Dataset Viewer
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|---|---|---|---|---|---|---|---|---|---|---|
1309043
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which of the following statements is (are) correct?\n\n(x) The opportunity cost of the first 50 tables is 400 chairs and the opportunity cost of the first 800 chairs is 20 tables.\n\n(y) If the economy produces 80 tables and 800 chairs instead of 50 tables and 1,400 chairs, then the opportunity cost of the 30 additional tables is 600 chairs.\n\n(z) The opportunity cost of the 200th chair is equal to 1/40th of a table and the opportunity cost of the 30th table is more than 8 chairs but less than 10 chairs.\n\na. (x), (y) and (z)\n\nb. (x) and (y), only\n\nc. (x) and (z), only\n\nd. (y) and (z), only\n\ne. (x) only\n\nProduction Possibilities\n\n\nTables Chairs\n100 0\n80 800\n50 1,400\n 0 1,800 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 0,
"question": "Which of the following statements is (are) correct?\n\n(x) The opportunity cost of the first 50 tables is 400 chairs and the opportunity cost of the first 800 chairs is 20 tables.\n\n(y) If the economy produces 80 tables and 800 chairs instead of 50 tables and 1,400 chairs, then the opportunity cost of the 30 additional tables is 600 chairs.\n\n(z) The opportunity cost of the 200th chair is equal to 1/40th of a table and the opportunity cost of the 30th table is more than 8 chairs but less than 10 chairs.\n\na. (x), (y) and (z)\n\nb. (x) and (y), only\n\nc. (x) and (z), only\n\nd. (y) and (z), only\n\ne. (x) only\n\nProduction Possibilities\n\n\nTables Chairs\n100 0\n80 800\n50 1,400\n 0 1,800",
"split": "train"
}
| null | null |
1131067
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Write an equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilibrium, bounces to it maximum height of 6 inches above equilibrium and returns to its lowest point in a total of 2 seconds. (think about amplitude and period) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6*sin(πt)",
"style": "rule"
}
|
{
"answer": "6*sin(πt)",
"index": 1,
"question": "Write an equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilibrium, bounces to it maximum height of 6 inches above equilibrium and returns to its lowest point in a total of 2 seconds. (think about amplitude and period)",
"split": "train"
}
| null | null |
2022282
|
Expression
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Balance the following reaction equation: {eq}N_2H_4 \\to NH_3 + N_2\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3N_2H_4 -> 4NH_3 + N_2",
"style": "rule"
}
|
{
"answer": "3N_2H_4 -> 4NH_3 + N_2",
"index": 2,
"question": "Balance the following reaction equation: {eq}N_2H_4 \\to NH_3 + N_2\n\n{/eq}",
"split": "train"
}
| null | null |
667568
|
String
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "Identify the term:\n\nThis WBC secretes histamine. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "mast cells",
"style": "rule"
}
|
{
"answer": "mast cells",
"index": 3,
"question": "Identify the term:\n\nThis WBC secretes histamine.",
"split": "train"
}
| null | null |
1319302
|
Float
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "How far is saturn from the sun in scientific notation? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.4 x 10 ^ 9 kilometers",
"style": "rule"
}
|
{
"answer": "1.4 x 10 ^ 9 kilometers",
"index": 4,
"question": "How far is saturn from the sun in scientific notation?",
"split": "train"
}
| null | null |
879860
|
Boolean
|
Mathematics
|
PhD
|
general-reasoner
|
[
{
"content": "Suppose $X$ is Nötherian, integral, separated, and regular in codimension one. If $\\imath:Y\\to X$ and $\\jmath:Z\\to X$ are closed immersions and $Y$ and $Z$ are integral schemes such that there exists a homeomorphism $\\lvert\\varphi\\rvert:\\lvert Y\\rvert\\to \\lvert Z\\rvert$ such that $\\lvert\\jmath\\rvert\\circ\\lvert\\varphi\\rvert=\\lvert\\imath\\rvert$, can $\\lvert\\varphi\\rvert$ be extended to a morphism of schemes $\\varphi:Y\\to Z$ such that $\\jmath\\circ\\varphi=\\imath$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 5,
"question": "Suppose $X$ is Nötherian, integral, separated, and regular in codimension one. If $\\imath:Y\\to X$ and $\\jmath:Z\\to X$ are closed immersions and $Y$ and $Z$ are integral schemes such that there exists a homeomorphism $\\lvert\\varphi\\rvert:\\lvert Y\\rvert\\to \\lvert Z\\rvert$ such that $\\lvert\\jmath\\rvert\\circ\\lvert\\varphi\\rvert=\\lvert\\imath\\rvert$, can $\\lvert\\varphi\\rvert$ be extended to a morphism of schemes $\\varphi:Y\\to Z$ such that $\\jmath\\circ\\varphi=\\imath$?",
"split": "train"
}
| null | null |
712060
|
String
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "Which unit, megagrams or grams, would be more suitable for expressing the mass of an automobile? Why? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "megagram",
"style": "rule"
}
|
{
"answer": "megagram",
"index": 6,
"question": "Which unit, megagrams or grams, would be more suitable for expressing the mass of an automobile? Why?",
"split": "train"
}
| null | null |
632240
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose $X_1$ and $X_2$ are independent exponential random variables with $E(X_1)=\\theta$ and $E(X_2)=2\\theta$. Find a most powerful test of $H_0: \\theta=2$ versus $H_\\alpha: \\theta=4$. Given that $\\frac{L(\\theta_0;x_1,x_2)}{L(\\theta_\\alpha;x_1,x_2)}= 4e^{-\\frac{2x_1+x_2}{8}}$ and $2X_1+X_2$ is a sufficient statistic, give the decision rule for $\\alpha = 0.05$. How do I relate this quantity to the $\\alpha = 0.05$ to find the decision rule? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Reject $H_0$ when $2X_1 + X_2 > T$, where $T$ satisfies $\\mathbb{P}(\\Gamma(2,4) > T) = 0.05$",
"style": "rule"
}
|
{
"answer": "Reject $H_0$ when $2X_1 + X_2 > T$, where $T$ satisfies $\\mathbb{P}(\\Gamma(2,4) > T) = 0.05$",
"index": 7,
"question": "Suppose $X_1$ and $X_2$ are independent exponential random variables with $E(X_1)=\\theta$ and $E(X_2)=2\\theta$. Find a most powerful test of $H_0: \\theta=2$ versus $H_\\alpha: \\theta=4$. Given that $\\frac{L(\\theta_0;x_1,x_2)}{L(\\theta_\\alpha;x_1,x_2)}= 4e^{-\\frac{2x_1+x_2}{8}}$ and $2X_1+X_2$ is a sufficient statistic, give the decision rule for $\\alpha = 0.05$. How do I relate this quantity to the $\\alpha = 0.05$ to find the decision rule?",
"split": "train"
}
| null | null |
2004481
|
Integer
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Assuming that the gases are ideal, calculate the amount of work done (in joules) in the following reaction. Is work done on or by the system?\n\nA reaction in the Mond process for purifying nickel(0) tetracarbonyl at {eq}50-100 ^{\\circ} C\n\n{/eq}.\n\nAssume one mole of nickel is used and a constant temperature of {eq}75 ^{\\circ} C\n\n{/eq} is maintained.\n\n{eq}Ni(s) + 4CO(g) \\rightarrow Ni(CO)_4(g)\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "8684J",
"style": "rule"
}
|
{
"answer": "8684J",
"index": 8,
"question": "Assuming that the gases are ideal, calculate the amount of work done (in joules) in the following reaction. Is work done on or by the system?\n\nA reaction in the Mond process for purifying nickel(0) tetracarbonyl at {eq}50-100 ^{\\circ} C\n\n{/eq}.\n\nAssume one mole of nickel is used and a constant temperature of {eq}75 ^{\\circ} C\n\n{/eq} is maintained.\n\n{eq}Ni(s) + 4CO(g) \\rightarrow Ni(CO)_4(g)\n\n{/eq}",
"split": "train"
}
| null | null |
1389551
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "A cash strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming your indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$8,645.09",
"style": "rule"
}
|
{
"answer": "$8,645.09",
"index": 9,
"question": "A cash strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming your indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept?",
"split": "train"
}
| null | null |
403774
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Kathy is changing the tire of her car on a steep hill 20 m high. She trips and drops the 10 kg spare tire which rolls down the hill. What is the speed of the tire at the top of the next hill if the height of the hill is 5 m high? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "17.16 m/s",
"style": "rule"
}
|
{
"answer": "17.16 m/s",
"index": 10,
"question": "Kathy is changing the tire of her car on a steep hill 20 m high. She trips and drops the 10 kg spare tire which rolls down the hill. What is the speed of the tire at the top of the next hill if the height of the hill is 5 m high?",
"split": "train"
}
| null | null |
574118
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "The problem with attempting to control interest rates while also controlling the exchange rate and maintaining free and open international capital flows is that\n\nA. Capital will flow into those countries that maintain a rate of interest above the global mean rate (risk-adjusted) causing the nation to move off the peg\n\nB. Capital will flow out of those countries that maintain a rate of interest below the global mean (risk-adjusted) causing the nation to move off the peg\n\nC. Any attempt to fix the rate of interest will almost certainly cause the exchange rate to adjust\n\nD. All of the above Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "D",
"style": "rule"
}
|
{
"answer": "D",
"index": 11,
"question": "The problem with attempting to control interest rates while also controlling the exchange rate and maintaining free and open international capital flows is that\n\nA. Capital will flow into those countries that maintain a rate of interest above the global mean rate (risk-adjusted) causing the nation to move off the peg\n\nB. Capital will flow out of those countries that maintain a rate of interest below the global mean (risk-adjusted) causing the nation to move off the peg\n\nC. Any attempt to fix the rate of interest will almost certainly cause the exchange rate to adjust\n\nD. All of the above",
