id
stringlengths 2
47
| answer_type
stringclasses 11
values | category
stringclasses 16
values | difficulty
stringclasses 5
values | data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict | verifications
int64 0
7
⌀ | domain
stringlengths 3
84
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|
1009412
|
Other
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Draw the structure of this compound: 5-(1, 2-dimethylpropyl) nonane. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "<img>/cimages/multimages/16/structu4508016055418417594.jpg</img>",
"style": "rule"
}
|
{
"answer": "<img>/cimages/multimages/16/structu4508016055418417594.jpg</img>",
"index": 400,
"question": "Draw the structure of this compound: 5-(1, 2-dimethylpropyl) nonane.",
"split": "train"
}
| null | null |
1079415
|
Boolean
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Consider a country that has been producing a lot of oil and suppose that from one year to the next, its oil wells run out. The country will be poorer than previously. According to the two definitions above, is it in a recession? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 401,
"question": "Consider a country that has been producing a lot of oil and suppose that from one year to the next, its oil wells run out. The country will be poorer than previously. According to the two definitions above, is it in a recession?",
"split": "train"
}
| null | null |
1239088
|
Expression
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Balance the following in basic solution:\n\n{eq}SO_3{^{2-}}{_{(aq)}} + Cu(OH)_2{_{(s)}} \\longrightarrow SO_4{^{2-}}{_{(aq)}} + Cu(OH){_{(s)}}\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "SO_3^{2-} + 2Cu(OH)_2 \\rightarrow SO_4^{2-} + 2Cu(OH) +H_2O",
"style": "rule"
}
|
{
"answer": "SO_3^{2-} + 2Cu(OH)_2 \\rightarrow SO_4^{2-} + 2Cu(OH) +H_2O",
"index": 402,
"question": "Balance the following in basic solution:\n\n{eq}SO_3{^{2-}}{_{(aq)}} + Cu(OH)_2{_{(s)}} \\longrightarrow SO_4{^{2-}}{_{(aq)}} + Cu(OH){_{(s)}}\n\n{/eq}.",
"split": "train"
}
| null | null |
1762165
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "If 36 kJ of energy is given off when pointing a laser at an exciting chemical equation on the projector screen, how many photons were emitted? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.27e+23",
"style": "rule"
}
|
{
"answer": "1.27e+23",
"index": 403,
"question": "If 36 kJ of energy is given off when pointing a laser at an exciting chemical equation on the projector screen, how many photons were emitted?",
"split": "train"
}
| null | null |
1955560
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Which of the following is not a reason for economic income and accounting income to differ?\n\n- Transaction basis\n\n- The monetary assumption\n\n- Conservatism\n\n- Earnings management Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"answer": "B",
"index": 404,
"question": "Which of the following is not a reason for economic income and accounting income to differ?\n\n- Transaction basis\n\n- The monetary assumption\n\n- Conservatism\n\n- Earnings management",
"split": "train"
}
| null | null |
1471918
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given the point ($x,y$), ($L_h$), ($d_e$), v, ($\\theta_d$), and ($x_d,y_d$), and knowing that the line '$d_e$' runs perpendicular to a tangent trajectory at ($x_d,y_d$) with an angle '$\\theta_e$', is it possible to find '$\\theta_e$' without knowing '$\\theta$'? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\theta_e=\\theta_d-\\theta",
"style": "rule"
}
|
{
"answer": "\\theta_e=\\theta_d-\\theta",
"index": 405,
"question": "Given the point ($x,y$), ($L_h$), ($d_e$), v, ($\\theta_d$), and ($x_d,y_d$), and knowing that the line '$d_e$' runs perpendicular to a tangent trajectory at ($x_d,y_d$) with an angle '$\\theta_e$', is it possible to find '$\\theta_e$' without knowing '$\\theta$'?",
"split": "train"
}
| null | null |
1339400
|
Float
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "Suppose that you invest $5000 each year for 5 years and that you expect to earn an interest rate of 5.5%. How much money should you have in 15years? Show all work Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$50,288.21",
"style": "rule"
}
|
{
"answer": "$50,288.21",
"index": 406,
"question": "Suppose that you invest $5000 each year for 5 years and that you expect to earn an interest rate of 5.5%. How much money should you have in 15years? Show all work",
"split": "train"
}
| null | null |
1249785
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "The reaction of {eq}CH_4\n\n{/eq} in {eq}2CH_4(g) \\rightarrow C_2H_2(g) + 3H_2(g)\n\n{/eq} is carried out at a different temperature with an initial concentration of {eq}[CH_4]\n\n{/eq} = 0.087 M. At equilibrium, the concentration of {eq}H_2\n\n{/eq} is 0.012 M. Find the equilibrium constant at this temperature. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.11e-6",
"style": "rule"
}
|
{
"answer": "1.11e-6",
"index": 407,
"question": "The reaction of {eq}CH_4\n\n{/eq} in {eq}2CH_4(g) \\rightarrow C_2H_2(g) + 3H_2(g)\n\n{/eq} is carried out at a different temperature with an initial concentration of {eq}[CH_4]\n\n{/eq} = 0.087 M. At equilibrium, the concentration of {eq}H_2\n\n{/eq} is 0.012 M. Find the equilibrium constant at this temperature.",
"split": "train"
}
| null | null |
1333409
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let {eq}X{/eq} be the number of flaws on the surface of a randomly selected boiler of a certain type and suppose {eq}X{/eq} is a Poisson distributed random variable with parameter {eq}\\mu{/eq} = 5. Find {eq}P(2 \\leq X \\leq 5){/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.5755",
"style": "rule"
}
|
{
"answer": "0.5755",
"index": 408,
"question": "Let {eq}X{/eq} be the number of flaws on the surface of a randomly selected boiler of a certain type and suppose {eq}X{/eq} is a Poisson distributed random variable with parameter {eq}\\mu{/eq} = 5. Find {eq}P(2 \\leq X \\leq 5){/eq}.",
"split": "train"
}
| null | null |
197182
|
Percentage
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Calculate the percentage by mass of sulfur in tetraoxosulphate(IV) acid, {eq}\\rm H_2SO_4{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "33%",
"style": "rule"
}
|
{
"answer": "33%",
"index": 409,
"question": "Calculate the percentage by mass of sulfur in tetraoxosulphate(IV) acid, {eq}\\rm H_2SO_4{/eq}.",
"split": "train"
}
| null | null |
708841
|
String
|
Physics
|
Primary School
|
general-reasoner
|
[
{
"content": "Would a rug have static or dynamic friction? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "static friction",
"style": "rule"
}
|
{
"answer": "static friction",
"index": 410,
"question": "Would a rug have static or dynamic friction?",
"split": "train"
}
| null | null |
1400548
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "In the goods market,\n\na) Inflation uniquely determines the equilibrium level of employment.\n\nb) Wage bargaining is central to our understanding of equilibrium.\n\nc) The working age population that is employed is irrelevant.\n\nd) The higher the interest rate the lower the equilibrium level of output. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 411,
"question": "In the goods market,\n\na) Inflation uniquely determines the equilibrium level of employment.\n\nb) Wage bargaining is central to our understanding of equilibrium.\n\nc) The working age population that is employed is irrelevant.\n\nd) The higher the interest rate the lower the equilibrium level of output.",
"split": "train"
}
| null | null |
390481
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Where is the mistake in using second-order Taylor polynomials to evaluate the limit\n$$ \\lim_{(x,y)\\to(0,0)} \\frac {e^{x+y^2}-1-\\sin \\left ( x + \\frac{y^2}{2} \\right )}{x^2+y^2} $$\nwhen the polar coordinate approach suggests the limit does not exist? Specifically, the proposed solution uses the Taylor expansions $ e^{x+y^2} \\approx 1 + x + \\frac{1}{2}x^2 + y^2 $ and $ \\sin \\left ( x + \\frac{y^2}{2} \\right ) \\approx x + \\frac{1}{2}y^2 $ to conclude the limit is $1/2$, while my polar coordinate calculation suggests the limit depends on the angle and thus does not exist. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1/2",
"style": "rule"
}
|
{
"answer": "1/2",
"index": 412,
"question": "Where is the mistake in using second-order Taylor polynomials to evaluate the limit\n$$ \\lim_{(x,y)\\to(0,0)} \\frac {e^{x+y^2}-1-\\sin \\left ( x + \\frac{y^2}{2} \\right )}{x^2+y^2} $$\nwhen the polar coordinate approach suggests the limit does not exist? Specifically, the proposed solution uses the Taylor expansions $ e^{x+y^2} \\approx 1 + x + \\frac{1}{2}x^2 + y^2 $ and $ \\sin \\left ( x + \\frac{y^2}{2} \\right ) \\approx x + \\frac{1}{2}y^2 $ to conclude the limit is $1/2$, while my polar coordinate calculation suggests the limit depends on the angle and thus does not exist.",
"split": "train"
}
| null | null |
80152
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Evaluate the line integral {eq}\\int_C \\ F \\cdot dr{/eq}, where F is given by the vector function {eq}F(x, y, z)=3sin(x) \\ i - 4cos(y) \\ j - xz \\ k{/eq} and C is given by the vector function {eq}r(t)=t^6i - t^5j + t^4k, \\ 0 \\leq t \\leq 1{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "19/7 - 3cos(1) + 4sin(1)",
"style": "rule"
}
|
{
"answer": "19/7 - 3cos(1) + 4sin(1)",
"index": 413,
"question": "Evaluate the line integral {eq}\\int_C \\ F \\cdot dr{/eq}, where F is given by the vector function {eq}F(x, y, z)=3sin(x) \\ i - 4cos(y) \\ j - xz \\ k{/eq} and C is given by the vector function {eq}r(t)=t^6i - t^5j + t^4k, \\ 0 \\leq t \\leq 1{/eq}.",
"split": "train"
}
| null | null |
1565125
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the (pseudo)inverse of\n$\\left(\n\\begin{array}{cc}\n\\frac{9}{4} & 5 \\\\\n-\\frac{9}{2} & \\frac{3}{4} \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{4}{387}\\left(\n\\begin{array}{cc}\n3 & -20 \\\\\n18 & 9 \\\\\n\\end{array}\n\\right)",
"style": "rule"
}
|
{
"answer": "\\frac{4}{387}\\left(\n\\begin{array}{cc}\n3 & -20 \\\\\n18 & 9 \\\\\n\\end{array}\n\\right)",
"index": 414,
"question": "Compute the (pseudo)inverse of\n$\\left(\n\\begin{array}{cc}\n\\frac{9}{4} & 5 \\\\\n-\\frac{9}{2} & \\frac{3}{4} \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
