prompt string | prompt_id string | chosen list | rejected list | messages list | id string | task string | dataset string | n_turns int64 | reward_score_chosen float64 | reward_score_rejected float64 | reward_margin float64 | is_difficult int64 | score_chosen float64 | score_rejected float64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly one of the triplets... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84_5_4 | Math_CoT | MATH | 7 | 23.625 | -32.25 | 55.875 | 0 | 23.625 | -32.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Next year, there will be twice as many people going to the fair as are going this year, and the number of people who went to the fair last year was 200 less than those going next ye... | e4b31f400feb1e56d7fdfbb83e8b643fa6e167afa6446d1e9ed35013f9c3bef7 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNext year, there will be twice as many people going to the fair as are going this year, and the number of people who went to the fair last year was 200 less... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNext year, there will be twice as many people going to the fair as are going this year, and the number of people who went to the fair last year was 200 less... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNext year, there will be twice as many people going to the fair as are going this year, and the number of people who went to the fair last year was 200 less... | e4b31f400feb1e56d7fdfbb83e8b643fa6e167afa6446d1e9ed35013f9c3bef7_5_2 | Math_CoT | gsm8k | 3 | 30.875 | -21.125 | 52 | 0 | 30.875 | -21.125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Cathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one week and Cathy took her shif... | 2f55044dc7018c1739c78c11114b00d0e51847d28d98d5618e5b3ee77500c7b6 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | 2f55044dc7018c1739c78c11114b00d0e51847d28d98d5618e5b3ee77500c7b6_2_2 | Math_CoT | gsm8k | 3 | 25.625 | -25.375 | 51 | 0 | 25.625 | -25.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The number of cards in a card game was 500. Two friends Ellis and Orion, playing together, divided the cards in the ratio of 11:9. How many more cards did Ellis get than Orion? | a06a0845908a96bfa1e6edd3a3df77a8bcb6cdbd8911f27016a5969cc0cd47d6 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe number of cards in a card game was 500. Two friends Ellis and Orion, playing together, divided the cards in the ratio of 11:9. How many more cards did E... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe number of cards in a card game was 500. Two friends Ellis and Orion, playing together, divided the cards in the ratio of 11:9. How many more cards did E... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe number of cards in a card game was 500. Two friends Ellis and Orion, playing together, divided the cards in the ratio of 11:9. How many more cards did E... | a06a0845908a96bfa1e6edd3a3df77a8bcb6cdbd8911f27016a5969cc0cd47d6_2_2 | Math_CoT | gsm8k | 3 | 31.75 | -16.75 | 48.5 | 0 | 31.75 | -16.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Ursula bought five hot dogs at $1.50 each and three salads at $2.50 each. If she had two $10 bills, how much change did she get back? | c549e98e4f9b1bb2628e06e838f9319366cdad16efc85c717b4b876288e07f79 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nUrsula bought five hot dogs at $1.50 each and three salads at $2.50 each. If she had two $10 bills, how much change did she get back?",
"role": "user"
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nUrsula bought five hot dogs at $1.50 each and three salads at $2.50 each. If she had two $10 bills, how much change did she get back?",
"role": "user"
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nUrsula bought five hot dogs at $1.50 each and three salads at $2.50 each. If she had two $10 bills, how much change did she get back?",
"role": "user"
