0896 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | /cimages/multimages/16/clo3-8395402040312351495.png |
[
{
"content": "The domain and range of the function \\( y=f(x) \\) are both \\( \\mathbb{R} \\). The function \\( y=f(x) \\) is increasing. Let the solution set of the equation \\( f(x)=x \\) be \\( P \\), and the solution set of the equation \\( f[f(x)]=x \\) be \\( Q \\). Determine the correct relationship bet... | A |
[
{
"content": "Is it possible to construct a sphere within an $n$-simplex such that the sphere touches the boundary of the simplex at exactly one point and is contained within the simplex at all other points?",
"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... | Sales Revenue: 1,800,000
Cost of Goods Sold: -1,100,000
Gross Profit: 700,000
Selling expenses: -220,000
Interest expense: -40,000
General and admin expense: -50,000
Operating Income: 390,000
Interest revenue: 80,000
Gain on sale of investments: 50,000
Write-off of obsolete equipment: -30,000
Income before extraordinar... |
[
{
"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... | 9.55e-10 |
[
{
"content": "Evaluate the limit: $$\\lim \\limits_{n \\to \\infty}\\left(1-e^{\\left(\\frac{t+ \\log^2(n)}{t-\\log(n)}\\right)}\\right)^n$$",
"role": "user"
}
] | e^{-e^{-t}} |
[
{
"content": "Evaluate the integral \\( \\int_{-2}^2 \\frac{x^2}{3}\\ln\\frac{2+x}{2-x}\\,dx \\) by hand, without using a calculator.",
"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... | 80 mph |
[
{
"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... | 7.5N |
[
{
"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-chlorobutane |
[
{
"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... | $2,403.85 |
[
{
"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... | Temporarily |
[
{
"content": "Evaluate the asymptotic behavior of the integral \\( \\int_0^{at} \\frac{e^{-u}}{(t-\\frac{u}{a})^\\beta} \\, \\mathrm{d}u \\) as \\( t \\to \\infty \\), where \\( \\beta < 1 \\).",
"role": "user"
}
] | t^{-\beta} |
[
{
"content": "Consider the sequence \\((a_n)\\) defined by \\(a_1 = 3\\) and \\(a_{n+1} = 3^{a_n}\\) for all \\(n\\). Determine the last two digits of \\(a_n\\).",
"role": "user"
}
] | 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... | 12.70 |
[
{
"content": "Determine whether the statement is true or false: Let $V$ be a space of polynomials of degree $\\leq 3$. Let $T$ and $D$ be linear operators on $V$ such that $T(f(t))=f(t+1)$ and $D(f(t))=f'(t)$. Then $T$ is a polynomial in $D$. Is this statement true?",
"role": "user"
}
] | True |
[
{
"content": "Evaluate the limit \\( \\lim _{n \\rightarrow \\infty }\\int ^{n}_{-n} \\left(\\sin\\left(\\frac{x}{n}\\right)\\right)^{n^{2}}\\,dx \\) using the inequality \\( r^{k} \\leq \\exp(-k(1-r)) \\), where \\( 0\\leq r \\leq 1 \\) and \\( k\\in \\mathbb{N} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the natural number \\( x = 5^n - 1 \\) such that \\( x \\) has exactly three distinct prime factors, one of which is 11.",
"role": "user"
}
] | 3124 |
[
{
"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... | B = (-0.667)i + (-0.667)j + (-0.889)k |
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