"split": "train"
}
| null | null |
584181
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "The pOH of an aqueous solution of 0.381 M ammonia is Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.419",
"style": "rule"
}
|
{
"answer": "0.419",
"index": 12,
"question": "The pOH of an aqueous solution of 0.381 M ammonia is",
"split": "train"
}
| null | null |
1579870
|
Multiple Choice
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "Semester Exams,Which Statement Best compares the two passages. Screenshot below,Giving Brainliest. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "D. Both passages have a theme of the hardships of war",
"style": "rule"
}
|
{
"answer": "D. Both passages have a theme of the hardships of war",
"index": 13,
"question": "Semester Exams,Which Statement Best compares the two passages. Screenshot below,Giving Brainliest.",
"split": "train"
}
| null | null |
2040558
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the local maximum and minimum values and the saddle points of the function f(x,y) = xy - x^2 - y^2 - 2x - 2y + 4. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "local maximum at (-2,-2)",
"style": "rule"
}
|
{
"answer": "local maximum at (-2,-2)",
"index": 14,
"question": "Find the local maximum and minimum values and the saddle points of the function f(x,y) = xy - x^2 - y^2 - 2x - 2y + 4.",
"split": "train"
}
| null | null |
736606
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "For the reaction, calculate how many grams of the product form when 1.6 g of {eq}Cl_2\n\n{/eq} completely reacts. Assume that there is more than enough of the other reactant.\n\n{eq}2Na(s) + Cl_2(g) \\to 2NaCl(s)\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.64 g NaCl",
"style": "rule"
}
|
{
"answer": "2.64 g NaCl",
"index": 15,
"question": "For the reaction, calculate how many grams of the product form when 1.6 g of {eq}Cl_2\n\n{/eq} completely reacts. Assume that there is more than enough of the other reactant.\n\n{eq}2Na(s) + Cl_2(g) \\to 2NaCl(s)\n\n{/eq}",
"split": "train"
}
| null | null |
1378988
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A solenoid with 400 turns has a radius of 0.060 m and is 50 cm long. If this solenoid carries a current of 18 A, what is the magnitude of the magnetic field near the center of the solenoid?\n\n{eq}(\\mu_0 = 4\\pi \\times 10^{-7} T \\cdot m/A)\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.018 T",
"style": "rule"
}
|
{
"answer": "0.018 T",
"index": 16,
"question": "A solenoid with 400 turns has a radius of 0.060 m and is 50 cm long. If this solenoid carries a current of 18 A, what is the magnitude of the magnetic field near the center of the solenoid?\n\n{eq}(\\mu_0 = 4\\pi \\times 10^{-7} T \\cdot m/A)\n\n{/eq}",
"split": "train"
}
| null | null |
129410
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "On July 1, 2017, Metlock Limited issued bonds with a face value of $1,100,000 due in 20 years, paying interest at a face rate of 9% on January 1 and July 1 each year. The bonds were issued to yield 11.00%. The company's year-end was September 30. The company used the effective interest method of amortization. Calculate the premium or discount on the bonds. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$176,468.05",
"style": "rule"
}
|
{
"answer": "$176,468.05",
"index": 17,
"question": "On July 1, 2017, Metlock Limited issued bonds with a face value of $1,100,000 due in 20 years, paying interest at a face rate of 9% on January 1 and July 1 each year. The bonds were issued to yield 11.00%. The company's year-end was September 30. The company used the effective interest method of amortization. Calculate the premium or discount on the bonds.",
"split": "train"
}
| null | null |
1664757
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "When 15.00 g of of an unknown fuel (MM - 60.0 g/mol) is burned in a calorimeter with a heat capacity of 66.0 kJ/ C, the temperature of the calorimeter assembly rises by 6.93 C. What is the standard enthalpy of combustion for the fuel, in kJ/mol? Enter your answer with no units. Make sure to indicate the sign (positive or negative). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "+1829.52",
"style": "rule"
}
|
{
"answer": "+1829.52",
"index": 18,
"question": "When 15.00 g of of an unknown fuel (MM - 60.0 g/mol) is burned in a calorimeter with a heat capacity of 66.0 kJ/ C, the temperature of the calorimeter assembly rises by 6.93 C. What is the standard enthalpy of combustion for the fuel, in kJ/mol? Enter your answer with no units. Make sure to indicate the sign (positive or negative).",
"split": "train"
}
| null | null |
1609839
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Dungeons and Dragons Gaming Co. is expected to pay a dividend in year 1 of $1.4, a dividend in year 2 of $2.1, and a dividend in year 3 of $3.5. After year 3, dividends are expected to grow at the rate of 4.4% per year. An appropriate required return for the stock is 10%.\n\nUsing the multistage dividend discount model, what should be the price of the stock today? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$54.66",
"style": "rule"
}
|
{
"answer": "$54.66",
"index": 19,
"question": "Dungeons and Dragons Gaming Co. is expected to pay a dividend in year 1 of $1.4, a dividend in year 2 of $2.1, and a dividend in year 3 of $3.5. After year 3, dividends are expected to grow at the rate of 4.4% per year. An appropriate required return for the stock is 10%.\n\nUsing the multistage dividend discount model, what should be the price of the stock today?",
"split": "train"
}
| null | null |
1131704
|
String
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "What is the limit of #x^2e^x# as x goes to infinity? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "∞",
"style": "rule"
}
|
{
"answer": "∞",
"index": 20,
"question": "What is the limit of #x^2e^x# as x goes to infinity?",
"split": "train"
}
| null | null |
1904374
|
Percentage
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "If the firm could reduce the average age of its inventory from 73 days, to 63 day, by how much would it reduce its dollar investment in working capital? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.74%",
"style": "rule"
}
|
{
"answer": "2.74%",
"index": 21,
"question": "If the firm could reduce the average age of its inventory from 73 days, to 63 day, by how much would it reduce its dollar investment in working capital?",
"split": "train"
}
| null | null |
256471
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Suppose in the current year that there is a nation-wide drought for apple growers and a statewide bumper crop for oranges in both Florida and California. Which of the following statements correctly reflects the subsequent developments in the U.S. orange market?\n\na. Both equilibrium output and price will increase.\n\nb. Both equilibrium output and price will decrease.\n\nc. Both equilibrium output and price may decrease.\n\nd. Equilibrium output may decrease and price will increase.\n\ne. Equilibrium output will increase and price may increase. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "e",
"style": "rule"
}
|
{
"answer": "e",
"index": 22,
"question": "Suppose in the current year that there is a nation-wide drought for apple growers and a statewide bumper crop for oranges in both Florida and California. Which of the following statements correctly reflects the subsequent developments in the U.S. orange market?\n\na. Both equilibrium output and price will increase.\n\nb. Both equilibrium output and price will decrease.\n\nc. Both equilibrium output and price may decrease.\n\nd. Equilibrium output may decrease and price will increase.\n\ne. Equilibrium output will increase and price may increase.",
"split": "train"
}
| null | null |
1268723
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the volume of the solid revolution generated by revolving the region bounded by {eq}y = (x + 6)/(x^2 + 8x - 20), y = 0, x = 3, and\\ x= 5 about the {eq}y- axis. Provide a graphical display of calculation. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "18.773",
"style": "rule"
}
|
{
"answer": "18.773",
"index": 23,
"question": "Find the volume of the solid revolution generated by revolving the region bounded by {eq}y = (x + 6)/(x^2 + 8x - 20), y = 0, x = 3, and\\ x= 5 about the {eq}y- axis. Provide a graphical display of calculation.",
"split": "train"
}
| null | null |
1759167
|
Float
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is {eq}p = \\sqrt{49 + 3.8x}\n\n{/eq} dollars. Determine the producers' surplus if the market price is set at $12 per unit. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5701.75",
"style": "rule"
}
|
{
"answer": "5701.75",
"index": 24,
"question": "A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is {eq}p = \\sqrt{49 + 3.8x}\n\n{/eq} dollars. Determine the producers' surplus if the market price is set at $12 per unit.",
"split": "train"
}
| null | null |
1628036
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Use Work and Mechanical Energy to derive the expression for the experimentally determined moment of inertia. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "I=m[\\frac{v^2-u^2}{\\omega_i^2-\\omega_f^2}]+2mg[\\frac{h_f-h_i}{\\omega_i^2-\\omega_f^2}]",
"style": "rule"
}
|
{
"answer": "I=m[\\frac{v^2-u^2}{\\omega_i^2-\\omega_f^2}]+2mg[\\frac{h_f-h_i}{\\omega_i^2-\\omega_f^2}]",