563134
|
Percentage
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A sample of limestone and other solid materials is heated and the limestone decomposes to give calcium oxide and carbon dioxide: {eq}CaCO_3 \\rightarrow CaO + CO_2\n\n{/eq} a {eq}1.506 \\ g\n\n{/eq} sample of limestone containing material produces {eq}284 \\ mL\n\n{/eq} of {eq}CO_2\n\n{/eq} at {eq}STP\n\n{/eq}.\n\n(a) What is the mass percent of {eq}CaCO_3\n\n{/eq} in the original sample? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "84.1%",
"style": "rule"
}
|
{
"answer": "84.1%",
"index": 415,
"question": "A sample of limestone and other solid materials is heated and the limestone decomposes to give calcium oxide and carbon dioxide: {eq}CaCO_3 \\rightarrow CaO + CO_2\n\n{/eq} a {eq}1.506 \\ g\n\n{/eq} sample of limestone containing material produces {eq}284 \\ mL\n\n{/eq} of {eq}CO_2\n\n{/eq} at {eq}STP\n\n{/eq}.\n\n(a) What is the mass percent of {eq}CaCO_3\n\n{/eq} in the original sample?",
"split": "train"
}
| null | null |
517441
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Jack and a Jill are standing on flat ground in front of an empty well that extends a depth s below the ground. Jill tosses a penny down the well with an initial velocity, u{eq}_0\n\n{/eq}, while Jack decides to toss a penny up with an initial velocity v{eq}_0\n\n{/eq}.\n\nHow long does it take for Jack and Jill s pennies to hit the bottom of the well?\n\nExpress your answer in terms of know quantities such as v{eq}_0\n\n{/eq}, u{eq}_0\n\n{/eq}, s, and g, where g is the acceleration due to gravity. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Jill: {eq}t = \\sqrt{\\dfrac{u_0^2}{g^2} + \\dfrac{2 \\, s}{g}} - \\dfrac{u_0}{g}{/eq}\nJack: {eq}t = \\sqrt{\\dfrac{v_0^2}{g^2} + \\dfrac{2 \\, s}{g}} + \\dfrac{v_0}{g}{/eq}",
"style": "rule"
}
|
{
"answer": "Jill: {eq}t = \\sqrt{\\dfrac{u_0^2}{g^2} + \\dfrac{2 \\, s}{g}} - \\dfrac{u_0}{g}{/eq}\nJack: {eq}t = \\sqrt{\\dfrac{v_0^2}{g^2} + \\dfrac{2 \\, s}{g}} + \\dfrac{v_0}{g}{/eq}",
"index": 416,
"question": "Jack and a Jill are standing on flat ground in front of an empty well that extends a depth s below the ground. Jill tosses a penny down the well with an initial velocity, u{eq}_0\n\n{/eq}, while Jack decides to toss a penny up with an initial velocity v{eq}_0\n\n{/eq}.\n\nHow long does it take for Jack and Jill s pennies to hit the bottom of the well?\n\nExpress your answer in terms of know quantities such as v{eq}_0\n\n{/eq}, u{eq}_0\n\n{/eq}, s, and g, where g is the acceleration due to gravity.",
"split": "train"
}
| null | null |
537501
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I would like to calculate the value of this infinite product: $$\\prod_{n=1}^\\infty \\bigg(\\frac{n+1}{n}\\bigg)^{\\frac{1}{n}}$$ According to Wolfram, it seems to converge at around $3.514$, but I have no idea how to start proving this. Any hints? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\exp\\pars{\\int_{0}^{1}{H_{t} \\over t}\\dd t}$",
"style": "rule"
}
|
{
"answer": "$\\exp\\pars{\\int_{0}^{1}{H_{t} \\over t}\\dd t}$",
"index": 417,
"question": "I would like to calculate the value of this infinite product: $$\\prod_{n=1}^\\infty \\bigg(\\frac{n+1}{n}\\bigg)^{\\frac{1}{n}}$$ According to Wolfram, it seems to converge at around $3.514$, but I have no idea how to start proving this. Any hints?",
"split": "train"
}
| null | null |
606928
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the area of the surface of the part of the hyperbolic paraboloid z = y^2 - x^2 that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 9. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{\\pi}{6}(37^{3/2}-5^{3/2})",
"style": "rule"
}
|
{
"answer": "\\frac{\\pi}{6}(37^{3/2}-5^{3/2})",
"index": 418,
"question": "Find the area of the surface of the part of the hyperbolic paraboloid z = y^2 - x^2 that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 9.",
"split": "train"
}
| null | null |
1568819
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use Green's theorem to evaluate the line integral {eq}\\displaystyle \\int_C(4y + \\cos(1 = e^{\\sin x})) dx + (2x - \\sec^2 y) dy, where C is the circle {eq}x^2 + y^2 = 9{/eq} going from (0, 3) to (0, 3) counterclockwise. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-18pi",
"style": "rule"
}
|
{
"answer": "-18pi",
"index": 419,
"question": "Use Green's theorem to evaluate the line integral {eq}\\displaystyle \\int_C(4y + \\cos(1 = e^{\\sin x})) dx + (2x - \\sec^2 y) dy, where C is the circle {eq}x^2 + y^2 = 9{/eq} going from (0, 3) to (0, 3) counterclockwise.",
"split": "train"
}
| null | null |
911303
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose we have a sequence of càdlàg functions $(x_n)_{n\\in\\mathbb{N}}\\subset \\mathbb{D}[0,1]$ that converges in the Skorokhod topology to $x\\in \\mathbb{D}[0,1]$. Do we then know that $x_n \\to x$ in $L^1[0,1]$? If not, can you provide a counterexample? Does $\\int_0^1 |x(\\alpha_n(t)) - x(t)| dt$ necessarily go to $0$ as $n \\to \\infty$, where $\\alpha_n$ is a homeomorphism $[0,1]\\to[0,1]$ satisfying the Skorokhod condition? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 420,
"question": "Suppose we have a sequence of càdlàg functions $(x_n)_{n\\in\\mathbb{N}}\\subset \\mathbb{D}[0,1]$ that converges in the Skorokhod topology to $x\\in \\mathbb{D}[0,1]$. Do we then know that $x_n \\to x$ in $L^1[0,1]$? If not, can you provide a counterexample? Does $\\int_0^1 |x(\\alpha_n(t)) - x(t)| dt$ necessarily go to $0$ as $n \\to \\infty$, where $\\alpha_n$ is a homeomorphism $[0,1]\\to[0,1]$ satisfying the Skorokhod condition?",
"split": "train"
}
| null | null |
1744943
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do you find the integral of arccos(x)x? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "x^2/2arc cosx+1/4arc sinx-x/4sqrt(1-x^2)+C",
"style": "rule"
}
|
{
"answer": "x^2/2arc cosx+1/4arc sinx-x/4sqrt(1-x^2)+C",
"index": 421,
"question": "How do you find the integral of arccos(x)x?",
"split": "train"
}
| null | null |
2051341
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "In our calculation of cash flow from assets, we need to consider the balance(s) of:\n\nA. inventory\n\nB. none of them is included\n\nC. accounts payable\n\nD. sales\n\nE. all are included Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "E",
"style": "rule"
}
|
{
"answer": "E",
"index": 422,
"question": "In our calculation of cash flow from assets, we need to consider the balance(s) of:\n\nA. inventory\n\nB. none of them is included\n\nC. accounts payable\n\nD. sales\n\nE. all are included",
"split": "train"
}
| null | null |
1128430
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A small circular loop of 5mm radius is placed 1 m away from a 60 Hz power line. The voltage induced on this loop is measured at 0.6 microvolt. What is the current on the power line? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "101.321 A",
"style": "rule"
}
|
{
"answer": "101.321 A",
"index": 423,
"question": "A small circular loop of 5mm radius is placed 1 m away from a 60 Hz power line. The voltage induced on this loop is measured at 0.6 microvolt. What is the current on the power line?",
"split": "train"
}
| null | null |
95732
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I'm trying to look at the number of turns taken to either win or reach gambler's ruin, and I don't quite know how to get that number or an approximation of it. Instinctively I want to model this using Poisson but I can't quite see how to make the jump. Can anyone offer any suggestions? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$T=\\\\frac{PN-i}{p-q}$ where $P$ is the probability of the player obtaining total money $N$ starting with initial capital $i$.",
"style": "rule"
}
|
{
"answer": "$T=\\\\frac{PN-i}{p-q}$ where $P$ is the probability of the player obtaining total money $N$ starting with initial capital $i$.",
"index": 424,
"question": "I'm trying to look at the number of turns taken to either win or reach gambler's ruin, and I don't quite know how to get that number or an approximation of it. Instinctively I want to model this using Poisson but I can't quite see how to make the jump. Can anyone offer any suggestions?",
"split": "train"
}
| null | null |
678964
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "Using a 0.20 M acetate buffer with a pH of 4.7, you add 0.79 mL of 0.12 M HCl to 75 mL of the buffer. What is the new pH of the solution? (Enter your answer to three significant figures.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "4.69",
"style": "rule"
}
|
{
"answer": "4.69",
"index": 425,
"question": "Using a 0.20 M acetate buffer with a pH of 4.7, you add 0.79 mL of 0.12 M HCl to 75 mL of the buffer. What is the new pH of the solution? (Enter your answer to three significant figures.)",
"split": "train"
}
| null | null |
471338
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{ccccccc}\n-9 & -10 & -10 & 6 & -1 & -3 & -2 \\\\\n7 & 0 & -7 & 5 & -3 & 3 & 3 \\\\\n10 & -10 & -9 & 5 & -10 & -1 & 2 \\\\\n-6 & -8 & -5 & 7 & 3 & -8 & -2 \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\left(\n\\begin{array}{ccccccc}\n1 & 0 & 0 & 0 & -\\frac{704}{1541} & \\frac{163}{1541} & \\frac{341}{1541} \\\\\n0 & 1 & 0 & 0 & \\frac{1303}{3082} & \\frac{1006}{1541} & \\frac{645}{3082} \\\\\n0 & 0 & 1 & 0 & \\frac{1080}{1541} & -\\frac{3407}{3082} & -\\frac{661}{3082} \\\\\n0 & 0 & 0 & 1 & \\frac{1573}{1541} & -\\frac{3377}{3082} & -\\frac{31}{3082} \\\\\n\\end{array}\n\\right)$",
"style": "rule"
}
|
{
"answer": "$\\left(\n\\begin{array}{ccccccc}\n1 & 0 & 0 & 0 & -\\frac{704}{1541} & \\frac{163}{1541} & \\frac{341}{1541} \\\\\n0 & 1 & 0 & 0 & \\frac{1303}{3082} & \\frac{1006}{1541} & \\frac{645}{3082} \\\\\n0 & 0 & 1 & 0 & \\frac{1080}{1541} & -\\frac{3407}{3082} & -\\frac{661}{3082} \\\\\n0 & 0 & 0 & 1 & \\frac{1573}{1541} & -\\frac{3377}{3082} & -\\frac{31}{3082} \\\\\n\\end{array}\n\\right)$",
"index": 426,
"question": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{ccccccc}\n-9 & -10 & -10 & 6 & -1 & -3 & -2 \\\\\n7 & 0 & -7 & 5 & -3 & 3 & 3 \\\\\n10 & -10 & -9 & 5 & -10 & -1 & 2 \\\\\n-6 & -8 & -5 & 7 & 3 & -8 & -2 \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
1021372