... | c549e98e4f9b1bb2628e06e838f9319366cdad16efc85c717b4b876288e07f79_1_1 | Math_CoT | gsm8k | 1 | 25.875 | -21.75 | 47.625 | 0 | 25.875 | -21.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
There are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm? | ac4c1c81f54928f4d82deaa34078de891e1d3faf55f944093cc8da33c5582421 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | ac4c1c81f54928f4d82deaa34078de891e1d3faf55f944093cc8da33c5582421_1_1 | Math_CoT | numglue | 1 | 21 | -25.625 | 46.625 | 0 | 21 | -25.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Frank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sold 5 cars each day. Then t... | 713ed26f1974acce248e017f3836c09133c6a0b97c7eeeeb258e7bdf15fb3f66 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFrank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sol... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFrank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sol... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFrank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sol... | 713ed26f1974acce248e017f3836c09133c6a0b97c7eeeeb258e7bdf15fb3f66_3_3 | Math_CoT | gsm8k | 5 | 26.75 | -18.625 | 45.375 | 0 | 26.75 | -18.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $F(x)$ be a polynomial such that $F(6) = 15$ and\[\frac{F(3x)}{F(x+3)} = 9-\frac{48x+54}{x^2+5x+6}\]for $x \in \mathbb{R}$ such that both sides are defined. Find $F(12)$. | b0c6f65f23b1bd207f0d583d1a63499f5a76ab2f02882892e65c9ee1f220ea4b | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | 179039f9f3fe76d239c864a993975421cc94a7063b898418cd99e641817051f0_1_1 | Math_CoT | MATH | 1 | 24.125 | -20.75 | 44.875 | 0 | 24.125 | -20.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Andy works in the pro shop at a tennis resort, where he earns $9 an hour. In addition to this, he gets paid $15 for each racquet he restrings, $10 for changing out the grommets on a... | 29a0635284ef0b9f104908c809791ac6563b55217088d3d51742121ce3e42140 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAndy works in the pro shop at a tennis resort, where he earns $9 an hour. In addition to this, he gets paid $15 for each racquet he restrings, $10 for chang... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAndy works in the pro shop at a tennis resort, where he earns $9 an hour. In addition to this, he gets paid $15 for each racquet he restrings, $10 for chang... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAndy works in the pro shop at a tennis resort, where he earns $9 an hour. In addition to this, he gets paid $15 for each racquet he restrings, $10 for chang... | 29a0635284ef0b9f104908c809791ac6563b55217088d3d51742121ce3e42140_1_1 | Math_CoT | gsm8k | 1 | 33.5 | -10.5 | 44 | 0 | 33.5 | -10.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$? | 30f590b851107c6e21414e92a1a5d8092eeb5588709f7febfe436d847565d697 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | 30f590b851107c6e21414e92a1a5d8092eeb5588709f7febfe436d847565d697_5_5 | Math_CoT | MATH | 9 | 28 | -15.9375 | 43.9375 | 0 | 28 | -15.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory course and 30 have not ta... | 042b468c6396aceb77acf819d15059214b1b920c71c64df600d7ee2f402b5381 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory ... | 042b468c6396aceb77acf819d15059214b1b920c71c64df600d7ee2f402b5381_3_3 | Math_CoT | mathqa | 5 | 28.625 | -14.9375 | 43.5625 | 0 | 28.625 | -14.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Johnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. How many days will pass ... | b74a67accd33ee6b6320512ac108d105750f807acbefa7eb80fa62d8a7d5d5d7 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | b74a67accd33ee6b6320512ac108d105750f807acbefa7eb80fa62d8a7d5d5d7_5_5 | Math_CoT | gsm8k | 9 | 14.5 | -29 | 43.5 | 0 | 14.5 | -29 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
the length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ? | 5a1401f2c23fc9688ef6a39bf4400dbe2601b2a666ae5f8fd4882b24017791fe | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ?",
