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
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|
1234162
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The Starship Enterprise returns from a warp drive to ordinary space with a forward speed of {eq}53\\text{ km/s}\n\n{/eq}. To the crew's great surprise, a Klingon ship is {eq}150\\text{ km}\n\n{/eq} directly ahead, traveling in the same direction at a mere {eq}22\\text{ km/s}\n\n{/eq}. Without evasive action, the Enterprise will overtake and collide with the Klingons in just about {eq}4.8\\text{ s}\n\n{/eq}. The Enterprise's computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant. Express your answer to two significant figures and include appropriate units.\n\nHint: Draw a position-versus-time graph showing the motions of both the Enterprise and the Klingon ship. Let {eq}x_{0} = 0\\text{ km}\n\n{/eq} be the location of the Enterprise as it returns from warp drive. How do you show graphically the situation in which the collision is \"barely avoided\"? Once you decide what it looks like graphically, express that situation mathematically. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6.5 km/s^2",
"style": "rule"
}
|
{
"answer": "6.5 km/s^2",
"index": 100,
"question": "The Starship Enterprise returns from a warp drive to ordinary space with a forward speed of {eq}53\\text{ km/s}\n\n{/eq}. To the crew's great surprise, a Klingon ship is {eq}150\\text{ km}\n\n{/eq} directly ahead, traveling in the same direction at a mere {eq}22\\text{ km/s}\n\n{/eq}. Without evasive action, the Enterprise will overtake and collide with the Klingons in just about {eq}4.8\\text{ s}\n\n{/eq}. The Enterprise's computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant. Express your answer to two significant figures and include appropriate units.\n\nHint: Draw a position-versus-time graph showing the motions of both the Enterprise and the Klingon ship. Let {eq}x_{0} = 0\\text{ km}\n\n{/eq} be the location of the Enterprise as it returns from warp drive. How do you show graphically the situation in which the collision is \"barely avoided\"? Once you decide what it looks like graphically, express that situation mathematically.",
"split": "train"
}
| null | null |
333850
|
Integer
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "How much energy is required to raise the temperature of 15.0 grams of solid aluminum from 22.8 degrees Celsius to 37.6 degrees Celsius? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "204J",
"style": "rule"
}
|
{
"answer": "204J",
"index": 101,
"question": "How much energy is required to raise the temperature of 15.0 grams of solid aluminum from 22.8 degrees Celsius to 37.6 degrees Celsius?",
"split": "train"
}
| null | null |
515178
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Calculate the pH of a 4.00x10^-8 M solution of HBr. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6.914",
"style": "rule"
}
|
{
"answer": "6.914",
"index": 102,
"question": "Calculate the pH of a 4.00x10^-8 M solution of HBr.",
"split": "train"
}
| null | null |
969019
|
Other
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Hall Company's fixed budget performance report for June follows.\n\nThe $660,000 budgeted expenses include $450,000 variable expenses and $210,000 fixed expenses. Actual expenses include $200,000 fixed expenses.\n\nPrepare a flexible budget performance report that shows any variances between budgeted results and actual results. List fixed and variable expenses separately.\n\n\n Fixed Budget Actual Results Variances\nSales (in units) 9,000 7,900 \nSales (in dollars) $720,000 $647,800 $72,200 U\nTotal expenses 660,000 606,850 53,150 F\nIncome from operations $ 60,000 $ 40,950 $19,050 U Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": " Accounts titleFlexible budget (A)Actual results (B)Variance (C = A - B)Favorable/Unfavorable\n Sales632,000647,80015,800Unfavorable\nLess: Variable costs395,000406,85011,850Unfavorable\n Contribution margin237,000240,9503,950Unfavorable\nLess: Fixed costs210,000200,00010,000Favorable\n Income from operations27,00040,95013,950 Unfavorable",
"style": "rule"
}
|
{
"answer": " Accounts titleFlexible budget (A)Actual results (B)Variance (C = A - B)Favorable/Unfavorable\n Sales632,000647,80015,800Unfavorable\nLess: Variable costs395,000406,85011,850Unfavorable\n Contribution margin237,000240,9503,950Unfavorable\nLess: Fixed costs210,000200,00010,000Favorable\n Income from operations27,00040,95013,950 Unfavorable",
"index": 103,
"question": "Hall Company's fixed budget performance report for June follows.\n\nThe $660,000 budgeted expenses include $450,000 variable expenses and $210,000 fixed expenses. Actual expenses include $200,000 fixed expenses.\n\nPrepare a flexible budget performance report that shows any variances between budgeted results and actual results. List fixed and variable expenses separately.\n\n\n Fixed Budget Actual Results Variances\nSales (in units) 9,000 7,900 \nSales (in dollars) $720,000 $647,800 $72,200 U\nTotal expenses 660,000 606,850 53,150 F\nIncome from operations $ 60,000 $ 40,950 $19,050 U",
"split": "train"
}
| null | null |
1167276
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A solid 0.3 kg ball rolls smoothly from rest (starting at height H = 6.0 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from end point does the ball hit the floor. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5.0 m",
"style": "rule"
}
|
{
"answer": "5.0 m",
"index": 104,
"question": "A solid 0.3 kg ball rolls smoothly from rest (starting at height H = 6.0 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from end point does the ball hit the floor.",
"split": "train"
}
| null | null |
1751237
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Is the stability region $-2 < (1+ \\lambda h)^2<0$ for the explicit midpoint method correct, and how do I find the correct stability region? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The stability region is defined by |1+z+0.5z^2|<=1, where z = Δtλ. The boundary of the stability region can be found by setting |1+z+0.5z^2|=1 and solving for the imaginary part b as a function of the real part a, where z=a+bi. This yields b=±sqrt(-a^2-2a+2sqrt(-a(a+2))). Plotting this expression will reveal the stability region.",
"style": "rule"
}
|
{
"answer": "The stability region is defined by |1+z+0.5z^2|<=1, where z = Δtλ. The boundary of the stability region can be found by setting |1+z+0.5z^2|=1 and solving for the imaginary part b as a function of the real part a, where z=a+bi. This yields b=±sqrt(-a^2-2a+2sqrt(-a(a+2))). Plotting this expression will reveal the stability region.",
"index": 105,
"question": "Is the stability region $-2 < (1+ \\lambda h)^2<0$ for the explicit midpoint method correct, and how do I find the correct stability region?",
"split": "train"
}
| null | null |
404480
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use the technology display to make a decision to reject or fail to reject the null hypothesis at {eq}\\alpha =.01. Make the decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 106,
"question": "Use the technology display to make a decision to reject or fail to reject the null hypothesis at {eq}\\alpha =.01. Make the decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal.",
"split": "train"
}
| null | null |
818894
|
Integer
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "An estimate of the efficiency-loss ratio of taxes on labor income is 15 percent.\n\nThe efficiency-loss ratio of taxes on capital income is estimated to be 45 percent.\n\nAssuming that these estimates are accurate, calculate the change in well-being that would result from a $10 billion reduction in taxes on capital income, accompanied by a $10 billion increase in taxes on labor income. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3 billion",
"style": "rule"
}
|
{
"answer": "3 billion",
"index": 107,
"question": "An estimate of the efficiency-loss ratio of taxes on labor income is 15 percent.\n\nThe efficiency-loss ratio of taxes on capital income is estimated to be 45 percent.\n\nAssuming that these estimates are accurate, calculate the change in well-being that would result from a $10 billion reduction in taxes on capital income, accompanied by a $10 billion increase in taxes on labor income.",
"split": "train"
}
| null | null |
911052
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Ball A (mass = 10 kg) makes a head-on, elastic collision with ball B, which is initially at rest. As a result of the collision, ball A rebounds with a speed equal to one-fourth its original speed. What is the mass of ball B? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "16.7 kg",
"style": "rule"
}
|
{
"answer": "16.7 kg",
"index": 108,
"question": "Ball A (mass = 10 kg) makes a head-on, elastic collision with ball B, which is initially at rest. As a result of the collision, ball A rebounds with a speed equal to one-fourth its original speed. What is the mass of ball B?",
"split": "train"
}
| null | null |
411229
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given a 3D cartesian system with known origo position and z-direction $\\vec{e}_z' = (\\cos\\theta\\sin\\phi, \\sin\\theta\\sin\\phi, \\cos\\phi)$ in global coordinates, and knowing there is no rotation around the z-axis, how can I find rotation angles $\\alpha, \\beta$ around the x and y axes respectively such that $R = R_xR_y$, where $R_x$ and $R_y$ are the rotation matrices around the x and y axes? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "β = sin⁻¹(x₃), α = Atan2(y₃,-y₂) where (x₃,y₃,z₃) represents the new z-direction",
"style": "rule"
}
|
{
"answer": "β = sin⁻¹(x₃), α = Atan2(y₃,-y₂) where (x₃,y₃,z₃) represents the new z-direction",
"index": 109,