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "The temperature at a point (x, y, z) on a given surface is given by {eq}T (x, y, z) = x^2 + \\frac{y}{x} + z^3 {/eq} where T is measured in degree C and x, y, z are in meters. Find the rate of change in the temperature at the point P (5, 1, 10) in the direction of the point Q (7, 5, 6) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-14741/75",
"style": "rule"
}
|
{
"answer": "-14741/75",
"index": 427,
"question": "The temperature at a point (x, y, z) on a given surface is given by {eq}T (x, y, z) = x^2 + \\frac{y}{x} + z^3 {/eq} where T is measured in degree C and x, y, z are in meters. Find the rate of change in the temperature at the point P (5, 1, 10) in the direction of the point Q (7, 5, 6)",
"split": "train"
}
| null | null |
2035633
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{cccccc}\n-1 & 3 & -7 & 0 & -7 & 3 \\\\\n1 & 2 & -5 & -7 & 7 & 6 \\\\\n3 & -4 & 5 & 1 & 9 & 4 \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\left(\\begin{array}{cccccc}1 & 0 & 0 & -\\frac{23}{5} & \\frac{38}{5} & \\frac{11}{5} \\\\ 0 & 1 & 0 & -\\frac{31}{5} & \\frac{36}{5} & -\\frac{3}{5} \\\\ 0 & 0 & 1 & -2 & 3 & -1 \\\\ \\end{array}\\right)$",
"style": "rule"
}
|
{
"answer": "$\\left(\\begin{array}{cccccc}1 & 0 & 0 & -\\frac{23}{5} & \\frac{38}{5} & \\frac{11}{5} \\\\ 0 & 1 & 0 & -\\frac{31}{5} & \\frac{36}{5} & -\\frac{3}{5} \\\\ 0 & 0 & 1 & -2 & 3 & -1 \\\\ \\end{array}\\right)$",
"index": 428,
"question": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{cccccc}\n-1 & 3 & -7 & 0 & -7 & 3 \\\\\n1 & 2 & -5 & -7 & 7 & 6 \\\\\n3 & -4 & 5 & 1 & 9 & 4 \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
1772860
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the line integral of the vector field {eq}\\mathbf F = \\langle 9y,\\ -9x \\rangle{/eq} over the circle {eq}x^2 + y^2 = 16{/eq} oriented clockwise. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "288\\pi",
"style": "rule"
}
|
{
"answer": "288\\pi",
"index": 429,
"question": "Compute the line integral of the vector field {eq}\\mathbf F = \\langle 9y,\\ -9x \\rangle{/eq} over the circle {eq}x^2 + y^2 = 16{/eq} oriented clockwise.",
"split": "train"
}
| null | null |
966928
|
Percentage
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r*) is 2.5%. If the yield on 3-year treasury bonds equals the 1-year yield plus 1.5%, what inflation rate is expected after Year 1? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5.45%",
"style": "rule"
}
|
{
"answer": "5.45%",
"index": 430,
"question": "Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r*) is 2.5%. If the yield on 3-year treasury bonds equals the 1-year yield plus 1.5%, what inflation rate is expected after Year 1?",
"split": "train"
}
| null | null |
1586969
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "What are the chances that you actually have the disease, given that you tested positive for a serious disease with a 99% accurate test and the disease strikes only one in 10,000 people? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.00981",
"style": "rule"
}
|
{
"answer": "0.00981",
"index": 431,
"question": "What are the chances that you actually have the disease, given that you tested positive for a serious disease with a 99% accurate test and the disease strikes only one in 10,000 people?",
"split": "train"
}
| null | null |
594924
|
Boolean
|
History
|
Junior High School
|
general-reasoner
|
[
{
"content": "Women were banned from performing Kabuki dance in 1629 because many of the performers came from the \"pleasure quarters\" where prostitution was a way of life and public morality was considered to be at risk. So men took over and played all the parts. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "True",
"style": "rule"
}
|
{
"answer": "True",
"index": 432,
"question": "Women were banned from performing Kabuki dance in 1629 because many of the performers came from the \"pleasure quarters\" where prostitution was a way of life and public morality was considered to be at risk. So men took over and played all the parts.",
"split": "train"
}
| null | null |
283107
|
List
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Selected accounts from the Pearson, Gomez, and Litt Partnership adjusted trial balance for the year ended December 31 follow.\n\n\n \n \n Accounts payable\n $5,000\n \n \n Accounts receivable\n $10,000\n \n \n Cash\n 40,000\n \n \n Gomez, Capital\n 15,000\n \n \n Land\n 25,000\n \n \n Long-term notes payable\n 20,000\n \n \n Pearson, Capital\n 30,000\n \n \n Litt, Capital\n 5,000\n \n \n\nOrganize a classified balance sheet. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Pearson, Gomez and Litt Partnership\nBalance Sheet\nAs on December 31, XXXX\n\nAssets\nCurrent Assets:\nAccounts Receivable $10,000\nCash $40,000\nTotal current assets $50,000\nNon-current Assets:\nLand $25,000\nTotal assets $75,000\nLiabilities\nCurrent Liabilities:\nAccounts Payable $5,000\nNon-current liabilities:\nLong-term notes payable $20,000\nTotal liabilities $25,000\nStockholder's Equity:\nPearson capital $30,000\nGomez capital $15,000\nLitt capital $5,000\nTotal Stockholder's Equity $50,000\nTotal liabilities and Stockholder's Equity $75,000",
"style": "rule"
}
|
{
"answer": "Pearson, Gomez and Litt Partnership\nBalance Sheet\nAs on December 31, XXXX\n\nAssets\nCurrent Assets:\nAccounts Receivable $10,000\nCash $40,000\nTotal current assets $50,000\nNon-current Assets:\nLand $25,000\nTotal assets $75,000\nLiabilities\nCurrent Liabilities:\nAccounts Payable $5,000\nNon-current liabilities:\nLong-term notes payable $20,000\nTotal liabilities $25,000\nStockholder's Equity:\nPearson capital $30,000\nGomez capital $15,000\nLitt capital $5,000\nTotal Stockholder's Equity $50,000\nTotal liabilities and Stockholder's Equity $75,000",
"index": 433,
"question": "Selected accounts from the Pearson, Gomez, and Litt Partnership adjusted trial balance for the year ended December 31 follow.\n\n\n \n \n Accounts payable\n $5,000\n \n \n Accounts receivable\n $10,000\n \n \n Cash\n 40,000\n \n \n Gomez, Capital\n 15,000\n \n \n Land\n 25,000\n \n \n Long-term notes payable\n 20,000\n \n \n Pearson, Capital\n 30,000\n \n \n Litt, Capital\n 5,000\n \n \n\nOrganize a classified balance sheet.",
"split": "train"
}
| null | null |
154766
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 500 ml stock solution of {eq}\\rm NaOH\n\n{/eq} has a purity of {eq}70\\%\n\n{/eq} and a density of {eq}\\rm 1.9\\ g/ml\n\n{/eq}. Calculate the concentration that would be in a 1 L solution. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "16.6 M",
"style": "rule"
}
|
{
"answer": "16.6 M",
"index": 434,
"question": "A 500 ml stock solution of {eq}\\rm NaOH\n\n{/eq} has a purity of {eq}70\\%\n\n{/eq} and a density of {eq}\\rm 1.9\\ g/ml\n\n{/eq}. Calculate the concentration that would be in a 1 L solution.",
"split": "train"
}
| null | null |
1542173
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Judging from the way the data were collected, which test would likely be most appropriate? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 435,
"question": "Judging from the way the data were collected, which test would likely be most appropriate?",
"split": "train"
}
| null | null |
1849928
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the eigenvalues of the following matrix:\n$\\left(\n\\begin{array}{cc}\n-\\frac{3}{2} & 7 \\\\\n-\\frac{9}{2} & -1 \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\lambda = \\frac{i \\sqrt{503}}{4}-\\frac{5}{4}$ or $\\lambda =-\\frac{i \\sqrt{503}}{4}-\\frac{5}{4}$",
"style": "rule"
}
|
{
"answer": "$\\lambda = \\frac{i \\sqrt{503}}{4}-\\frac{5}{4}$ or $\\lambda =-\\frac{i \\sqrt{503}}{4}-\\frac{5}{4}$",
"index": 436,
"question": "Find the eigenvalues of the following matrix:\n$\\left(\n\\begin{array}{cc}\n-\\frac{3}{2} & 7 \\\\\n-\\frac{9}{2} & -1 \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
100727
|
Other
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Draw Lewis dot structure for {eq}\\rm BrCl_2^-\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "[Image: Lewis dot structure of BrCl2-]",
"style": "rule"
}
|
{
"answer": "[Image: Lewis dot structure of BrCl2-]",
"index": 437,
"question": "Draw Lewis dot structure for {eq}\\rm BrCl_2^-\n\n{/eq}.",
"split": "train"
}
| null | null |
1069868
|
String
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Based on the raw SPSS output below, write a result section following the statistical results. Provide practical suggestions based on statistical findings.\n\nGroup Statistics\n\n{eq}\\begin{array}{|l|c|c|}\n\n\\hline\n\n&\\text{Location}&\\text{N}&\\text{Mean}&\\text{Std. Deviation}&\\text{Std. Error Mean}\\\\\n\n\\hline\n\n\\text{Place}&\\text{Urban}&65&36.8308&5.94393&.73725\\\\\n\n\\text{Attachment}&\\text{Rural}&85&36.0941&5.52618&.59940\\\\\n\n\\text{Scale}\\\\\n\n\\hline\n\n\\end{array}\n\n{/eq}\n\nIndependent Sample t-Test\n\n\n Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference\n FSig.tdfSig. (2-tailed) Mean DifferenceStd. Error DifferenceLowerUpper\nPlace Attachment ScaleEqual variances assumed.119.730.783148.435.73665.940941.122752.59605\n Equal variances not assumed .775132.4.440.73665.950171.142812.61612 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Urban: Mean = 36.83, SD = 5.94, N = 65; Rural: Mean = 36.09, SD = 5.53, N = 85. The independent samples t-test indicated that the difference in place attachment scores between the urban and rural groups was not statistically significant (t(148) = 0.78, p = 0.435, 95% CI [1.12, 2.59]).",
"style": "rule"
}
|
{
"answer": "Urban: Mean = 36.83, SD = 5.94, N = 65; Rural: Mean = 36.09, SD = 5.53, N = 85. The independent samples t-test indicated that the difference in place attachment scores between the urban and rural groups was not statistically significant (t(148) = 0.78, p = 0.435, 95% CI [1.12, 2.59]).",
"index": 438,