"role": "user"
},
{
"content": "Ste... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ?",
"role": "user"
},
{
"content": "Ste... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ?",
"role": "user"
},
{
"content": "Ste... | 5a1401f2c23fc9688ef6a39bf4400dbe2601b2a666ae5f8fd4882b24017791fe_3_3 | Math_CoT | mathqa | 5 | 29.5 | -13.9375 | 43.4375 | 0 | 29.5 | -13.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle? | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65_5_4 | Math_CoT | MATH | 7 | 27.875 | -15.5625 | 43.4375 | 0 | 27.875 | -15.5625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Given that $2^x+ 2^x+ 2^x+ 2^x= 128$, what is the value of $(x + 1)(x - 1)$? | a2ba829ebcd0c398e28bf1fcff8ab6cb5af158adf4b90f07366ec2e37735fd2d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nGiven that $2^x+ 2^x+ 2^x+ 2^x= 128$, what is the value of $(x + 1)(x - 1)$?",
"role": "user"
},
{
"content": "Step 1: Let's simplify the equati... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nGiven that $2^x+ 2^x+ 2^x+ 2^x= 128$, what is the value of $(x + 1)(x - 1)$?",
"role": "user"
},
{
"content": "Step 1: I see that there are four... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nGiven that $2^x+ 2^x+ 2^x+ 2^x= 128$, what is the value of $(x + 1)(x - 1)$?",
"role": "user"
},
{
"content": "Step 1: Let's simplify the equati... | a2ba829ebcd0c398e28bf1fcff8ab6cb5af158adf4b90f07366ec2e37735fd2d_1_1 | Math_CoT | MATH | 1 | 25 | -17.625 | 42.625 | 0 | 25 | -17.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A squirrel had stashed 210 acorns to last him the three winter months. It divided the pile into thirds, one for each month, and then took some from each third, leaving 60 acorns for... | d712e79a03deba0778f93558144f4c97d6cccc45c61497aeca43a0328f94f9a0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA squirrel had stashed 210 acorns to last him the three winter months. It divided the pile into thirds, one for each month, and then took some from each thi... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA squirrel had stashed 210 acorns to last him the three winter months. It divided the pile into thirds, one for each month, and then took some from each thi... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA squirrel had stashed 210 acorns to last him the three winter months. It divided the pile into thirds, one for each month, and then took some from each thi... | d712e79a03deba0778f93558144f4c97d6cccc45c61497aeca43a0328f94f9a0_3_3 | Math_CoT | gsm8k | 5 | 27.125 | -15.375 | 42.5 | 0 | 27.125 | -15.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Miranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the heels. If she paid $260 in t... | c0253a6cb013ac8fa4ab3acf087967cc71e8017d44a7f72922ee42f1c8373433 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | c0253a6cb013ac8fa4ab3acf087967cc71e8017d44a7f72922ee42f1c8373433_3_3 | Math_CoT | gsm8k | 5 | 25 | -17.5 | 42.5 | 0 | 25 | -17.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
There are 37 baskets. There are 17 apples in each basket. How many apples are there in all? | 9d32448d9a710ef1d356b28ad7526641ccf63a99a2cf598f88070dea9cf9690f | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 37 baskets. There are 17 apples in each basket. How many apples are there in all?",
"role": "user"
},
{
"content": "Step 1: Calculate ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 37 baskets. There are 17 apples in each basket. How many apples are there in all?",
"role": "user"
},
{
"content": "Step 1: First, let... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 37 baskets. There are 17 apples in each basket. How many apples are there in all?",
"role": "user"
},
{
"content": "Step 1: Calculate ... | 9d32448d9a710ef1d356b28ad7526641ccf63a99a2cf598f88070dea9cf9690f_1_1 | Math_CoT | numglue | 1 | 20.25 | -22.25 | 42.5 | 0 | 20.25 | -22.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.