"question": "Given a 3D cartesian system with known origo position and z-direction $\\vec{e}_z' = (\\cos\\theta\\sin\\phi, \\sin\\theta\\sin\\phi, \\cos\\phi)$ in global coordinates, and knowing there is no rotation around the z-axis, how can I find rotation angles $\\alpha, \\beta$ around the x and y axes respectively such that $R = R_xR_y$, where $R_x$ and $R_y$ are the rotation matrices around the x and y axes?",
"split": "train"
}
| null | null |
1470061
|
Integer
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "If a net force of {eq}34\\ \\rm N\n\n{/eq} acts for {eq}15\n\n{/eq} seconds on a {eq}15\\ \\rm kg\n\n{/eq} object which is initially at rest, how far will the object move in that time? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "255 m",
"style": "rule"
}
|
{
"answer": "255 m",
"index": 110,
"question": "If a net force of {eq}34\\ \\rm N\n\n{/eq} acts for {eq}15\n\n{/eq} seconds on a {eq}15\\ \\rm kg\n\n{/eq} object which is initially at rest, how far will the object move in that time?",
"split": "train"
}
| null | null |
1172983
|
Multiple Choice
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "_____ is the movement of water across a membrane.\n\nSelect all that apply.\n\na. Diffusion\n\nb. Facilitated diffusion\n\nc. Osmosis\n\nd. Active transport Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 111,
"question": "_____ is the movement of water across a membrane.\n\nSelect all that apply.\n\na. Diffusion\n\nb. Facilitated diffusion\n\nc. Osmosis\n\nd. Active transport",
"split": "train"
}
| null | null |
1432606
|
Multiple Choice
|
Philosophy
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which of the following is an example of inductive reasoning?\n \n\nA.\tJune is the coolest summer month where I live, so it will probably be cool this June.\nB.\tIt was cool on the first day of summer, so the entire summer will be cool.\nC.\tI heard on the radio that the first day of summer will be cool, so it will be cool that day.\nD.\tIt has been cool every day this summer so far, so tomorrow will likely be cool too. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 112,
"question": "Which of the following is an example of inductive reasoning?\n \n\nA.\tJune is the coolest summer month where I live, so it will probably be cool this June.\nB.\tIt was cool on the first day of summer, so the entire summer will be cool.\nC.\tI heard on the radio that the first day of summer will be cool, so it will be cool that day.\nD.\tIt has been cool every day this summer so far, so tomorrow will likely be cool too.",
"split": "train"
}
| null | null |
1241169
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A student measures the {eq}\\rm\n\nAl^{3+}\n\n{/eq} concentration in a saturated aqueous solution of aluminum hydroxide to be {eq}\\rm\n\n2.84 \\times 10^{-9}\\ M\n\n{/eq}.\n\nBased on her data, the solubility product constant for aluminum hydroxide is _____. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.76e-33",
"style": "rule"
}
|
{
"answer": "1.76e-33",
"index": 113,
"question": "A student measures the {eq}\\rm\n\nAl^{3+}\n\n{/eq} concentration in a saturated aqueous solution of aluminum hydroxide to be {eq}\\rm\n\n2.84 \\times 10^{-9}\\ M\n\n{/eq}.\n\nBased on her data, the solubility product constant for aluminum hydroxide is _____.",
"split": "train"
}
| null | null |
1126854
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Assume that the uncovered interest parity condition holds. Also assume that the Australian interest rate is greater than the U.K. interest rate. Given this information, we know that investors expect:\n\na. the pound to appreciate.\n\nb. the Australian interest rate to fall.\n\nc. the pound to depreciate.\n\nd. the Australian dollar-pound exchange rate to remain fixed.\n\ne. None of the above. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 114,
"question": "Assume that the uncovered interest parity condition holds. Also assume that the Australian interest rate is greater than the U.K. interest rate. Given this information, we know that investors expect:\n\na. the pound to appreciate.\n\nb. the Australian interest rate to fall.\n\nc. the pound to depreciate.\n\nd. the Australian dollar-pound exchange rate to remain fixed.\n\ne. None of the above.",
"split": "train"
}
| null | null |
616193
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.95 L/s, with an output pressure of 3.25 {eq}\\times\n\n{/eq} 10{eq}^5\n\n{/eq} N/m{eq}^2\n\n{/eq}. The water enters a hose with a 2.8 cm inside diameter and rises 2.9 m above the pump. What is its pressure at this point N/m{eq}^2\n\n{/eq}? You may neglect frictional losses. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.97e5 N/m^2",
"style": "rule"
}
|
{
"answer": "2.97e5 N/m^2",
"index": 115,
"question": "A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.95 L/s, with an output pressure of 3.25 {eq}\\times\n\n{/eq} 10{eq}^5\n\n{/eq} N/m{eq}^2\n\n{/eq}. The water enters a hose with a 2.8 cm inside diameter and rises 2.9 m above the pump. What is its pressure at this point N/m{eq}^2\n\n{/eq}? You may neglect frictional losses.",
"split": "train"
}
| null | null |
1351328
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $Q$ be a finite quiver with vertex set $I$. Let $kQ = \\bigoplus_{n \\ge 0} k^{(n)}Q$ be the vector space direct sum decomposition of the path algebra $kQ$, where $k^{(n)}Q$ is the $k$-linear span of all paths of length $n$. Find a closed formula for the Poincaré series $P_{kQ}(t) = \\sum_{n \\ge 0} \\text{dim}_k (k^{(n)}Q) \\cdot t^n$ in terms of the adjacency matrix $A_Q = \\|a_{i,j}\\|_{i, j \\in I}$, where $a_{i, j}$ is the number of edges $j \\to i$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The generating function is the sum of the entries of the matrix $\\sum_{n\\ge0} A^nt^n=({\rm Id}-At)^{-1}$",
"style": "rule"
}
|
{
"answer": "The generating function is the sum of the entries of the matrix $\\sum_{n\\ge0} A^nt^n=({\rm Id}-At)^{-1}$",
"index": 116,
"question": "Let $Q$ be a finite quiver with vertex set $I$. Let $kQ = \\bigoplus_{n \\ge 0} k^{(n)}Q$ be the vector space direct sum decomposition of the path algebra $kQ$, where $k^{(n)}Q$ is the $k$-linear span of all paths of length $n$. Find a closed formula for the Poincaré series $P_{kQ}(t) = \\sum_{n \\ge 0} \\text{dim}_k (k^{(n)}Q) \\cdot t^n$ in terms of the adjacency matrix $A_Q = \\|a_{i,j}\\|_{i, j \\in I}$, where $a_{i, j}$ is the number of edges $j \\to i$.",
"split": "train"
}
| null | null |
1746352
|
Expression
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Define asset turnover Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Net Sales / Total Assets",
"style": "rule"
}
|
{
"answer": "Net Sales / Total Assets",
"index": 117,
"question": "Define asset turnover",
"split": "train"
}
| null | null |
1388974
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Your company has a required rate of return 7%. The company has completed a new project that is expected to grow dividends at a rate of 50% the first year and 25% the following year, after which growth should be at a constant rate of 6%. The last dividend paid was $1.00. What is the value per share of your firm's stock? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "176.85",
"style": "rule"
}
|
{
"answer": "176.85",
"index": 118,
"question": "Your company has a required rate of return 7%. The company has completed a new project that is expected to grow dividends at a rate of 50% the first year and 25% the following year, after which growth should be at a constant rate of 6%. The last dividend paid was $1.00. What is the value per share of your firm's stock?",
"split": "train"
}
| null | null |
1323766
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "At room temperature, what fraction of the nitrogen molecules in the air are moving at less than 300 m/s? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.218",
"style": "rule"
}
|
{
"answer": "0.218",
"index": 119,
"question": "At room temperature, what fraction of the nitrogen molecules in the air are moving at less than 300 m/s?",
"split": "train"
}
| null | null |
1529896
|
Expression
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Find the market equilibrium point. The supply function for a product is 2p - q - 30 = 0, while the demand function for the same product is (p + 10)(q + 30) = 8400. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(60, 90)",
"style": "rule"
}
|
{
"answer": "(60, 90)",
"index": 120,
"question": "Find the market equilibrium point. The supply function for a product is 2p - q - 30 = 0, while the demand function for the same product is (p + 10)(q + 30) = 8400.",
"split": "train"
}
| null | null |
1798038
|
String
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is the amount assigned to each share of stock that is printed on the stock certificate called? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "par value",
"style": "rule"
}
|
{
"answer": "par value",
"index": 121,
"question": "What is the amount assigned to each share of stock that is printed on the stock certificate called?",
"split": "train"
}
| null | null |
1333333
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find {eq}f{/eq} given {eq}f''(x) = 4 - \\sqrt[3]{x}{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "f(x)=2x^2-(4x^(7/2))/35+Cx+C1",
"style": "rule"
}
|
{
"answer": "f(x)=2x^2-(4x^(7/2))/35+Cx+C1",
"index": 122,
"question": "Find {eq}f{/eq} given {eq}f''(x) = 4 - \\sqrt[3]{x}{/eq}.",
"split": "train"
}
| null | null |
1961066
|
List
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A mixture of 0.2 mole O2 and 0.4 mole N2 gas is enclosed in a vessel of certain volume at 27C and 800 torr. If volume of mixture is doubled at same temperature then determine pressure of mixture and individual gases? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "400 torr, 130 torr, 270 torr",