"index": 25,
"question": "Use Work and Mechanical Energy to derive the expression for the experimentally determined moment of inertia.",
"split": "train"
}
| null | null |
88656
|
Float
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "The allowance account before adjustment has a debit balance of $5,700. Bad debt expense for the upcoming year is estimated to be 3% of net sales, which is $162,600.\nWhat is the amount of the adjusting entry to provide for doubtful accounts? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$10,578",
"style": "rule"
}
|
{
"answer": "$10,578",
"index": 26,
"question": "The allowance account before adjustment has a debit balance of $5,700. Bad debt expense for the upcoming year is estimated to be 3% of net sales, which is $162,600.\nWhat is the amount of the adjusting entry to provide for doubtful accounts?",
"split": "train"
}
| null | null |
146835
|
Percentage
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the standard deviation of PG&E's monthly returns. The past five monthly returns for PG&E are -3.19%, 3.93%, 3.79%, 6.50%, and 3.60%. (Do not round intermediate calculations and round your final answer to 2 decimal places.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.24%",
"style": "rule"
}
|
{
"answer": "3.24%",
"index": 27,
"question": "Compute the standard deviation of PG&E's monthly returns. The past five monthly returns for PG&E are -3.19%, 3.93%, 3.79%, 6.50%, and 3.60%. (Do not round intermediate calculations and round your final answer to 2 decimal places.)",
"split": "train"
}
| null | null |
466331
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "NextToo is considering an investment that will require purchasing a piece of equipment for $1,200 and last for two years. The investment will pay $1,000 at the end of each of the two years before taxes. Taxes are 30%, and the $1,200 equipment is deductible for tax purposes over the two year period using straight line depreciation. That would be $600 of depreciation year year. NextToo requires a 10% return on investments. What is the Net Present Value of the investment?\n\n- $327\n\n- $15\n\n- $223\n\n- <$506> Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 28,
"question": "NextToo is considering an investment that will require purchasing a piece of equipment for $1,200 and last for two years. The investment will pay $1,000 at the end of each of the two years before taxes. Taxes are 30%, and the $1,200 equipment is deductible for tax purposes over the two year period using straight line depreciation. That would be $600 of depreciation year year. NextToo requires a 10% return on investments. What is the Net Present Value of the investment?\n\n- $327\n\n- $15\n\n- $223\n\n- <$506>",
"split": "train"
}
| null | null |
353164
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "After {eq}54.0\n\n{/eq} min, {eq}28.0\\%\n\n{/eq} of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "113.95 min",
"style": "rule"
}
|
{
"answer": "113.95 min",
"index": 29,
"question": "After {eq}54.0\n\n{/eq} min, {eq}28.0\\%\n\n{/eq} of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?",
"split": "train"
}
| null | null |
696321
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Antonio is analyzing a project with an initial cost of $34,000 and cash inflows of $28,000 a year for 2 years. This project is an extension of the firm's current operations and thus is equally as risky as the current firm. The firm uses only debt and common stock to finance its operations and maintains a debt-equity ratio of 0.8. The pre-tax cost of debt is 10.2 percent and the cost of equity is 12.6 percent. The tax rate is 34 percent.\n\nWhat is the projected net present value of this project? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "14601.56",
"style": "rule"
}
|
{
"answer": "14601.56",
"index": 30,
"question": "Antonio is analyzing a project with an initial cost of $34,000 and cash inflows of $28,000 a year for 2 years. This project is an extension of the firm's current operations and thus is equally as risky as the current firm. The firm uses only debt and common stock to finance its operations and maintains a debt-equity ratio of 0.8. The pre-tax cost of debt is 10.2 percent and the cost of equity is 12.6 percent. The tax rate is 34 percent.\n\nWhat is the projected net present value of this project?",
"split": "train"
}
| null | null |
518551
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Solve the following:\n\n{eq}t\\frac{dx}{dt} -x-3y = t\\frac{dy}{dt} -x+y = 0\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "x=t/4(C1+3C2), y=t/4(C1-C2)",
"style": "rule"
}
|
{
"answer": "x=t/4(C1+3C2), y=t/4(C1-C2)",
"index": 31,
"question": "Solve the following:\n\n{eq}t\\frac{dx}{dt} -x-3y = t\\frac{dy}{dt} -x+y = 0\n{/eq}",
"split": "train"
}
| null | null |
1440537
|
Boolean
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "True or False; If an engine consists of two isotherms and two isochores and operates between 20 and 4 L/mol, the work of expansion at 1000 K exceeds that of compression at 500 K by less than 100%. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "True",
"style": "rule"
}
|
{
"answer": "True",
"index": 32,
"question": "True or False; If an engine consists of two isotherms and two isochores and operates between 20 and 4 L/mol, the work of expansion at 1000 K exceeds that of compression at 500 K by less than 100%.",
"split": "train"
}
| null | null |
1388635
|
Multiple Choice
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which one of the following species has the same electron configuration as the Al{eq}^{3+}\n\n{/eq} cation?\n\nA. F\n\nB. Cl\n\nC. S{eq}_2\n\n{/eq}\n\nD. O\n\nE. Mg{eq}^+\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "F",
"style": "rule"
}
|
{
"answer": "F",
"index": 33,
"question": "Which one of the following species has the same electron configuration as the Al{eq}^{3+}\n\n{/eq} cation?\n\nA. F\n\nB. Cl\n\nC. S{eq}_2\n\n{/eq}\n\nD. O\n\nE. Mg{eq}^+\n\n{/eq}",
"split": "train"
}
| null | null |
731652
|
Multiple Choice
|
Philosophy
|
Senior High School
|
general-reasoner
|
[
{
"content": "Statements: The national norm is 100 beds per thousand populations but in this state, 150 beds per thousand are available in the hospitals. Conclusions: Our national norm is appropriate. The state's health system is taking adequate care in this regard. Options are: answer A Only conclusion I follows; answer B Only conclusion II follows; answer C Either I or II follows; answer D Neither I nor II follows; answer E Both I and II follow Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"answer": "B",
"index": 34,
"question": "Statements: The national norm is 100 beds per thousand populations but in this state, 150 beds per thousand are available in the hospitals. Conclusions: Our national norm is appropriate. The state's health system is taking adequate care in this regard. Options are: answer A Only conclusion I follows; answer B Only conclusion II follows; answer C Either I or II follows; answer D Neither I nor II follows; answer E Both I and II follow",
"split": "train"
}
| null | null |
1948663
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A race car is making a U-turn at constant speed. The coefficient of friction between the tires and the track is 1.89. If the radius of the curve is 16.1 m, what is the maximum speed at which the car can turn without sliding? Assume that the car is performing uniform circular motion. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "17.26 m/s",
"style": "rule"
}
|
{
"answer": "17.26 m/s",
"index": 35,
"question": "A race car is making a U-turn at constant speed. The coefficient of friction between the tires and the track is 1.89. If the radius of the curve is 16.1 m, what is the maximum speed at which the car can turn without sliding? Assume that the car is performing uniform circular motion.",
"split": "train"
}
| null | null |
540001
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "How much energy is produced when the sun converts one kg of hydrogen into helium?. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6.3e14 J",
"style": "rule"
}
|
{
"answer": "6.3e14 J",
"index": 36,
"question": "How much energy is produced when the sun converts one kg of hydrogen into helium?.",
"split": "train"
}
| null | null |
773326
|
Multiple Choice
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "Eight months ago, you purchased 400 shares of Winston stock at a price of $46.40 a share. The company pays quarterly dividends of $1.05 a share. Today, you sold all of your shares for $48.30 a share. What is your total percentage return on this investment?\n\na. 8.62%\n\nb. 12.08%\n\nc. 10.12%\n\nd. 4.09%\n\ne. 7.34% Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 37,
"question": "Eight months ago, you purchased 400 shares of Winston stock at a price of $46.40 a share. The company pays quarterly dividends of $1.05 a share. Today, you sold all of your shares for $48.30 a share. What is your total percentage return on this investment?\n\na. 8.62%\n\nb. 12.08%\n\nc. 10.12%\n\nd. 4.09%\n\ne. 7.34%",
"split": "train"
}
| null | null |
1752791
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Find the pH of a one-liter aqueous solution to which has been added 0.2 moles of acetic acid ({eq}CH_3COOH\n\n{/eq}).\n\nTemperature: 25 degrees Celsius, {eq}pK_a\n\n{/eq} = 4.76, {eq}pK_w\n\n{/eq} = 14.0. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.7",
"style": "rule"
}
|
{
"answer": "2.7",
"index": 38,
"question": "Find the pH of a one-liter aqueous solution to which has been added 0.2 moles of acetic acid ({eq}CH_3COOH\n\n{/eq}).\n\nTemperature: 25 degrees Celsius, {eq}pK_a\n\n{/eq} = 4.76, {eq}pK_w\n\n{/eq} = 14.0.",