[asy]
import three;
triple A,B,C,D,EE,F,G,H;
A = (0,0,0);
B = (1,0,0);
C = (1,1,0);
D= (0,1,0);
... | 85302d63b9bd502fcf1abe1549d6d4396dae18535831e22aabc370456f0ba635 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | c74a284cb9ef426be17ad18a6976b11146716cd372f5de4cf7237aa5082768f4_1_1 | Math_CoT | MATH | 1 | 23.625 | -18.875 | 42.5 | 0 | 23.625 | -18.875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
by travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for ... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0_5_4 | Math_CoT | mathqa | 7 | 29.5 | -12.75 | 42.25 | 0 | 29.5 | -12.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Find the area of a triangle with side lengths 8, 9, and 9. | 3e2b78835369c0c4991569956b83ae41d7b75d69d617e708cdd012a918ca8036 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the area of a triangle with side lengths 8, 9, and 9.",
"role": "user"
},
{
"content": "Step 1: Determine whether the given side lengths fo... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the area of a triangle with side lengths 8, 9, and 9.",
"role": "user"
},
{
"content": "Step 1: Determine whether the given side lengths fo... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the area of a triangle with side lengths 8, 9, and 9.",
"role": "user"
},
{
"content": "Step 1: Determine whether the given side lengths fo... | 3e2b78835369c0c4991569956b83ae41d7b75d69d617e708cdd012a918ca8036_3_3 | Math_CoT | MATH | 5 | 25.875 | -16.375 | 42.25 | 0 | 25.875 | -16.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ? | ad7bcb52da8f9388db9b2d2bbf2d1ae8988e71b87460f9df79294992f5324776 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nhow much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?",
"role... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nhow much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?",
"role... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nhow much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?",
"role... | ad7bcb52da8f9388db9b2d2bbf2d1ae8988e71b87460f9df79294992f5324776_2_2 | Math_CoT | mathqa | 3 | 34.5 | -7.71875 | 42.21875 | 0 | 34.5 | -7.71875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The volume of a cylinder is $54\pi$ $\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder? Express your answer in ter... | 7bfbf1c2156aa751a58b4b3e8845597fb656691c2951b47f6e0727e9b37a857d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | 6fae99e7b660f95daef959e3fcfa4eca870bc7e31b24bb07b0f56a9099c98f7c_1_1 | Math_CoT | MATH | 1 | 30.5 | -11.6875 | 42.1875 | 0 | 30.5 | -11.6875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Javier exercised for 50 minutes every day for one week. Sanda exercised for 90 minutes on each of three days. How many minutes did Javier and Sanda exercise in total? | 239a8b0201acb66eaf6dbb8f791d28ea031f271d85b1ec3cb385c2c08408302c | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJavier exercised for 50 minutes every day for one week. Sanda exercised for 90 minutes on each of three days. How many minutes did Javier and Sanda exercise... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJavier exercised for 50 minutes every day for one week. Sanda exercised for 90 minutes on each of three days. How many minutes did Javier and Sanda exercise... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJavier exercised for 50 minutes every day for one week. Sanda exercised for 90 minutes on each of three days. How many minutes did Javier and Sanda exercise... | 239a8b0201acb66eaf6dbb8f791d28ea031f271d85b1ec3cb385c2c08408302c_1_1 | Math_CoT | gsm8k | 1 | 25 | -17.125 | 42.125 | 0 | 25 | -17.125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the square, in inches?
[asy]
... | 07250bc7d40d262c7a4ba3e7a1ff54154a76698786919cbad0aa0a7dd989dae4 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | b286c7e996799b46a31ce129516b3c46f42275de111b378e39371d526fbbe71f_1_1 | Math_CoT | MATH | 1 | 33 | -9.0625 | 42.0625 | 0 | 33 | -9.0625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $S$ denote the value of the sum
\[\sum_{n = 1}^{9800} \frac{1}{\sqrt{n + \sqrt{n^2 - 1}}}\]
