prompt list | ground_truth string |
|---|---|
[
{
"content": "Given a positive definite matrix $A$, if the inverse is expressed as $A^{-1} = \\frac{1}{\\text{det}(A)} \\cdot B$, determine whether matrix $B$ is also positive definite.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\to 0^+} \\frac{1}{x}\\int_0^x \\frac{f(t)}{t}\\, dt \\), where \\( f \\) is integrable on \\([0,1]\\) and \\( \\lim_{x\\to 0} f(x)=L \\).",
"role": "user"
}
] | L |
[
{
"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... | E(r_p) = 6% + 10% * \beta_{1,p} + 5% * \beta_{2,p} |
[
{
"content": "In triangle $A_1A_2A_3$, construct the following points:\n\n- Let $B_1$, $B_2$, and $B_3$ be the midpoints of sides $A_1A_2$, $A_2A_3$, and $A_3A_1$, respectively.\n- Let $C_1$, $C_2$, and $C_3$ be the midpoints of segments $A_1B_1$, $A_2B_2$, and $A_3B_3$, respectively.\n- Define $D_1$ as the int... | \dfrac{25}{49} |
[
{
"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... | {eq}Ni^{2+} + SO_4^{2-} + 4NH_3 -> NiSO_4(NH_3)_4{/eq} |
[
{
"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... | 118.5 ft |
[
{
"content": "Determine all real values of \\(\\alpha\\) such that for every continuous function \\(f: [0,1] \\to [0,1]\\), there exists a point \\(c \\in [0,1]\\) satisfying \\(f(c) = \\alpha c\\).",
"role": "user"
}
] | [1, \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... | 596 L |
[
{
"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... | $15.7 trillion |
[
{
"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... | 1.4L |
[
{
"content": "Calculate the surface area of the portion of the cylinder given by $x^2+y^2 = 2x$ that is contained within the sphere $x^2 + y^2 + z^2 = 4$.",
"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... | $191,544 |
[
{
"content": "Given that the function \\( f(x) \\) satisfies the condition \\( f\\left(\\frac{a+2b}{3}\\right)=\\frac{f(a)+2f(b)}{3} \\) for any real numbers \\( a \\) and \\( b \\), find the value of \\( f(2021) \\) if \\( f(1)=5 \\) and \\( f(4)=2 \\).",
"role": "user"
}
] | -2015 |
[
{
"content": "Find the minimum value of the expression \\(|z+1|+|z-1|+|z-i|\\), where \\(z\\) is a complex number.",
"role": "user"
}
] | 1 + \sqrt{3} |
[
{
"content": "Evaluate the infinite product: \\[ \\lim_{n \\to \\infty} \\prod_{k=2}^{n} \\left(1 - \\frac{1}{k^2}\\right). \\]",
"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... | 46.375 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/structu4508016055418417594.jpg</img> |
[
{
"content": "For a positive integer $p$, define the positive integer $n$ to be $p$-safe if $n$ differs in absolute value by more than $2$ from all multiples of $p$. For example, the set of $10$-safe numbers is $\\{ 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 23, \\ldots\\}$. Find the number of positive integers less th... | 958 |
[
{
"content": "Let \\( p \\) be an odd prime such that \\( p \\equiv 1 \\pmod{4} \\). Compute \\( \\sum_{k=1}^{p-1} \\left\\{ \\frac{k^2}{p} \\right\\} \\), where \\( \\{ x \\} = x - \\lfloor x \\rfloor \\) and \\( \\lfloor x \\rfloor \\) is the greatest integer less than or equal to \\( x \\).",
"role": "us... | \dfrac{p-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... | 0.043 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... | 412.7 nm |
[
{
"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... | Key:
A: A allele
B: B allele
O: O allele
Parental genotypes: A/O x B/O
Parental phenotypes: Type A x Type B
Punnett square:
| | A | O |
|---|----|----|
| B | A/B| B/O|
| O | A/O| O/O|
Offspring genotypes:
- A/B: 25%
- B/O: 25%
- A/O: 25%
- O/O: 25%
Genotypic ratio: 1:1:1:1 (A/B:B/O:A/O:O/O)
Offspring phe... |
[
{
"content": "Verify the asymptotic approximation \\(\\int^{1}_{0}t^{-\\frac{1}{2}} \\cos(t) e^{-xt^{\\frac{1}{2}}} \\, dt \\sim \\frac{2}{x}\\) as \\(x \\rightarrow \\infty\\) using Watson's Lemma or another suitable method.",
"role": "user"
}
] | \dfrac{2}{x} |
[
{
"content": "Determine the limit of the sequence \\(\\left(\\frac{n!}{n!+2}\\right)^{n!}\\) as \\(n\\) approaches infinity.",
"role": "user"
}
] | e^{-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... | 10.66 |
[
{
