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
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|
1922683
|
List
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "List three documents that the accounting department should have access to in order to pay an invoice. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1. Purchase requisition\n2. Purchase order\n3. Receiving report",
"style": "rule"
}
|
{
"answer": "1. Purchase requisition\n2. Purchase order\n3. Receiving report",
"index": 300,
"question": "List three documents that the accounting department should have access to in order to pay an invoice.",
"split": "train"
}
| null | null |
664138
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "The economy is experiencing substantial unemployment. If policy does not change, then we would expect to see what level of inflation and what level of unemployment in the long run?\n\na. higher; higher\n\nb. lower; lower\n\nc. higher; lower\n\nd. lower; higher Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 301,
"question": "The economy is experiencing substantial unemployment. If policy does not change, then we would expect to see what level of inflation and what level of unemployment in the long run?\n\na. higher; higher\n\nb. lower; lower\n\nc. higher; lower\n\nd. lower; higher",
"split": "train"
}
| null | null |
504926
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Convert the following measurement: 0.017 g/L = _____ mg/dL Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.7 mg/dL",
"style": "rule"
}
|
{
"answer": "1.7 mg/dL",
"index": 302,
"question": "Convert the following measurement: 0.017 g/L = _____ mg/dL",
"split": "train"
}
| null | null |
694638
|
Boolean
|
Other
|
Senior High School
|
general-reasoner
|
[
{
"content": "The kings of the earth gave their power to the harlot.\nTrue\nFalse Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "False",
"style": "rule"
}
|
{
"answer": "False",
"index": 303,
"question": "The kings of the earth gave their power to the harlot.\nTrue\nFalse",
"split": "train"
}
| null | null |
1187702
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Suppose you can throw a ball a maximum horizontal distance L when standing on level ground. How far can you throw it from the top of a building of height h = L if you throw it at 27.9 degrees? (Ignore your height and any effects due to air resistance.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.24v_0^2",
"style": "rule"
}
|
{
"answer": "0.24v_0^2",
"index": 304,
"question": "Suppose you can throw a ball a maximum horizontal distance L when standing on level ground. How far can you throw it from the top of a building of height h = L if you throw it at 27.9 degrees? (Ignore your height and any effects due to air resistance.)",
"split": "train"
}
| null | null |
361275
|
Multiple Choice
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "Two chemical, A and B, are combined, forming chemical C. The rate of the reaction is jointly proportional to the amount of Aand B not yet converted to C. Initially there are 200 grams of A and 300 grams of Band, during the reaction, for each gram of A used up in the conversion, there are three gram of B used up. An experiment shows that 75 grams of C are produced in the first ten minutes, the amount of chemical C, X(t), produced by timed is.\n\nSelect the correct answer.{eq}a) X =800(1-e^{-400kt})/(2-e^{-400kt}), where k =ln(29/26)/4000\\\\\n\nb) X =800(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\\n\nc) X =400(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\\n\nd) X =400(1-e^{-400kt})/(4-e^{-400kt}), where k =ln(29/26)/4000\\\\\n\ne) X =600(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 305,
"question": "Two chemical, A and B, are combined, forming chemical C. The rate of the reaction is jointly proportional to the amount of Aand B not yet converted to C. Initially there are 200 grams of A and 300 grams of Band, during the reaction, for each gram of A used up in the conversion, there are three gram of B used up. An experiment shows that 75 grams of C are produced in the first ten minutes, the amount of chemical C, X(t), produced by timed is.\n\nSelect the correct answer.{eq}a) X =800(1-e^{-400kt})/(2-e^{-400kt}), where k =ln(29/26)/4000\\\\\n\nb) X =800(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\\n\nc) X =400(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\\n\nd) X =400(1-e^{-400kt})/(4-e^{-400kt}), where k =ln(29/26)/4000\\\\\n\ne) X =600(1-e^{-800kt})/(4-e^{-800kt}), where k =ln(29/20)/8000\\\\{/eq}",
"split": "train"
}
| null | null |
664296
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "In a sample where p is 0.30, and the standard error of percentage is ± 0.04, what is the 93.86% confidence interval (Use Z table)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a",
"style": "rule"
}
|
{
"answer": "a",
"index": 306,
"question": "In a sample where p is 0.30, and the standard error of percentage is ± 0.04, what is the 93.86% confidence interval (Use Z table)?",
"split": "train"
}
| null | null |
581248
|
Multiple Choice
|
Law
|
University
|
general-reasoner
|
[
{
"content": "Which third-party intervention is commonly used in national emergency disputes?\n\nA) fact-finding\n\nB) mediation\n\nC) binding arbitration\n\nD) nonbinding arbitration Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 307,
"question": "Which third-party intervention is commonly used in national emergency disputes?\n\nA) fact-finding\n\nB) mediation\n\nC) binding arbitration\n\nD) nonbinding arbitration",
"split": "train"
}
| null | null |
599900
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How long will you wait from now if you invest $26,000 at 9.25 percent until you have $161,000, expecting to receive the $26,000 in two years? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "22.6 years",
"style": "rule"
}
|
{
"answer": "22.6 years",
"index": 308,
"question": "How long will you wait from now if you invest $26,000 at 9.25 percent until you have $161,000, expecting to receive the $26,000 in two years?",
"split": "train"
}
| null | null |
733808
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A 1.10-m-diameter MRI solenoid with a length of 2.10 m has a magnetic field of 1.80 T along its axis. If the current is turned off in a time of 1.2 s, what is the emf in one turn of the solenoid's windings? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.42 V",
"style": "rule"
}
|
{
"answer": "1.42 V",
"index": 309,
"question": "A 1.10-m-diameter MRI solenoid with a length of 2.10 m has a magnetic field of 1.80 T along its axis. If the current is turned off in a time of 1.2 s, what is the emf in one turn of the solenoid's windings?",
"split": "train"
}
| null | null |
904951
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "When a mass of 2 kg is attached to a spring whose constant is 12 N/m, it comes to rest at the equilibrium position. Starting at t = 0, a force equal to f(t) = 4 sin(t) is applied to the system. Find the equation of motion if damping is numerically equal to 10 times the instantaneous velocity. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1/5 sin(t) - 1/5cos(t)",
"style": "rule"
}
|
{
"answer": "1/5 sin(t) - 1/5cos(t)",
"index": 310,
"question": "When a mass of 2 kg is attached to a spring whose constant is 12 N/m, it comes to rest at the equilibrium position. Starting at t = 0, a force equal to f(t) = 4 sin(t) is applied to the system. Find the equation of motion if damping is numerically equal to 10 times the instantaneous velocity.",
"split": "train"
}
| null | null |
598796
|
Percentage
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "Year-to-date, Oracle had earned a 1.40 percent return. During the same time period, Valero Energy earned 7.68 percent and McDonald's earned 0.44 percent. If you have a portfolio made up of 20 percent Oracle, 30 percent Valero Energy, and 50 percent McDonald's, what is your portfolio return? (Round answer to 2 decimal places.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.80%",
"style": "rule"
}
|
{
"answer": "2.80%",
"index": 311,
"question": "Year-to-date, Oracle had earned a 1.40 percent return. During the same time period, Valero Energy earned 7.68 percent and McDonald's earned 0.44 percent. If you have a portfolio made up of 20 percent Oracle, 30 percent Valero Energy, and 50 percent McDonald's, what is your portfolio return? (Round answer to 2 decimal places.)",
"split": "train"
}
| null | null |
189792
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Can the integral $$\\int_0^1 \\frac{\\sin x}{x} dx$$ be calculated analytically? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$$\\int_0^1 \\frac{\\sin x}{x} dx=\\int_0^1\\left(1-\\frac{x^2}{3!}+\\frac{x^4}{5!}-...\\right)dx=1-\\frac{1}{3\\cdot3!}+\\frac{1}{5\\cdot5!}-...$$",
"style": "rule"
}
|
{
"answer": "$$\\int_0^1 \\frac{\\sin x}{x} dx=\\int_0^1\\left(1-\\frac{x^2}{3!}+\\frac{x^4}{5!}-...\\right)dx=1-\\frac{1}{3\\cdot3!}+\\frac{1}{5\\cdot5!}-...$$",
"index": 312,
"question": "Can the integral $$\\int_0^1 \\frac{\\sin x}{x} dx$$ be calculated analytically?",
"split": "train"
}
| null | null |
1557276
|
List
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "How do you say 'I will help you' in Spanish? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Te ayudaré (informal), Lo ayudaré (formal, male), La ayudaré (formal, female), Los/Las ayudaré (plural)",
"style": "rule"
}
|
{