"question": "Based on the raw SPSS output below, write a result section following the statistical results. Provide practical suggestions based on statistical findings.\n\nGroup Statistics\n\n{eq}\\begin{array}{|l|c|c|}\n\n\\hline\n\n&\\text{Location}&\\text{N}&\\text{Mean}&\\text{Std. Deviation}&\\text{Std. Error Mean}\\\\\n\n\\hline\n\n\\text{Place}&\\text{Urban}&65&36.8308&5.94393&.73725\\\\\n\n\\text{Attachment}&\\text{Rural}&85&36.0941&5.52618&.59940\\\\\n\n\\text{Scale}\\\\\n\n\\hline\n\n\\end{array}\n\n{/eq}\n\nIndependent Sample t-Test\n\n\n Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference\n FSig.tdfSig. (2-tailed) Mean DifferenceStd. Error DifferenceLowerUpper\nPlace Attachment ScaleEqual variances assumed.119.730.783148.435.73665.940941.122752.59605\n Equal variances not assumed .775132.4.440.73665.950171.142812.61612",
"split": "train"
}
| null | null |
159319
|
Integer
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is the #pH# of an aqueous solution prepared from a #600*mg# mass of #NaOH# dissolved in #75*mL# of water? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "13",
"style": "rule"
}
|
{
"answer": "13",
"index": 439,
"question": "What is the #pH# of an aqueous solution prepared from a #600*mg# mass of #NaOH# dissolved in #75*mL# of water?",
"split": "train"
}
| null | null |
1159569
|
List
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "When did Leonardo da Vinci paint The Virgin of the Rocks? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1490s and 1508",
"style": "rule"
}
|
{
"answer": "1490s and 1508",
"index": 440,
"question": "When did Leonardo da Vinci paint The Virgin of the Rocks?",
"split": "train"
}
| null | null |
1767858
|
Float
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Ajika plc has been using an overhead absorption rate of 18.25 per machine hour in its production department. During the year the overhead expenditure amounted to 628,240 and 28,848 machine hours were used. How much overhead is under or over absorbed? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$101,764 under-absorbed",
"style": "rule"
}
|
{
"answer": "$101,764 under-absorbed",
"index": 441,
"question": "Ajika plc has been using an overhead absorption rate of 18.25 per machine hour in its production department. During the year the overhead expenditure amounted to 628,240 and 28,848 machine hours were used. How much overhead is under or over absorbed?",
"split": "train"
}
| null | null |
1341859
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Serial correlation:\n\na. measures the relationship between the current return on security with that of second security.\n\nb. involves multiple securities within the same industry.\n\nc. indicates a tendency for continuation when the correlation is positive.\n\nd. indicates a tendency toward reversal when the correlation coefficient is zero.\n\ne. supports weak form efficiency when the correlation coefficient is near zero. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 442,
"question": "Serial correlation:\n\na. measures the relationship between the current return on security with that of second security.\n\nb. involves multiple securities within the same industry.\n\nc. indicates a tendency for continuation when the correlation is positive.\n\nd. indicates a tendency toward reversal when the correlation coefficient is zero.\n\ne. supports weak form efficiency when the correlation coefficient is near zero.",
"split": "train"
}
| null | null |
2019703
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A refrigerator operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 120 and 800 kPa. If the rate of heat removal from the refrigerated space is 32 kJ/s, what is the mass flow rate of the refrigerant? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.226 kg/s",
"style": "rule"
}
|
{
"answer": "0.226 kg/s",
"index": 443,
"question": "A refrigerator operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 120 and 800 kPa. If the rate of heat removal from the refrigerated space is 32 kJ/s, what is the mass flow rate of the refrigerant?",
"split": "train"
}
| null | null |
1879869
|
List
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Data for December concerning Ash Corporation's two major business segments, Fibers and Feedstocks, appear below:\n\n\nSales revenues, Fibers $950,000\nSales revenues, Feedstocks $900,000\nVariable expenses, Fibers $525,000\nVariable expenses, Feedstocks $424,000\nTraceable fixed expenses, Fibers $148,000\nTraceable fixed expenses, Feedstocks $156,000\nCommon fixed expenses totaled $292,000 and were allocated as follows: $155,000 to the Fibers business segment and $137,000 to the Feedstocks business segment.\n\nRequired:\n\nPrepare a segmented income statement in the contribution format for the company. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Sales: Fibers $950,000, Feedstocks $900,000, Total $1,850,000; Variable Expenses: Fibers $525,000, Feedstocks $424,000, Total $949,000; Contribution Margin: Fibers $425,000, Feedstocks $476,000, Total $901,000; Traceable Fixed Expense: Fibers $148,000, Feedstocks $156,000, Total $304,000; Responsibility Margin: Fibers $277,000, Feedstocks $320,000, Total $597,000; Common Fixed Expenses: Fibers $155,000, Feedstocks $137,000, Total $292,000; Operating Income: Fibers $122,000, Feedstocks $183,000, Total $305,000",
"style": "rule"
}
|
{
"answer": "Sales: Fibers $950,000, Feedstocks $900,000, Total $1,850,000; Variable Expenses: Fibers $525,000, Feedstocks $424,000, Total $949,000; Contribution Margin: Fibers $425,000, Feedstocks $476,000, Total $901,000; Traceable Fixed Expense: Fibers $148,000, Feedstocks $156,000, Total $304,000; Responsibility Margin: Fibers $277,000, Feedstocks $320,000, Total $597,000; Common Fixed Expenses: Fibers $155,000, Feedstocks $137,000, Total $292,000; Operating Income: Fibers $122,000, Feedstocks $183,000, Total $305,000",
"index": 444,
"question": "Data for December concerning Ash Corporation's two major business segments, Fibers and Feedstocks, appear below:\n\n\nSales revenues, Fibers $950,000\nSales revenues, Feedstocks $900,000\nVariable expenses, Fibers $525,000\nVariable expenses, Feedstocks $424,000\nTraceable fixed expenses, Fibers $148,000\nTraceable fixed expenses, Feedstocks $156,000\nCommon fixed expenses totaled $292,000 and were allocated as follows: $155,000 to the Fibers business segment and $137,000 to the Feedstocks business segment.\n\nRequired:\n\nPrepare a segmented income statement in the contribution format for the company.",
"split": "train"
}
| null | null |
619407
|
Multiple Choice
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "The dissolution of gases in water is virtually always exothermic because:\n\na. one of the two endothermic steps (separation of solute particles) in the solution-formation process is unnecessary.\n\nb. the exothermic step in the solution-formation process is unnecessary.\n\nc. gases react exothermically with water.\n\nd. neither of the two endothermic steps in the solution-formation process is necessary.\n\ne. all three steps in the solution-formation process are exothermic. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 445,
"question": "The dissolution of gases in water is virtually always exothermic because:\n\na. one of the two endothermic steps (separation of solute particles) in the solution-formation process is unnecessary.\n\nb. the exothermic step in the solution-formation process is unnecessary.\n\nc. gases react exothermically with water.\n\nd. neither of the two endothermic steps in the solution-formation process is necessary.\n\ne. all three steps in the solution-formation process are exothermic.",
"split": "train"
}
| null | null |
1280485
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "If we intercept an electron having total energy 1533 MeV that came from Vega, which is 26 ly from us, how far in light-years was the trip in the rest frame of the electron? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.009 ly",
"style": "rule"
}
|
{
"answer": "0.009 ly",
"index": 446,
"question": "If we intercept an electron having total energy 1533 MeV that came from Vega, which is 26 ly from us, how far in light-years was the trip in the rest frame of the electron?",
"split": "train"
}
| null | null |
1291945
|
String
|
Health
|
Senior High School
|
general-reasoner
|
[
{
"content": "After impairing memory, focus, and reasoning, alcohol next causes a deterioration in __________. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "muscle control",
"style": "rule"
}
|
{
"answer": "muscle control",
"index": 447,
"question": "After impairing memory, focus, and reasoning, alcohol next causes a deterioration in __________.",
"split": "train"
}
| null | null |
295296
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A solenoid that is {eq}\\displaystyle \\rm 54 \\ cm\n\n{/eq} long has a cross-sectional area of {eq}\\displaystyle \\rm 17 \\ cm^2\n\n{/eq}. The magnetic field inside the solenoid has a magnitude of {eq}\\displaystyle \\rm 130 \\ mT\n\n{/eq}. What is the total energy stored by the magnetic field inside the solenoid? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6.2 J",
"style": "rule"
}
|
{
"answer": "6.2 J",
"index": 448,
"question": "A solenoid that is {eq}\\displaystyle \\rm 54 \\ cm\n\n{/eq} long has a cross-sectional area of {eq}\\displaystyle \\rm 17 \\ cm^2\n\n{/eq}. The magnetic field inside the solenoid has a magnitude of {eq}\\displaystyle \\rm 130 \\ mT\n\n{/eq}. What is the total energy stored by the magnetic field inside the solenoid?",
"split": "train"
}
| null | null |
1040903
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "A plane with equation {eq}\\frac{x}{a}+\\frac{y}{b}+\\frac{z}{c}=1 (a,b,c > 0){/eq} together with positive coordinate planes forms a tetrahedron of volume {eq}V=\\frac{1}{6} abc{/eq}. Find the plane that minimizes {eq}V{/eq} if the plane is constrained to pass through a point {eq}P=(3,7,6){/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "567",
"style": "rule"
}
|
{
"answer": "567",
"index": 449,
"question": "A plane with equation {eq}\\frac{x}{a}+\\frac{y}{b}+\\frac{z}{c}=1 (a,b,c > 0){/eq} together with positive coordinate planes forms a tetrahedron of volume {eq}V=\\frac{1}{6} abc{/eq}. Find the plane that minimizes {eq}V{/eq} if the plane is constrained to pass through a point {eq}P=(3,7,6){/eq}.",
"split": "train"
}
| null | null |
653309
|
List
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Find the partial pressure in a solution containing ethanol and 1-propanol with a total vapor pressure of #\"56.3 torr\"#? The pure vapor pressures are #\"100.0 torr\"# and #\"37.6 torr\"#, respectively, and the solution has a mol fraction of #0.300# of ethanol. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "30.0 torr, 26.3 torr",