"content": "Working 22 hours in the second week of June, Xenia was able to earn $\\$$47.60 more than during the first week of June when she worked 15 hours. If her hourly wage was constant, how many dollars did she earn during the first two weeks of June? Express your answer to the nearest hundredth.",
"r... | \$ 251.60 |
[
{
"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... | 0.00457 M |
[
{
"content": "Determine whether the following statement is true or false: For any perfect graph \\( G \\), the independence number of \\( G \\) is equal to the chromatic number of its complement.",
"role": "user"
}
] | True |
[
{
"content": "Find the focus of the parabola $y = 4x^2 - 3.$",
"role": "user"
}
] | \left( 0, -\frac{47}{16} \right) |
[
{
"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... | $71.95 |
[
{
"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... | 276.25 N |
[
{
"content": "Find the sum of all possible values of \\( \\frac{b}{c}+\\frac{d}{a} \\) given that \\( a, b, c, d \\) are real numbers satisfying \\( \\frac{a}{b}+\\frac{b}{c}+\\frac{c}{d}+\\frac{d}{a}=17 \\) and \\( \\frac{a}{c}+\\frac{c}{a}+\\frac{b}{d}+\\frac{d}{b}=20 \\).",
"role": "user"
}
] | 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... | 4.04 g |
[
{
"content": "Let \\( S \\) be a subset of \\( \\{1, 2, 3, \\ldots, 100\\} \\). For any two distinct elements \\( a \\) and \\( b \\) in \\( S \\), there exists a positive integer \\( k \\) and two distinct elements \\( c \\) and \\( d \\) in \\( S \\) (where \\( c \\) and \\( d \\) may be equal to \\( a \\) or... | 50 |
[
{
"content": "Suppose $H$ is a subgroup of order $(n-1)!$ in $S_n$. Determine if there exists an $i \\in \\{1, 2, \\ldots, n\\}$ such that $H = \\mathbb{Stab}(i)$ for all $n \\ge 7$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "If $g(x)$ is a differentiable real-valued function satisfying $g''(x) - 3g'(x) > 3$ for all $x \\geq 0$ and $g'(0) = -1$, determine the nature of the function $h(x) = g(x) + x$ for $x > 0$:\n\n(A) $h(x)$ is an increasing function of $x$.\n(B) $h(x)$ is a decreasing function of $x$.\n(C) There is i... | A |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.8 MV |
[
{
"content": "Consider an irreducible plane real algebraic curve $R$ without isolated points, such that for any point $(x,y)$ on the curve, the point $(x,-y)$ is also on the curve. Is it possible to find a polynomial $f(x,y)$ defining the zero set $R$ such that $f(x,y) = f(x,-y)$ for all $(x,y) \\in \\mathbb{R}... | 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... | 16 seconds |
[
{
"content": "Given the equation \\(2\\tan^2x - 5\\sec x = 1\\), which has exactly 7 distinct solutions for \\(x\\in[0,\\frac{n\\pi}{2}]\\), where \\(n\\in\\mathbb{N}\\), find the greatest possible value of \\(n\\).",
"role": "user"
}
] | 15 |
[
{
"content": "Are symmetric matrices with constant diagonals, where all diagonal entries are 1 and non-diagonal entries are between 0 and 1, guaranteed to have all eigenvalues greater than or equal to 0, making them positive semidefinite?",
"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... | 0.09 m |
[
{
"content": "Determine the number of zeros in the right half-plane \\( \\text{Re} \\, z > 0 \\) for the polynomial:\n\\[\nf(z) = z^3 - z + 1\n\\]",
"role": "user"
}
] | 2 |
[
{
"content": "Is it true that a point $x^*$ is an accumulation point of the sequence $\\{x_n\\}$ if and only if there exists a subsequence $x_{a_n}$ such that $\\lim_{n\\rightarrow\\infty} x_{a_n}=x^*$?",
"role": "user"
}
] | True |
[
{
"content": "Find the equation of the plane passing through $(-1,1,1)$ and $(1,-1,1),$ and which is perpendicular to the plane $x + 2y + 3z = 5.$ Enter your answer in the form\n\\[Ax + By + Cz + D = 0,\\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\\gcd(|A|,|B|,|C|,|D|) = 1.$",
"role": "u... | x + y - z + 1 = 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... | 16.79 g |
[
{
"content": "Given the elliptic curve \\(E\\) over \\(\\mathbb{F}_{11}\\) defined by \\(y^2 = x^3 + 5\\) and the function \\(f(x,y)=\\frac{2x+y-3}{3x-y+2}\\), calculate \\(f(\\mathcal{O})\\) using projective coordinates.",
"role": "user"
}
] | 10 |