"answer": "Te ayudaré (informal), Lo ayudaré (formal, male), La ayudaré (formal, female), Los/Las ayudaré (plural)",
"index": 313,
"question": "How do you say 'I will help you' in Spanish?",
"split": "train"
}
| null | null |
452228
|
Integer
|
History
|
Junior High School
|
general-reasoner
|
[
{
"content": "How many people were injured in the Newark Riots? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "727",
"style": "rule"
}
|
{
"answer": "727",
"index": 314,
"question": "How many people were injured in the Newark Riots?",
"split": "train"
}
| null | null |
1842407
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "How many atoms are in 2.70 moles of iron (fe) atoms? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "16.2594 X 10^23",
"style": "rule"
}
|
{
"answer": "16.2594 X 10^23",
"index": 315,
"question": "How many atoms are in 2.70 moles of iron (fe) atoms?",
"split": "train"
}
| null | null |
2092406
|
Multiple Choice
|
Physics
|
Primary School
|
general-reasoner
|
[
{
"content": "How are Saturn and Jupiter alike?\n \n\nThey both have rock surfaces.\nThey both rotate very slowly.\nThey both have rings.\nThey both have very low densities. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 316,
"question": "How are Saturn and Jupiter alike?\n \n\nThey both have rock surfaces.\nThey both rotate very slowly.\nThey both have rings.\nThey both have very low densities.",
"split": "train"
}
| null | null |
2031406
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What volume of 0.125 M HNOa_3 in milliliters, is required to react completely with 1.30 g of Ba(OH)_2? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "121.6 mL",
"style": "rule"
}
|
{
"answer": "121.6 mL",
"index": 317,
"question": "What volume of 0.125 M HNOa_3 in milliliters, is required to react completely with 1.30 g of Ba(OH)_2?",
"split": "train"
}
| null | null |
837754
|
Expression
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "How many atoms of C are present in 315.93 g ({eq}6.79 \\times 10^{24}\n\n{/eq} molecules) of CO? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6.79*10^24 atoms C",
"style": "rule"
}
|
{
"answer": "6.79*10^24 atoms C",
"index": 318,
"question": "How many atoms of C are present in 315.93 g ({eq}6.79 \\times 10^{24}\n\n{/eq} molecules) of CO?",
"split": "train"
}
| null | null |
2054257
|
Integer
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "A company has a Supplies account balance of $1,000 on January 1, 2011. During 2011, it purchased $3,000 of supplies. As of December 31, 2011, a supplies inventory shows $1,300 of supplies available. Prepare the adjusting journal entry to correctly report the balance of the Supplies account and the Supplies Expense account as of December 31, 2011. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$2,700",
"style": "rule"
}
|
{
"answer": "$2,700",
"index": 319,
"question": "A company has a Supplies account balance of $1,000 on January 1, 2011. During 2011, it purchased $3,000 of supplies. As of December 31, 2011, a supplies inventory shows $1,300 of supplies available. Prepare the adjusting journal entry to correctly report the balance of the Supplies account and the Supplies Expense account as of December 31, 2011.",
"split": "train"
}
| null | null |
2032316
|
String
|
Psychology
|
Senior High School
|
general-reasoner
|
[
{
"content": "What branch of psychology studies abnormal behavior? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Abnormal Psychology",
"style": "rule"
}
|
{
"answer": "Abnormal Psychology",
"index": 320,
"question": "What branch of psychology studies abnormal behavior?",
"split": "train"
}
| null | null |
769455
|
Multiple Choice
|
Business
|
Junior High School
|
general-reasoner
|
[
{
"content": "Select the list that has the steps of the closing process in the right order. a. Do final walk-through Purchase homeowners insurance Sign closing documents b. Apply for mortgage Apply for mortgage Do final walk-through Sign closing documents Purchase homeowners insurance 3. Apply for mortgage Purchase homeowners insurance Do final walk-through Sign closing documents Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 321,
"question": "Select the list that has the steps of the closing process in the right order. a. Do final walk-through Purchase homeowners insurance Sign closing documents b. Apply for mortgage Apply for mortgage Do final walk-through Sign closing documents Purchase homeowners insurance 3. Apply for mortgage Purchase homeowners insurance Do final walk-through Sign closing documents",
"split": "train"
}
| null | null |
1451684
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A square wire loop that is 0.1 m on a side has a current of 3 A running in it. The current is running clockwise. Find the magnitude and direction of the magnetic field at the center of the loop. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.39e-5 T, inward",
"style": "rule"
}
|
{
"answer": "3.39e-5 T, inward",
"index": 322,
"question": "A square wire loop that is 0.1 m on a side has a current of 3 A running in it. The current is running clockwise. Find the magnitude and direction of the magnetic field at the center of the loop.",
"split": "train"
}
| null | null |
1304079
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Light with a wavelength of 551 nm is incident on a single slit of width 2.25 micrometers. A screen is located 0.55 m behind the slid and an interference has formed on it. What is the distance between the central bright spot and the first dark fringe? Express your answer in meters. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.135 m",
"style": "rule"
}
|
{
"answer": "0.135 m",
"index": 323,
"question": "Light with a wavelength of 551 nm is incident on a single slit of width 2.25 micrometers. A screen is located 0.55 m behind the slid and an interference has formed on it. What is the distance between the central bright spot and the first dark fringe? Express your answer in meters.",
"split": "train"
}
| null | null |
1875417
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "How far above the surface of Earth would you weigh 63.6 percent of your surface weight? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.25 times Earth's radius",
"style": "rule"
}
|
{
"answer": "0.25 times Earth's radius",
"index": 324,
"question": "How far above the surface of Earth would you weigh 63.6 percent of your surface weight?",
"split": "train"
}
| null | null |
717867
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The maximum applied force of compression that one man's thighbone can endure without breaking is {eq}7.6 \\times 10^4\\, N\n\n{/eq}. The minimum effective cross-sectional area of the bone is {eq}3 \\times 10^{-4}\\, m^2\n\n{/eq}, its length is {eq}0.54\\, m\n\n{/eq}, and Young's modulus is {eq}Y = 9.4 \\times 10^9\\, N/m^2\n\n{/eq}. The mass of the man is {eq}61\\, kg\n\n{/eq}. He falls straight down without rotating, strikes the ground stiff-legged on one foot, and comes to a halt without rotating.\n\nTo see that it is easy to break a thighbone when falling in this fashion, find the maximum distance through which his center of gravity can fall without his breaking a bone. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.91 m",
"style": "rule"
}
|
{
"answer": "0.91 m",
"index": 325,
"question": "The maximum applied force of compression that one man's thighbone can endure without breaking is {eq}7.6 \\times 10^4\\, N\n\n{/eq}. The minimum effective cross-sectional area of the bone is {eq}3 \\times 10^{-4}\\, m^2\n\n{/eq}, its length is {eq}0.54\\, m\n\n{/eq}, and Young's modulus is {eq}Y = 9.4 \\times 10^9\\, N/m^2\n\n{/eq}. The mass of the man is {eq}61\\, kg\n\n{/eq}. He falls straight down without rotating, strikes the ground stiff-legged on one foot, and comes to a halt without rotating.\n\nTo see that it is easy to break a thighbone when falling in this fashion, find the maximum distance through which his center of gravity can fall without his breaking a bone.",
"split": "train"
}
| null | null |
443454
|
Integer
|
Business
|
University
|
general-reasoner
|
[
{
"content": "You are evaluating a project for The Farstroke golf club, guaranteed to correct that nasty slice. You estimate the sales price of The Farstroke to be $450 per unit and sales volume to be 1,200 units in year 1; 1,325 units in year 2; and 1,000 units in year 3. The project has a 3-year life. Variable costs amount to $250 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $150,000 in assets, which can be depreciated using bonus depreciation. The actual market value of these assets at the end of year 3 is expected to be $30,000. NWC requirements at the beginning of each year will be approximately 20% of the projected sales during the coming year. The tax rate is 21% and the required return on the project is 10 percent. What change in NWC occurs at the end of year 1? (Enter a decrease as a negative amount using a minus sign.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$11,250",
"style": "rule"
}
|
{
"answer": "$11,250",
"index": 326,
"question": "You are evaluating a project for The Farstroke golf club, guaranteed to correct that nasty slice. You estimate the sales price of The Farstroke to be $450 per unit and sales volume to be 1,200 units in year 1; 1,325 units in year 2; and 1,000 units in year 3. The project has a 3-year life. Variable costs amount to $250 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $150,000 in assets, which can be depreciated using bonus depreciation. The actual market value of these assets at the end of year 3 is expected to be $30,000. NWC requirements at the beginning of each year will be approximately 20% of the projected sales during the coming year. The tax rate is 21% and the required return on the project is 10 percent. What change in NWC occurs at the end of year 1? (Enter a decrease as a negative amount using a minus sign.)",