"split": "train"
}
| null | null |
492022
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use a triple integral to find the volume of the solid bounded below by the cone {eq}z = \\sqrt{x^2+y^2} {/eq} and bounded above by the sphere {eq}x^2 +y^2 +z^2 = 392 {/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{10976\\pi}{3}(\\sqrt2-1)",
"style": "rule"
}
|
{
"answer": "\\frac{10976\\pi}{3}(\\sqrt2-1)",
"index": 39,
"question": "Use a triple integral to find the volume of the solid bounded below by the cone {eq}z = \\sqrt{x^2+y^2} {/eq} and bounded above by the sphere {eq}x^2 +y^2 +z^2 = 392 {/eq}.",
"split": "train"
}
| null | null |
333240
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A thin nonconducting rod of length {eq}l\n\n{/eq} carries a nonuniform charge density {eq}\\lambda = Ax^2\n\n{/eq}. The rod lies on the positive {eq}x\n\n{/eq}-axis with one end at the origin and the other end at {eq}x = l\n\n{/eq}. A point charge {eq}q_0\n\n{/eq} lies on the {eq}x\n\n{/eq}-axis at the point {eq}x_0 (x_0 > l)\n\n{/eq}. Find the magnitude of the force acting on charge {eq}q_0\n\n{/eq}. Derive an expression for the magnitude of the force on charge {eq}q_0\n\n{/eq} and use the following set of values to determine its value:\n\n{eq}q_0 = 4.070 \\times10^{-6} \\ C; \\\\\n\nA = 8.150\\times10^{-6} \\ C/m3; \\\\\n\nl = 0.7430 \\ m; \\\\\n\nx_0 = 0.8820 \\ m;\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.6555 N",
"style": "rule"
}
|
{
"answer": "0.6555 N",
"index": 40,
"question": "A thin nonconducting rod of length {eq}l\n\n{/eq} carries a nonuniform charge density {eq}\\lambda = Ax^2\n\n{/eq}. The rod lies on the positive {eq}x\n\n{/eq}-axis with one end at the origin and the other end at {eq}x = l\n\n{/eq}. A point charge {eq}q_0\n\n{/eq} lies on the {eq}x\n\n{/eq}-axis at the point {eq}x_0 (x_0 > l)\n\n{/eq}. Find the magnitude of the force acting on charge {eq}q_0\n\n{/eq}. Derive an expression for the magnitude of the force on charge {eq}q_0\n\n{/eq} and use the following set of values to determine its value:\n\n{eq}q_0 = 4.070 \\times10^{-6} \\ C; \\\\\n\nA = 8.150\\times10^{-6} \\ C/m3; \\\\\n\nl = 0.7430 \\ m; \\\\\n\nx_0 = 0.8820 \\ m;\n\n{/eq}",
"split": "train"
}
| null | null |
727263
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A gun is fired with an angle of elevation of {eq}30^{\\circ}\n\n{/eq}. What is the muzzle speed if the maximum height of the shell is 548 m? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "207.3 m/s",
"style": "rule"
}
|
{
"answer": "207.3 m/s",
"index": 41,
"question": "A gun is fired with an angle of elevation of {eq}30^{\\circ}\n\n{/eq}. What is the muzzle speed if the maximum height of the shell is 548 m?",
"split": "train"
}
| null | null |
990032
|
Multiple Choice
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "What particle is emitted in radioactive decay? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 42,
"question": "What particle is emitted in radioactive decay?",
"split": "train"
}
| null | null |
565029
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "The hollow plastic sphere at right has inner radius a, outer radius b, and uniform charge density \\rho. Find the electric potential difference between a and b. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-(\\rho/(3*\\epsilon_0)) * (3*a^2/2 - b^2/2 - a^3/b)",
"style": "rule"
}
|
{
"answer": "-(\\rho/(3*\\epsilon_0)) * (3*a^2/2 - b^2/2 - a^3/b)",
"index": 43,
"question": "The hollow plastic sphere at right has inner radius a, outer radius b, and uniform charge density \\rho. Find the electric potential difference between a and b.",
"split": "train"
}
| null | null |
478327
|
Float
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "As a train accelerates away from a station, it reaches a speed of 4.7 m/s in 5.0s. If the train's acceleration remains constant, what is its speed after an additional 6.0 s has elapsed? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "10 m/s",
"style": "rule"
}
|
{
"answer": "10 m/s",
"index": 44,
"question": "As a train accelerates away from a station, it reaches a speed of 4.7 m/s in 5.0s. If the train's acceleration remains constant, what is its speed after an additional 6.0 s has elapsed?",
"split": "train"
}
| null | null |
1150216
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose that n balls are tossed, one at a time, into n bins such that each ball is equally likely to fall into any bin and that the tosses are independent. What is the probability that the first bin is empty? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(1-1/n)^n",
"style": "rule"
}
|
{
"answer": "(1-1/n)^n",
"index": 45,
"question": "Suppose that n balls are tossed, one at a time, into n bins such that each ball is equally likely to fall into any bin and that the tosses are independent. What is the probability that the first bin is empty?",
"split": "train"
}
| null | null |
1062465
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "You want to borrow $4,700 for 24 months and can afford monthly payments of $210, but no more. Assuming monthly compounding, what is the highest APR rate you can afford? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 46,
"question": "You want to borrow $4,700 for 24 months and can afford monthly payments of $210, but no more. Assuming monthly compounding, what is the highest APR rate you can afford?",
"split": "train"
}
| null | null |
1638613
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the jacobian of the vector valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = x$, $g(x,y,z) = \\sqrt[3]{\\frac{x}{y z^2}}$, and $h(x,y,z) = \\sin ^{-1}\\left(\\frac{y}{z^2}\\right)$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\begin{pmatrix}\n1 & 0 & 0 \\\\\n\\frac{1}{3 y z^2 \\sqrt[3]{\\frac{x}{y z^2}}^2} & -\\frac{x}{3 y^2 z^2 \\sqrt[3]{\\frac{x}{y z^2}}^2} & -\\frac{2 x}{3 y z^3 \\sqrt[3]{\\frac{x}{y z^2}}^2} \\\\\n0 & \\frac{1}{z^2 \\sqrt{1-\\frac{y^2}{z^4}}} & -\\frac{2 y}{z^3 \\sqrt{1-\\frac{y^2}{z^4}}} \\\\\n\\end{pmatrix}",
"style": "rule"
}
|
{
"answer": "\\begin{pmatrix}\n1 & 0 & 0 \\\\\n\\frac{1}{3 y z^2 \\sqrt[3]{\\frac{x}{y z^2}}^2} & -\\frac{x}{3 y^2 z^2 \\sqrt[3]{\\frac{x}{y z^2}}^2} & -\\frac{2 x}{3 y z^3 \\sqrt[3]{\\frac{x}{y z^2}}^2} \\\\\n0 & \\frac{1}{z^2 \\sqrt{1-\\frac{y^2}{z^4}}} & -\\frac{2 y}{z^3 \\sqrt{1-\\frac{y^2}{z^4}}} \\\\\n\\end{pmatrix}",
"index": 47,
"question": "Find the jacobian of the vector valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = x$, $g(x,y,z) = \\sqrt[3]{\\frac{x}{y z^2}}$, and $h(x,y,z) = \\sin ^{-1}\\left(\\frac{y}{z^2}\\right)$",
"split": "train"
}
| null | null |
1810847
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Show that $$\\ {u}=\\frac{\\cos\\phi}{b}$$ and use this to show that u then solves the homogenous equation: $$\\frac {d^2u}{d{\\phi}^2}+{u}=0$$ given that the homogenous equation describes a hypothetical situation where light passes by the Sun in a straight line without changing direction, b is the minimum distance from the photon to the center of the star, and r = r(φ) is the distance when the angle is φ. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Given u = cos(phi)/b, du/d(phi) = -sin(phi)/b, and d^2u/d(phi^2) = -cos(phi)/b. Substituting into the homogeneous equation: d^2u/d(phi^2) + u = -cos(phi)/b + cos(phi)/b = 0. Therefore, u = cos(phi)/b satisfies the homogeneous equation.",
"style": "rule"
}
|
{
"answer": "Given u = cos(phi)/b, du/d(phi) = -sin(phi)/b, and d^2u/d(phi^2) = -cos(phi)/b. Substituting into the homogeneous equation: d^2u/d(phi^2) + u = -cos(phi)/b + cos(phi)/b = 0. Therefore, u = cos(phi)/b satisfies the homogeneous equation.",
"index": 48,
"question": "Show that $$\\ {u}=\\frac{\\cos\\phi}{b}$$ and use this to show that u then solves the homogenous equation: $$\\frac {d^2u}{d{\\phi}^2}+{u}=0$$ given that the homogenous equation describes a hypothetical situation where light passes by the Sun in a straight line without changing direction, b is the minimum distance from the photon to the center of the star, and r = r(φ) is the distance when the angle is φ.",
"split": "train"
}
| null | null |
1984151
|
Boolean
|
Law
|
Senior High School
|
general-reasoner
|
[
{
"content": "In the case of multiple wage attachments, a garnishment for a student loan has priority over any other garnishment. 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": 49,
"question": "In the case of multiple wage attachments, a garnishment for a student loan has priority over any other garnishment. True or False?",
"split": "train"
}
| null | null |
1256871
|
List
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Give some specific sets of quantum numbers and determine if the set given is possible. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Possible combinations:\nn=3, l=0, ml=0, ms=+1/2 or -1/2\nn=3, l=1, ml=-1, 0, or +1, ms=+1/2 or -1/2\nn=3, l=2, ml=-2, -1, 0, +1, or +2, ms=+1/2 or -1/2\nImpossible combination: n=3, l=2, ml=3, ms=+1/2 or -1/2",
"style": "rule"
}
|
{
"answer": "Possible combinations:\nn=3, l=0, ml=0, ms=+1/2 or -1/2\nn=3, l=1, ml=-1, 0, or +1, ms=+1/2 or -1/2\nn=3, l=2, ml=-2, -1, 0, +1, or +2, ms=+1/2 or -1/2\nImpossible combination: n=3, l=2, ml=3, ms=+1/2 or -1/2",
"index": 50,
"question": "Give some specific sets of quantum numbers and determine if the set given is possible.",
"split": "train"
}
| null | null |
1427464