"style": "rule"
}
|
{
"answer": "30.0 torr, 26.3 torr",
"index": 450,
"question": "Find the partial pressure in a solution containing ethanol and 1-propanol with a total vapor pressure of #\"56.3 torr\"#? The pure vapor pressures are #\"100.0 torr\"# and #\"37.6 torr\"#, respectively, and the solution has a mol fraction of #0.300# of ethanol.",
"split": "train"
}
| null | null |
89619
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A projectile is shot at an angle of #pi/8 # and a velocity of # 27 m/s#. How far away will the projectile land? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "52.59m",
"style": "rule"
}
|
{
"answer": "52.59m",
"index": 451,
"question": "A projectile is shot at an angle of #pi/8 # and a velocity of # 27 m/s#. How far away will the projectile land?",
"split": "train"
}
| null | null |
1550717
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Explain the finite population correlation factor. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{eq}CF = \\sqrt {\\frac{{N - n}}{{N - 1}}} {/eq}",
"style": "rule"
}
|
{
"answer": "{eq}CF = \\sqrt {\\frac{{N - n}}{{N - 1}}} {/eq}",
"index": 452,
"question": "Explain the finite population correlation factor.",
"split": "train"
}
| null | null |
398641
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "If an electron's position can be measured to a precision of {eq}5.0\\times 10^{-8}\n\n{/eq} m, how precisely can its speed be known? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.163*10^3 m/s",
"style": "rule"
}
|
{
"answer": "1.163*10^3 m/s",
"index": 453,
"question": "If an electron's position can be measured to a precision of {eq}5.0\\times 10^{-8}\n\n{/eq} m, how precisely can its speed be known?",
"split": "train"
}
| null | null |
1230819
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A #42.3*mL# volume of gas at #371.3*K# is cooled to #351.7*K#. What is the new volume? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "40.2 mL",
"style": "rule"
}
|
{
"answer": "40.2 mL",
"index": 454,
"question": "A #42.3*mL# volume of gas at #371.3*K# is cooled to #351.7*K#. What is the new volume?",
"split": "train"
}
| null | null |
1911444
|
List
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Determine the opportunity cost of additional production at different outputs.\n\n \n \n \n Possibility \n Cars (hundreds) \n Bicycles (hundreds) \n \n \n A \n 15 \n 0 \n \n \n B \n 11 \n 5 \n \n \n C \n 8 \n 7 \n \n \n D \n 5 \n 9 \n \n \n E \n 0 \n 11 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The opportunity costs of one bicycle at different points are: \nAt point B: 0.8 cars \nAt point C: 1.5 cars \nAt point D: 1.5 cars\nAt point E: 2.5 cars",
"style": "rule"
}
|
{
"answer": "The opportunity costs of one bicycle at different points are: \nAt point B: 0.8 cars \nAt point C: 1.5 cars \nAt point D: 1.5 cars\nAt point E: 2.5 cars",
"index": 455,
"question": "Determine the opportunity cost of additional production at different outputs.\n\n \n \n \n Possibility \n Cars (hundreds) \n Bicycles (hundreds) \n \n \n A \n 15 \n 0 \n \n \n B \n 11 \n 5 \n \n \n C \n 8 \n 7 \n \n \n D \n 5 \n 9 \n \n \n E \n 0 \n 11",
"split": "train"
}
| null | null |
2029917
|
Integer
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is the final temperature and state of water when 8.50 kJ of energy is added to 10.0 g of ice at {eq}0^{\\circ}C\n\n{/eq}?\n\nCs (ice) = 2.1 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq}\n\nHeat of vaporization (water) = 40.7 kJ/mol\n\nCa (water) = 4.184 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq}\n\nHeat of fusion (water) = 6.02 kJ/mol\n\nCs (steam) = 2.0 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "100 degrees Celcius",
"style": "rule"
}
|
{
"answer": "100 degrees Celcius",
"index": 456,
"question": "What is the final temperature and state of water when 8.50 kJ of energy is added to 10.0 g of ice at {eq}0^{\\circ}C\n\n{/eq}?\n\nCs (ice) = 2.1 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq}\n\nHeat of vaporization (water) = 40.7 kJ/mol\n\nCa (water) = 4.184 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq}\n\nHeat of fusion (water) = 6.02 kJ/mol\n\nCs (steam) = 2.0 {eq}J/g \\cdot ^{\\circ}C\n\n{/eq}",
"split": "train"
}
| null | null |
1445587
|
Integer
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 200 L kiln is used for vitrifying ceramics. It is currently operating at 1015 deg-C, and the pressure is 0.9750 atm. How many moles of air molecules are within the confines of the kiln? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2 mol",
"style": "rule"
}
|
{
"answer": "2 mol",
"index": 457,
"question": "A 200 L kiln is used for vitrifying ceramics. It is currently operating at 1015 deg-C, and the pressure is 0.9750 atm. How many moles of air molecules are within the confines of the kiln?",
"split": "train"
}
| null | null |
1338423
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A tank in the shape of an inverted right circular cone has height 14 meters and radius 12 meters. It is filled with 6 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is 1540kg/cubic m Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "23826441.87 J",
"style": "rule"
}
|
{
"answer": "23826441.87 J",
"index": 458,
"question": "A tank in the shape of an inverted right circular cone has height 14 meters and radius 12 meters. It is filled with 6 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is 1540kg/cubic m",
"split": "train"
}
| null | null |
623896
|
Expression
|
Mathematics
|
PhD
|
general-reasoner
|
[
{
"content": "Given a polynomial ODE $\\dot{x}=f(x)\\in\\mathbb{R}^n$ that possesses a Darboux polynomial $p(x)$ satisfying $\\dot{p}(x)=c(x)p(x)$ for some function $c(x)$ (the cofactor), how can one write $f(x)$ in terms of $p(x)$ and/or $c(x)$? Is there an equivalent statement for the case of ODE possessing a Darboux polynomial, analogous to the skew-gradient form $\\dot{x}=S(x)\\nabla H(x)$ for a first integral $H(x)$ (where $\\dot{H}(x)=0$ and $S(x)=-S(x)^T$)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$f=(\\alpha I + S) \\nabla p$, where $\\alpha = \\frac{cp}{|\\nabla p|^2}$ and $S$ is a skew symmetric matrix.",
"style": "rule"
}
|
{
"answer": "$f=(\\alpha I + S) \\nabla p$, where $\\alpha = \\frac{cp}{|\\nabla p|^2}$ and $S$ is a skew symmetric matrix.",
"index": 459,
"question": "Given a polynomial ODE $\\dot{x}=f(x)\\in\\mathbb{R}^n$ that possesses a Darboux polynomial $p(x)$ satisfying $\\dot{p}(x)=c(x)p(x)$ for some function $c(x)$ (the cofactor), how can one write $f(x)$ in terms of $p(x)$ and/or $c(x)$? Is there an equivalent statement for the case of ODE possessing a Darboux polynomial, analogous to the skew-gradient form $\\dot{x}=S(x)\\nabla H(x)$ for a first integral $H(x)$ (where $\\dot{H}(x)=0$ and $S(x)=-S(x)^T$)?",
"split": "train"
}
| null | null |
687254
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Suppose 25 mL of 0.1 M NH{eq}_3\n\n{/eq} was added to 35 mL of 0.2 M HCl. Calculate the pH of the resulting solution after reaching equilibrium. {eq}K_b = 1.8 \\times 10^{-5}\n\n{/eq} for ammonia. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.1",
"style": "rule"
}
|
{
"answer": "1.1",
"index": 460,
"question": "Suppose 25 mL of 0.1 M NH{eq}_3\n\n{/eq} was added to 35 mL of 0.2 M HCl. Calculate the pH of the resulting solution after reaching equilibrium. {eq}K_b = 1.8 \\times 10^{-5}\n\n{/eq} for ammonia.",
"split": "train"
}
| null | null |
2012048
|
String
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $\\sigma = (135) \\in S_6$. We know that $\\sigma$ can be written as transpositions, or 2-cycles, as $$(135)=(15)(13)$$ How do I write it as composite of elementary permutations? The definition of elementary permutation is the following Let $1\\le i < k$. Let $e_i$ be an element in $S_k$ such that $e_i (i) = i+1$ and $e_i (i+1) = i$. We call $e_i$ and elementary permutation. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(12)(23)(34)(45)(34)(12)",
"style": "rule"
}
|
{
"answer": "(12)(23)(34)(45)(34)(12)",
"index": 461,
"question": "Let $\\sigma = (135) \\in S_6$. We know that $\\sigma$ can be written as transpositions, or 2-cycles, as $$(135)=(15)(13)$$ How do I write it as composite of elementary permutations? The definition of elementary permutation is the following Let $1\\le i < k$. Let $e_i$ be an element in $S_k$ such that $e_i (i) = i+1$ and $e_i (i+1) = i$. We call $e_i$ and elementary permutation.",
"split": "train"
}
| null | null |
1642132
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How can I approximate the function $f(x)=\\sqrt{1-x^2}$ for $x\\rightarrow0$ using a Taylor expansion up to first-order terms, given that the linear term vanishes when expanding around $x=0$, and this loss of the linear term removes the relevant physics? Is there a workaround to this issue, beyond ad-hoc methods like approximating $x^2$ with $x$ before performing the expansion? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$f(x) = \\sqrt{1-x^2} \\approx 1-\\frac{x^2}{2}$",
"style": "rule"
}
|
{
"answer": "$f(x) = \\sqrt{1-x^2} \\approx 1-\\frac{x^2}{2}$",
"index": 462,
"question": "How can I approximate the function $f(x)=\\sqrt{1-x^2}$ for $x\\rightarrow0$ using a Taylor expansion up to first-order terms, given that the linear term vanishes when expanding around $x=0$, and this loss of the linear term removes the relevant physics? Is there a workaround to this issue, beyond ad-hoc methods like approximating $x^2$ with $x$ before performing the expansion?",
"split": "train"
}
| null | null |
51346
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "For the reaction represented by the equation #Cl_2 + 2KBr -> 2KCl + Br_2#, how many grams of potassium chloride can be produced from 300. g each of chlorine and potassium bromide? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "187.74g",
"style": "rule"
}
|
{
"answer": "187.74g",
"index": 463,
"question": "For the reaction represented by the equation #Cl_2 + 2KBr -> 2KCl + Br_2#, how many grams of potassium chloride can be produced from 300. g each of chlorine and potassium bromide?",
"split": "train"
}
| null | null |
1757860
|
String
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is the formula for sodium phosphide? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Na3P",