"split": "train"
}
| null | null |
712479
|
Float
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "Find the future value of an ordinary annuity that pays $150 per month for 15 years at an interest rate of 10% per year compounded monthly. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$62,170.552",
"style": "rule"
}
|
{
"answer": "$62,170.552",
"index": 327,
"question": "Find the future value of an ordinary annuity that pays $150 per month for 15 years at an interest rate of 10% per year compounded monthly.",
"split": "train"
}
| null | null |
1239264
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use the FTC part I to find the derivative of g(x), if {eq}g(x) = \\int^{x \\arccos x}_{\\tan x} \\frac{dt}{1 + \\sqrt[3] {t}}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{\\frac{1}{1+\\sqrt[3]{x\\arccos x}}\\left(-\\frac{x}{\\sqrt{1-x^2}}+\\arccos x\\right)-\\frac{1}{1+\\sqrt[3]{\\tan x}}\\sec^2 x}",
"style": "rule"
}
|
{
"answer": "{\\frac{1}{1+\\sqrt[3]{x\\arccos x}}\\left(-\\frac{x}{\\sqrt{1-x^2}}+\\arccos x\\right)-\\frac{1}{1+\\sqrt[3]{\\tan x}}\\sec^2 x}",
"index": 328,
"question": "Use the FTC part I to find the derivative of g(x), if {eq}g(x) = \\int^{x \\arccos x}_{\\tan x} \\frac{dt}{1 + \\sqrt[3] {t}}.",
"split": "train"
}
| null | null |
502272
|
Boolean
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Would reducing information asymmetries guarantee better markets? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 329,
"question": "Would reducing information asymmetries guarantee better markets?",
"split": "train"
}
| null | null |
1913390
|
Multiple Choice
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "External events include all of the following except:\n\na. Paying employees' salaries.\n\nb. Purchasing equipment.\n\nc. Using office supplies.\n\nd. Collecting an account receivable. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 330,
"question": "External events include all of the following except:\n\na. Paying employees' salaries.\n\nb. Purchasing equipment.\n\nc. Using office supplies.\n\nd. Collecting an account receivable.",
"split": "train"
}
| null | null |
874130
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The lower half of a 6-m-high cylindrical container is filled with water ( {eq}\\rho= 1000 kg/m^3\n\n{/eq} ) and the upper half with oil that has a specific gravity of 0.85. Determine the pressure difference between the top and bottom of the cylinder. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "54.445 kPa",
"style": "rule"
}
|
{
"answer": "54.445 kPa",
"index": 331,
"question": "The lower half of a 6-m-high cylindrical container is filled with water ( {eq}\\rho= 1000 kg/m^3\n\n{/eq} ) and the upper half with oil that has a specific gravity of 0.85. Determine the pressure difference between the top and bottom of the cylinder.",
"split": "train"
}
| null | null |
1248380
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Two point charges {eq}q_1\n\n{/eq} = {eq}q_2\n\n{/eq} = 2 {eq}\\mu\n\n{/eq}C are fixed at {eq}x_1\n\n{/eq} = + 3 and {eq}x_2\n\n{/eq} = -3. A third particle of mass 1 g and charge {eq}q_3\n\n{/eq} = -4 {eq}\\mu\n\n{/eq}C are released from rest at y = 4.0. Find the speed of the particle as it reaches the origin. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6 m/s",
"style": "rule"
}
|
{
"answer": "6 m/s",
"index": 332,
"question": "Two point charges {eq}q_1\n\n{/eq} = {eq}q_2\n\n{/eq} = 2 {eq}\\mu\n\n{/eq}C are fixed at {eq}x_1\n\n{/eq} = + 3 and {eq}x_2\n\n{/eq} = -3. A third particle of mass 1 g and charge {eq}q_3\n\n{/eq} = -4 {eq}\\mu\n\n{/eq}C are released from rest at y = 4.0. Find the speed of the particle as it reaches the origin.",
"split": "train"
}
| null | null |
1278377
|
Expression
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "How do you calculate the energy needed to heat water? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "q = cmΔT",
"style": "rule"
}
|
{
"answer": "q = cmΔT",
"index": 333,
"question": "How do you calculate the energy needed to heat water?",
"split": "train"
}
| null | null |
1974121
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Integrate by partial fraction method: \\(\\int \\frac{ -2 x + 4 }{ x \\left( x + 5 \\right) \\left( x - 1\\right)} d x\\) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-4/5ln|x|+7/15ln|x+5|+1/3ln|x-1|+C",
"style": "rule"
}
|
{
"answer": "-4/5ln|x|+7/15ln|x+5|+1/3ln|x-1|+C",
"index": 334,
"question": "Integrate by partial fraction method: \\(\\int \\frac{ -2 x + 4 }{ x \\left( x + 5 \\right) \\left( x - 1\\right)} d x\\)",
"split": "train"
}
| null | null |
381037
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "How do you determine the OH (aq) concentration in 1.0 M aniline (#C_6H_5NH_2#) solution. (The #K_b# for aniline is #4.0 x 10^-10#? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.14e-5 mol/l",
"style": "rule"
}
|
{
"answer": "2.14e-5 mol/l",
"index": 335,
"question": "How do you determine the OH (aq) concentration in 1.0 M aniline (#C_6H_5NH_2#) solution. (The #K_b# for aniline is #4.0 x 10^-10#?",
"split": "train"
}
| null | null |
368925
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $b\\in\\mathbb{R}$ and consider the matrix $\\begin{vmatrix} 4 &-1 & b\\\\ -1& 2& -2\\\\ 0& -2& 1 \\end{vmatrix}$. For what values of $b\\in\\mathbb{R}$ is the matrix positive definite? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The matrix is never definite positive (nor semi-definite) for any value of b",
"style": "rule"
}
|
{
"answer": "The matrix is never definite positive (nor semi-definite) for any value of b",
"index": 336,
"question": "Let $b\\in\\mathbb{R}$ and consider the matrix $\\begin{vmatrix} 4 &-1 & b\\\\ -1& 2& -2\\\\ 0& -2& 1 \\end{vmatrix}$. For what values of $b\\in\\mathbb{R}$ is the matrix positive definite?",
"split": "train"
}
| null | null |
1203368
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Use the Fundamental Theorem of Calculus to find {eq}\\int_1^4 {{{\\cos \\sqrt x } \\over {\\sqrt x }}} \\ dx Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2(sin(2)-sin(1))",
"style": "rule"
}
|
{
"answer": "2(sin(2)-sin(1))",
"index": 337,
"question": "Use the Fundamental Theorem of Calculus to find {eq}\\int_1^4 {{{\\cos \\sqrt x } \\over {\\sqrt x }}} \\ dx",
"split": "train"
}
| null | null |
695453
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The average of the total deficit of the middle five deficit is closest to the deficit of which country ? Options are: answer A Korea; answer B South Africa; answer C UAE; answer D None of these Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 338,
"question": "The average of the total deficit of the middle five deficit is closest to the deficit of which country ? Options are: answer A Korea; answer B South Africa; answer C UAE; answer D None of these",
"split": "train"
}
| null | null |
1779184
|
Multiple Choice
|
History
|
Senior High School
|
general-reasoner
|
[
{
"content": "Question 26\n \n\nUse the video\nConcerning law and punishment, Taizong favored\npunishment.\nquick execution as\nOlenient, less harsh\nO harsh, strict\nNo answer text provided. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 339,
"question": "Question 26\n \n\nUse the video\nConcerning law and punishment, Taizong favored\npunishment.\nquick execution as\nOlenient, less harsh\nO harsh, strict\nNo answer text provided.",
"split": "train"
}
| null | null |
1871058
|
String
|
Biology
|
Junior High School
|
general-reasoner
|
[
{
"content": "What plant cell structures capture sunlight to produce sugars? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Chloroplasts",
"style": "rule"
}
|
{
"answer": "Chloroplasts",
"index": 340,
"question": "What plant cell structures capture sunlight to produce sugars?",
"split": "train"
}
| null | null |
1363989
|
String
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "What part of speech is really? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "adverb",
"style": "rule"
}
|
{
"answer": "adverb",
"index": 341,
"question": "What part of speech is really?",
"split": "train"
}
| null | null |
1119378
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "If I have a group $G$ and a set $X$ then I can define an action $\\alpha:G \\times X \\rightarrow X$ like $(g, x)=gx$ I can also define it's corresponding morphism $\\alpha':G \\rightarrow S_X$. Does this have to be surjective? In the exercise, I have that $p$ is the lowest prime that divides $|G|$, I have an $H$ such that $|G:H|=p$ and $X=G/H$. Is my reasoning correct in showing that the corresponding morphism $\\alpha':G \\rightarrow S_X$ is not surjective when $G = \\mathbb{Z}_{15}$, $p=3$, $H \\cong \\mathbb{Z_5}$, and $X=\\{\\bar{0}, \\bar{1}, \\bar{2}\\}$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "No",
"style": "rule"
}
|
{
"answer": "No",
"index": 342,