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I'm trying to evaluate: $$\\iint_D \\left(\\sqrt{a^2-x^2-y^2}-\\sqrt{x^2+y^2}~\\right)dxdy$$ where $D_{xy}$ is the disk $x^2+y^2\\le a^2$. I chose $\\varphi (r,\\theta)=(ra\\cos\\theta,ra\\sin\\theta)$, where $0\\le r\\le 1$ and $0\\le \\theta\\le 2\\pi$ to be the change of variables. The determinant of the Jacobian is $ra^2$ and \\begin{align*} &\\iint_{D_{xy}}\\left(\\sqrt{a^2-x^2-y^2}-\\sqrt{x^2+y^2}~\\right)dxdy \\\\&=\\int_0^{2\\pi}\\int^1_0\\left(\\sqrt{a^2-r^2a^2}-ra\\right)ra^2 drd\\theta\\\\ &=2\\pi a^3\\int^1_0 \\left(r\\sqrt{1-r^2}-r^2 \\right)dr\\\\ &=2\\pi a^3\\left(\\int^1_0r\\sqrt{1-r^2}dr-\\int^1_0r^2dr\\right)\\\\ &=2\\pi a^3\\left( \\frac{1}{3}-\\frac{1}{3} \\right)\\\\ &=0 \\end{align*} Where am I mistaken? The answer is $\\pi a^3/3$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 51,
"question": "I'm trying to evaluate: $$\\iint_D \\left(\\sqrt{a^2-x^2-y^2}-\\sqrt{x^2+y^2}~\\right)dxdy$$ where $D_{xy}$ is the disk $x^2+y^2\\le a^2$. I chose $\\varphi (r,\\theta)=(ra\\cos\\theta,ra\\sin\\theta)$, where $0\\le r\\le 1$ and $0\\le \\theta\\le 2\\pi$ to be the change of variables. The determinant of the Jacobian is $ra^2$ and \\begin{align*} &\\iint_{D_{xy}}\\left(\\sqrt{a^2-x^2-y^2}-\\sqrt{x^2+y^2}~\\right)dxdy \\\\&=\\int_0^{2\\pi}\\int^1_0\\left(\\sqrt{a^2-r^2a^2}-ra\\right)ra^2 drd\\theta\\\\ &=2\\pi a^3\\int^1_0 \\left(r\\sqrt{1-r^2}-r^2 \\right)dr\\\\ &=2\\pi a^3\\left(\\int^1_0r\\sqrt{1-r^2}dr-\\int^1_0r^2dr\\right)\\\\ &=2\\pi a^3\\left( \\frac{1}{3}-\\frac{1}{3} \\right)\\\\ &=0 \\end{align*} Where am I mistaken? The answer is $\\pi a^3/3$.",
"split": "train"
}
| null | null |
207059
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Integral for the mass of a lamina bounded by the curves y = x^2, y = x + 2 where the density is given by ρ(x,y) = kx? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "9k/4",
"style": "rule"
}
|
{
"answer": "9k/4",
"index": 52,
"question": "Integral for the mass of a lamina bounded by the curves y = x^2, y = x + 2 where the density is given by ρ(x,y) = kx?",
"split": "train"
}
| null | null |
1693465
|
Percentage
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Lorge Corporation has collected the following information after its first year of sales. Sales were $2,100,000 on 105,000 units; selling expenses $250,000 (40% variable and 60% fixed); direct materials $1,045,700; direct labor $250,000; administrative expenses $270,000 (20% variable and 80% fixed); and manufacturing overhead $329,000 (70% variable and 30% fixed). The top management has asked you to do a CVP analysis so that it can make plans for the coming year. It has been projected that unit sales will increase by 10% next year.\n\nThe company is considering a purchase of equipment that would reduce direct labor costs by $100,000 and would change its manufacturing overhead costs to 30% variable and 70% fixed (assume the total manufacturing overhead cost is $329,000, as above). It is also considering switching to a pure commission basis for its sales staff. This would change selling expenses to 90% variable and 10% fixed (assume total selling expense is $250,000, as above).\n\nCompute the contribution margin ratio. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "20%",
"style": "rule"
}
|
{
"answer": "20%",
"index": 53,
"question": "Lorge Corporation has collected the following information after its first year of sales. Sales were $2,100,000 on 105,000 units; selling expenses $250,000 (40% variable and 60% fixed); direct materials $1,045,700; direct labor $250,000; administrative expenses $270,000 (20% variable and 80% fixed); and manufacturing overhead $329,000 (70% variable and 30% fixed). The top management has asked you to do a CVP analysis so that it can make plans for the coming year. It has been projected that unit sales will increase by 10% next year.\n\nThe company is considering a purchase of equipment that would reduce direct labor costs by $100,000 and would change its manufacturing overhead costs to 30% variable and 70% fixed (assume the total manufacturing overhead cost is $329,000, as above). It is also considering switching to a pure commission basis for its sales staff. This would change selling expenses to 90% variable and 10% fixed (assume total selling expense is $250,000, as above).\n\nCompute the contribution margin ratio.",
"split": "train"
}
| null | null |
1802115
|
String
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Closed. This question is off-topic. It is not currently accepting answers. This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. Closed 8 years ago. Improve this question Is the closure of $\\Bbb R$ equal to $\\Bbb R$ itself or the extended real numbers $\\bar{\\Bbb R}$? Thanks for any comment. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\Bbb R$",
"style": "rule"
}
|
{
"answer": "$\\Bbb R$",
"index": 54,
"question": "Closed. This question is off-topic. It is not currently accepting answers. This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. Closed 8 years ago. Improve this question Is the closure of $\\Bbb R$ equal to $\\Bbb R$ itself or the extended real numbers $\\bar{\\Bbb R}$? Thanks for any comment.",
"split": "train"
}
| null | null |
129235
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "At a particular location in the room, there is an electric field = {eq}\\displaystyle \\langle 7940,\\ 0,\\ 0 \\rangle\\ N/C\n\n{/eq}. Where would you place a single negative point particle of charge {eq}2.0\\ \\mu C\n\n{/eq} in order to produce this electric field? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.505 m on the right side of origin on the x-axis",
"style": "rule"
}
|
{
"answer": "1.505 m on the right side of origin on the x-axis",
"index": 55,
"question": "At a particular location in the room, there is an electric field = {eq}\\displaystyle \\langle 7940,\\ 0,\\ 0 \\rangle\\ N/C\n\n{/eq}. Where would you place a single negative point particle of charge {eq}2.0\\ \\mu C\n\n{/eq} in order to produce this electric field?",
"split": "train"
}
| null | null |
379436
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do I proceed to discover an expression for $I_l$ given $$I_l = V_1 \\int_0^1 P_l(x)dx+V_2 \\int_{-1}^0 P_l(x)dx$$ and $$\\Phi(r,x) = K\\sum_{l=0}^\\infty r^l P_l(x) I_l $$ where I am solving for the potential of a conducting sphere with hemispheres at opposite potentials? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\frac{\\sqrt{\\pi}}{2\\Gamma(1-\\frac{l}{2})\\Gamma(\\frac{l+3}{2})}$",
"style": "rule"
}
|
{
"answer": "$\\frac{\\sqrt{\\pi}}{2\\Gamma(1-\\frac{l}{2})\\Gamma(\\frac{l+3}{2})}$",
"index": 56,
"question": "How do I proceed to discover an expression for $I_l$ given $$I_l = V_1 \\int_0^1 P_l(x)dx+V_2 \\int_{-1}^0 P_l(x)dx$$ and $$\\Phi(r,x) = K\\sum_{l=0}^\\infty r^l P_l(x) I_l $$ where I am solving for the potential of a conducting sphere with hemispheres at opposite potentials?",
"split": "train"
}
| null | null |
1686544
|
Expression
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Write the equation that represents \"nitrogen and oxygen react to form nitrogen dioxide.\" Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "N_2 + 2O_2 -> 2NO_2",
"style": "rule"
}
|
{
"answer": "N_2 + 2O_2 -> 2NO_2",
"index": 57,
"question": "Write the equation that represents \"nitrogen and oxygen react to form nitrogen dioxide.\"",
"split": "train"
}
| null | null |
1584848
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is 334 degrees Celsius. If the efficiency of this ideal engine is 27%, find the temperature of the cold reservoir in degrees Celsius. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "630",
"style": "rule"
}
|
{
"answer": "630",
"index": 58,
"question": "A Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is 334 degrees Celsius. If the efficiency of this ideal engine is 27%, find the temperature of the cold reservoir in degrees Celsius.",
"split": "train"
}
| null | null |
1779388
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use power series methods to express {eq}S=\\int_{0}^{1}\\frac{\\sin (x)}{x}dx{/eq} as an alternating series {eq}\\sum_{n=0}^{\\infty } a_{n}{/eq} with rational terms alternating in sign and satisfying the condition {eq}\\left | a_{n} \\right |\\rightarrow 0{/eq}, then use the alternating series test remainder estimate to approximate S by a rational number with {eq}\\left | Sin T\\right |< \\frac{1}{500}{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)!(2n+1)}",
"style": "rule"
}
|
{
"answer": "\\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)!(2n+1)}",
"index": 59,
"question": "Use power series methods to express {eq}S=\\int_{0}^{1}\\frac{\\sin (x)}{x}dx{/eq} as an alternating series {eq}\\sum_{n=0}^{\\infty } a_{n}{/eq} with rational terms alternating in sign and satisfying the condition {eq}\\left | a_{n} \\right |\\rightarrow 0{/eq}, then use the alternating series test remainder estimate to approximate S by a rational number with {eq}\\left | Sin T\\right |< \\frac{1}{500}{/eq}",
"split": "train"
}
| null | null |
1538372
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "What is the length of the longest pipe that can be carried horizontally around a corner from a 9 ft wide hallway into a 6 ft wide hallway? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "21.07",
"style": "rule"
}
|
{
"answer": "21.07",
"index": 60,
"question": "What is the length of the longest pipe that can be carried horizontally around a corner from a 9 ft wide hallway into a 6 ft wide hallway?",
"split": "train"
}
| null | null |
1404084
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let {eq}f(x, y) = x^2 - 2xy + y^2{/eq}. Find the local extrema Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 61,
"question": "Let {eq}f(x, y) = x^2 - 2xy + y^2{/eq}. Find the local extrema",
"split": "train"
}
| null | null |
1622905
|