"style": "rule"
}
|
{
"answer": "400 torr, 130 torr, 270 torr",
"index": 123,
"question": "A mixture of 0.2 mole O2 and 0.4 mole N2 gas is enclosed in a vessel of certain volume at 27C and 800 torr. If volume of mixture is doubled at same temperature then determine pressure of mixture and individual gases?",
"split": "train"
}
| null | null |
695635
|
List
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the Maclaurin series of the function {eq}\\displaystyle (2 x^2) (e^{\\displaystyle -8 x})\n\n{eq}. Then, find the coefficients from {eq}\\displaystyle c_1\n\n{eq} to {eq}\\displaystyle c_5\n\n{eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c1=0, c2=2, c3=-16, c4=64, c5=-512/3",
"style": "rule"
}
|
{
"answer": "c1=0, c2=2, c3=-16, c4=64, c5=-512/3",
"index": 124,
"question": "Find the Maclaurin series of the function {eq}\\displaystyle (2 x^2) (e^{\\displaystyle -8 x})\n\n{eq}. Then, find the coefficients from {eq}\\displaystyle c_1\n\n{eq} to {eq}\\displaystyle c_5\n\n{eq}.",
"split": "train"
}
| null | null |
752663
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and are then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of internal kinetic friction, so the oscillation is damped. The particles eventually stop vibrating when the distance between them is 3d. Assume the system of the spring and two charged particles is isolated. Find the increase in internal energy that appears in the spring during the oscillations. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5Cq^2/9d",
"style": "rule"
}
|
{
"answer": "5Cq^2/9d",
"index": 125,
"question": "A light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and are then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of internal kinetic friction, so the oscillation is damped. The particles eventually stop vibrating when the distance between them is 3d. Assume the system of the spring and two charged particles is isolated. Find the increase in internal energy that appears in the spring during the oscillations.",
"split": "train"
}
| null | null |
748386
|
Expression
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "A corporate manager decides to build a new store on a lot owned by the corporation that could be sold to a local developer for $250,000. The lot was purchased for $50,000. How do you determine the value of the new store project? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "NPV = \\displaystyle \\frac{CF1}{1 + I} + \\frac{CF2}{(1 + I)^2} + \\frac{CF3}{(1 + I)^3} + ... + \\frac{CFn}{(1 + I)^n} - Total\\:initial\\:costs",
"style": "rule"
}
|
{
"answer": "NPV = \\displaystyle \\frac{CF1}{1 + I} + \\frac{CF2}{(1 + I)^2} + \\frac{CF3}{(1 + I)^3} + ... + \\frac{CFn}{(1 + I)^n} - Total\\:initial\\:costs",
"index": 126,
"question": "A corporate manager decides to build a new store on a lot owned by the corporation that could be sold to a local developer for $250,000. The lot was purchased for $50,000. How do you determine the value of the new store project?",
"split": "train"
}
| null | null |
523483
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use the Divergence Theorem to calculate the surface integral {eq}\\displaystyle \\iint_S \\mathbf F \\cdot d\\mathbf S\n\n{/eq}; that is, calculate the flux of {eq}\\mathbf F\n\n{/eq} across {eq}S\n\n{/eq}.\n\n{eq}\\mathbf F(x,\\ y,\\ z) = x^2 y\\mathbf i + x y^2\\mathbf j + 3 x y z \\mathbf k,\\ S\n\n{/eq} is the surface of the tetrahedron bounded by the planes {eq}x = 0,\\ y = 0,\\ z = 0\n\n{/eq}, and {eq}\\displaystyle x + 4 y + z = 4\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "56/15",
"style": "rule"
}
|
{
"answer": "56/15",
"index": 127,
"question": "Use the Divergence Theorem to calculate the surface integral {eq}\\displaystyle \\iint_S \\mathbf F \\cdot d\\mathbf S\n\n{/eq}; that is, calculate the flux of {eq}\\mathbf F\n\n{/eq} across {eq}S\n\n{/eq}.\n\n{eq}\\mathbf F(x,\\ y,\\ z) = x^2 y\\mathbf i + x y^2\\mathbf j + 3 x y z \\mathbf k,\\ S\n\n{/eq} is the surface of the tetrahedron bounded by the planes {eq}x = 0,\\ y = 0,\\ z = 0\n\n{/eq}, and {eq}\\displaystyle x + 4 y + z = 4\n\n{/eq}.",
"split": "train"
}
| null | null |
1998751
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How to determine a parametrization of the border of the $R$ region in a clockwise direction, where $R$ is defined by $y\\geq \\left | x \\right |+2$ and $y\\leq 4-x^{2}$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$(1-|t|, |1-|t||+2)$ for $0\\le t<2$ and $(t-3,-t^2+6t-5)$ for $2 \\le t < 4$",
"style": "rule"
}
|
{
"answer": "$(1-|t|, |1-|t||+2)$ for $0\\le t<2$ and $(t-3,-t^2+6t-5)$ for $2 \\le t < 4$",
"index": 128,
"question": "How to determine a parametrization of the border of the $R$ region in a clockwise direction, where $R$ is defined by $y\\geq \\left | x \\right |+2$ and $y\\leq 4-x^{2}$?",
"split": "train"
}
| null | null |
953743
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,500 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #7/4 #, what is the maximum mass that can be pulled up at one time? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "224.1kg",
"style": "rule"
}
|
{
"answer": "224.1kg",
"index": 129,
"question": "A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,500 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #7/4 #, what is the maximum mass that can be pulled up at one time?",
"split": "train"
}
| null | null |
202497
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How can we construct a 2x2 positive semi-definite matrix $A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ such that $x^TAx = x^2a+xyb+xyc+dy^2 \\geq 0$ for all vectors $(x, y)$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A matrix is positive semi-definite if $x^TAx \\geq 0$ for all vectors $x$. An example of 2x2 positive semi-definite matrix is $\\begin{pmatrix}1&0\\\\ 0&1\\end{pmatrix}$",
"style": "rule"
}
|
{
"answer": "A matrix is positive semi-definite if $x^TAx \\geq 0$ for all vectors $x$. An example of 2x2 positive semi-definite matrix is $\\begin{pmatrix}1&0\\\\ 0&1\\end{pmatrix}$",
"index": 130,
"question": "How can we construct a 2x2 positive semi-definite matrix $A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ such that $x^TAx = x^2a+xyb+xyc+dy^2 \\geq 0$ for all vectors $(x, y)$?",
"split": "train"
}
| null | null |
1716666
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Consider the titration of 25.0 mL of 0.215 M KOH with 0.116 M HCl. Calculate the pH after 5.0 mL of HCl has been added. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "13.20",
"style": "rule"
}
|
{
"answer": "13.20",
"index": 131,
"question": "Consider the titration of 25.0 mL of 0.215 M KOH with 0.116 M HCl. Calculate the pH after 5.0 mL of HCl has been added.",
"split": "train"
}
| null | null |
418867
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose I have two non-negative r.v.s $X,Y \\geq 1$ and I know $\\mathbb{E}(X^2 | Y) = (Y-1) ^ 2$. Does this mean $\\mathbb{E}(X | Y) = Y - 1$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "No",
"style": "rule"
}
|
{
"answer": "No",
"index": 132,
"question": "Suppose I have two non-negative r.v.s $X,Y \\geq 1$ and I know $\\mathbb{E}(X^2 | Y) = (Y-1) ^ 2$. Does this mean $\\mathbb{E}(X | Y) = Y - 1$?",
"split": "train"
}
| null | null |
6845
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "A scientist makes 300.0 mL of an acetate buffer using {eq}[CH_3COOH] = [NaCH_3COO]\n\n{/eq} = 0.075 M. How many mL of 5.0 M {eq}NaOH\n\n{/eq} can be added before its buffering capacity is exhausted? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "4.5 mL",
"style": "rule"
}
|
{
"answer": "4.5 mL",
"index": 133,
"question": "A scientist makes 300.0 mL of an acetate buffer using {eq}[CH_3COOH] = [NaCH_3COO]\n\n{/eq} = 0.075 M. How many mL of 5.0 M {eq}NaOH\n\n{/eq} can be added before its buffering capacity is exhausted?",
"split": "train"
}
| null | null |
1958878
|
Percentage
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An engine rejects energy {eq}1,933\\ J\n\n{/eq} to the cold reservoir while performing {eq}731\\ J\n\n{/eq} of work. Calculate the engine's efficiency. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "27.44%",
"style": "rule"
}
|
{
"answer": "27.44%",
"index": 134,
"question": "An engine rejects energy {eq}1,933\\ J\n\n{/eq} to the cold reservoir while performing {eq}731\\ J\n\n{/eq} of work. Calculate the engine's efficiency.",
"split": "train"
}
| null | null |
1614663
|
Float
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Calculate the present value of $15,000 received in 5 years discounted at 8%. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$10,207.5",
"style": "rule"
}
|
{
"answer": "$10,207.5",
"index": 135,
"question": "Calculate the present value of $15,000 received in 5 years discounted at 8%.",
"split": "train"
}
| null | null |
626294
|
Percentage
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "An investment offers a total return of 12 percent over the coming year. Janet Jello thinks the total real return on this investment will be only 8.8 percent. What does Janet believe the inflation rate will be over the next year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.20%",
"style": "rule"
}
|
{
"answer": "3.20%",
"index": 136,
"question": "An investment offers a total return of 12 percent over the coming year. Janet Jello thinks the total real return on this investment will be only 8.8 percent. What does Janet believe the inflation rate will be over the next year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)",
"split": "train"
}
| null | null |
1308715
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two objects have masses of #36 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81 m# to #27 m#? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-1.07e-21 J",