"question": "If I have a group $G$ and a set $X$ then I can define an action $\\alpha:G \\times X \\rightarrow X$ like $(g, x)=gx$ I can also define it's corresponding morphism $\\alpha':G \\rightarrow S_X$. Does this have to be surjective? In the exercise, I have that $p$ is the lowest prime that divides $|G|$, I have an $H$ such that $|G:H|=p$ and $X=G/H$. Is my reasoning correct in showing that the corresponding morphism $\\alpha':G \\rightarrow S_X$ is not surjective when $G = \\mathbb{Z}_{15}$, $p=3$, $H \\cong \\mathbb{Z_5}$, and $X=\\{\\bar{0}, \\bar{1}, \\bar{2}\\}$?",
"split": "train"
}
| null | null |
68055
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Determine the molar solubility of {eq}MnS\n\n{/eq} in a solution containing 0.0350 M {eq}Na_2S\n\n{/eq}. ({eq}K_{sp}\n\n{/eq} of {eq}MnS = 2.50 \\times 10^{-10}\n\n{/eq}) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "7.14e-9 mol/L",
"style": "rule"
}
|
{
"answer": "7.14e-9 mol/L",
"index": 343,
"question": "Determine the molar solubility of {eq}MnS\n\n{/eq} in a solution containing 0.0350 M {eq}Na_2S\n\n{/eq}. ({eq}K_{sp}\n\n{/eq} of {eq}MnS = 2.50 \\times 10^{-10}\n\n{/eq})",
"split": "train"
}
| null | null |
1054213
|
List
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "1. Gonyo Inc., which produces and sells a single product, has provided the following contribution format income statement for December:\n\n\n Sales (3,200 units) $252,800\n Variable costs 118,400\n Contribution Margin 134,400\n Fixed costs 113,600\n Net Operating Income $ 20,800\nRedo the company's contribution format income statement assuming that the company sells 3,400 units. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Sales: $268,600\nVariable Costs: $125,800\nContribution Margin: $142,800\nFixed Costs: $113,600\nNet Operating Income: $29,200",
"style": "rule"
}
|
{
"answer": "Sales: $268,600\nVariable Costs: $125,800\nContribution Margin: $142,800\nFixed Costs: $113,600\nNet Operating Income: $29,200",
"index": 344,
"question": "1. Gonyo Inc., which produces and sells a single product, has provided the following contribution format income statement for December:\n\n\n Sales (3,200 units) $252,800\n Variable costs 118,400\n Contribution Margin 134,400\n Fixed costs 113,600\n Net Operating Income $ 20,800\nRedo the company's contribution format income statement assuming that the company sells 3,400 units.",
"split": "train"
}
| null | null |
1220101
|
Percentage
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $850. What is the bond's nominal (annual) coupon interest rate?\n\na. 6.27%\n\nb. 6.60%\n\nc. 6.95%\n\nd 7.32%\n\ne. 7.70% Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "7.70%",
"style": "rule"
}
|
{
"answer": "7.70%",
"index": 345,
"question": "O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $850. What is the bond's nominal (annual) coupon interest rate?\n\na. 6.27%\n\nb. 6.60%\n\nc. 6.95%\n\nd 7.32%\n\ne. 7.70%",
"split": "train"
}
| null | null |
528764
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I'm trying to calculate the inverse laplace transform: $$\\large \\mathcal{L}^{-1}\\left(-\\sqrt{\\frac ks}e^{-\\sqrt{\\frac sk}x}\\right)$$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$$f(t)=\\frac{a}{\\sqrt t}e^{-\\frac{b}{t}}$$",
"style": "rule"
}
|
{
"answer": "$$f(t)=\\frac{a}{\\sqrt t}e^{-\\frac{b}{t}}$$",
"index": 346,
"question": "I'm trying to calculate the inverse laplace transform: $$\\large \\mathcal{L}^{-1}\\left(-\\sqrt{\\frac ks}e^{-\\sqrt{\\frac sk}x}\\right)$$",
"split": "train"
}
| null | null |
1694126
|
List
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Where do I get information on a company's financial performance immediately after it enters the stock market? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Market regulator's website and the company's investor relations webpage",
"style": "rule"
}
|
{
"answer": "Market regulator's website and the company's investor relations webpage",
"index": 347,
"question": "Where do I get information on a company's financial performance immediately after it enters the stock market?",
"split": "train"
}
| null | null |
537827
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "It is desired to make a nonreflecting lens {eq}(n = 1.51)\n\n{/eq} for an infrared radiation detector. If the coating material has an index of refraction of {eq}1.37\n\n{/eq}, what is the minimum thickness of the coating for radiation with a frequency of {eq}3.65 \\times 10^{14} \\ Hz\n\n{/eq}? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "150 nm",
"style": "rule"
}
|
{
"answer": "150 nm",
"index": 348,
"question": "It is desired to make a nonreflecting lens {eq}(n = 1.51)\n\n{/eq} for an infrared radiation detector. If the coating material has an index of refraction of {eq}1.37\n\n{/eq}, what is the minimum thickness of the coating for radiation with a frequency of {eq}3.65 \\times 10^{14} \\ Hz\n\n{/eq}?",
"split": "train"
}
| null | null |
1494688
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Solve.\n\n{eq}\\frac {dy}{dx} = \\frac{e^{2x-y}}{e^{x+y}}\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "y = - \\frac{ \\ln( C' -2e^{x}) }{2}",
"style": "rule"
}
|
{
"answer": "y = - \\frac{ \\ln( C' -2e^{x}) }{2}",
"index": 349,
"question": "Solve.\n\n{eq}\\frac {dy}{dx} = \\frac{e^{2x-y}}{e^{x+y}}\n\n{/eq}",
"split": "train"
}
| null | null |
1906963
|
String
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "So the Gaussian integral basically states that: $$ I = \\int_{-\\infty}^{\\infty} e^{-x^2} \\ dx =\\sqrt{\\pi}$$ So the way to solve this is by converting to polar co-ordinates and doing a double integration. Since I haven’t learnt double integration, I have searched a lot to solve this kind of integral using single integration. But to no avail. I have even tried it myself a couple of times but have been unsuccessful. So here’s my question, is it possible to integrate the above using only single integration and if so how? If this is not possible to integrate using single integration then what is the reason behind it. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "√π",
"style": "rule"
}
|
{
"answer": "√π",
"index": 350,
"question": "So the Gaussian integral basically states that: $$ I = \\int_{-\\infty}^{\\infty} e^{-x^2} \\ dx =\\sqrt{\\pi}$$ So the way to solve this is by converting to polar co-ordinates and doing a double integration. Since I haven’t learnt double integration, I have searched a lot to solve this kind of integral using single integration. But to no avail. I have even tried it myself a couple of times but have been unsuccessful. So here’s my question, is it possible to integrate the above using only single integration and if so how? If this is not possible to integrate using single integration then what is the reason behind it.",
"split": "train"
}
| null | null |
1963220
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The minute hand on a watch is in length. What is the displacement vector of the tip of the minute hand from 8:00AM to 8:20 AM? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\Delta r = \\frac{\\sqrt{3}L}{2} \\hat{i} - \\frac{3L}{2}\\hat{j}",
"style": "rule"
}
|
{
"answer": "\\Delta r = \\frac{\\sqrt{3}L}{2} \\hat{i} - \\frac{3L}{2}\\hat{j}",
"index": 351,
"question": "The minute hand on a watch is in length. What is the displacement vector of the tip of the minute hand from 8:00AM to 8:20 AM?",
"split": "train"
}
| null | null |
1288562
|
Multiple Choice
|
Biology
|
Junior High School
|
general-reasoner
|
[
{
"content": "How long does it take for your liver to get rid of the alcohol in one standard drink.\n \n\na. 10 minutes? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 352,
"question": "How long does it take for your liver to get rid of the alcohol in one standard drink.\n \n\na. 10 minutes?",
"split": "train"
}
| null | null |
629857
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Two uniformly charged insulating rods are bent in a semicircular shape with radius r = 12.9 cm. If they are positioned so they form a circle but do not touch and have opposite charges of {eq}+7.43 \\mu C\n\n{/eq} and {eq}-7.43 \\mu C\n\n{/eq}, find the magnitude of the electric field at the center of the composite circular charge configuration. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5.12e6 N/C",
"style": "rule"
}
|
{
"answer": "5.12e6 N/C",
"index": 353,
"question": "Two uniformly charged insulating rods are bent in a semicircular shape with radius r = 12.9 cm. If they are positioned so they form a circle but do not touch and have opposite charges of {eq}+7.43 \\mu C\n\n{/eq} and {eq}-7.43 \\mu C\n\n{/eq}, find the magnitude of the electric field at the center of the composite circular charge configuration.",
"split": "train"
}
| null | null |
1088702
|
Float
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "You are considering buying 100 shares of WalMart stock. In any given week, the stock can either increase in value by 3.8% or decrease in value by 2.2%. The probability that the stock increases is 0.63; otherwise, the stock decreases in price. How the stock performs in any given week is independent of how it has performed in the past. What is the expected return in a randomly chosen week? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.0158",
"style": "rule"
}
|
{
"answer": "0.0158",
"index": 354,
"question": "You are considering buying 100 shares of WalMart stock. In any given week, the stock can either increase in value by 3.8% or decrease in value by 2.2%. The probability that the stock increases is 0.63; otherwise, the stock decreases in price. How the stock performs in any given week is independent of how it has performed in the past. What is the expected return in a randomly chosen week?",
"split": "train"