Integer
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "The revenues and expenses of Ousel Travel Service for the year ended November 30, 2016, follow.\n\n\nFees earned$742,000\nOffice expense309,000\nMiscellaneous expense12,000\nWages expense461,000\nPrepare an income statement for the year ended November 30. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Net loss: ($40,000)",
"style": "rule"
}
|
{
"answer": "Net loss: ($40,000)",
"index": 62,
"question": "The revenues and expenses of Ousel Travel Service for the year ended November 30, 2016, follow.\n\n\nFees earned$742,000\nOffice expense309,000\nMiscellaneous expense12,000\nWages expense461,000\nPrepare an income statement for the year ended November 30.",
"split": "train"
}
| null | null |
53170
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Calculate the mass (in grams) of 0.0971 mole of ammonia, NH{eq}_{3}\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.65 g",
"style": "rule"
}
|
{
"answer": "1.65 g",
"index": 63,
"question": "Calculate the mass (in grams) of 0.0971 mole of ammonia, NH{eq}_{3}\n\n{/eq}.",
"split": "train"
}
| null | null |
1631777
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Set up the integral for the area {eq}\\rm A(R) {/eq} of the region {eq}\\rm R {/eq} bounded by the circles {eq}y^2 + x^2 = 1, \\ \\ y^2 + x^2 = 4 {/eq}, below by the {eq}x {/eq}-axis and to the left by the {eq}y {/eq}-axis using a vertical strip. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\displaystyle\\int_{-2}^{-1}\\int_{-\\sqrt{4-x^2}}^0\\;dydx + \\displaystyle\\int_{-1}^{0}\\int_{-\\sqrt{4-x^2}}^{-\\sqrt{1-x^2}}\\;dydx",
"style": "rule"
}
|
{
"answer": "\\displaystyle\\int_{-2}^{-1}\\int_{-\\sqrt{4-x^2}}^0\\;dydx + \\displaystyle\\int_{-1}^{0}\\int_{-\\sqrt{4-x^2}}^{-\\sqrt{1-x^2}}\\;dydx",
"index": 64,
"question": "Set up the integral for the area {eq}\\rm A(R) {/eq} of the region {eq}\\rm R {/eq} bounded by the circles {eq}y^2 + x^2 = 1, \\ \\ y^2 + x^2 = 4 {/eq}, below by the {eq}x {/eq}-axis and to the left by the {eq}y {/eq}-axis using a vertical strip.",
"split": "train"
}
| null | null |
1808790
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 24.0 kg wombat is moving horizontally at 1.90 m/s when it strikes an empty aluminum can attached to a wall and comes to rest after crumpling the can by 4.00 cm against the wall. What was the average force exerted on the can? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1080 N",
"style": "rule"
}
|
{
"answer": "1080 N",
"index": 65,
"question": "A 24.0 kg wombat is moving horizontally at 1.90 m/s when it strikes an empty aluminum can attached to a wall and comes to rest after crumpling the can by 4.00 cm against the wall. What was the average force exerted on the can?",
"split": "train"
}
| null | null |
588488
|
Multiple Choice
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "If there is s large amount of lactose present, how does bacteria respond?\n \n\nA the gene for beta-galactosidase turns on.\n\nB the gene for beta-galactosidase turns off.\n\nC beta-galactosidase production increases.\n\nD lactose is produced. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 66,
"question": "If there is s large amount of lactose present, how does bacteria respond?\n \n\nA the gene for beta-galactosidase turns on.\n\nB the gene for beta-galactosidase turns off.\n\nC beta-galactosidase production increases.\n\nD lactose is produced.",
"split": "train"
}
| null | null |
1211937
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "After takeoff, an airplane climbs at an angle of 30 degrees at a speed of 215 ft/sec. How long does it take for the airplane to reach an altitude of 13,000 ft? (round your answer to one decimal place.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "120.9 s",
"style": "rule"
}
|
{
"answer": "120.9 s",
"index": 67,
"question": "After takeoff, an airplane climbs at an angle of 30 degrees at a speed of 215 ft/sec. How long does it take for the airplane to reach an altitude of 13,000 ft? (round your answer to one decimal place.)",
"split": "train"
}
| null | null |
986124
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "How much force must be exerted at the right end to pick up the lever and load if it pivots at the left end? The 2.00 meter long lever weighs 1.50 N and is uniform. There is an 8.00 N weight resting on the 40.0 cm mark. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.35 N",
"style": "rule"
}
|
{
"answer": "2.35 N",
"index": 68,
"question": "How much force must be exerted at the right end to pick up the lever and load if it pivots at the left end? The 2.00 meter long lever weighs 1.50 N and is uniform. There is an 8.00 N weight resting on the 40.0 cm mark.",
"split": "train"
}
| null | null |
2028912
|
Multiple Choice
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "When the following equation is balanced using the smallest possible integers, what is the coefficient in front?\n\n{eq}\\displaystyle \\rm C_2H_6 + O_2 \\to CO_2 + H_2O\n\n{/eq}\n\n(a) 1\n\n(b) 7\n\n(c) 4\n\n(d) 6\n\n(e) 2 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(e)",
"style": "rule"
}
|
{
"answer": "(e)",
"index": 69,
"question": "When the following equation is balanced using the smallest possible integers, what is the coefficient in front?\n\n{eq}\\displaystyle \\rm C_2H_6 + O_2 \\to CO_2 + H_2O\n\n{/eq}\n\n(a) 1\n\n(b) 7\n\n(c) 4\n\n(d) 6\n\n(e) 2",
"split": "train"
}
| null | null |
1541803
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Slow U.S. economic growth rate impacts the size of the Fed's balance sheet as:\n\na. The Fed reduces the discount rate to 0%,\n\nb. Banks maintain high levels of excess reserves,\n\nc. Businesses reduce spending, keeping more money in their demand accounts,\n\nd. Individuals move money from checking ti saving accounts. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 70,
"question": "Slow U.S. economic growth rate impacts the size of the Fed's balance sheet as:\n\na. The Fed reduces the discount rate to 0%,\n\nb. Banks maintain high levels of excess reserves,\n\nc. Businesses reduce spending, keeping more money in their demand accounts,\n\nd. Individuals move money from checking ti saving accounts.",
"split": "train"
}
| null | null |
1196135
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the (pseudo)inverse of\n$\\left(\n\\begin{array}{ccc}\n-1 & 4 & -4 \\\\\n1 & 3 & 1 \\\\\n1 & 2 & -2 \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{1}{24}\\left(\n\\begin{array}{ccc}\n-8 & 0 & 16 \\\\\n3 & 6 & -3 \\\\\n-1 & 6 & -7 \\\\\n\\end{array}\n\\right)",
"style": "rule"
}
|
{
"answer": "\\frac{1}{24}\\left(\n\\begin{array}{ccc}\n-8 & 0 & 16 \\\\\n3 & 6 & -3 \\\\\n-1 & 6 & -7 \\\\\n\\end{array}\n\\right)",
"index": 71,
"question": "Compute the (pseudo)inverse of\n$\\left(\n\\begin{array}{ccc}\n-1 & 4 & -4 \\\\\n1 & 3 & 1 \\\\\n1 & 2 & -2 \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
1507858
|
Integer
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "A project will produce cash inflows of $1,750 a year for four years. The project initially costs $10,600 to get started. In year five, the project will be closed and as a result should produce a cash inflow of $8,500. What is the net present value of this project if the required rate of return is 14.75%? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-$1,300",
"style": "rule"
}
|
{
"answer": "-$1,300",
"index": 72,
"question": "A project will produce cash inflows of $1,750 a year for four years. The project initially costs $10,600 to get started. In year five, the project will be closed and as a result should produce a cash inflow of $8,500. What is the net present value of this project if the required rate of return is 14.75%?",
"split": "train"
}
| null | null |
958236
|
Integer
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "It takes a boat 5 hours to travel upstream. It takes the same boat 4 hours to travel the same distance downstream. If the current is 1 mile per hour, what is the speed of the boat in still water? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "9 mph",
"style": "rule"
}
|
{
"answer": "9 mph",
"index": 73,
"question": "It takes a boat 5 hours to travel upstream. It takes the same boat 4 hours to travel the same distance downstream. If the current is 1 mile per hour, what is the speed of the boat in still water?",
"split": "train"
}
| null | null |
1365733
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do you find the integral ln(x)/(x^2)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "#-lnx /x -1/x +C#",
"style": "rule"
}
|
{
"answer": "#-lnx /x -1/x +C#",
"index": 74,
"question": "How do you find the integral ln(x)/(x^2)?",
"split": "train"
}
| null | null |
84215
|
Fraction
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "An object of mass m travels along the parabola {eq}y=6x^{2}\n\n{/eq} with a constant speed of {eq}6 \\, units/s\n\n{/eq}. What is the force on the object due to its acceleration at {eq}(2^{\\frac{1}{2}}, 12)\n\n{/eq}? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{eq}F = \\frac{432m}{4913}{/eq}",
"style": "rule"
}
|
{
"answer": "{eq}F = \\frac{432m}{4913}{/eq}",
"index": 75,
"question": "An object of mass m travels along the parabola {eq}y=6x^{2}\n\n{/eq} with a constant speed of {eq}6 \\, units/s\n\n{/eq}. What is the force on the object due to its acceleration at {eq}(2^{\\frac{1}{2}}, 12)\n\n{/eq}?",
"split": "train"
}
| null | null |
270053
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Solve the differential equation y ln y dx - x dy = 0 with initial condition (1, 2) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "y = \\frac{2}{e} e^{x}",
"style": "rule"
}
|
{