"style": "rule"
}
|
{
"answer": "Na3P",
"index": 464,
"question": "What is the formula for sodium phosphide?",
"split": "train"
}
| null | null |
1916108
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of {eq}5\\times10^{10}\n\n{/eq} m (inside the orbit of Mercury), at which point its speed is {eq}9.2\\times10^{4}\n\n{/eq} m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is {eq}6\\times10^{12}\n\n{/eq} m from the Sun? (This is the approximate distance of Pluto from the Sun.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "767 m/s",
"style": "rule"
}
|
{
"answer": "767 m/s",
"index": 465,
"question": "A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of {eq}5\\times10^{10}\n\n{/eq} m (inside the orbit of Mercury), at which point its speed is {eq}9.2\\times10^{4}\n\n{/eq} m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is {eq}6\\times10^{12}\n\n{/eq} m from the Sun? (This is the approximate distance of Pluto from the Sun.)",
"split": "train"
}
| null | null |
1716615
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do you integrate #(6x^2+1)/(x^2(x-1)^2)# using partial fractions? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-1/x+2lnx-2ln(x-1)-7/(x-1) +C",
"style": "rule"
}
|
{
"answer": "-1/x+2lnx-2ln(x-1)-7/(x-1) +C",
"index": 466,
"question": "How do you integrate #(6x^2+1)/(x^2(x-1)^2)# using partial fractions?",
"split": "train"
}
| null | null |
195411
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose $\\mathcal{H}$ is a separable Hilbert space over $\\mathbb{C}$ with scalar product $(\\cdot,\\cdot)$. Let $(U_n),\\, n\\in \\mathbb{N},$ and $U$ be unitary operators on $\\mathcal{H}$ and $D\\subset \\mathcal{H}$ be dense such that $$ (x, U_n y) \\longrightarrow (x,U y) \\quad(n\\to \\infty)$$ for all $x,y\\in D$. Can we already conclude that $U_n \\to U$ weakly, that is, the above equation holds for all $x,y\\in\\mathcal{H}$? If not, is there a reasonable further assumption that would be sufficient to imply weak convergence? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 467,
"question": "Suppose $\\mathcal{H}$ is a separable Hilbert space over $\\mathbb{C}$ with scalar product $(\\cdot,\\cdot)$. Let $(U_n),\\, n\\in \\mathbb{N},$ and $U$ be unitary operators on $\\mathcal{H}$ and $D\\subset \\mathcal{H}$ be dense such that $$ (x, U_n y) \\longrightarrow (x,U y) \\quad(n\\to \\infty)$$ for all $x,y\\in D$. Can we already conclude that $U_n \\to U$ weakly, that is, the above equation holds for all $x,y\\in\\mathcal{H}$? If not, is there a reasonable further assumption that would be sufficient to imply weak convergence?",
"split": "train"
}
| null | null |
1173434
|
Boolean
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Do you think that Apple Co.'s current ratio of 1.12 could pose a problem for the company? The current ratio tells me that for every one dollar in liabilities, Apple has $1.12 in their current assets. So can they easily meet their obligations? Why, or why not? Are they in good shape? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "No",
"style": "rule"
}
|
{
"answer": "No",
"index": 468,
"question": "Do you think that Apple Co.'s current ratio of 1.12 could pose a problem for the company? The current ratio tells me that for every one dollar in liabilities, Apple has $1.12 in their current assets. So can they easily meet their obligations? Why, or why not? Are they in good shape?",
"split": "train"
}
| null | null |
857540
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "What is the relationship between the number of employees who assemble a subassembly and the number produced, given the following data:\n\nNumber of Assemblers | One-hour Production (units)\n------- | --------\n2 | 9\n4 | 15\n1 | 4\n1 | 4\n5 | 16\n3 | 11\n\nThe dependent variable is production. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.9827",
"style": "rule"
}
|
{
"answer": "0.9827",
"index": 469,
"question": "What is the relationship between the number of employees who assemble a subassembly and the number produced, given the following data:\n\nNumber of Assemblers | One-hour Production (units)\n------- | --------\n2 | 9\n4 | 15\n1 | 4\n1 | 4\n5 | 16\n3 | 11\n\nThe dependent variable is production.",
"split": "train"
}
| null | null |
120368
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Differentiate {eq}y=\\sqrt{(1-x^2)}sin^{-1}x{/eq} with respect to x. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{eq}1 - \\frac{x \\sin^{-1}x}{\\sqrt{1-x^2}}{/eq}",
"style": "rule"
}
|
{
"answer": "{eq}1 - \\frac{x \\sin^{-1}x}{\\sqrt{1-x^2}}{/eq}",
"index": 470,
"question": "Differentiate {eq}y=\\sqrt{(1-x^2)}sin^{-1}x{/eq} with respect to x.",
"split": "train"
}
| null | null |
1139753
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "A triangle has adjacent sides of 3 inches and 4 inches with an included angle of {eq}\\pi/4{/eq}. The possible errors in measurement are 1/18 inch for the sides and 0.02 radians for the angle. Approximate the maximum possible error in the computation of the area. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.2253",
"style": "rule"
}
|
{
"answer": "0.2253",
"index": 471,
"question": "A triangle has adjacent sides of 3 inches and 4 inches with an included angle of {eq}\\pi/4{/eq}. The possible errors in measurement are 1/18 inch for the sides and 0.02 radians for the angle. Approximate the maximum possible error in the computation of the area.",
"split": "train"
}
| null | null |
932275
|
Percentage
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "An investment offers a total return of 14 percent over the coming year. Alan Wingspan thinks the total real return on this investment will be only 8 percent. What does Alan believe the inflation rate will be over the next year? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5.5%",
"style": "rule"
}
|
{
"answer": "5.5%",
"index": 472,
"question": "An investment offers a total return of 14 percent over the coming year. Alan Wingspan thinks the total real return on this investment will be only 8 percent. What does Alan believe the inflation rate will be over the next year?",
"split": "train"
}
| null | null |
1789668
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "Calculate the pH in a solution prepared by dissolving 0.10 mol of solid NH{eq}_4\n\n{/eq}Cl in 0.500 L of 0.40 M NH{eq}_3\n\n{/eq}. Assume that there is no volume change. Without using the Henderson-Hasselbalch equation. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "9.6",
"style": "rule"
}
|
{
"answer": "9.6",
"index": 473,
"question": "Calculate the pH in a solution prepared by dissolving 0.10 mol of solid NH{eq}_4\n\n{/eq}Cl in 0.500 L of 0.40 M NH{eq}_3\n\n{/eq}. Assume that there is no volume change. Without using the Henderson-Hasselbalch equation.",
"split": "train"
}
| null | null |
153022
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two point charges {eq}q_1\\ = 8.0\\ \\mu\\text{C} {/eq} and {eq}q_2\\ = -5.0\\ \\mu\\text{C} {/eq}, are separated by a distance of {eq}r\\ = 10.0\\ \\text{cm}{/eq}.\nWhat is the magnitude of the electrostatic force? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "36 N",
"style": "rule"
}
|
{
"answer": "36 N",
"index": 474,
"question": "Two point charges {eq}q_1\\ = 8.0\\ \\mu\\text{C} {/eq} and {eq}q_2\\ = -5.0\\ \\mu\\text{C} {/eq}, are separated by a distance of {eq}r\\ = 10.0\\ \\text{cm}{/eq}.\nWhat is the magnitude of the electrostatic force?",
"split": "train"
}
| null | null |
460302
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "The journal entry in the buyer's books to record the honoring by the seller of an account deemed uncollectible in a factoring agreement with recourse would include a\n\nA. debit to Bad Debt Expense\n\nB. debit to Allowance for Uncollectible Accounts\n\nC. debit to Cash\n\nD. debit to Loss of Factoring Agreement Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"answer": "B",
"index": 475,
"question": "The journal entry in the buyer's books to record the honoring by the seller of an account deemed uncollectible in a factoring agreement with recourse would include a\n\nA. debit to Bad Debt Expense\n\nB. debit to Allowance for Uncollectible Accounts\n\nC. debit to Cash\n\nD. debit to Loss of Factoring Agreement",
"split": "train"
}
| null | null |
683326
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the function f(t) satisfying the differential equation f'(t) - f(t) = 7t and the condition f(3) = 1. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "f(t) = -7t - 7 + (29/e^3)*e^t",
"style": "rule"
}
|
{
"answer": "f(t) = -7t - 7 + (29/e^3)*e^t",
"index": 476,
"question": "Find the function f(t) satisfying the differential equation f'(t) - f(t) = 7t and the condition f(3) = 1.",
"split": "train"
}
| null | null |
1000189
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "At the 0.05 significance level, can the watchdog agency conclude the mean number of complaints per airport is differ than 15 per month? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 477,
"question": "At the 0.05 significance level, can the watchdog agency conclude the mean number of complaints per airport is differ than 15 per month?",
"split": "train"
}
| null | null |
208399
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Some politicians argue for imposing trade restrictions in the hope that doing so will reduce the trade deficit of Canada. Assuming Canada has a floating exchange rate, the imposition of trade barriers:\n\na. increases the supply of dollars, causing a depreciation of the exchange rate, which shifts the net exports curve to the left. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nb. decreases the supply of dollars, causing an appreciation of the exchange rate, which shifts the net exports curve right. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nc. decreases the supply of dollars, causing an appreciation of the exchange rate, which shifts the net exports curve to the left. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nd. increases the supply of dollars, causing a depreciation of the exchange rate, which shifts the net exports curve to the right. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 478,