}
| null | null |
348170
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Seller X sells her good for $40. The price index is currently 140. If the price of Seller X's good rises to $50 and the price index rises by the same percentage, according to the producer misperception explanation of the upward-sloping SRAS curve, what would the seller think of the relative price of her good?\n\nA) It has risen.\n\nB) It has remained constant.\n\nC) It has fallen.\n\nD) Either Parts B or C could be correct, depending on the expectations.\n\nE) There is not enough information to answer this question. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 355,
"question": "Seller X sells her good for $40. The price index is currently 140. If the price of Seller X's good rises to $50 and the price index rises by the same percentage, according to the producer misperception explanation of the upward-sloping SRAS curve, what would the seller think of the relative price of her good?\n\nA) It has risen.\n\nB) It has remained constant.\n\nC) It has fallen.\n\nD) Either Parts B or C could be correct, depending on the expectations.\n\nE) There is not enough information to answer this question.",
"split": "train"
}
| null | null |
1027945
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.)\n\n{eq}\\displaystyle\n\n\\int_4^7 \\frac{x}{1 + x^3}dx \\\\ \\lim_{n \\to \\infty}\\sum_{i = 1}^n \\boxed{\\space}.\n\n{/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{4 + \\frac{3i}{n} }{1 + \\left( 4 + \\frac{3i}{n} \\right)^3 } \\right) \\frac{3}{n}",
"style": "rule"
}
|
{
"answer": "\\lim_{n \\to \\infty} \\sum_{i=1}^{n} \\left( \\frac{4 + \\frac{3i}{n} }{1 + \\left( 4 + \\frac{3i}{n} \\right)^3 } \\right) \\frac{3}{n}",
"index": 356,
"question": "Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.)\n\n{eq}\\displaystyle\n\n\\int_4^7 \\frac{x}{1 + x^3}dx \\\\ \\lim_{n \\to \\infty}\\sum_{i = 1}^n \\boxed{\\space}.\n\n{/eq}",
"split": "train"
}
| null | null |
1338385
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Which of the following always correspond(s) to a fall in the short run output?\n\na) The AS shifts right.\n\nb) The resulting price level falls.\n\nc) The AD shifts up.\n\nd) None of the answers is correct. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 357,
"question": "Which of the following always correspond(s) to a fall in the short run output?\n\na) The AS shifts right.\n\nb) The resulting price level falls.\n\nc) The AD shifts up.\n\nd) None of the answers is correct.",
"split": "train"
}
| null | null |
313079
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "The rate constant for a reaction involving {eq}\\rm\n\nNO_2\n\n{/eq} is {eq}\\rm\n\n7.45 \\times 10^2\\ M/s\n\n{/eq} at {eq}\\rm\n\n300 ^\\circ C\n\n{/eq}. How long (in seconds) would it take for the concentration of {eq}\\rm\n\nNO_2\n\n{/eq} to decrease from {eq}\\rm\n\n2.15\\ M\n\n{/eq} to {eq}\\rm\n\n1.28\\ M\n\n{/eq}? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.17e-3 s",
"style": "rule"
}
|
{
"answer": "1.17e-3 s",
"index": 358,
"question": "The rate constant for a reaction involving {eq}\\rm\n\nNO_2\n\n{/eq} is {eq}\\rm\n\n7.45 \\times 10^2\\ M/s\n\n{/eq} at {eq}\\rm\n\n300 ^\\circ C\n\n{/eq}. How long (in seconds) would it take for the concentration of {eq}\\rm\n\nNO_2\n\n{/eq} to decrease from {eq}\\rm\n\n2.15\\ M\n\n{/eq} to {eq}\\rm\n\n1.28\\ M\n\n{/eq}?",
"split": "train"
}
| null | null |
1212294
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $N$ be an integer. Given the indices of the congruence subgroups $\\Gamma(N),\\Gamma_1(N),\\Gamma_0(N)$ in $\\mathrm{SL}_2(\\mathbb{Z})$, can I compute the indices $[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}(N)],[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}_1(N)],[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}_0(N)]$, where $\\bar{\\Gamma}$ denotes the image of $\\Gamma$ in $\\mathrm{PSL}_2(\\mathbb{Z})$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$[PSL(2,\\mathbb{Z}):\\Gamma (m)]=\\frac{m^3}{2}\\prod_{p\\mid m}\\left(1-\\frac{1}{p^2}, \\right), [PSL(2,\\mathbb{Z}):\\Gamma_1 (m)]=\\frac{m^2}{2}\\prod_{p\\mid m}\\left(1-\\frac{1}{p^2}, \\right), [PSL(2,\\mathbb{Z}):\\Gamma_0 (m)]=m\\prod_{p\\mid m}\\left(1+\\frac{1}{p}, \\right)$",
"style": "rule"
}
|
{
"answer": "$[PSL(2,\\mathbb{Z}):\\Gamma (m)]=\\frac{m^3}{2}\\prod_{p\\mid m}\\left(1-\\frac{1}{p^2}, \\right), [PSL(2,\\mathbb{Z}):\\Gamma_1 (m)]=\\frac{m^2}{2}\\prod_{p\\mid m}\\left(1-\\frac{1}{p^2}, \\right), [PSL(2,\\mathbb{Z}):\\Gamma_0 (m)]=m\\prod_{p\\mid m}\\left(1+\\frac{1}{p}, \\right)$",
"index": 359,
"question": "Let $N$ be an integer. Given the indices of the congruence subgroups $\\Gamma(N),\\Gamma_1(N),\\Gamma_0(N)$ in $\\mathrm{SL}_2(\\mathbb{Z})$, can I compute the indices $[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}(N)],[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}_1(N)],[\\mathrm{PSL}_2(\\mathbb{Z}):\\bar{ \\Gamma}_0(N)]$, where $\\bar{\\Gamma}$ denotes the image of $\\Gamma$ in $\\mathrm{PSL}_2(\\mathbb{Z})$?",
"split": "train"
}
| null | null |
2017530
|
List
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A uniform bridge of weight {eq}1200 \\ kN {/eq} and of length {eq}17 \\ m {/eq} rests on supports at each end which are {eq}1 \\ m {/eq} wide. A stationary lorry of weight {eq}60 \\ kN {/eq} has it's centre of mass {eq}3.0 \\ m {/eq} from the centre of the bridge. Calculate the support force on the bridge at each end. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The support force on the left end is 641 kN and the support force on the right end is 619 kN.",
"style": "rule"
}
|
{
"answer": "The support force on the left end is 641 kN and the support force on the right end is 619 kN.",
"index": 360,
"question": "A uniform bridge of weight {eq}1200 \\ kN {/eq} and of length {eq}17 \\ m {/eq} rests on supports at each end which are {eq}1 \\ m {/eq} wide. A stationary lorry of weight {eq}60 \\ kN {/eq} has it's centre of mass {eq}3.0 \\ m {/eq} from the centre of the bridge. Calculate the support force on the bridge at each end.",
"split": "train"
}
| null | null |
147659
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Evaluate the line integral {eq}\\int_C \\mathbf F \\cdot d\\mathbf r{/eq}, where {eq}\\mathbf F(x,y,z) = \\sin x \\mathbf i + \\cos y \\mathbf j + xz \\mathbf k{/eq} and {eq}C{/eq} is given by the vector function {eq}\\mathbf r(t) = t^4 \\mathbf i - t^4 \\mathbf j + t \\mathbf k ; \\quad 0 \\leq t \\leq 1{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-0.22",
"style": "rule"
}
|
{
"answer": "-0.22",
"index": 361,
"question": "Evaluate the line integral {eq}\\int_C \\mathbf F \\cdot d\\mathbf r{/eq}, where {eq}\\mathbf F(x,y,z) = \\sin x \\mathbf i + \\cos y \\mathbf j + xz \\mathbf k{/eq} and {eq}C{/eq} is given by the vector function {eq}\\mathbf r(t) = t^4 \\mathbf i - t^4 \\mathbf j + t \\mathbf k ; \\quad 0 \\leq t \\leq 1{/eq}",
"split": "train"
}
| null | null |
685008
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Is there a way to compute the convergence orders $p$ and $q$ using numerical data, given the error estimate $u(x,t)= u_{h,k} + C_1 h^{p} +C_2 k^{q}$ where $u_{h,k}$ is a numerical approximation to the solution function $u(x,t)$, $h$ is the size of the partitions on $x\\in [a,b]$, $k$ is the size of the partitions on $t\\in [0,T]$, and $C_1$ and $C_2$ are constants that do not depend on $h$ and $k$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "p = \\frac{\\ln |u_{h,k} - u_{h/2,k} |}{\\ln | u_{h/2,k} - u_{h/4,k} |}/\\ln 2, and q = \\frac{\\ln |u_{h,k} - u_{h,k/2} |}{\\ln | u_{h,k/2} - u_{h,k/2} |}/\\ln 2",
"style": "rule"
}
|
{
"answer": "p = \\frac{\\ln |u_{h,k} - u_{h/2,k} |}{\\ln | u_{h/2,k} - u_{h/4,k} |}/\\ln 2, and q = \\frac{\\ln |u_{h,k} - u_{h,k/2} |}{\\ln | u_{h,k/2} - u_{h,k/2} |}/\\ln 2",
"index": 362,
"question": "Is there a way to compute the convergence orders $p$ and $q$ using numerical data, given the error estimate $u(x,t)= u_{h,k} + C_1 h^{p} +C_2 k^{q}$ where $u_{h,k}$ is a numerical approximation to the solution function $u(x,t)$, $h$ is the size of the partitions on $x\\in [a,b]$, $k$ is the size of the partitions on $t\\in [0,T]$, and $C_1$ and $C_2$ are constants that do not depend on $h$ and $k$?",
"split": "train"
}
| null | null |
1932152
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the trace of\n$\\left(\n\\begin{array}{cccc}\n\\frac{3}{\\sqrt{2}} & \\frac{13}{\\sqrt{2}} & -7 \\sqrt{2} & \\frac{7}{\\sqrt{2}} \\\\\n-\\frac{5}{\\sqrt{2}} & 6 \\sqrt{2} & \\frac{7}{\\sqrt{2}} & \\frac{9}{\\sqrt{2}} \\\\\n\\frac{3}{\\sqrt{2}} & -\\frac{5}{\\sqrt{2}} & -\\frac{7}{\\sqrt{2}} & -\\frac{9}{\\sqrt{2}} \\\\\n7 \\sqrt{2} & -\\sqrt{2} & 2 \\sqrt{2} & -\\frac{5}{\\sqrt{2}} \\\\\n\\end{array}\n\\right)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "6 \\sqrt{2} - \\frac{9}{\\sqrt{2}}",
"style": "rule"
}
|
{
"answer": "6 \\sqrt{2} - \\frac{9}{\\sqrt{2}}",
"index": 363,
"question": "Compute the trace of\n$\\left(\n\\begin{array}{cccc}\n\\frac{3}{\\sqrt{2}} & \\frac{13}{\\sqrt{2}} & -7 \\sqrt{2} & \\frac{7}{\\sqrt{2}} \\\\\n-\\frac{5}{\\sqrt{2}} & 6 \\sqrt{2} & \\frac{7}{\\sqrt{2}} & \\frac{9}{\\sqrt{2}} \\\\\n\\frac{3}{\\sqrt{2}} & -\\frac{5}{\\sqrt{2}} & -\\frac{7}{\\sqrt{2}} & -\\frac{9}{\\sqrt{2}} \\\\\n7 \\sqrt{2} & -\\sqrt{2} & 2 \\sqrt{2} & -\\frac{5}{\\sqrt{2}} \\\\\n\\end{array}\n\\right)$.",
"split": "train"
}
| null | null |
1741402