"answer": "y = \\frac{2}{e} e^{x}",
"index": 76,
"question": "Solve the differential equation y ln y dx - x dy = 0 with initial condition (1, 2)",
"split": "train"
}
| null | null |
585924
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Prove by definition that the supremum of the set $S:=\\lbrace{\\frac{1}{a} - \\frac{3}{b}:a,b \\in \\mathbb{N}}\\rbrace $ is $\\sup(S)=1$. Specifically, prove that if $u<\\sup(S)=1$ then $\\exists s\\in S$ such that $u<s\\leq \\sup(S)$.\nThe definition of \"prove by definition\" requires:\ni) Prove that $\\sup(S)=1$ is an upper bound (i.e. $s\\leq \\sup(S)=1 \\forall s \\in S$).\nii) Then prove such number (i) IS the least upper bound (i.e. if $u<\\sup(S)=1$ then $\\exists s \\in S$ such that $u<s\\leq \\sup(S)=1$).\nAssume (i) is already proven. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 77,
"question": "Prove by definition that the supremum of the set $S:=\\lbrace{\\frac{1}{a} - \\frac{3}{b}:a,b \\in \\mathbb{N}}\\rbrace $ is $\\sup(S)=1$. Specifically, prove that if $u<\\sup(S)=1$ then $\\exists s\\in S$ such that $u<s\\leq \\sup(S)$.\nThe definition of \"prove by definition\" requires:\ni) Prove that $\\sup(S)=1$ is an upper bound (i.e. $s\\leq \\sup(S)=1 \\forall s \\in S$).\nii) Then prove such number (i) IS the least upper bound (i.e. if $u<\\sup(S)=1$ then $\\exists s \\in S$ such that $u<s\\leq \\sup(S)=1$).\nAssume (i) is already proven.",
"split": "train"
}
| null | null |
1584889
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Is there any standard function that outputs $1$ if an inequality is true and $0$ otherwise? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Indicator function $\\Bbb{1}_{x>D}$",
"style": "rule"
}
|
{
"answer": "Indicator function $\\Bbb{1}_{x>D}$",
"index": 78,
"question": "Is there any standard function that outputs $1$ if an inequality is true and $0$ otherwise?",
"split": "train"
}
| null | null |
2066005
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How to find the complex integration of a function over a closed contour when there are infinitely many singularities inside the contour, specifically for the integral $$\\int_{|z|=1} \\frac{1}{\\sin(\\frac{1}{z})} dz$$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{\\pi i}{3}",
"style": "rule"
}
|
{
"answer": "\\frac{\\pi i}{3}",
"index": 79,
"question": "How to find the complex integration of a function over a closed contour when there are infinitely many singularities inside the contour, specifically for the integral $$\\int_{|z|=1} \\frac{1}{\\sin(\\frac{1}{z})} dz$$?",
"split": "train"
}
| null | null |
1483642
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "NPV Project K costs $55,000, its expected cash inflows are $11,000 per year for 9 years, and its WACC is 9%.\n\nWhat is the project's NPV?\n\nRound your answer to the nearest cent.\n\n$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "10947.72",
"style": "rule"
}
|
{
"answer": "10947.72",
"index": 80,
"question": "NPV Project K costs $55,000, its expected cash inflows are $11,000 per year for 9 years, and its WACC is 9%.\n\nWhat is the project's NPV?\n\nRound your answer to the nearest cent.\n\n$",
"split": "train"
}
| null | null |
69045
|
Float
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Amanda likes to eat bananas and apples with her lunch between classes. She also keeps a close eye on her spending each week since she is in college and cannot afford the time to work too much. She has budgeted a certain amount of money each week for apples and bananas. If she spends all of this budget on apples, she can purchase 7 apples. If she spends all of the budget on bananas, she can afford 11 bananas. What is Amanda's opportunity cost of a banana? Round your answer to the nearest tenth. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.6 apples",
"style": "rule"
}
|
{
"answer": "0.6 apples",
"index": 81,
"question": "Amanda likes to eat bananas and apples with her lunch between classes. She also keeps a close eye on her spending each week since she is in college and cannot afford the time to work too much. She has budgeted a certain amount of money each week for apples and bananas. If she spends all of this budget on apples, she can purchase 7 apples. If she spends all of the budget on bananas, she can afford 11 bananas. What is Amanda's opportunity cost of a banana? Round your answer to the nearest tenth.",
"split": "train"
}
| null | null |
1823993
|
Expression
|
Other STEM
|
University
|
general-reasoner
|
[
{
"content": "I want to correct visual odometry (VO) trajectory with GPS and assign each point of the VO curve a computed GPS coordinate. Data I have: I have a curve that represents the VO trajectory (blue in the picture) - this trajectory was calculated via some computer vision algorithms and I know coordinates of every point of this curve. Then I only have two GPS coordinates - the start and finish of the \"ground truth\" (ie. I don't know exactly the whole red curve - I only picture it for clarity). What I need: How can I correct (stretch/contract etc.) the blue VO curve so that it nears the red ground truth curve as close as possible? Here is the situation (GPS start is the same as VO start): Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$f(\\begin{bmatrix} x \\\\ y \\end {bmatrix}) = S + \\frac{\\|G-S \\|}{\\|F-S\\|}R (\\begin{bmatrix} x \\\\ y \\end {bmatrix} - S)$",
"style": "rule"
}
|
{
"answer": "$f(\\begin{bmatrix} x \\\\ y \\end {bmatrix}) = S + \\frac{\\|G-S \\|}{\\|F-S\\|}R (\\begin{bmatrix} x \\\\ y \\end {bmatrix} - S)$",
"index": 82,
"question": "I want to correct visual odometry (VO) trajectory with GPS and assign each point of the VO curve a computed GPS coordinate. Data I have: I have a curve that represents the VO trajectory (blue in the picture) - this trajectory was calculated via some computer vision algorithms and I know coordinates of every point of this curve. Then I only have two GPS coordinates - the start and finish of the \"ground truth\" (ie. I don't know exactly the whole red curve - I only picture it for clarity). What I need: How can I correct (stretch/contract etc.) the blue VO curve so that it nears the red ground truth curve as close as possible? Here is the situation (GPS start is the same as VO start):",
"split": "train"
}
| null | null |
1935339
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Which of the following is false?\n\nA. Fixed costs increase in the long run.\n\nB. In the long run, both the amount of capital and labor used by the firm can be changed.\n\nC. Long-run average variable costs equal long-run average total costs.\n\nD. As a firm produces more output, eventually it experiences diseconomies of scale. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 83,
"question": "Which of the following is false?\n\nA. Fixed costs increase in the long run.\n\nB. In the long run, both the amount of capital and labor used by the firm can be changed.\n\nC. Long-run average variable costs equal long-run average total costs.\n\nD. As a firm produces more output, eventually it experiences diseconomies of scale.",
"split": "train"
}
| null | null |
928969
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A portable CD player was recently introduced that has a \"special power saving technology.\" The manufacturer claims that with only two standard AA batteries (together: 3.0 V, 20 kJ energy storage), the player can be played for about 25 hours. What is the approximate resistance in the CD player's electrical circuitry? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "39Ω",
"style": "rule"
}
|
{
"answer": "39Ω",
"index": 84,
"question": "A portable CD player was recently introduced that has a \"special power saving technology.\" The manufacturer claims that with only two standard AA batteries (together: 3.0 V, 20 kJ energy storage), the player can be played for about 25 hours. What is the approximate resistance in the CD player's electrical circuitry?",
"split": "train"
}
| null | null |
1563943
|
Multiple Choice
|
History
|
Junior High School
|
general-reasoner
|
[
{
"content": "Which statement best describes the relationship between the pope and the monarchs of Europe during the medieval period?\n \n \nThe monarchs controlled the pope and the bishops. \nThey kept one another from gaining too much power.\nThey helped one another maintain power over people.\nThe pope controlled the flow of money for the monarchs. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 85,
"question": "Which statement best describes the relationship between the pope and the monarchs of Europe during the medieval period?\n \n \nThe monarchs controlled the pope and the bishops. \nThey kept one another from gaining too much power.\nThey helped one another maintain power over people.\nThe pope controlled the flow of money for the monarchs.",
"split": "train"
}
| null | null |
1770987
|
Float
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "Marcia plans on saving $100 at the beginning of every month for the next 20 years. If she can earn a 7% annual return (assume monthly compounding), then how much will she have in her account at the end of 20 years? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$52,396.54",
"style": "rule"
}
|
{
"answer": "$52,396.54",
"index": 86,
"question": "Marcia plans on saving $100 at the beginning of every month for the next 20 years. If she can earn a 7% annual return (assume monthly compounding), then how much will she have in her account at the end of 20 years?",
"split": "train"
}
| null | null |
2073102
|
Integer
|
History
|
Junior High School
|
general-reasoner
|
[
{
"content": "How many siblings did Booker T. Washington have? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 87,