"style": "rule"
}
|
{
"answer": "-1.07e-21 J",
"index": 137,
"question": "Two objects have masses of #36 MG# and #18 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81 m# to #27 m#?",
"split": "train"
}
| null | null |
1972347
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Evaluate the indefinite integral: $$\\int{1\\over (x+a)^2\\cdot(x+b)^2} dx$$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$$\\frac{1}{(a-b)^2} \\left( \\frac{1}{x+a} - \\frac{1}{x+b} \\right) + \\frac{2}{(a-b)^3}\\ln\\left|\\frac{x+b}{x+a}\\right| + C$$",
"style": "rule"
}
|
{
"answer": "$$\\frac{1}{(a-b)^2} \\left( \\frac{1}{x+a} - \\frac{1}{x+b} \\right) + \\frac{2}{(a-b)^3}\\ln\\left|\\frac{x+b}{x+a}\\right| + C$$",
"index": 138,
"question": "Evaluate the indefinite integral: $$\\int{1\\over (x+a)^2\\cdot(x+b)^2} dx$$",
"split": "train"
}
| null | null |
484912
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two flat surfaces are exposed to a uniform, horizontal magnetic field of magnitude 0.50 T. When viewed edge-on, the first surface is tilted at an angle of 11 degrees from the horizontal, and a net magnetic flux of {eq}8.20 \\times 10^{-3}\n\n{/eq} Wb passes through it. The same net magnetic flux passes through the second surface. Determine the area of the first surface. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.086 m^2",
"style": "rule"
}
|
{
"answer": "0.086 m^2",
"index": 139,
"question": "Two flat surfaces are exposed to a uniform, horizontal magnetic field of magnitude 0.50 T. When viewed edge-on, the first surface is tilted at an angle of 11 degrees from the horizontal, and a net magnetic flux of {eq}8.20 \\times 10^{-3}\n\n{/eq} Wb passes through it. The same net magnetic flux passes through the second surface. Determine the area of the first surface.",
"split": "train"
}
| null | null |
1838514
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is travelling 35.4 m/s when it strikes a person's head (1.5 m above the ground), how tall is the building? Neglect air resistance. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "65 m",
"style": "rule"
}
|
{
"answer": "65 m",
"index": 140,
"question": "A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is travelling 35.4 m/s when it strikes a person's head (1.5 m above the ground), how tall is the building? Neglect air resistance.",
"split": "train"
}
| null | null |
1013795
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $A=\\begin{pmatrix} 1 & 1 & -1\\\\ -1 & 3 & -1\\\\ -1 & 1 & 1 \\end{pmatrix}$ and $f\\in L(\\mathbb R^3)$ be canonically associated to $A$. Given the diagonal matrix $B=\\begin{pmatrix} 1 & 0 & 0\\\\ 0 & 2 & 0\\\\ 0 & 0 & 2 \\end{pmatrix}$ and $P=\\begin{pmatrix} 1 & -1 & 1\\\\ 0 & 1 & -1\\\\ -1 & 2 & -1 \\end{pmatrix}$, how to calculate $A^n$ for all $n\\in \\mathbb N$ using the formula $A^n=PB^nP^{-1}$? Why does such a $P$ exist? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$A^n = P B^n P^{-1}$, where $B^n = \\begin{pmatrix} 1^n & 0 & 0 \\\\ 0 & 2^n & 0 \\\\ 0 & 0 & 2^n \\end{pmatrix}$",
"style": "rule"
}
|
{
"answer": "$A^n = P B^n P^{-1}$, where $B^n = \\begin{pmatrix} 1^n & 0 & 0 \\\\ 0 & 2^n & 0 \\\\ 0 & 0 & 2^n \\end{pmatrix}$",
"index": 141,
"question": "Let $A=\\begin{pmatrix} 1 & 1 & -1\\\\ -1 & 3 & -1\\\\ -1 & 1 & 1 \\end{pmatrix}$ and $f\\in L(\\mathbb R^3)$ be canonically associated to $A$. Given the diagonal matrix $B=\\begin{pmatrix} 1 & 0 & 0\\\\ 0 & 2 & 0\\\\ 0 & 0 & 2 \\end{pmatrix}$ and $P=\\begin{pmatrix} 1 & -1 & 1\\\\ 0 & 1 & -1\\\\ -1 & 2 & -1 \\end{pmatrix}$, how to calculate $A^n$ for all $n\\in \\mathbb N$ using the formula $A^n=PB^nP^{-1}$? Why does such a $P$ exist?",
"split": "train"
}
| null | null |
5255
|
Multiple Choice
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Three identical charges of 3.0 {eq}\\mu\n\n{/eq}C are placed at the vertices of an equilateral triangle which measures 30 cm on a side. What is the magnitude of the electrostatic force which acts on an one of the charges?\n\nA) 2.4 N\n\nB) 1.6 N\n\nC) 1.8 N\n\nD) 2.2 N\n\nE) 2.0 N Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"answer": "B",
"index": 142,
"question": "Three identical charges of 3.0 {eq}\\mu\n\n{/eq}C are placed at the vertices of an equilateral triangle which measures 30 cm on a side. What is the magnitude of the electrostatic force which acts on an one of the charges?\n\nA) 2.4 N\n\nB) 1.6 N\n\nC) 1.8 N\n\nD) 2.2 N\n\nE) 2.0 N",
"split": "train"
}
| null | null |
2100135
|
String
|
Biology
|
University
|
general-reasoner
|
[
{
"content": "In 1961, two neurosurgeons were able to reduce seizure activity in epileptic patients by severing the corpus callosum. the neurosurgeons were: Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Vogel and Bogen",
"style": "rule"
}
|
{
"answer": "Vogel and Bogen",
"index": 143,
"question": "In 1961, two neurosurgeons were able to reduce seizure activity in epileptic patients by severing the corpus callosum. the neurosurgeons were:",
"split": "train"
}
| null | null |
371017
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{cccccc}\n8 & -1 & 9 & -5 & -2 & 7 \\\\\n0 & -1 & 7 & -4 & 5 & -9 \\\\\n9 & 0 & 10 & -7 & -7 & 10 \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\left(\n\\begin{array}{cccccc}\n1 & 0 & 0 & \\frac{2}{31} & -\\frac{28}{31} & \\frac{70}{31} \\\\\n0 & 1 & 0 & -\\frac{81}{62} & -\\frac{261}{62} & \\frac{55}{31} \\\\\n0 & 0 & 1 & -\\frac{47}{62} & \\frac{7}{62} & -\\frac{32}{31} \\\\\n\\end{array}\n\\right)$",
"style": "rule"
}
|
{
"answer": "$\\left(\n\\begin{array}{cccccc}\n1 & 0 & 0 & \\frac{2}{31} & -\\frac{28}{31} & \\frac{70}{31} \\\\\n0 & 1 & 0 & -\\frac{81}{62} & -\\frac{261}{62} & \\frac{55}{31} \\\\\n0 & 0 & 1 & -\\frac{47}{62} & \\frac{7}{62} & -\\frac{32}{31} \\\\\n\\end{array}\n\\right)$",
"index": 144,
"question": "Convert the following matrix to reduced row echelon form:\n$\\left(\n\\begin{array}{cccccc}\n8 & -1 & 9 & -5 & -2 & 7 \\\\\n0 & -1 & 7 & -4 & 5 & -9 \\\\\n9 & 0 & 10 & -7 & -7 & 10 \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
1402034
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Consider a 35 year coupon bond that pays $80 annual coupons (beginning one year from today). What is the future value of the coupons at maturity if you can invest them at 8%? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$13785.3",
"style": "rule"
}
|
{
"answer": "$13785.3",
"index": 145,
"question": "Consider a 35 year coupon bond that pays $80 annual coupons (beginning one year from today). What is the future value of the coupons at maturity if you can invest them at 8%?",
"split": "train"
}
| null | null |
378724
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find an equation of the plane tangent to the paraboloid f(x, y, z) = 32 - 3x^2 - 4y^2 - z at (2, 1, 16). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "T(x,y) = 48-12x-8y",
"style": "rule"
}
|
{
"answer": "T(x,y) = 48-12x-8y",
"index": 146,
"question": "Find an equation of the plane tangent to the paraboloid f(x, y, z) = 32 - 3x^2 - 4y^2 - z at (2, 1, 16).",
"split": "train"
}
| null | null |
649984
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Consider the flow of a fluid with viscosity{eq}\\mu\n\n{/eq} through a circular pipe. The velocity profile in the pipe is given as u(r) = umax(1 - r^n/R^n), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at the position r. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "F/L = 2nμπu_max",
"style": "rule"
}
|
{
"answer": "F/L = 2nμπu_max",
"index": 147,
"question": "Consider the flow of a fluid with viscosity{eq}\\mu\n\n{/eq} through a circular pipe. The velocity profile in the pipe is given as u(r) = umax(1 - r^n/R^n), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at the position r. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe.",
"split": "train"
}
| null | null |
1698187
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two long, straight parallel wires 9.6 cm apart carry currents of equal magnitude I. The parallel wires repel each other with a force per unit length of 4.4 nN/m. Find I. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "46 mA",
"style": "rule"
}
|
{
"answer": "46 mA",
"index": 148,
"question": "Two long, straight parallel wires 9.6 cm apart carry currents of equal magnitude I. The parallel wires repel each other with a force per unit length of 4.4 nN/m. Find I.",
"split": "train"
}
| null | null |
337786
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Set up the integrals that represent the area inside r = 6, but outside r = 12 cos(θ). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\int_{\\frac{\\pi}{3}}^{\\frac{2\\pi}{3}} \\int_{6}^{12 \\cos \\theta} r \\ dr \\ d \\theta",
"style": "rule"
}
|
{
"answer": "\\int_{\\frac{\\pi}{3}}^{\\frac{2\\pi}{3}} \\int_{6}^{12 \\cos \\theta} r \\ dr \\ d \\theta",
"index": 149,
"question": "Set up the integrals that represent the area inside r = 6, but outside r = 12 cos(θ).",
"split": "train"
}
| null | null |
1531128
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A model train with a mass of #1 kg# is moving along a track at #4 (cm)/s#. If the curvature of the track changes from a radius of #144 cm# to #60 cm#, by how much must the centripetal force applied by the tracks change? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.0016N",
"style": "rule"
}
|
{
"answer": "0.0016N",
"index": 150,
"question": "A model train with a mass of #1 kg# is moving along a track at #4 (cm)/s#. If the curvature of the track changes from a radius of #144 cm# to #60 cm#, by how much must the centripetal force applied by the tracks change?",
"split": "train"
}
| null | null |
24720
|
Fraction