[
{
"content": "Determine the conditions under which the sequence defined by \\(x_{n+2}=|x_{n+1}-x_{n-1}|\\) has a period of 1.",
"role": "user"
}
] | x_0 = x_1 = x_2 = 0 |
[
{
"content": "Is it true that an absolutely convergent series converges to the same value regardless of the order in which its terms are added?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $X_1, X_2, \\ldots$ be i.i.d. non-negative random variables. Assume that $$P( X_n > n \\ \\text{i.o.} ) = 0.$$ Does this imply that $$\\limsup_{n \\to \\infty} X_n < \\limsup_{n \\to \\infty} n = \\infty$$? Answer yes or no.",
"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... | 15916 |
[
{
"content": "Determine whether the following proposition is true or false: Let \\(f:[-1,1]\\to \\mathbb{R}\\) be a function such that \\(\\exists I_{n}=\\int_{-1}^{1/n}f(x)dx \\forall n\\in \\mathbb{N}.\\) If \\(\\lim_{x\\to 0}f(x)=0; \\lim_{n\\to \\infty}I_{n}=A\\) then \\(\\Rightarrow \\int_{-1}^{1}f(x)dx=A.... | False |
[
{
"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... | 1.441e-8 cm |
[
{
"content": "William is taking the 25-question, multiple choice American Mathematics Competition. Each question has five answer choices. William guesses random answers for the last four questions. What is the probability that he will get at least one of these final four questions right?",
"role": "user"
... | \frac{369}{625} |
[
{
"content": "Determine whether the necessary and sufficient condition for the integer \\( \\sum_{k=0}^{n}\\left(a^{2}+1\\right)^{3 k} a_{k} \\) to be divisible by \\( a^{2}+a+1 \\) (or by \\( a^{2}-a+1 \\)) is that the integer \\( \\sum_{k=0}^{n}(-1)^{k} a_{k} \\) is divisible by \\( a^{2}+a+1 \\) (or by \\( a... | 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... | 395.075 kV/m |
[
{
"content": "In triangle \\( \\triangle ABC \\) with side lengths 8, 10, and 12, there is a point \\( P \\) inside the triangle. Perpendiculars are drawn from \\( P \\) to \\( AB \\), \\( BC \\), and \\( CA \\), with feet at \\( D \\), \\( E \\), and \\( F \\) respectively. When \\( AD^2 + BE^2 + CF^2 \\) reac... | B |
[
{
"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... | sodium cyanide |
[
{
"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 kg.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... | 2.60e8 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... | $1,382.43 |
[
{
"content": "Find the holomorphic function \\( f(z) = u(x,y) + iv(x,y) \\) such that \\( xu + yv = (x^2 + y^2)e^x \\cos y \\).",
"role": "user"
}
] | z e^z |
[
{
"content": "If the sum of the squares of nonnegative real numbers $a,b,$ and $c$ is $13$, and $ab + bc + ca = 6$, then what is the sum of $a,b,$ and $c$?",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -7.85e-3 C |
[
{
"content": "Determine whether $y + x = 3$ is a solution to the differential equation \\( \\frac{dy}{dx} = \\frac{y+x-2}{y+x-4} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Is the uniform limit of a sequence of Lipschitz functions with bounded derivatives necessarily differentiable everywhere?",
"role": "user"
}
] | No |
[
{
"content": "A regular $48$-gon is inscribed in a circle with radius $1$. The set $X$ consists of the distances from the circle's center to each side of the polygon. The set $Y$ contains the distances to its diagonals. Let $S$ be the union of $X$ and $Y$. Calculate the sum of the squares of all elements in $S$... | \dfrac{23}{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... | 28000 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... | $73.42 |
[
{
"content": "Given a Poisson random variable \\( Z \\) with parameter \\( \\mathbb{E}Z \\) and another random variable \\( G \\) that converges in distribution to \\( Z \\) with an error bound \\( d_{TV}(G,Z) \\leq c \\), where \\( c \\) is a constant and \\( d_{TV} \\) is the total variation distance, find an... | c |
[
{
"content": "Suppose \\( \\mu \\) is a finite measure and for some \\( \\gamma > 0 \\), we have \\( \\sup_n \\int |f_n|^{1 + \\gamma}d\\mu < \\infty \\). Does it follow that the sequence \\( \\{f_n\\} \\) is uniformly integrable?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the values of \\( p \\) for which the series \\( \\sum \\frac{1}{n(\\log(n))^p} \\) converges.",