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Twone produces and sells three products. Last month's results are as follows:\n\n\n P1 P2 P3\nRevenues $104,000 $208,000 $208,000\nVariable costs $41,600 $93,600 $83,200\nFixed costs total $140,000. What is Twone's margin of safety? (Assume the current product mix.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$278,621",
"style": "rule"
}
|
{
"answer": "$278,621",
"index": 364,
"question": "Twone produces and sells three products. Last month's results are as follows:\n\n\n P1 P2 P3\nRevenues $104,000 $208,000 $208,000\nVariable costs $41,600 $93,600 $83,200\nFixed costs total $140,000. What is Twone's margin of safety? (Assume the current product mix.)",
"split": "train"
}
| null | null |
1495402
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The angular speed of a rotating platform changes from {eq}\\displaystyle\n\n\\omega_0 = 3.6 \\text{ rad/s to } \\omega = 6.4 \\text{ rad/s }\n\n{/eq} at a constant rate as the platform moves through an angle {eq}\\displaystyle\n\n\\Delta{\\theta} = 5.5\\text{ radians }\n\n{/eq}. The platform has a radius of {eq}\\displaystyle\n\nR = 12 cm\n\n{/eq}. Calculate the angular acceleration of the platform {eq}\\displaystyle\n\na\n\n{/eq} in {eq}\\displaystyle\n\nrad/s^2\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.54 rad/s^2",
"style": "rule"
}
|
{
"answer": "2.54 rad/s^2",
"index": 365,
"question": "The angular speed of a rotating platform changes from {eq}\\displaystyle\n\n\\omega_0 = 3.6 \\text{ rad/s to } \\omega = 6.4 \\text{ rad/s }\n\n{/eq} at a constant rate as the platform moves through an angle {eq}\\displaystyle\n\n\\Delta{\\theta} = 5.5\\text{ radians }\n\n{/eq}. The platform has a radius of {eq}\\displaystyle\n\nR = 12 cm\n\n{/eq}. Calculate the angular acceleration of the platform {eq}\\displaystyle\n\na\n\n{/eq} in {eq}\\displaystyle\n\nrad/s^2\n\n{/eq}.",
"split": "train"
}
| null | null |
1719229
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $A \\in \\mathbb R^{4\\times 4}$ have characteristic polynomial $(x^2+1)^2$. Which of the following is true?\n(A) $A$ is diagonalizable over $\\mathbb C$ but not over $\\mathbb R$\n(B) $A$ is nilpotent\n(C) $A$ is invertible\n(D) There is no such matrix $A$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 366,
"question": "Let $A \\in \\mathbb R^{4\\times 4}$ have characteristic polynomial $(x^2+1)^2$. Which of the following is true?\n(A) $A$ is diagonalizable over $\\mathbb C$ but not over $\\mathbb R$\n(B) $A$ is nilpotent\n(C) $A$ is invertible\n(D) There is no such matrix $A$.",
"split": "train"
}
| null | null |
1385550
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "To transform a unit square into a parallelogram in which (a) the diagonals are parallel to the unit square's diagonals, (b) the longest diagonal is equal in length to either of the unit square's diagonals, and (c) the diagonals intersect at the midpoint of the longest diagonal, what is/are the transformation equation(s) using basic algebra? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "ax_n + by_n = x'_n and cx_n + dy_n = y'_n",
"style": "rule"
}
|
{
"answer": "ax_n + by_n = x'_n and cx_n + dy_n = y'_n",
"index": 367,
"question": "To transform a unit square into a parallelogram in which (a) the diagonals are parallel to the unit square's diagonals, (b) the longest diagonal is equal in length to either of the unit square's diagonals, and (c) the diagonals intersect at the midpoint of the longest diagonal, what is/are the transformation equation(s) using basic algebra?",
"split": "train"
}
| null | null |
2106041
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Sketch the region of integration and set up the integral in polar coordinates. Don't integrate.\n\n{eq}\\int_{1}^{2}\\int_{0}^{\\sqrt{4-x^{2}}}\\frac{1}{\\sqrt{x^{2}+y^{2}}}dy\\ dx\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{\\int_{0}^{\\frac{\\pi}{2}}\\int_{1}^{2}\\frac{1}{r}rdrd\\theta} = {\\int_{0}^{\\frac{\\pi}{2}}drd\\theta}",
"style": "rule"
}
|
{
"answer": "{\\int_{0}^{\\frac{\\pi}{2}}\\int_{1}^{2}\\frac{1}{r}rdrd\\theta} = {\\int_{0}^{\\frac{\\pi}{2}}drd\\theta}",
"index": 368,
"question": "Sketch the region of integration and set up the integral in polar coordinates. Don't integrate.\n\n{eq}\\int_{1}^{2}\\int_{0}^{\\sqrt{4-x^{2}}}\\frac{1}{\\sqrt{x^{2}+y^{2}}}dy\\ dx\n\n{/eq}",
"split": "train"
}
| null | null |
1122432
|
List
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "Dna is compacted and condensed in order to make it easier to proceed through the cell cycle. what is the correct sequence from loosely compacted dna to highly condensed dna? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1. Single DNA strand\n2. DNA combines with histones to form chromatin\n3. Chromatin binds to a centromere\n4. Two copies of condensed chromatin bind at the centromere during prophase\n5. The two chromatin condense further and form a chromosome in metaphase",
"style": "rule"
}
|
{
"answer": "1. Single DNA strand\n2. DNA combines with histones to form chromatin\n3. Chromatin binds to a centromere\n4. Two copies of condensed chromatin bind at the centromere during prophase\n5. The two chromatin condense further and form a chromosome in metaphase",
"index": 369,
"question": "Dna is compacted and condensed in order to make it easier to proceed through the cell cycle. what is the correct sequence from loosely compacted dna to highly condensed dna?",
"split": "train"
}
| null | null |
894954
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the Laplace Transform of the following function:\n\n{eq}\\displaystyle \\ f(t) = \\left \\{ \\begin{array}{ ll }\n\n0, & 0 \\leq t < 1 \\\\\n\nt - 1, & 1 \\leq t < 2 \\\\\n\n3 - t, & 2 \\leq t < 3 \\\\\n\n0, & 3 \\leq t\n\n\\end{array} \\right .\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "F(s) = (e^(-s) - e^(-2s) + e^(-3s))/s^2 - (e^(-2s) + e^(-3s))/s",
"style": "rule"
}
|
{
"answer": "F(s) = (e^(-s) - e^(-2s) + e^(-3s))/s^2 - (e^(-2s) + e^(-3s))/s",
"index": 370,
"question": "Find the Laplace Transform of the following function:\n\n{eq}\\displaystyle \\ f(t) = \\left \\{ \\begin{array}{ ll }\n\n0, & 0 \\leq t < 1 \\\\\n\nt - 1, & 1 \\leq t < 2 \\\\\n\n3 - t, & 2 \\leq t < 3 \\\\\n\n0, & 3 \\leq t\n\n\\end{array} \\right .\n\n{/eq}",
"split": "train"
}
| null | null |
1849213
|
Multiple Choice
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "Which work is the best example of an adaptation? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 371,
"question": "Which work is the best example of an adaptation?",
"split": "train"
}
| null | null |
272388
|
Multiple Choice
|
Psychology
|
Senior High School
|
general-reasoner
|
[
{
"content": "People who claim to have been abducted by space aliens—often shortly after going to bed—commonly recall being floated off their beds. It is most likely that they have incorporated ________ into their memories. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 372,
"question": "People who claim to have been abducted by space aliens—often shortly after going to bed—commonly recall being floated off their beds. It is most likely that they have incorporated ________ into their memories.",
"split": "train"
}
| null | null |
1280050
|
Percentage
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Rotorua Products, Ltd., of New Zealand markets agricultural products for the burgeoning Asian consumer market. The company's current assets, current liabilities, and sales have been reported as follows over the last five years (Year 5 is the most recent year):\n\n \n \n \n \n Year 1 \n Year 2 \n Year 3 \n Year 4 \n Year 5 \n \n \n Sales \n $ \n 4,635,640 \n \n $ \n 4,775,600 \n \n $ \n 5,097,510 \n \n $ \n 5,554,070 \n \n $ \n 5,798,480 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Cash \n $ \n 96,781 \n \n $ \n 89,547 \n \n $ \n 100,485 \n \n $ \n 73,353 \n \n $ \n 80,182 \n \n \n \n Accounts receivable, net \n \n 402,926 \n \n \n 433,719 \n \n \n 451,015 \n \n \n 497,308 \n \n \n 569,205 \n \n \n \n Inventory \n \n 819,533 \n \n \n 871,581 \n \n \n 822,039 \n \n \n 897,999 \n \n \n 898,668 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Total current assets \n $ \n 1,319,240 \n \n $ \n 1,394,847 \n \n $ \n 1,373,539 \n \n $ \n 1,468,660 \n \n $ \n 1,548,055 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Current liabilities \n $ \n 312,533 \n \n $ \n 340,279 \n \n $ \n 343,680 \n \n $ \n 319,165 \n \n $ \n 403,051 \n \n \n \n\n\n1. Express all of the asset, liability, and sales data in trend percentages. Use Year 1 as the base year. (Round your percentage answers to 1 decimal place (i.e., 0.1234 should be entered as 12.3).) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Sales: Year 1: 100.0, Year 2: 103.0, Year 3: 110.0, Year 4: 119.8, Year 5: 125.1\nCash: Year 1: 100.0, Year 2: 92.5, Year 3: 103.8, Year 4: 75.8, Year 5: 82.8\nAccounts receivable, net: Year 1: 100.0, Year 2: 107.6, Year 3: 111.9, Year 4: 123.4, Year 5: 141.3\nInventory: Year 1: 100.0, Year 2: 106.4, Year 3: 100.3, Year 4: 109.6, Year 5: 109.7\nTotal current assets: Year 1: 100.0, Year 2: 105.7, Year 3: 104.1, Year 4: 111.3, Year 5: 117.3\nCurrent liabilities: Year 1: 100.0, Year 2: 108.9, Year 3: 110.0, Year 4: 102.1, Year 5: 129.0",
"style": "rule"
}
|
{