$S$ can be expressed as $p + q \sqrt{r}$, where $p, q,$ and $r$ are positive integers... | 701722a48156550bcbd06e3b926c7f7cf28466788a1b4acac7e390d3f7fb2762 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $S$ denote the value of the sum\n\\[\\sum_{n = 1}^{9800} \\frac{1}{\\sqrt{n + \\sqrt{n^2 - 1}}}\\]\n$S$ can be expressed as $p + q \\sqrt{r}$, where $p,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $S$ denote the value of the sum\n\\[\\sum_{n = 1}^{9800} \\frac{1}{\\sqrt{n + \\sqrt{n^2 - 1}}}\\]\n$S$ can be expressed as $p + q \\sqrt{r}$, where $p,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $S$ denote the value of the sum\n\\[\\sum_{n = 1}^{9800} \\frac{1}{\\sqrt{n + \\sqrt{n^2 - 1}}}\\]\n$S$ can be expressed as $p + q \\sqrt{r}$, where $p,... | 701722a48156550bcbd06e3b926c7f7cf28466788a1b4acac7e390d3f7fb2762_5_3 | Math_CoT | MATH | 5 | 29.875 | -12.1875 | 42.0625 | 0 | 29.875 | -12.1875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ... | b85f3df4f4353b27777f9fdd2e8c5f8cfe88d436838948bc251d79143ea20ee2 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . ... | b85f3df4f4353b27777f9fdd2e8c5f8cfe88d436838948bc251d79143ea20ee2_2_2 | Math_CoT | mathqa | 3 | 33.25 | -8.625 | 41.875 | 0 | 33.25 | -8.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Three real numbers $a,b,$ and $c$ satisfy the equations $a+b+c=2$, $ab+ac+bc=-7$ and $abc=-14$. What is the largest of the three numbers? Express your answer in simplest radical f... | 80d1be92258ffc24cf0197fe67374d7f968919e3effe71e4a2c020f5228baf22 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThree real numbers $a,b,$ and $c$ satisfy the equations $a+b+c=2$, $ab+ac+bc=-7$ and $abc=-14$. What is the largest of the three numbers? Express your ans... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThree real numbers $a,b,$ and $c$ satisfy the equations $a+b+c=2$, $ab+ac+bc=-7$ and $abc=-14$. What is the largest of the three numbers? Express your ans... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThree real numbers $a,b,$ and $c$ satisfy the equations $a+b+c=2$, $ab+ac+bc=-7$ and $abc=-14$. What is the largest of the three numbers? Express your ans... | 80d1be92258ffc24cf0197fe67374d7f968919e3effe71e4a2c020f5228baf22_5_1 | Math_CoT | MATH | 1 | 27.875 | -14 | 41.875 | 0 | 27.875 | -14 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$? | 30f590b851107c6e21414e92a1a5d8092eeb5588709f7febfe436d847565d697 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?",
"role": "user"
},
{
"content": "Step 1: We ca... | 30f590b851107c6e21414e92a1a5d8092eeb5588709f7febfe436d847565d697_5_4 | Math_CoT | MATH | 7 | 29.875 | -11.9375 | 41.8125 | 0 | 29.875 | -11.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a certain city the rate of taxation is the following: $x\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield the greatest take home pay... | d605686aa8c30ccca5014c048aede1b4018b075d4c011eaac85ea22f4571b4fa | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | d605686aa8c30ccca5014c048aede1b4018b075d4c011eaac85ea22f4571b4fa_3_1 | Math_CoT | MATH | 1 | 27.125 | -14.6875 | 41.8125 | 0 | 27.125 | -14.6875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Nadia walked 18 kilometers, which was twice as far as Hannah walked. How many kilometers did the two girls walk in total? | d6d2998bb5655bf6e4714ff319f33fc084eb3d0e8beed0d597c06d41088656d1 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNadia walked 18 kilometers, which was twice as far as Hannah walked. How many kilometers did the two girls walk in total?",
"role": "user"
},
{
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNadia walked 18 kilometers, which was twice as far as Hannah walked. How many kilometers did the two girls walk in total?",
"role": "user"
},
{
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nNadia walked 18 kilometers, which was twice as far as Hannah walked. How many kilometers did the two girls walk in total?",
"role": "user"
},
{
... | d6d2998bb5655bf6e4714ff319f33fc084eb3d0e8beed0d597c06d41088656d1_3_3 | Math_CoT | gsm8k | 5 | 27 | -14.75 | 41.75 | 0 | 27 | -14.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the total length of the rubber... | 8196ca477d835bd9084de2861b8ac262e3cd2cbfde1a1852363e4fd87ddf878d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | 8196ca477d835bd9084de2861b8ac262e3cd2cbfde1a1852363e4fd87ddf878d_3_2 | Math_CoT | gsm8k | 3 | 32.75 | -8.75 | 41.5 | 0 | 32.75 | -8.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Find the equation of the directrix of the parabola $y = 8x^2 + 2.$ | 02a47a548d46b5c34aec4a58a910b75950181ce68470fc86a953ea4eb8a2039a | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the equation of the directrix of the parabola $y = 8x^2 + 2.$",