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A variable force of {eq}x^2 - 2x\n\n{/eq} pounds moves an object along a straight line when it is {eq}x\n\n{/eq} feet from the origin. Determine the work {eq}W\n\n{/eq} done in moving the object from {eq}x = 2\n\n{/eq} to {eq}x = 3\n\n{/eq} feet. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "4/3 ft⋅lb",
"style": "rule"
}
|
{
"answer": "4/3 ft⋅lb",
"index": 151,
"question": "A variable force of {eq}x^2 - 2x\n\n{/eq} pounds moves an object along a straight line when it is {eq}x\n\n{/eq} feet from the origin. Determine the work {eq}W\n\n{/eq} done in moving the object from {eq}x = 2\n\n{/eq} to {eq}x = 3\n\n{/eq} feet.",
"split": "train"
}
| null | null |
1432523
|
Integer
|
Business
|
University
|
general-reasoner
|
[
{
"content": "The following data refer to Industrial Manufacturing Pty Ltd for the current year:\n\n \n \n \n Sales revenue \n $3,157,500 \n \n \n Raw material inventory, 1 January \n 133,500 \n \n \n Purchases of raw material \n 1,096,500 \n \n \n Raw material inventory, 31 December \n 88,500 \n \n \n Direct labor cost incurred \n 711,000 \n \n \n Selling and administrative expenses \n 403,500 \n \n \n Indirect labor cost incurred \n 225,000 \n \n \n Council rates \n 135,000 \n \n \n Depreciation of factory building \n 187,500 \n \n \n Income tax expense \n 37,500 \n \n \n Indirect material used \n 67,500 \n \n \n Depreciation of factory equipment \n 90,000 \n \n \n Insurance on factory and equipment \n 60,000 \n \n \n Electricity for factory \n 105,000 \n \n \n Work in process inventory, 1 January \n 0 \n \n \n Work in process inventory, 31 December \n 60,000 \n \n \n Finished goods inventory, 1 January \n 52,500 \n \n \n Finished goods inventory, 31 December \n 60,000 \n \n \n Applied manufacturing overhead \n 866,250 \n \n \n\n\nSuppose that only half of the $90,000 depreciation on equipment was related to factory machinery, and the other half was related to selling and administrative equipment. How would this have changed the schedule of cost of goods manufactured? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$45,000 reduction",
"style": "rule"
}
|
{
"answer": "$45,000 reduction",
"index": 152,
"question": "The following data refer to Industrial Manufacturing Pty Ltd for the current year:\n\n \n \n \n Sales revenue \n $3,157,500 \n \n \n Raw material inventory, 1 January \n 133,500 \n \n \n Purchases of raw material \n 1,096,500 \n \n \n Raw material inventory, 31 December \n 88,500 \n \n \n Direct labor cost incurred \n 711,000 \n \n \n Selling and administrative expenses \n 403,500 \n \n \n Indirect labor cost incurred \n 225,000 \n \n \n Council rates \n 135,000 \n \n \n Depreciation of factory building \n 187,500 \n \n \n Income tax expense \n 37,500 \n \n \n Indirect material used \n 67,500 \n \n \n Depreciation of factory equipment \n 90,000 \n \n \n Insurance on factory and equipment \n 60,000 \n \n \n Electricity for factory \n 105,000 \n \n \n Work in process inventory, 1 January \n 0 \n \n \n Work in process inventory, 31 December \n 60,000 \n \n \n Finished goods inventory, 1 January \n 52,500 \n \n \n Finished goods inventory, 31 December \n 60,000 \n \n \n Applied manufacturing overhead \n 866,250 \n \n \n\n\nSuppose that only half of the $90,000 depreciation on equipment was related to factory machinery, and the other half was related to selling and administrative equipment. How would this have changed the schedule of cost of goods manufactured?",
"split": "train"
}
| null | null |
892090
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Determine whether the integral is convergent or divergent. Evaluate if the integral is convergent: {eq}\\int_{0}^{\\frac{\\pi}{4}} (\\cos(x))(\\sqrt{(\\sin{x})} {/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1/(3*sqrt(2))",
"style": "rule"
}
|
{
"answer": "1/(3*sqrt(2))",
"index": 153,
"question": "Determine whether the integral is convergent or divergent. Evaluate if the integral is convergent: {eq}\\int_{0}^{\\frac{\\pi}{4}} (\\cos(x))(\\sqrt{(\\sin{x})} {/eq}",
"split": "train"
}
| null | null |
1687450
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $G$ be a weighted graph with edge weights greater than one and $G’$ be the graph constructed by squaring the weights of edges in $G$. Let $T$ and $T’$ be the minimum spanning trees of $G$ and $G’$, respectively, with total weights $t$ and $t’$. Which of the following statements is TRUE?\n(A) $T’ = T$ with total weight $t’ = t^2$\n(B) $T’ = T$ with total weight $t’ < t^2$\n(C) $T’ \\neq T$ but total weight $t’ = t^2$\n(D) None of the above. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"answer": "B",
"index": 154,
"question": "Let $G$ be a weighted graph with edge weights greater than one and $G’$ be the graph constructed by squaring the weights of edges in $G$. Let $T$ and $T’$ be the minimum spanning trees of $G$ and $G’$, respectively, with total weights $t$ and $t’$. Which of the following statements is TRUE?\n(A) $T’ = T$ with total weight $t’ = t^2$\n(B) $T’ = T$ with total weight $t’ < t^2$\n(C) $T’ \\neq T$ but total weight $t’ = t^2$\n(D) None of the above.",
"split": "train"
}
| null | null |
1265902
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A force 50 N is required to maintain a spring stretched from its natural length 9 cm to a length of 13 cm. How much work is done in stretching the spring from 9 cm to 11 cm? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "25 J",
"style": "rule"
}
|
{
"answer": "25 J",
"index": 155,
"question": "A force 50 N is required to maintain a spring stretched from its natural length 9 cm to a length of 13 cm. How much work is done in stretching the spring from 9 cm to 11 cm?",
"split": "train"
}
| null | null |
1884294
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A circular conductor with radius r = 1 m and current I = {eq}{I}_{0}\n\n{/eq} is embedded in a external magnetic field B = 5 T. What is the maximum value of the magnetic potential energy of the conductor? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5πI_0 J",
"style": "rule"
}
|
{
"answer": "5πI_0 J",
"index": 156,
"question": "A circular conductor with radius r = 1 m and current I = {eq}{I}_{0}\n\n{/eq} is embedded in a external magnetic field B = 5 T. What is the maximum value of the magnetic potential energy of the conductor?",
"split": "train"
}
| null | null |
2059639
|
Multiple Choice
|
Psychology
|
Senior High School
|
general-reasoner
|
[
{
"content": "Karl is going to visit the local community mental health center. He is most likely to see a:\n\na. pastoral counselor\n\nb. psychoanalyst\n\nc. psychiatrist\n\nd. clinical psychologist Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 157,
"question": "Karl is going to visit the local community mental health center. He is most likely to see a:\n\na. pastoral counselor\n\nb. psychoanalyst\n\nc. psychiatrist\n\nd. clinical psychologist",
"split": "train"
}
| null | null |
1463907
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Verify {eq}\\int_{-\\infty }^{\\infty }xe^{-x}{/eq} to improper t integrate Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-∞",
"style": "rule"
}
|
{
"answer": "-∞",
"index": 158,
"question": "Verify {eq}\\int_{-\\infty }^{\\infty }xe^{-x}{/eq} to improper t integrate",
"split": "train"
}
| null | null |
1262419
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given the process $X_t = (2+t+\\exp(W_t))_t$ where $W_t$ is Brownian motion, find functions $\\sigma, \\tau$ such that $X_t = X_0 + \\int_0^t \\sigma(W_s,s)dW_s + \\int_0^t\\tau(W_s,s)ds$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$dX_t = \\exp(W_t)dW_t + (1+0.5\\exp(W_t))dt = (X_t-2-t)dW_t + (1+0.5(X_t - 2 - t))dt$",
"style": "rule"
}
|
{
"answer": "$dX_t = \\exp(W_t)dW_t + (1+0.5\\exp(W_t))dt = (X_t-2-t)dW_t + (1+0.5(X_t - 2 - t))dt$",
"index": 159,
"question": "Given the process $X_t = (2+t+\\exp(W_t))_t$ where $W_t$ is Brownian motion, find functions $\\sigma, \\tau$ such that $X_t = X_0 + \\int_0^t \\sigma(W_s,s)dW_s + \\int_0^t\\tau(W_s,s)ds$.",
"split": "train"
}
| null | null |
1972187
|
List
|
Business
|
University
|
general-reasoner
|
[
{
"content": "A machine costing $209, 400 with a four-year life and an estimated $17,000 salvage value is installed in Luther Company's factory on January 1. The factory manager estimates the machine will produce 481,000 units of product during its life. It actually produces the following units 122.300 in 1st year, 122, 500 in 2nd year, 120, 400 in 3rd year, 125, 800 in 4th year. The total number of units produced by the end of year 4 exceeds the original estimate-this difference was not predicted (The machine must not be depreciated below its estimated salvage value.)\n\nRequired: Compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method (Round your per unit depreciation to 2 decimal places. Round your answers to the nearest whole dollar.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Year 1: $48,920\nYear 2: $49,000\nYear 3: $48,160\nYear 4: $46,320\nTotal: $192,400",
"style": "rule"
}
|
{
"answer": "Year 1: $48,920\nYear 2: $49,000\nYear 3: $48,160\nYear 4: $46,320\nTotal: $192,400",
"index": 160,
"question": "A machine costing $209, 400 with a four-year life and an estimated $17,000 salvage value is installed in Luther Company's factory on January 1. The factory manager estimates the machine will produce 481,000 units of product during its life. It actually produces the following units 122.300 in 1st year, 122, 500 in 2nd year, 120, 400 in 3rd year, 125, 800 in 4th year. The total number of units produced by the end of year 4 exceeds the original estimate-this difference was not predicted (The machine must not be depreciated below its estimated salvage value.)\n\nRequired: Compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method (Round your per unit depreciation to 2 decimal places. Round your answers to the nearest whole dollar.)",