"role": "user"
}
] | p > 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.95c |
[
{
"content": "Evaluate the line integral \\( \\int_{C}{(3x+2y) \\, dx + (2x-y) \\, dy} \\) along the curve \\( y = \\sin\\left(\\frac{\\pi x}{2}\\right) \\) from \\((0,0)\\) to \\((1,1)\\).",
"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... | -$595 |
[
{
"content": "Let $\\mathbb{F}_{243}$ be the field of 243 elements. Determine the number of elements $\\alpha \\in \\mathbb{F}_{243}$ such that $\\alpha^9 = \\alpha$. Provide your answer as a single integer.",
"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... | 9.68% |
[
{
"content": "Is it always true that for a differentiable function $f(x)$, the maximum absolute value of its first derivative is greater than the maximum absolute value of its second derivative? That is, does the inequality $$\\max\\left|\\frac{df(x)}{dx}\\right| > \\max\\left|\\frac{d^2f(x)}{dx^2}\\right|$$ ho... | No |
[
{
"content": "Compute the limit: \\[ \\lim_{n \\to \\infty} \\frac{1}{n} \\sum_{k=1}^{\\left\\lfloor \\frac{n}{2} \\right\\rfloor} \\cos \\left(\\frac{k \\pi}{n}\\right) \\]",
"role": "user"
}
] | \dfrac{1}{\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... | 1.99 |
[
{
"content": "Determine whether the following statement is true: For $u \\in L^\\infty(\\mathbb{R}^d)$ and $a > 0$, is it true that \\( \\|u^{a}\\|_{L^\\infty(\\mathbb{R}^d)} = \\|u\\|_{L^\\infty(\\mathbb{R}^d)}^a \\)? Justify your answer.",
"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... | $2,963 |
[
{
"content": "Determine if there exists a rational number $c$ such that \\[ c = \\sqrt{\\frac{p^2 + 2a^2q^2 - a^2}{a^2q^2}} \\] where $p$ and $q$ are integers, and $a$ is a rational number.",
"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... | 39 N |
[
{
"content": "Find the characteristic of a ring $R$ (not necessarily unital) that satisfies the equation $r^4 - 2r^3 + r^2 = 0$ for all $r \\in R$. Provide your answer as a single integer.",
"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... | 18602 |
[
{
"content": "In a Markov chain with infinite states, where the transition probabilities are given by $p_{0,1}=1$ and $p_{i,i+1}=p_{i,i-1}=0.5$ for $i \\geq 1$, calculate the expected time to reach state $n$ starting from state $x$, given that $0<x<n$. Provide your answer as a single numerical value.",
"rol... | n^2 - 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... | 174.39 |
[
{
"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... | pH, salt content, buffering system, stabilizing, and reducing properties |
[
{
"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... | $14,195 |
[
{
"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... | 62.5Ag[ (6H+3) / 2 ] |
[
{
"content": "In triangle $\\triangle ABC$, point $D$ is the midpoint of $AC$. Given that $AB = 3$, $BD = BC$, and the area of $\\triangle ABC$ is 3, determine the measure of $\\angle A$. Express your answer in degrees.",
"role": "user"
}
] | 45 |
[
{
"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... | $6667 |
[
{
"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... | 99.84 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... | 3.68 years |
[
{
"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... | $598,999.90 |
[
{
"content": "Suppose $f$ and $g$ are polynomials in $n$ variables, where $n \\ge 2$, over a field $E$. If $f$ and $g$ are relatively prime over $E$, are they still relatively prime over a field extension $F$ of $E$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the minimum value of \\(x^2 + y^2 + z^2\\) subject to the constraint \\(yz + zx + xy = 3a^2\\) using the Lagrange multiplier method.",
"role": "user"
}
] | 3a^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... | London Dispersion |
[
{
"content": "Determine whether there exists a rectangle that can be divided into 100 smaller rectangles, all similar to the original rectangle, with no two of the smaller rectangles being identical.",
"role": "user"
}
] | Yes |
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