"answer": "Sales: Year 1: 100.0, Year 2: 103.0, Year 3: 110.0, Year 4: 119.8, Year 5: 125.1\nCash: Year 1: 100.0, Year 2: 92.5, Year 3: 103.8, Year 4: 75.8, Year 5: 82.8\nAccounts receivable, net: Year 1: 100.0, Year 2: 107.6, Year 3: 111.9, Year 4: 123.4, Year 5: 141.3\nInventory: Year 1: 100.0, Year 2: 106.4, Year 3: 100.3, Year 4: 109.6, Year 5: 109.7\nTotal current assets: Year 1: 100.0, Year 2: 105.7, Year 3: 104.1, Year 4: 111.3, Year 5: 117.3\nCurrent liabilities: Year 1: 100.0, Year 2: 108.9, Year 3: 110.0, Year 4: 102.1, Year 5: 129.0",
"index": 373,
"question": "Rotorua Products, Ltd., of New Zealand markets agricultural products for the burgeoning Asian consumer market. The company's current assets, current liabilities, and sales have been reported as follows over the last five years (Year 5 is the most recent year):\n\n \n \n \n \n Year 1 \n Year 2 \n Year 3 \n Year 4 \n Year 5 \n \n \n Sales \n $ \n 4,635,640 \n \n $ \n 4,775,600 \n \n $ \n 5,097,510 \n \n $ \n 5,554,070 \n \n $ \n 5,798,480 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Cash \n $ \n 96,781 \n \n $ \n 89,547 \n \n $ \n 100,485 \n \n $ \n 73,353 \n \n $ \n 80,182 \n \n \n \n Accounts receivable, net \n \n 402,926 \n \n \n 433,719 \n \n \n 451,015 \n \n \n 497,308 \n \n \n 569,205 \n \n \n \n Inventory \n \n 819,533 \n \n \n 871,581 \n \n \n 822,039 \n \n \n 897,999 \n \n \n 898,668 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Total current assets \n $ \n 1,319,240 \n \n $ \n 1,394,847 \n \n $ \n 1,373,539 \n \n $ \n 1,468,660 \n \n $ \n 1,548,055 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Current liabilities \n $ \n 312,533 \n \n $ \n 340,279 \n \n $ \n 343,680 \n \n $ \n 319,165 \n \n $ \n 403,051 \n \n \n \n\n\n1. Express all of the asset, liability, and sales data in trend percentages. Use Year 1 as the base year. (Round your percentage answers to 1 decimal place (i.e., 0.1234 should be entered as 12.3).)",
"split": "train"
}
| null | null |
1138268
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I am given the following $$ \\begin{cases} u_x+u_y=1-u, x>0\\\\ u(x,x+x^2)=sinx\\\\ \\end{cases} $$ I am trying to solve it using method of characteristics. So I got the following equations: $$ \\begin{cases} x_t=1\\Rightarrow x(t,s)=t+f_1(s)\\\\ y_t=1\\Rightarrow x(t,s)=t+f_2(s)\\\\ u_t=1-u \\end{cases} $$ But the third equation is again a pde Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "u(x,y)=1-e^{-x+φ(x-y)}",
"style": "rule"
}
|
{
"answer": "u(x,y)=1-e^{-x+φ(x-y)}",
"index": 374,
"question": "I am given the following $$ \\begin{cases} u_x+u_y=1-u, x>0\\\\ u(x,x+x^2)=sinx\\\\ \\end{cases} $$ I am trying to solve it using method of characteristics. So I got the following equations: $$ \\begin{cases} x_t=1\\Rightarrow x(t,s)=t+f_1(s)\\\\ y_t=1\\Rightarrow x(t,s)=t+f_2(s)\\\\ u_t=1-u \\end{cases} $$ But the third equation is again a pde",
"split": "train"
}
| null | null |
376055
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Find the density of sulfur hexafluoride at {eq}\\rm\n\n95.0\\ kPa\n\n{/eq} and {eq}\\rm\n\n273 ^\\circ C\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.07 g/L",
"style": "rule"
}
|
{
"answer": "3.07 g/L",
"index": 375,
"question": "Find the density of sulfur hexafluoride at {eq}\\rm\n\n95.0\\ kPa\n\n{/eq} and {eq}\\rm\n\n273 ^\\circ C\n\n{/eq}.",
"split": "train"
}
| null | null |
1666317
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "The enthalpy change for the process: {eq}H_2O(s) <--> H_2O(l)\n\n{/eq} is 6.01 kJ/mol. What is the minimum value for the standard entropy change, on the basis of your conclusions about the spontaneity of the process? Explain. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "22.014 J/mol.K",
"style": "rule"
}
|
{
"answer": "22.014 J/mol.K",
"index": 376,
"question": "The enthalpy change for the process: {eq}H_2O(s) <--> H_2O(l)\n\n{/eq} is 6.01 kJ/mol. What is the minimum value for the standard entropy change, on the basis of your conclusions about the spontaneity of the process? Explain.",
"split": "train"
}
| null | null |
1108319
|
Multiple Choice
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which of the below substances will have the least entropy associated with it, in its current state of matter and temperature?\n\na. Substance 1: Ne (g) Temperature of 284 K\n\nb. Substance 2: H2O (l) Temperature of 306 K\n\nc. Substance 3: Hg (g) Temperature of 307 K\n\nd. Substance 4: He (g) Temperature of 279 K Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 377,
"question": "Which of the below substances will have the least entropy associated with it, in its current state of matter and temperature?\n\na. Substance 1: Ne (g) Temperature of 284 K\n\nb. Substance 2: H2O (l) Temperature of 306 K\n\nc. Substance 3: Hg (g) Temperature of 307 K\n\nd. Substance 4: He (g) Temperature of 279 K",
"split": "train"
}
| null | null |
126858
|
Multiple Choice
|
Philosophy
|
Senior High School
|
general-reasoner
|
[
{
"content": "Morality is best defined as _____.\n\na. society's responsibility toward a person\n\nb. a person's responsibility toward society\n\nc. the rules or principles that define right and wrong conduct\n\nd. the goodness or badness of human action or behavior Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 378,
"question": "Morality is best defined as _____.\n\na. society's responsibility toward a person\n\nb. a person's responsibility toward society\n\nc. the rules or principles that define right and wrong conduct\n\nd. the goodness or badness of human action or behavior",
"split": "train"
}
| null | null |
1363479
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute {eq}\\iint_S F \\ dS{/eq} for {eq}F= \\langle e^y, z, x \\rangle, \\ G(r, s)=(rs, r+s, r): 0 \\leq r \\leq s, \\ 0 \\leq x \\leq 1{/eq}, oriented by {eq}T_r \\times T_s{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "e+7/60+(-1-e^2)/2",
"style": "rule"
}
|
{
"answer": "e+7/60+(-1-e^2)/2",
"index": 379,
"question": "Compute {eq}\\iint_S F \\ dS{/eq} for {eq}F= \\langle e^y, z, x \\rangle, \\ G(r, s)=(rs, r+s, r): 0 \\leq r \\leq s, \\ 0 \\leq x \\leq 1{/eq}, oriented by {eq}T_r \\times T_s{/eq}.",
"split": "train"
}
| null | null |
614806
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What is the theoretical yield in grams of NaCl given the following information?\n\n1) 24.94mL of HCl\n\n2) 24.80mL of NaOH\n\nConcentration of HCl is 1.093 M\n\nConcentration of NaOH is .9138 M Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.32 g",
"style": "rule"
}
|
{
"answer": "1.32 g",
"index": 380,
"question": "What is the theoretical yield in grams of NaCl given the following information?\n\n1) 24.94mL of HCl\n\n2) 24.80mL of NaOH\n\nConcentration of HCl is 1.093 M\n\nConcentration of NaOH is .9138 M",
"split": "train"
}
| null | null |
1556271
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Is the differential equation (1 - 3/y + x) dy/dx + y = 3/x - 1 exact? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 381,
"question": "Is the differential equation (1 - 3/y + x) dy/dx + y = 3/x - 1 exact?",
"split": "train"
}
| null | null |
184489
|
Integer
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Consider a market for a good with the following demand and supply functions: {eq}Q_D = 20 - 2P ~and~ Q_S = 5 + P\n\n{/eq}.\n\nDetermine the effect of a $6 tax paid by firms and calculate the loss of welfare for consumers, producers, and in total. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$48",
"style": "rule"
}
|
{
"answer": "$48",
"index": 382,
"question": "Consider a market for a good with the following demand and supply functions: {eq}Q_D = 20 - 2P ~and~ Q_S = 5 + P\n\n{/eq}.\n\nDetermine the effect of a $6 tax paid by firms and calculate the loss of welfare for consumers, producers, and in total.",
"split": "train"
}
| null | null |
236072
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find a solution to the limit $$\\lim_{x \\rightarrow \\infty} \\left(\\frac{20x}{20x+4}\\right)^{8x}$$ using only knowledge from a first quarter (or semester) calculus course which hasn't covered series expansions or Taylor series, but has covered L'Hopital's rule. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "e^{-8/5}",
"style": "rule"
}
|
{
"answer": "e^{-8/5}",
"index": 383,
"question": "Find a solution to the limit $$\\lim_{x \\rightarrow \\infty} \\left(\\frac{20x}{20x+4}\\right)^{8x}$$ using only knowledge from a first quarter (or semester) calculus course which hasn't covered series expansions or Taylor series, but has covered L'Hopital's rule.",
"split": "train"
}
| null | null |
613660
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Bayou Okra Farms just paid a dividend of $2.65 on its stock. The growth rate in dividends is expected to be constant 4.5 percent per year indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter. What is the current share price? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$40.73",
"style": "rule"
}
|
{
"answer": "$40.73",
"index": 384,
"question": "Bayou Okra Farms just paid a dividend of $2.65 on its stock. The growth rate in dividends is expected to be constant 4.5 percent per year indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter. What is the current share price?",
"split": "train"
}
| null | null |
1072628
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let {eq}\\; \\mathrm{F}(x, y, z) = z \\tan^{-1} (y^2) \\mathrm{i} + z^3 \\ln(x^2 + 1) \\mathrm{j} + z \\mathrm{k}\n\n{/eq}. Find the flux of {eq}\\mathrm{F}\n\n{/eq} across the part of the paraboloid {eq}x^2 + y^2 + z = 2\n\n{/eq} that lies above the plane {eq}z = 1\n\n{/eq} and is oriented upward. (Give your answer correct to at least three decimal places.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3π/2",