"split": "train"
}
| null | null |
1619111
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "find the coefficient of $z^n$ in expansion of $e^z \\cos z$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\frac{1}{n!} \\sum_{0\\leq 2k\\leq n} \\binom{n}{k}(-1)^k$",
"style": "rule"
}
|
{
"answer": "$\\frac{1}{n!} \\sum_{0\\leq 2k\\leq n} \\binom{n}{k}(-1)^k$",
"index": 161,
"question": "find the coefficient of $z^n$ in expansion of $e^z \\cos z$",
"split": "train"
}
| null | null |
546798
|
String
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "Drug side effects are endless and can vary depending on the ____________. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Individuals",
"style": "rule"
}
|
{
"answer": "Individuals",
"index": 162,
"question": "Drug side effects are endless and can vary depending on the ____________.",
"split": "train"
}
| null | null |
2011553
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The specific weight {eq}\\frac {wt}{vol}\n\n{/eq} of brass is {eq}520\\frac{Ib}{ft^{3}}\n\n{/eq}. Determine its density {eq}\\frac{mass}{vol}\n\n{/eq} in SI units. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "8327.1 kg/m^3",
"style": "rule"
}
|
{
"answer": "8327.1 kg/m^3",
"index": 163,
"question": "The specific weight {eq}\\frac {wt}{vol}\n\n{/eq} of brass is {eq}520\\frac{Ib}{ft^{3}}\n\n{/eq}. Determine its density {eq}\\frac{mass}{vol}\n\n{/eq} in SI units.",
"split": "train"
}
| null | null |
90492
|
Integer
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Suppose that demand for a good is given by Q=137-1P, while supply for the good is given by Q=2P-8. If a price ceiling of $11.13 is imposed, what will be the area of the deadweight loss? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "4152",
"style": "rule"
}
|
{
"answer": "4152",
"index": 164,
"question": "Suppose that demand for a good is given by Q=137-1P, while supply for the good is given by Q=2P-8. If a price ceiling of $11.13 is imposed, what will be the area of the deadweight loss?",
"split": "train"
}
| null | null |
1449529
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Why are some producers forced to sell their products at the prevailing market price?\n\na) Price takers find market analysis is too costly.\n\nb) They can increase output without affecting quality.\n\nc) High degree of similarity to competitors products.\n\nd) They are very small players in the overall market Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 165,
"question": "Why are some producers forced to sell their products at the prevailing market price?\n\na) Price takers find market analysis is too costly.\n\nb) They can increase output without affecting quality.\n\nc) High degree of similarity to competitors products.\n\nd) They are very small players in the overall market",
"split": "train"
}
| null | null |
1171778
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 1700 kg roller coaster car starts from rest at a height H = 20.0 m (see figure) above the bottom of a 15.0 m diameter loop. If friction is negligible, determine the downward force of the rails on the car when the upside-down car is at the top of the loop. N Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5555.6 N",
"style": "rule"
}
|
{
"answer": "5555.6 N",
"index": 166,
"question": "A 1700 kg roller coaster car starts from rest at a height H = 20.0 m (see figure) above the bottom of a 15.0 m diameter loop. If friction is negligible, determine the downward force of the rails on the car when the upside-down car is at the top of the loop. N",
"split": "train"
}
| null | null |
873027
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the present value of the rate of flow of money $f(x) = 500e^{0.04x}$ dollars per year over a 10-year period at 7% compounded continuously. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$4319.70",
"style": "rule"
}
|
{
"answer": "$4319.70",
"index": 167,
"question": "Find the present value of the rate of flow of money $f(x) = 500e^{0.04x}$ dollars per year over a 10-year period at 7% compounded continuously.",
"split": "train"
}
| null | null |
555080
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is Stefan Boltzmann law? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "L=A*sigma*T^4",
"style": "rule"
}
|
{
"answer": "L=A*sigma*T^4",
"index": 168,
"question": "What is Stefan Boltzmann law?",
"split": "train"
}
| null | null |
1678101
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Determine the time required for a 1.25 cm diameter Carbon Steel (1% C) sphere to cool from 500 {eq}^o{/eq}C to 100 {eq}^o{/eq}C if exposed to a cooling airflow at 25 {eq}^o{/eq}C. Assume h = 110 W/m{eq}^2{/eq}-K. Assume the thermal conductivity of 1% C steel is 40 W/m-K. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "128.99s",
"style": "rule"
}
|
{
"answer": "128.99s",
"index": 169,
"question": "Determine the time required for a 1.25 cm diameter Carbon Steel (1% C) sphere to cool from 500 {eq}^o{/eq}C to 100 {eq}^o{/eq}C if exposed to a cooling airflow at 25 {eq}^o{/eq}C. Assume h = 110 W/m{eq}^2{/eq}-K. Assume the thermal conductivity of 1% C steel is 40 W/m-K.",
"split": "train"
}
| null | null |
580323
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How many partitions of $n$ distinct objects are there, given that all parts are equinumerous, excluding the empty partition and the identity partition? What is the number of such partitions when $n = p^2$ with $p$ prime, specifically when $n = 9,$ or $25,$ or $49$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\frac{(p^2)!}{(p!)^{p+1}}$",
"style": "rule"
}
|
{
"answer": "$\\frac{(p^2)!}{(p!)^{p+1}}$",
"index": 170,
"question": "How many partitions of $n$ distinct objects are there, given that all parts are equinumerous, excluding the empty partition and the identity partition? What is the number of such partitions when $n = p^2$ with $p$ prime, specifically when $n = 9,$ or $25,$ or $49$?",
"split": "train"
}
| null | null |
983999
|
List
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Construct a {eq}95\\%{/eq} confidence interval for the mean incubation period of the SARS virus interpret the interval, based on the information that the mean incubation period was {eq}5{/eq} days, with a standard deviation of {eq}14.7{/eq} days from interviews with {eq}96{/eq} SARS patients. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(2.0218, 7.9781)",
"style": "rule"
}
|
{
"answer": "(2.0218, 7.9781)",
"index": 171,
"question": "Construct a {eq}95\\%{/eq} confidence interval for the mean incubation period of the SARS virus interpret the interval, based on the information that the mean incubation period was {eq}5{/eq} days, with a standard deviation of {eq}14.7{/eq} days from interviews with {eq}96{/eq} SARS patients.",
"split": "train"
}
| null | null |
304711
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "When the voltage across a resistor is {eq}v\n\n{/eq} the power delivered is {eq}p\n\n{/eq}. If the voltage if doubled to {eq}2v\n\n{/eq}, the power delivered becomes _____. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2P",
"style": "rule"
}
|
{
"answer": "2P",
"index": 172,
"question": "When the voltage across a resistor is {eq}v\n\n{/eq} the power delivered is {eq}p\n\n{/eq}. If the voltage if doubled to {eq}2v\n\n{/eq}, the power delivered becomes _____.",
"split": "train"
}
| null | null |
1545494
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the area of the surface obtained by rotating the curve, {eq}x = 2e^{2y} {/eq}, from y=0 to y=4 about the y-axis. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "111666151.831 sq units",
"style": "rule"
}
|
{
"answer": "111666151.831 sq units",
"index": 173,
"question": "Find the area of the surface obtained by rotating the curve, {eq}x = 2e^{2y} {/eq}, from y=0 to y=4 about the y-axis.",
"split": "train"
}
| null | null |
2080386
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Why does a firm in a competitive industry charge the market price?\n\na. If a firm charges less than the market price, it loses potential revenue,\n\nb. If a firm charges more than the market price, it loses all its market power,\n\nc. The firm can only sell limited number of units of output, so it wants to sell at the market price in order to lower its costs,\n\nd. All of the above are correct. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "None",
"style": "rule"
}
|
{
"answer": "None",
"index": 174,
"question": "Why does a firm in a competitive industry charge the market price?\n\na. If a firm charges less than the market price, it loses potential revenue,\n\nb. If a firm charges more than the market price, it loses all its market power,\n\nc. The firm can only sell limited number of units of output, so it wants to sell at the market price in order to lower its costs,\n\nd. All of the above are correct.",
"split": "train"
}
| null | null |
1986691
|
List
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A force {eq}\\vec{F} = 2\\vec{i} + \\vec{j} - 3\\vec{k}{/eq} is applied to a spacecraft with velocity {eq}\\vec{V} = 3\\vec{i} - \\vec{j}{/eq}. Express {eq}\\vec{F}{/eq} as a vectors parallel and orthogonal to two vectors parallel and orthogonal to {eq}\\vec{V}{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The parallel component is (1.5i - 0.5j) N and the orthogonal component is (0.5i + 1.5j - 3k) N",
"style": "rule"
}
|
{
"answer": "The parallel component is (1.5i - 0.5j) N and the orthogonal component is (0.5i + 1.5j - 3k) N",
"index": 175,
"question": "A force {eq}\\vec{F} = 2\\vec{i} + \\vec{j} - 3\\vec{k}{/eq} is applied to a spacecraft with velocity {eq}\\vec{V} = 3\\vec{i} - \\vec{j}{/eq}. Express {eq}\\vec{F}{/eq} as a vectors parallel and orthogonal to two vectors parallel and orthogonal to {eq}\\vec{V}{/eq}.",