"question": "Some politicians argue for imposing trade restrictions in the hope that doing so will reduce the trade deficit of Canada. Assuming Canada has a floating exchange rate, the imposition of trade barriers:\n\na. increases the supply of dollars, causing a depreciation of the exchange rate, which shifts the net exports curve to the left. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nb. decreases the supply of dollars, causing an appreciation of the exchange rate, which shifts the net exports curve right. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nc. decreases the supply of dollars, causing an appreciation of the exchange rate, which shifts the net exports curve to the left. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.\n\nd. increases the supply of dollars, causing a depreciation of the exchange rate, which shifts the net exports curve to the right. The quantity of net exports will either rise or fall depending on the relative size of the shifts in the curves.",
"split": "train"
}
| null | null |
982547
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Shares in a certain company are currently priced at 90 pence each. One year from now, their price will either have risen by 20% (with a probability of 0.5) or fallen 20% (with a probability of 0.5). Take the annual risk-free interest rate as r = 0.05 (compounded continuously).\n\nCalculate the expected discounted payment from selling one share a year from now. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "85.61",
"style": "rule"
}
|
{
"answer": "85.61",
"index": 479,
"question": "Shares in a certain company are currently priced at 90 pence each. One year from now, their price will either have risen by 20% (with a probability of 0.5) or fallen 20% (with a probability of 0.5). Take the annual risk-free interest rate as r = 0.05 (compounded continuously).\n\nCalculate the expected discounted payment from selling one share a year from now.",
"split": "train"
}
| null | null |
1429057
|
Multiple Choice
|
Other
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is one major factor that can result in biased news stories?\n \n\nA. Sensationalism.\n\nB. Pressure from the public.\n\nC. Bribes from interest groups.\n\nD. Opinion Polls. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 480,
"question": "What is one major factor that can result in biased news stories?\n \n\nA. Sensationalism.\n\nB. Pressure from the public.\n\nC. Bribes from interest groups.\n\nD. Opinion Polls.",
"split": "train"
}
| null | null |
907165
|
Float
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "How much potential energy does DeAnna, with a mass 62.0 kg, gain when he climbs a gymnasium rope, a distance of 3.5 m? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.13e+3 J",
"style": "rule"
}
|
{
"answer": "2.13e+3 J",
"index": 481,
"question": "How much potential energy does DeAnna, with a mass 62.0 kg, gain when he climbs a gymnasium rope, a distance of 3.5 m?",
"split": "train"
}
| null | null |
1361715
|
Float
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Sampson Manufacturing has fixed costs of $72,400 and variable costs are 66% of sales.\n\nWhat are the required sales if the company desires net income of $60,000? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$389,412",
"style": "rule"
}
|
{
"answer": "$389,412",
"index": 482,
"question": "Sampson Manufacturing has fixed costs of $72,400 and variable costs are 66% of sales.\n\nWhat are the required sales if the company desires net income of $60,000?",
"split": "train"
}
| null | null |
171467
|
Integer
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "If the utility function for the consumer is: U = min{10 x1, 50 x2} P1= 4 , P2=6 and I=2,000, what is the level of maximized utility? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3846",
"style": "rule"
}
|
{
"answer": "3846",
"index": 483,
"question": "If the utility function for the consumer is: U = min{10 x1, 50 x2} P1= 4 , P2=6 and I=2,000, what is the level of maximized utility?",
"split": "train"
}
| null | null |
1959527
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose the Department of Transportation decides to take the sample for this time and this time they want to have a margin of error of no more than {eq}0.07{/eq} (or {eq}7\\%{/eq}) for the {eq}95\\%{/eq} confidence interval. How big does the sample have to be? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "196",
"style": "rule"
}
|
{
"answer": "196",
"index": 484,
"question": "Suppose the Department of Transportation decides to take the sample for this time and this time they want to have a margin of error of no more than {eq}0.07{/eq} (or {eq}7\\%{/eq}) for the {eq}95\\%{/eq} confidence interval. How big does the sample have to be?",
"split": "train"
}
| null | null |
1255750
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find $\\displaystyle \\int \\dfrac{1}{2\\sin(x)-3\\cos(x)}dx$. How will we get $du = \\dfrac{1}{\\cos(x)+1}dx $ in the integrand using $u = \\tan \\left(\\dfrac{x}{2} \\right)$, $\\cos(x) = \\dfrac{1-u^2}{1+u^2}$ and $\\sin(x) = \\dfrac{2u}{1+u^2}$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$2\\int\\frac{du}{3u^2+4u-3}$",
"style": "rule"
}
|
{
"answer": "$2\\int\\frac{du}{3u^2+4u-3}$",
"index": 485,
"question": "Find $\\displaystyle \\int \\dfrac{1}{2\\sin(x)-3\\cos(x)}dx$. How will we get $du = \\dfrac{1}{\\cos(x)+1}dx $ in the integrand using $u = \\tan \\left(\\dfrac{x}{2} \\right)$, $\\cos(x) = \\dfrac{1-u^2}{1+u^2}$ and $\\sin(x) = \\dfrac{2u}{1+u^2}$?",
"split": "train"
}
| null | null |
672377
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An {eq}8.0 \\times 10^{-2} \\ kg\n\n{/eq} arrow hits the target at 25 m/s and penetrates 3.8 cm before stopping. What average force did the target exert on the arrow? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "658 N",
"style": "rule"
}
|
{
"answer": "658 N",
"index": 486,
"question": "An {eq}8.0 \\times 10^{-2} \\ kg\n\n{/eq} arrow hits the target at 25 m/s and penetrates 3.8 cm before stopping. What average force did the target exert on the arrow?",
"split": "train"
}
| null | null |
207855
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the vector equation for the line of intersection of the planes 5x + 2y + z = 4 and 5x + 5z = 4. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "<4/5+10t, -20t, -10t>",
"style": "rule"
}
|
{
"answer": "<4/5+10t, -20t, -10t>",
"index": 487,
"question": "Find the vector equation for the line of intersection of the planes 5x + 2y + z = 4 and 5x + 5z = 4.",
"split": "train"
}
| null | null |
28863
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given a Undirected Weighted Planar Graph with $N$ nodes and $N-1$ edges each having different weight. Between two nodes there is exactly one path that goes through the edges and nodes such that no node appears in the path more than once. Given some nodes $A_1, A_2, ..., A_K$. Two nodes are taken at random from these nodes. How to calculate the expected distance between those two randomly chosen nodes? (The answer will be in a form of rational numbers) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Let \\( d_w(v, u) \\) represent the shortest weighted distance between nodes v and u in graph G. The expected distance between two randomly chosen nodes from the set \\( \\{A_1, ..., A_K\\} \\) is given by: $$\\sum_{1\\le i<j\\le K} p_{ij} d_w(A_i, A_j)$$ where \\( p_{ij} \\) represents the probability of choosing the pair \\( (A_i, A_j) \\). In the special case where each node \\( A_i \\) has a probability \\( r_i \\) of being selected (e.g., \\( r_i = 1/K \\) for a uniform distribution), then \\( p_{ii} = r_i^2 \\) and \\( p_{ij} = 2r_ir_j \\) for \\( i < j \\).",
"style": "rule"
}
|
{
"answer": "Let \\( d_w(v, u) \\) represent the shortest weighted distance between nodes v and u in graph G. The expected distance between two randomly chosen nodes from the set \\( \\{A_1, ..., A_K\\} \\) is given by: $$\\sum_{1\\le i<j\\le K} p_{ij} d_w(A_i, A_j)$$ where \\( p_{ij} \\) represents the probability of choosing the pair \\( (A_i, A_j) \\). In the special case where each node \\( A_i \\) has a probability \\( r_i \\) of being selected (e.g., \\( r_i = 1/K \\) for a uniform distribution), then \\( p_{ii} = r_i^2 \\) and \\( p_{ij} = 2r_ir_j \\) for \\( i < j \\).",
"index": 488,
"question": "Given a Undirected Weighted Planar Graph with $N$ nodes and $N-1$ edges each having different weight. Between two nodes there is exactly one path that goes through the edges and nodes such that no node appears in the path more than once. Given some nodes $A_1, A_2, ..., A_K$. Two nodes are taken at random from these nodes. How to calculate the expected distance between those two randomly chosen nodes? (The answer will be in a form of rational numbers)",
"split": "train"
}
| null | null |
1108681
|
Boolean
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Economics consider the Fed's sequential targeting strategy to be transparent because the Federal Reserve announces its strategy, policy intentions and operating targets after each FOMC meeting. True or false? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "False",
"style": "rule"
}
|
{
"answer": "False",
"index": 489,
"question": "Economics consider the Fed's sequential targeting strategy to be transparent because the Federal Reserve announces its strategy, policy intentions and operating targets after each FOMC meeting. True or false?",
"split": "train"
}
| null | null |
936294
|
Integer
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "S is a cash basis, calendar year taxpayer. She operates Cloth R Us. All of the store's profits come from the sale of fabric. Sales are $2 million. During the year she paid the following expenses: 1. $3,000 premium for liability insurance covering her business. The coverage runs from December 1, 2015 through November 30, 2018. 2. $10,000 for cloth, all of which is still on hand at the end of the taxable year. 3. $2,000 for \"points\" related to obtaining a loan for the purchase of her personal residence. 4. $1,200 for \"points\" related to obtaining a loan on rental property. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$1,000",
"style": "rule"
}
|
{
"answer": "$1,000",
"index": 490,