"style": "rule"
}
|
{
"answer": "3π/2",
"index": 385,
"question": "Let {eq}\\; \\mathrm{F}(x, y, z) = z \\tan^{-1} (y^2) \\mathrm{i} + z^3 \\ln(x^2 + 1) \\mathrm{j} + z \\mathrm{k}\n\n{/eq}. Find the flux of {eq}\\mathrm{F}\n\n{/eq} across the part of the paraboloid {eq}x^2 + y^2 + z = 2\n\n{/eq} that lies above the plane {eq}z = 1\n\n{/eq} and is oriented upward. (Give your answer correct to at least three decimal places.)",
"split": "train"
}
| null | null |
523989
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I am wondering how the exact expression for the sum $$S=\\sum_{k=1}^{\\infty}\\frac{1}{k(3k-1)} = \\frac{1}{6}\\Big(-\\sqrt{3} π + 9 \\ln(3)\\Big)$$ is obtained, using math not beyond second year university. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{1}{6}\\Big(-\\sqrt{3} \\pi + 9 \\ln(3)\\Big)",
"style": "rule"
}
|
{
"answer": "\\frac{1}{6}\\Big(-\\sqrt{3} \\pi + 9 \\ln(3)\\Big)",
"index": 386,
"question": "I am wondering how the exact expression for the sum $$S=\\sum_{k=1}^{\\infty}\\frac{1}{k(3k-1)} = \\frac{1}{6}\\Big(-\\sqrt{3} π + 9 \\ln(3)\\Big)$$ is obtained, using math not beyond second year university.",
"split": "train"
}
| null | null |
1114854
|
Expression
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "How do you calculate the total resistance in a series circuit with more than one resistor? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Rtotal = R1 + R2 + R3, where R1, R2, and R3 are the resistances of the individual resistors.",
"style": "rule"
}
|
{
"answer": "Rtotal = R1 + R2 + R3, where R1, R2, and R3 are the resistances of the individual resistors.",
"index": 387,
"question": "How do you calculate the total resistance in a series circuit with more than one resistor?",
"split": "train"
}
| null | null |
720766
|
Multiple Choice
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "Moore Corporation uses the balance sheet approach for recording uncollectible. An aging schedule reveals an estimated $12,750 of uncollectible. Allowance for Doubtful Accounts has a credit balance of $3,700 before adjustment.\n\nWhat is the ending balance of Allowance for Doubtful Accounts after adjustment?\n\nA. $16,450\n\nB. $9,050\n\nC. $10,450\n\nD. $12,750 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 388,
"question": "Moore Corporation uses the balance sheet approach for recording uncollectible. An aging schedule reveals an estimated $12,750 of uncollectible. Allowance for Doubtful Accounts has a credit balance of $3,700 before adjustment.\n\nWhat is the ending balance of Allowance for Doubtful Accounts after adjustment?\n\nA. $16,450\n\nB. $9,050\n\nC. $10,450\n\nD. $12,750",
"split": "train"
}
| null | null |
1829422
|
String
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "A certain ionic compound is found to contain .012 mol of sodium, .012 mol of sulfur, and .018 mol of oxygen. What is its empirical formula? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Na2S2O3",
"style": "rule"
}
|
{
"answer": "Na2S2O3",
"index": 389,
"question": "A certain ionic compound is found to contain .012 mol of sodium, .012 mol of sulfur, and .018 mol of oxygen. What is its empirical formula?",
"split": "train"
}
| null | null |
1704629
|
Integer
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "How many different values of ml are possible when the principal quantum number is n = 5? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "16",
"style": "rule"
}
|
{
"answer": "16",
"index": 390,
"question": "How many different values of ml are possible when the principal quantum number is n = 5?",
"split": "train"
}
| null | null |
1507566
|
Integer
|
Mathematics
|
PhD
|
general-reasoner
|
[
{
"content": "How can I determine the optimal dimension $k$ such that $S^2 \\times S^2$ embeds in $\\mathbb{R}^k$? Specifically, is there a way to show that the tubular neighborhood of $S^2$ in $\\mathbb{R}^3$ is trivial in this context, or is there a different approach to finding the optimal dimension ($5$ or $6$)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 391,
"question": "How can I determine the optimal dimension $k$ such that $S^2 \\times S^2$ embeds in $\\mathbb{R}^k$? Specifically, is there a way to show that the tubular neighborhood of $S^2$ in $\\mathbb{R}^3$ is trivial in this context, or is there a different approach to finding the optimal dimension ($5$ or $6$)?",
"split": "train"
}
| null | null |
668098
|
List
|
History
|
Junior High School
|
general-reasoner
|
[
{
"content": "What weapons were used in the Battle of Megiddo in WWI? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Light and heavy machine guns and thousands of rifles were used in the Battle of Megiddo in WWI.",
"style": "rule"
}
|
{
"answer": "Light and heavy machine guns and thousands of rifles were used in the Battle of Megiddo in WWI.",
"index": 392,
"question": "What weapons were used in the Battle of Megiddo in WWI?",
"split": "train"
}
| null | null |
36002
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A 50 g bullet traveling with an initial velocity of 400 m/s penetrates into a wall with an average force of 4 {eq}\\times\n\n{/eq} 10{eq}^4\n\n{/eq} N. It goes out of the wall with a velocity of 50 m/s. What is the thickness of the wall? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "9.84 cm",
"style": "rule"
}
|
{
"answer": "9.84 cm",
"index": 393,
"question": "A 50 g bullet traveling with an initial velocity of 400 m/s penetrates into a wall with an average force of 4 {eq}\\times\n\n{/eq} 10{eq}^4\n\n{/eq} N. It goes out of the wall with a velocity of 50 m/s. What is the thickness of the wall?",
"split": "train"
}
| null | null |
52243
|
Boolean
|
Engineering
|
Senior High School
|
general-reasoner
|
[
{
"content": "Technician A says that all components in the high voltage battery box are completely insulated from the rest of the vehicle for safety. Technician B says that the high voltage battery box is located under the hood in some vehicles. Which technician is correct? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Technician A",
"style": "rule"
}
|
{
"answer": "Technician A",
"index": 394,
"question": "Technician A says that all components in the high voltage battery box are completely insulated from the rest of the vehicle for safety. Technician B says that the high voltage battery box is located under the hood in some vehicles. Which technician is correct?",
"split": "train"
}
| null | null |
1037770
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "2NOBr(g) {eq}\\rightleftharpoons\n\n{/eq} 2NO(g) + Br{eq}_2\n\n{/eq}(g) and the value of Kc = 1.98 at a temperature of 282 K. What is the value of Kp? (Hint: Use the value of R in the appropriate units.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "45.84",
"style": "rule"
}
|
{
"answer": "45.84",
"index": 395,
"question": "2NOBr(g) {eq}\\rightleftharpoons\n\n{/eq} 2NO(g) + Br{eq}_2\n\n{/eq}(g) and the value of Kc = 1.98 at a temperature of 282 K. What is the value of Kp? (Hint: Use the value of R in the appropriate units.)",
"split": "train"
}
| null | null |
693857
|
Percentage
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "If the {eq}K_a\n\n{/eq} of a monoprotic weak acid is {eq}8.4 \\times 10^{-6}\n\n{/eq}, what is the percent ionization of a 0.31 M solution of this acid? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "52%",
"style": "rule"
}
|
{
"answer": "52%",
"index": 396,
"question": "If the {eq}K_a\n\n{/eq} of a monoprotic weak acid is {eq}8.4 \\times 10^{-6}\n\n{/eq}, what is the percent ionization of a 0.31 M solution of this acid?",
"split": "train"
}
| null | null |
373
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let {eq}R{/eq} be the region above the {eq}xy{/eq}-plane bounded below by the cone {eq}z^2 = x^2 + y^2{/eq} and between the spheres {eq}x^2 + y^2 + z^2 = 4{/eq} and {eq}x^2 + y^2 + z^2 = 9{/eq}. Compute the integral of {eq}f(x, y, z) = \\frac{1}{(x^2 + y^2 + z^2)^2}{/eq} over this region. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{\\pi}{6} (2-\\sqrt{2})",
"style": "rule"
}
|
{
"answer": "\\frac{\\pi}{6} (2-\\sqrt{2})",
"index": 397,
"question": "Let {eq}R{/eq} be the region above the {eq}xy{/eq}-plane bounded below by the cone {eq}z^2 = x^2 + y^2{/eq} and between the spheres {eq}x^2 + y^2 + z^2 = 4{/eq} and {eq}x^2 + y^2 + z^2 = 9{/eq}. Compute the integral of {eq}f(x, y, z) = \\frac{1}{(x^2 + y^2 + z^2)^2}{/eq} over this region.",
"split": "train"
}
| null | null |
1901266
|
Fraction
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Set up an integral to find the area of the region bounded by the polar curve {eq}r = 4 + 3\\cos \\theta{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\frac{ 41 \\pi }{2}",
"style": "rule"
}
|
{
"answer": "\\frac{ 41 \\pi }{2}",
"index": 398,
"question": "Set up an integral to find the area of the region bounded by the polar curve {eq}r = 4 + 3\\cos \\theta{/eq}",
"split": "train"
}
| null | null |
2049512
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find a parametric representation for the part of the ellipsoid $9x^2 +4y^2+ z^2 = 1$ that lies above the xy-plane. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "x = u, y = v, z = \\sqrt{1-9u^2 - 4v^2}",
"style": "rule"
}
|
{
"answer": "x = u, y = v, z = \\sqrt{1-9u^2 - 4v^2}",
"index": 399,
"question": "Find a parametric representation for the part of the ellipsoid $9x^2 +4y^2+ z^2 = 1$ that lies above the xy-plane.",
"split": "train"
}
| null | null |
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