"split": "train"
}
| null | null |
1713444
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $X$ be a random variable having a normal distribution with mean $\\mu$ and standard deviation $\\sigma$. The observations $(x_i; i=1,2,\\cdots,n)$ have measurement errors that are normally distributed with zero mean and known standard deviation $\\delta$. Use the method of maximum likelihood to estimate $\\mu$ and $\\sigma^2$ from erroneous observations. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\widehat{\\sigma}^2 = \\max\\{s^2,\\delta^2\\} - \\delta ^2 = \\max\\{s^2-\\delta^2, 0\\}$",
"style": "rule"
}
|
{
"answer": "$\\widehat{\\sigma}^2 = \\max\\{s^2,\\delta^2\\} - \\delta ^2 = \\max\\{s^2-\\delta^2, 0\\}$",
"index": 176,
"question": "Let $X$ be a random variable having a normal distribution with mean $\\mu$ and standard deviation $\\sigma$. The observations $(x_i; i=1,2,\\cdots,n)$ have measurement errors that are normally distributed with zero mean and known standard deviation $\\delta$. Use the method of maximum likelihood to estimate $\\mu$ and $\\sigma^2$ from erroneous observations.",
"split": "train"
}
| null | null |
378891
|
Multiple Choice
|
History
|
Senior High School
|
general-reasoner
|
[
{
"content": "Who believed the masks he painted were magical and were mediators between humans and evil?\n \n\na. kirchner\nb. marc\nc. kandinsky\nd. picasso? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 177,
"question": "Who believed the masks he painted were magical and were mediators between humans and evil?\n \n\na. kirchner\nb. marc\nc. kandinsky\nd. picasso?",
"split": "train"
}
| null | null |
546561
|
Multiple Choice
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "The Dunkers is a religious group which moved from Germany to Pennsylvania in the 1700's. The Dunkers do not mate outside of their small group, and this has led to a change in the frequency of certain genes. The Pennsylvania Dunkers are now unique for other populations, including their German relatives. Which of these best describes this occurred? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 178,
"question": "The Dunkers is a religious group which moved from Germany to Pennsylvania in the 1700's. The Dunkers do not mate outside of their small group, and this has led to a change in the frequency of certain genes. The Pennsylvania Dunkers are now unique for other populations, including their German relatives. Which of these best describes this occurred?",
"split": "train"
}
| null | null |
824609
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The wavelength of yellow sodium light is 589 nm.\n\nWhat is its frequency? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5.09 * 10^14 Hz",
"style": "rule"
}
|
{
"answer": "5.09 * 10^14 Hz",
"index": 179,
"question": "The wavelength of yellow sodium light is 589 nm.\n\nWhat is its frequency?",
"split": "train"
}
| null | null |
1848114
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 4.6-kg block slides down an inclined plane that makes an angle of 26 with the horizontal. Starting from rest, the block slides a distance of 2.6 m in 4.9 s. Find the coefficient of kinetic friction between the block and plane. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.46",
"style": "rule"
}
|
{
"answer": "0.46",
"index": 180,
"question": "A 4.6-kg block slides down an inclined plane that makes an angle of 26 with the horizontal. Starting from rest, the block slides a distance of 2.6 m in 4.9 s. Find the coefficient of kinetic friction between the block and plane.",
"split": "train"
}
| null | null |
1417065
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the first four nonzero terms in the Maclaurin series for the function f(x) = ln(1 + x^3). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$x - \\frac{x^4}{4} + \\frac{x^7}{7} - \\frac{x^{10}}{10}$",
"style": "rule"
}
|
{
"answer": "$x - \\frac{x^4}{4} + \\frac{x^7}{7} - \\frac{x^{10}}{10}$",
"index": 181,
"question": "Find the first four nonzero terms in the Maclaurin series for the function f(x) = ln(1 + x^3).",
"split": "train"
}
| null | null |
2029325
|
String
|
Business
|
University
|
general-reasoner
|
[
{
"content": "The balance sheet caption for common stock is as follows. What accounts for the difference between issued shares and outstanding shares?\n\n\n Common stock, $10 par value 7,000,000 shares authorized\n 5,700,000shares issued\n 5,500,000 shares outstanding Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Treasury shares",
"style": "rule"
}
|
{
"answer": "Treasury shares",
"index": 182,
"question": "The balance sheet caption for common stock is as follows. What accounts for the difference between issued shares and outstanding shares?\n\n\n Common stock, $10 par value 7,000,000 shares authorized\n 5,700,000shares issued\n 5,500,000 shares outstanding",
"split": "train"
}
| null | null |
1404253
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Write the nuclear equation for lead-209 decaying by beta emission. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "^{209}_{82}Pb \\longrightarrow _{83}^{209} Bi+e^{-}+\\bar{\\nu_e}",
"style": "rule"
}
|
{
"answer": "^{209}_{82}Pb \\longrightarrow _{83}^{209} Bi+e^{-}+\\bar{\\nu_e}",
"index": 183,
"question": "Write the nuclear equation for lead-209 decaying by beta emission.",
"split": "train"
}
| null | null |
66581
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are {eq}m_1 = 8.8 \\; kg\n\n{/eq}, {eq}m_3 = 11.44 \\; kg\n\n{/eq}, {eq}m_4 = 16.016 \\; kg\n\n{/eq}, T{eq}_2\n\n{/eq} = 105 N, and T{eq}_4\n\n{/eq} = 230 N. What is the mass of the second penguin? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "14.27 kg",
"style": "rule"
}
|
{
"answer": "14.27 kg",
"index": 184,
"question": "Four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are {eq}m_1 = 8.8 \\; kg\n\n{/eq}, {eq}m_3 = 11.44 \\; kg\n\n{/eq}, {eq}m_4 = 16.016 \\; kg\n\n{/eq}, T{eq}_2\n\n{/eq} = 105 N, and T{eq}_4\n\n{/eq} = 230 N. What is the mass of the second penguin?",
"split": "train"
}
| null | null |
647618
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Silver nitrate and calcium chloride solutions produce a heavy, white precipitate when mixed. Chemical analysis indicates that the precipitate is silver chloride. What mass of silver chloride would be produced if 95 mL of 6.0 M silver nitrate is mixed with 40 mL of 6.0 M calcium chloride? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "68.79 grams",
"style": "rule"
}
|
{
"answer": "68.79 grams",
"index": 185,
"question": "Silver nitrate and calcium chloride solutions produce a heavy, white precipitate when mixed. Chemical analysis indicates that the precipitate is silver chloride. What mass of silver chloride would be produced if 95 mL of 6.0 M silver nitrate is mixed with 40 mL of 6.0 M calcium chloride?",
"split": "train"
}
| null | null |
287939
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given a joint probability density function of $X$ and $Y$ $$f(x,y)=\\begin{cases} \\frac{1}{a^2} & 0<x,y<a \\\\ 0, & \\text {otherwise} \\end{cases}$$ I want to find the cumulative distribution function of $W=\\max\\left(\\frac {X}{Y},\\frac {Y}{X}\\right)$. I can find the cdf of $Z=\\frac XY$ (is $F(z) =1-\\frac {z}{2}$ correct?), and I know how to find the CDF of max of two independent RVs. Is it correct to assume that the CDF of $W$ is equal to the CDF $X>Y$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$1-\\frac{1}{w}$",
"style": "rule"
}
|
{
"answer": "$1-\\frac{1}{w}$",
"index": 186,
"question": "Given a joint probability density function of $X$ and $Y$ $$f(x,y)=\\begin{cases} \\frac{1}{a^2} & 0<x,y<a \\\\ 0, & \\text {otherwise} \\end{cases}$$ I want to find the cumulative distribution function of $W=\\max\\left(\\frac {X}{Y},\\frac {Y}{X}\\right)$. I can find the cdf of $Z=\\frac XY$ (is $F(z) =1-\\frac {z}{2}$ correct?), and I know how to find the CDF of max of two independent RVs. Is it correct to assume that the CDF of $W$ is equal to the CDF $X>Y$?",
"split": "train"
}
| null | null |
1706173
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "In how many ways can I paint $n$ squares using $k$ colors, where it is not necessary to use all colors, and ways are considered different when the number of squares of at least one color differs? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\sum_{i=1}^{n-k}\\Big(k+\\binom{k}{2}(n-i-1)\\Big)$",
"style": "rule"
}
|
{
"answer": "$\\sum_{i=1}^{n-k}\\Big(k+\\binom{k}{2}(n-i-1)\\Big)$",
"index": 187,
"question": "In how many ways can I paint $n$ squares using $k$ colors, where it is not necessary to use all colors, and ways are considered different when the number of squares of at least one color differs?",
"split": "train"
}
| null | null |
775708
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I'm trying to find the general formula for a matrix raised to a certain power using diagonalization. My original matrix $A$ is: $$ \\begin{bmatrix} -3 & 2 \\\\ -12 & 7 \\end{bmatrix}. $$ My eigenvector matrix $P$ is: $$ \\begin{bmatrix} 1/2 & 1/3 \\\\ 1 & 1 \\end{bmatrix}. $$ I found the diagonal matrix $D$ to be: $$ \\begin{bmatrix} 1 & 0 \\\\ 0 & 3 \\end{bmatrix}. $$ And $P^{-1}$ is: $$ \\begin{bmatrix} 6 & -2 \\\\ -6 & 3 \\end{bmatrix}. $$ The final formula I got from multiplying $P D^n P^{-1}$ is $$ \\begin{bmatrix} 3- 6^n & -1+3^n \\\\ 6-18^n & -2+9^n \\end{bmatrix}. $$ It checks out in the case of $A^1$ but not $A^0$. Where did I go wrong? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\begin{bmatrix} 3-2\\cdot3^n & 3^n-1 \\\\ 6(1-3^{n}) & 3^{n+1}-2 \\end{bmatrix}$",
"style": "rule"
}
|
{
"answer": "$\\begin{bmatrix} 3-2\\cdot3^n & 3^n-1 \\\\ 6(1-3^{n}) & 3^{n+1}-2 \\end{bmatrix}$",
"index": 188,