"question": "How many siblings did Booker T. Washington have?",
"split": "train"
}
| null | null |
404414
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the volume of the solid generated by revolving the region bounded by {eq}\\; y = 2x^{\\frac{2}{3}} - x \\;{/eq} and {eq}\\; y = 0 \\;{/eq} around the {eq}x{/eq}-axis. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "128\\pi / 21",
"style": "rule"
}
|
{
"answer": "128\\pi / 21",
"index": 88,
"question": "Find the volume of the solid generated by revolving the region bounded by {eq}\\; y = 2x^{\\frac{2}{3}} - x \\;{/eq} and {eq}\\; y = 0 \\;{/eq} around the {eq}x{/eq}-axis.",
"split": "train"
}
| null | null |
201749
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Suppose you need to decide whether to keep a machine or replace it with a new one:\n\nOld machine: Old machine can operate for 5 years with operating cost of $120,000 per year.\n\nNew machine: Replacing old machine with new one requires capital cost of $250,000 in year zero (zero salvage value for old machine).\n\nCapital cost is depreciable from year 0 to year 5 (over six years) based on MACRS 5-year life depreciation with the half year convention. New machine can produce with lower operating cost of $45,000 per year for 5 years (from year 1 to year 5). Assume both machines produce similar good with similar value that yields similar revenue. Consider income tax of 38% and minimum rate of return 10%. Construct incremental analysis and conclude which alternative is more economically satisfactory? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-$3357.48",
"style": "rule"
}
|
{
"answer": "-$3357.48",
"index": 89,
"question": "Suppose you need to decide whether to keep a machine or replace it with a new one:\n\nOld machine: Old machine can operate for 5 years with operating cost of $120,000 per year.\n\nNew machine: Replacing old machine with new one requires capital cost of $250,000 in year zero (zero salvage value for old machine).\n\nCapital cost is depreciable from year 0 to year 5 (over six years) based on MACRS 5-year life depreciation with the half year convention. New machine can produce with lower operating cost of $45,000 per year for 5 years (from year 1 to year 5). Assume both machines produce similar good with similar value that yields similar revenue. Consider income tax of 38% and minimum rate of return 10%. Construct incremental analysis and conclude which alternative is more economically satisfactory?",
"split": "train"
}
| null | null |
1461439
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Liquid helium has a very low boiling point, 4.2 K, as well as a very low latent heat of vaporization, {eq}2.00 \\times 10^4\n\n{/eq} J/kg. If energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of 10.0 W, how long does it take to boil away 2.00 kg of the liquid? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "4,000 s",
"style": "rule"
}
|
{
"answer": "4,000 s",
"index": 90,
"question": "Liquid helium has a very low boiling point, 4.2 K, as well as a very low latent heat of vaporization, {eq}2.00 \\times 10^4\n\n{/eq} J/kg. If energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of 10.0 W, how long does it take to boil away 2.00 kg of the liquid?",
"split": "train"
}
| null | null |
604267
|
String
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "In the sentence, \"Tim's family took a trip to Paris last September,\" what is the direct object? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Trip",
"style": "rule"
}
|
{
"answer": "Trip",
"index": 91,
"question": "In the sentence, \"Tim's family took a trip to Paris last September,\" what is the direct object?",
"split": "train"
}
| null | null |
692158
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "If I treat the coefficients as an array of boolean values, I would achieve multiplication by using the AND operator and addition by using XOR. How would I go about finding the remainder? Is there, analogous to the other operations, a logic gate that would yield the appropriate result when applied to the coefficients? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 92,
"question": "If I treat the coefficients as an array of boolean values, I would achieve multiplication by using the AND operator and addition by using XOR. How would I go about finding the remainder? Is there, analogous to the other operations, a logic gate that would yield the appropriate result when applied to the coefficients?",
"split": "train"
}
| null | null |
1578469
|
String
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "Evidence from which type of data supports the common origin of all life on Earth? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Genetic Data",
"style": "rule"
}
|
{
"answer": "Genetic Data",
"index": 93,
"question": "Evidence from which type of data supports the common origin of all life on Earth?",
"split": "train"
}
| null | null |
1830700
|
List
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Construct a 90% confidence interval for the population mean of life insurance policy premiums, given a sample of 45 policy holders with an average premium of $345 and a sample standard deviation of $65. Make a statement about this in context of the problem. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(328.719, 361.281)",
"style": "rule"
}
|
{
"answer": "(328.719, 361.281)",
"index": 94,
"question": "Construct a 90% confidence interval for the population mean of life insurance policy premiums, given a sample of 45 policy holders with an average premium of $345 and a sample standard deviation of $65. Make a statement about this in context of the problem.",
"split": "train"
}
| null | null |
441779
|
Integer
|
Economics
|
Junior High School
|
general-reasoner
|
[
{
"content": "When 20,000 units are produced, variable costs are $8 per unit. Therefore, when 10,000 units are produced _____. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$8",
"style": "rule"
}
|
{
"answer": "$8",
"index": 95,
"question": "When 20,000 units are produced, variable costs are $8 per unit. Therefore, when 10,000 units are produced _____.",
"split": "train"
}
| null | null |
1247821
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An object, after being released from its circular path, travels the distance OA at the same time it would have moved from O to P on the circle. The speed of the object on and off the circle remains constant at the same value. Suppose that the radius of the circle is 3.6 m and the angle is 25C. What is the distance OA? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.570 m",
"style": "rule"
}
|
{
"answer": "1.570 m",
"index": 96,
"question": "An object, after being released from its circular path, travels the distance OA at the same time it would have moved from O to P on the circle. The speed of the object on and off the circle remains constant at the same value. Suppose that the radius of the circle is 3.6 m and the angle is 25C. What is the distance OA?",
"split": "train"
}
| null | null |
19688
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two charged particles {eq}q_1 = 21\\ nC\n\n{/eq} and {eq}q_2 = -4 q_1\n\n{/eq} are placed at {eq}x_1 = 20\\ cm\n\n{/eq} and {eq}x_2 = 70\\ cm\n\n{/eq}. At what point on the coordinate axis the net electric field by these two charges is zero? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(-30 cm, 0)",
"style": "rule"
}
|
{
"answer": "(-30 cm, 0)",
"index": 97,
"question": "Two charged particles {eq}q_1 = 21\\ nC\n\n{/eq} and {eq}q_2 = -4 q_1\n\n{/eq} are placed at {eq}x_1 = 20\\ cm\n\n{/eq} and {eq}x_2 = 70\\ cm\n\n{/eq}. At what point on the coordinate axis the net electric field by these two charges is zero?",
"split": "train"
}
| null | null |
190574
|
Percentage
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "You bought one of Great White Shark Repellant Co.'s 8 percent coupon bonds one year ago for $760. These bonds make annual payments and mature 12 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 9 percent. If the inflation rate was 3.4 percent over the past year, what was your total real return on investment? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "29.28%",
"style": "rule"
}
|
{
"answer": "29.28%",
"index": 98,
"question": "You bought one of Great White Shark Repellant Co.'s 8 percent coupon bonds one year ago for $760. These bonds make annual payments and mature 12 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 9 percent. If the inflation rate was 3.4 percent over the past year, what was your total real return on investment?",
"split": "train"
}
| null | null |
1832425
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A 149 g bullet is fired from a rifle having a barrel 0.504 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is {eq}F = a + bx - cx^2\n\n{/eq}, where {eq}a = 8130 N\n\n{/eq}, {eq}b = 123000 N/m\n\n{/eq}, {eq}c = 37800 N/m^2\n\n{/eq}, with {eq}x\n\n{/eq} in meters.\n\n\n\nDetermine the work done by the gas on the bullet as the bullet travels the length of the barrel. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "18106.40079 J",
"style": "rule"
}
|
{
"answer": "18106.40079 J",
"index": 99,
"question": "A 149 g bullet is fired from a rifle having a barrel 0.504 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is {eq}F = a + bx - cx^2\n\n{/eq}, where {eq}a = 8130 N\n\n{/eq}, {eq}b = 123000 N/m\n\n{/eq}, {eq}c = 37800 N/m^2\n\n{/eq}, with {eq}x\n\n{/eq} in meters.\n\n\n\nDetermine the work done by the gas on the bullet as the bullet travels the length of the barrel.",
"split": "train"
}
| null | null |
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