"question": "S is a cash basis, calendar year taxpayer. She operates Cloth R Us. All of the store's profits come from the sale of fabric. Sales are $2 million. During the year she paid the following expenses: 1. $3,000 premium for liability insurance covering her business. The coverage runs from December 1, 2015 through November 30, 2018. 2. $10,000 for cloth, all of which is still on hand at the end of the taxable year. 3. $2,000 for \"points\" related to obtaining a loan for the purchase of her personal residence. 4. $1,200 for \"points\" related to obtaining a loan on rental property.",
"split": "train"
}
| null | null |
905655
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How does the equation `[0.5495877475*(-100000.0*y + 161572687.0)/(25000.0*y - 199919.0)]` derived from the Python code `ymin = 1615.72687 ymax = -1607.73011 ec50 = 2.19835099 x,y = symbols('x y') expression = ((y-ymin)*(ec50+x))+abs(ymax)*x equation = solve(expression,x)` translate to the hand-calculated solution `x = \\frac{(y)(ec50) - (ymin)(ec50)}{\\mid{ymax}\\mid - y -ymin}`? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$x = \\frac{y\\cdot ec50 - ymin\\cdot ec50}{ymin - y -\\mid{ymax}\\mid}$",
"style": "rule"
}
|
{
"answer": "$x = \\frac{y\\cdot ec50 - ymin\\cdot ec50}{ymin - y -\\mid{ymax}\\mid}$",
"index": 491,
"question": "How does the equation `[0.5495877475*(-100000.0*y + 161572687.0)/(25000.0*y - 199919.0)]` derived from the Python code `ymin = 1615.72687 ymax = -1607.73011 ec50 = 2.19835099 x,y = symbols('x y') expression = ((y-ymin)*(ec50+x))+abs(ymax)*x equation = solve(expression,x)` translate to the hand-calculated solution `x = \\frac{(y)(ec50) - (ymin)(ec50)}{\\mid{ymax}\\mid - y -ymin}`?",
"split": "train"
}
| null | null |
84049
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which of the following applies to fiscal policy?\n\nA. Increasing T and G in a recession.T\n\nB. Increasing T and decreasing G in a recession.\n\nC. Increasing T and decreasing G in an overheated economy.\n\nD. Decreasing T and G in a recession. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 492,
"question": "Which of the following applies to fiscal policy?\n\nA. Increasing T and G in a recession.T\n\nB. Increasing T and decreasing G in a recession.\n\nC. Increasing T and decreasing G in an overheated economy.\n\nD. Decreasing T and G in a recession.",
"split": "train"
}
| null | null |
607784
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose that $E$ is a set that has the cardinality of the continuum and that If $A$ is an index set with $\\#A\\leq\\#\\mathbb R$ and $\\{X_{\\alpha}\\}_{\\alpha\\in A}$ is a family of sets such that $\\#X_{\\alpha}\\leq\\#\\mathbb R$ for each $\\alpha\\in A$, then $\\#(\\bigcup_{\\alpha\\in A}X_{\\alpha})\\leq\\#\\mathbb R$. Is there any way to prove that the set of countable subsets of $E$ has the cardinality of the continuum, using the result above? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 493,
"question": "Suppose that $E$ is a set that has the cardinality of the continuum and that If $A$ is an index set with $\\#A\\leq\\#\\mathbb R$ and $\\{X_{\\alpha}\\}_{\\alpha\\in A}$ is a family of sets such that $\\#X_{\\alpha}\\leq\\#\\mathbb R$ for each $\\alpha\\in A$, then $\\#(\\bigcup_{\\alpha\\in A}X_{\\alpha})\\leq\\#\\mathbb R$. Is there any way to prove that the set of countable subsets of $E$ has the cardinality of the continuum, using the result above?",
"split": "train"
}
| null | null |
52201
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Two charges are located in the {eq}xy\n\n{/eq}-plane. If {eq}q_1 = -3.65 \\, \\mathrm{nC}\n\n{/eq} and is located at {eq}x = 0.00 \\, \\mathrm{m}\n\n{/eq}, {eq}y = 0.960 \\, \\mathrm{m}\n\n{/eq} and the second charge has magnitude of {eq}q_2 = 4.40 \\, \\mathrm{nC}\n\n{/eq} and is located at {eq}x = 1.20 \\, \\mathrm{m}\n\n{/eq}, {eq}y = 0.600 \\, \\mathrm{m}\n\n{/eq}, calculate the {eq}x\n\n{/eq}- and {eq}y\n\n{/eq}-components, {eq}E_x\n\n{/eq} and {eq}E_y\n\n{/eq} of the electric field {eq}\\vec{E}\n\n{/eq} in component form at the origin {eq}(0, 0)\n\n{/eq}. The Coulomb force constant is {eq}1/(4\\pi\\epsilon_0) = 8.99 \\times 10^9 \\, \\mathrm{N \\cdot m^2/C^2}\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Ex = -19.7 N/C\nEy = 25.8 N/C",
"style": "rule"
}
|
{
"answer": "Ex = -19.7 N/C\nEy = 25.8 N/C",
"index": 494,
"question": "Two charges are located in the {eq}xy\n\n{/eq}-plane. If {eq}q_1 = -3.65 \\, \\mathrm{nC}\n\n{/eq} and is located at {eq}x = 0.00 \\, \\mathrm{m}\n\n{/eq}, {eq}y = 0.960 \\, \\mathrm{m}\n\n{/eq} and the second charge has magnitude of {eq}q_2 = 4.40 \\, \\mathrm{nC}\n\n{/eq} and is located at {eq}x = 1.20 \\, \\mathrm{m}\n\n{/eq}, {eq}y = 0.600 \\, \\mathrm{m}\n\n{/eq}, calculate the {eq}x\n\n{/eq}- and {eq}y\n\n{/eq}-components, {eq}E_x\n\n{/eq} and {eq}E_y\n\n{/eq} of the electric field {eq}\\vec{E}\n\n{/eq} in component form at the origin {eq}(0, 0)\n\n{/eq}. The Coulomb force constant is {eq}1/(4\\pi\\epsilon_0) = 8.99 \\times 10^9 \\, \\mathrm{N \\cdot m^2/C^2}\n\n{/eq}.",
"split": "train"
}
| null | null |
468428
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Three charged particles, each with mass 2.00 grams and charge 8.00 {eq}\\mu C\n\n{/eq}, are held in place at the corners of an equilateral triangle. One of the particles is released; it is repelled by the other two and has a speed of 118 m/s when it is very far away. Find the length of a side of the triangle. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "8.27 cm",
"style": "rule"
}
|
{
"answer": "8.27 cm",
"index": 495,
"question": "Three charged particles, each with mass 2.00 grams and charge 8.00 {eq}\\mu C\n\n{/eq}, are held in place at the corners of an equilateral triangle. One of the particles is released; it is repelled by the other two and has a speed of 118 m/s when it is very far away. Find the length of a side of the triangle.",
"split": "train"
}
| null | null |
1431778
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I have been given this equation in a past exam paper, in which I am solving for eigenfunctions & eigenvalues. The product rule has been applied to this section in the solution but I cannot work out which should be 'f' and which should be 'g'. The result is : after dividing through by , which I understand but how do I perform the product rule on my first equation? Thanks Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Consider \\(fg\\)’ = f’g+fg’\\) where \\(f = e^{-2x}\\) and \\(g = \\frac{dy}{dx}\\). Then, \\(f’ = \\frac{d}{dx} e^{-2x} = -2e^{-2x}\\) and \\(g’ = \\frac{d\\frac{dy}{dx}}{dx} = \\frac{d^2y}{dx^2}\\). Considering there is a negative sign as well, putting everything together, you get \\(-\\left[-2e^{-2x}\\cdot\\frac{dy}{dx}+e^{-2x}\\cdot\\frac{d^2y}{dx^2}\\right] = 2e^{-2x}\\cdot\\frac{dy}{dx}-e^{-2x}\\cdot\\frac{d^2y}{dx^2}\\)",
"style": "rule"
}
|
{
"answer": "Consider \\(fg\\)’ = f’g+fg’\\) where \\(f = e^{-2x}\\) and \\(g = \\frac{dy}{dx}\\). Then, \\(f’ = \\frac{d}{dx} e^{-2x} = -2e^{-2x}\\) and \\(g’ = \\frac{d\\frac{dy}{dx}}{dx} = \\frac{d^2y}{dx^2}\\). Considering there is a negative sign as well, putting everything together, you get \\(-\\left[-2e^{-2x}\\cdot\\frac{dy}{dx}+e^{-2x}\\cdot\\frac{d^2y}{dx^2}\\right] = 2e^{-2x}\\cdot\\frac{dy}{dx}-e^{-2x}\\cdot\\frac{d^2y}{dx^2}\\)",
"index": 496,
"question": "I have been given this equation in a past exam paper, in which I am solving for eigenfunctions & eigenvalues. The product rule has been applied to this section in the solution but I cannot work out which should be 'f' and which should be 'g'. The result is : after dividing through by , which I understand but how do I perform the product rule on my first equation? Thanks",
"split": "train"
}
| null | null |
974828
|
Integer
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "X Company is considering an upgrade to its computer equipment that will cost $19,000 but result in smaller operating costs. Estimated annual operating costs are as follows:\n\nYear: 1 No upgrade:$-6,000 Upgrade:$-7,000\n\nYear: 2 No upgrade:-8,000 Upgrade: -4,000\n\nYear: 3 No upgrade: -8,000 Upgrade:-3,000\n\nYear: 4 No upgrade: -8,000 Upgrade: -3,000\n\nYear: 5 No upgrade: -6,000 Upgrade: -3,000\n\nYear: 6 No upgrade: -5,000 Upgrade: -2,000\n\nYear: 7 No upgrade: -4,000 Upgrade: -2,000\n\nIf X Company decides to replace the equipment, what is the payback period (in years)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6",
"style": "rule"
}
|
{
"answer": "6",
"index": 497,
"question": "X Company is considering an upgrade to its computer equipment that will cost $19,000 but result in smaller operating costs. Estimated annual operating costs are as follows:\n\nYear: 1 No upgrade:$-6,000 Upgrade:$-7,000\n\nYear: 2 No upgrade:-8,000 Upgrade: -4,000\n\nYear: 3 No upgrade: -8,000 Upgrade:-3,000\n\nYear: 4 No upgrade: -8,000 Upgrade: -3,000\n\nYear: 5 No upgrade: -6,000 Upgrade: -3,000\n\nYear: 6 No upgrade: -5,000 Upgrade: -2,000\n\nYear: 7 No upgrade: -4,000 Upgrade: -2,000\n\nIf X Company decides to replace the equipment, what is the payback period (in years)?",
"split": "train"
}
| null | null |
1412713
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the indefinite integral.\n{eq}\\int t \\operatorname { ln } ( t + 3 ) d t{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{ t^2 \\ln( t + 3 )}{2} - \\frac{1}{2}\\left[ \\frac{t^2}{2}-3t + 9 \\ln| t + 3| \\right]+c",
"style": "rule"
}
|
{
"answer": "\\frac{ t^2 \\ln( t + 3 )}{2} - \\frac{1}{2}\\left[ \\frac{t^2}{2}-3t + 9 \\ln| t + 3| \\right]+c",
"index": 498,
"question": "Find the indefinite integral.\n{eq}\\int t \\operatorname { ln } ( t + 3 ) d t{/eq}",
"split": "train"
}
| null | null |
1491642
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How much must Stan save monthly in his 401K retirement fund over the next 30 years to be able to spend $5,000 monthly for 30 years during retirement while earning 10% annually on his retirement funds and 12% annually on his 401K savings? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$163.57",
"style": "rule"
}
|
{
"answer": "$163.57",
"index": 499,
"question": "How much must Stan save monthly in his 401K retirement fund over the next 30 years to be able to spend $5,000 monthly for 30 years during retirement while earning 10% annually on his retirement funds and 12% annually on his 401K savings?",
"split": "train"
}
| null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.