"question": "I'm trying to find the general formula for a matrix raised to a certain power using diagonalization. My original matrix $A$ is: $$ \\begin{bmatrix} -3 & 2 \\\\ -12 & 7 \\end{bmatrix}. $$ My eigenvector matrix $P$ is: $$ \\begin{bmatrix} 1/2 & 1/3 \\\\ 1 & 1 \\end{bmatrix}. $$ I found the diagonal matrix $D$ to be: $$ \\begin{bmatrix} 1 & 0 \\\\ 0 & 3 \\end{bmatrix}. $$ And $P^{-1}$ is: $$ \\begin{bmatrix} 6 & -2 \\\\ -6 & 3 \\end{bmatrix}. $$ The final formula I got from multiplying $P D^n P^{-1}$ is $$ \\begin{bmatrix} 3- 6^n & -1+3^n \\\\ 6-18^n & -2+9^n \\end{bmatrix}. $$ It checks out in the case of $A^1$ but not $A^0$. Where did I go wrong?",
"split": "train"
}
| null | null |
1923574
|
Multiple Choice
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "If an atom has 5 electrons in the 3rd orbital, what \"time\" on a clock would the 5th\n \n\nelectron be at? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 189,
"question": "If an atom has 5 electrons in the 3rd orbital, what \"time\" on a clock would the 5th\n \n\nelectron be at?",
"split": "train"
}
| null | null |
354825
|
Percentage
|
Business
|
University
|
general-reasoner
|
[
{
"content": "JB Chemical currently discharges liquid waste into Calgary's municipal sewer system. However, the Calgary municipal government has informed JB that a surcharge of $4 per thousand cubit liters will soon be imposed for the discharge of this waste. This has prompted management to evaluate the desirability of treating its own liquid waste.\n\nA proposed system consists of three elements. The first is a retention basin, which would permit unusual discharges to be held and treated before entering the downstream system. The second is a continuous self-cleaning rotary filter required where solids are removed. The third is an automated neutralization process required where materials are added to control the alkalinity-acidity range.\n\nThe system is designed to process 500,000 liters a day. However, management anticipates that only about 200,000 liters of liquid waste would be processed in a normal workday. The company operates 300 days per year. The initial investment in the system would be $450,000, and annual operating costs are predicted to be $150,000. The system has a predicted useful life of ten years and a salvage value of $50,000.\n\nRequired: Determine the project's approximate internal rate of return. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "25.77%",
"style": "rule"
}
|
{
"answer": "25.77%",
"index": 190,
"question": "JB Chemical currently discharges liquid waste into Calgary's municipal sewer system. However, the Calgary municipal government has informed JB that a surcharge of $4 per thousand cubit liters will soon be imposed for the discharge of this waste. This has prompted management to evaluate the desirability of treating its own liquid waste.\n\nA proposed system consists of three elements. The first is a retention basin, which would permit unusual discharges to be held and treated before entering the downstream system. The second is a continuous self-cleaning rotary filter required where solids are removed. The third is an automated neutralization process required where materials are added to control the alkalinity-acidity range.\n\nThe system is designed to process 500,000 liters a day. However, management anticipates that only about 200,000 liters of liquid waste would be processed in a normal workday. The company operates 300 days per year. The initial investment in the system would be $450,000, and annual operating costs are predicted to be $150,000. The system has a predicted useful life of ten years and a salvage value of $50,000.\n\nRequired: Determine the project's approximate internal rate of return.",
"split": "train"
}
| null | null |
1670395
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "If the gradient of f is f = xj - zi + yx k and the point P = (-9, -7, -10) lies on the level surface f(x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-9x - 10y + 63z + 479 = 0",
"style": "rule"
}
|
{
"answer": "-9x - 10y + 63z + 479 = 0",
"index": 191,
"question": "If the gradient of f is f = xj - zi + yx k and the point P = (-9, -7, -10) lies on the level surface f(x, y, z) = 0, find an equation for the tangent plane to the surface at the point P.",
"split": "train"
}
| null | null |
523259
|
String
|
Economics
|
Junior High School
|
general-reasoner
|
[
{
"content": "Which system has the least amount of government involvement in the economy? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Capitalism",
"style": "rule"
}
|
{
"answer": "Capitalism",
"index": 192,
"question": "Which system has the least amount of government involvement in the economy?",
"split": "train"
}
| null | null |
616425
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Which of the following is true about the hypothesis test of cost parameters? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 193,
"question": "Which of the following is true about the hypothesis test of cost parameters?",
"split": "train"
}
| null | null |
1039029
|
Boolean
|
Computer Science
|
Junior High School
|
general-reasoner
|
[
{
"content": "\"A {eq}r\n\n{/eq} sum can be used instead of filling out an application.\" Indicate whether the statement is 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": 194,
"question": "\"A {eq}r\n\n{/eq} sum can be used instead of filling out an application.\" Indicate whether the statement is true or false.",
"split": "train"
}
| null | null |
970697
|
List
|
Business
|
Junior High School
|
general-reasoner
|
[
{
"content": "List three things you should do before you attempt to return a defective product Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1. Contact the manufacturer and obtain an RMA (Return Merchandise Authorization) number.\n2. Carefully repackage the defective product in its original packaging, including all accessories and documentation.\n3. Ship the product to the manufacturer's specified address, ensuring you obtain a tracking number for the shipment.",
"style": "rule"
}
|
{
"answer": "1. Contact the manufacturer and obtain an RMA (Return Merchandise Authorization) number.\n2. Carefully repackage the defective product in its original packaging, including all accessories and documentation.\n3. Ship the product to the manufacturer's specified address, ensuring you obtain a tracking number for the shipment.",
"index": 195,
"question": "List three things you should do before you attempt to return a defective product",
"split": "train"
}
| null | null |
1587659
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Compared to hiring a white worker, an employer is $5 less happy when he hires a black worker and is $6 less happy when he hires a Hispanic worker. The frim faces hourly wage rates of $20 for whites, $16 for blacks, and $14 for Hispanics. Which of the following describes the firm's hiring decision?\n\na. The firm hires all white workers.b. The firm hires a mixture of white and black workers.c. The firm hires a mixture of white and Hispanic workers.d. The firm hires all black workers. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 196,
"question": "Compared to hiring a white worker, an employer is $5 less happy when he hires a black worker and is $6 less happy when he hires a Hispanic worker. The frim faces hourly wage rates of $20 for whites, $16 for blacks, and $14 for Hispanics. Which of the following describes the firm's hiring decision?\n\na. The firm hires all white workers.b. The firm hires a mixture of white and black workers.c. The firm hires a mixture of white and Hispanic workers.d. The firm hires all black workers.",
"split": "train"
}
| null | null |
1964600
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use the definition to find the expression for the area under the graph of {eq}\\displaystyle f{/eq} as a limit. Do not evaluate the limit.\n\n{eq}\\displaystyle f(x) = \\frac{6x}{x^2+4}, \\ 1 \\leq x \\leq 3{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\lim_{n \\to \\infty} \\sum_{i=1}^n \\left (\\frac{12n + 24i}{5n^2+ 4in + 4i^2} \\right )",
"style": "rule"
}
|
{
"answer": "\\lim_{n \\to \\infty} \\sum_{i=1}^n \\left (\\frac{12n + 24i}{5n^2+ 4in + 4i^2} \\right )",
"index": 197,
"question": "Use the definition to find the expression for the area under the graph of {eq}\\displaystyle f{/eq} as a limit. Do not evaluate the limit.\n\n{eq}\\displaystyle f(x) = \\frac{6x}{x^2+4}, \\ 1 \\leq x \\leq 3{/eq}.",
"split": "train"
}
| null | null |
876365
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "At a pressure of 570 mm Hg and a temperature of 25 degrees Celsius, a gas sample has a volume of 2270 ml. What is the final pressure, in mm Hg, at a volume of 1250 ml and a temperature of 175 degrees Celsius. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1556.25 mmHg",
"style": "rule"
}
|
{
"answer": "1556.25 mmHg",
"index": 198,
"question": "At a pressure of 570 mm Hg and a temperature of 25 degrees Celsius, a gas sample has a volume of 2270 ml. What is the final pressure, in mm Hg, at a volume of 1250 ml and a temperature of 175 degrees Celsius.",
"split": "train"
}
| null | null |
1754236
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "If 200g of Argon gas (Ar) expands from the initial temperature of 150 degrees Celcius and in the process does 3.15 kJ of work and absorbs 1.52 kJ of heat what is the final temperature of the gas? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "396.71K",
"style": "rule"
}
|
{
"answer": "396.71K",
"index": 199,
"question": "If 200g of Argon gas (Ar) expands from the initial temperature of 150 degrees Celcius and in the process does 3.15 kJ of work and absorbs 1.52 kJ of heat what is the final temperature of the gas?",
"split": "train"
}
| null | null |
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