"role": "user"
},
{
"content": "Step 1: To find the equation of the directr... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the equation of the directrix of the parabola $y = 8x^2 + 2.$",
"role": "user"
},
{
"content": "Step 1: To find the equation of the directr... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the equation of the directrix of the parabola $y = 8x^2 + 2.$",
"role": "user"
},
{
"content": "Step 1: To find the equation of the directr... | 02a47a548d46b5c34aec4a58a910b75950181ce68470fc86a953ea4eb8a2039a_3_3 | Math_CoT | MATH | 5 | 19.5 | -22 | 41.5 | 0 | 19.5 | -22 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
by travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for ... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0_5_5 | Math_CoT | mathqa | 9 | 26.75 | -14.5 | 41.25 | 0 | 26.75 | -14.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faste... | 3195c9c0a76ba7aff1a85007e877e7c8d31daadce3f5a41e20b17453a477d2d5 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked ... | 3195c9c0a76ba7aff1a85007e877e7c8d31daadce3f5a41e20b17453a477d2d5_3_2 | Math_CoT | mathqa | 3 | 28.875 | -12.375 | 41.25 | 0 | 28.875 | -12.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
For real numbers $t \neq 0,$ the point
\[(x,y) = \left( \frac{t + 1}{t}, \frac{t - 1}{t} \right)\]is plotted. All the plotted points lie on what kind of curve?
(A) Line
(B) Circle... | 407c49a905f1fe985b84a64133d02b2c352ef2232fa27c30df091215e0cb070e | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | 407c49a905f1fe985b84a64133d02b2c352ef2232fa27c30df091215e0cb070e_4_4 | Math_CoT | MATH | 7 | 25.75 | -15.5 | 41.25 | 0 | 25.75 | -15.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The four zeros of the polynomial $x^4 + jx^2 + kx + 225$ are distinct real numbers in arithmetic progression. Compute the value of $j.$ | 9a31ffe1f22e85b33d20e2a4245d98628d728250836d81b3685b337f6bf31f9f | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe four zeros of the polynomial $x^4 + jx^2 + kx + 225$ are distinct real numbers in arithmetic progression. Compute the value of $j.$",
"role": "user... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe four zeros of the polynomial $x^4 + jx^2 + kx + 225$ are distinct real numbers in arithmetic progression. Compute the value of $j.$",
"role": "user... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe four zeros of the polynomial $x^4 + jx^2 + kx + 225$ are distinct real numbers in arithmetic progression. Compute the value of $j.$",
"role": "user... | 949f8e463ba600dbd2d77a5765ce8f72e3e4ec73ab4422d8f5ccd8a8f5439af2_1_1 | Math_CoT | MATH | 1 | 31.75 | -9.1875 | 40.9375 | 0 | 31.75 | -9.1875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles that the set could have? | 8984b9f9308bdbd8ac4284029d71275862ad5062587278f2506b42d2a9dbb01c | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | 8984b9f9308bdbd8ac4284029d71275862ad5062587278f2506b42d2a9dbb01c_2_1 | Math_CoT | MATH | 1 | 28 | -12.9375 | 40.9375 | 0 | 28 | -12.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
1 number is 3 less than twice another number. The sum of the 2 numbers is 51. What is the larger number? | f1df918799a94fea45ecc6eb108dc662fd8ed65816e35e55044ece2ae63fb971 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n1 number is 3 less than twice another number. The sum of the 2 numbers is 51. What is the larger number?",
"role": "user"
},
{
"content": "Step ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n1 number is 3 less than twice another number. The sum of the 2 numbers is 51. What is the larger number?",
"role": "user"
},
{
"content": "Step ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n1 number is 3 less than twice another number. The sum of the 2 numbers is 51. What is the larger number?",
"role": "user"
},
{
"content": "Step ... | f1df918799a94fea45ecc6eb108dc662fd8ed65816e35e55044ece2ae63fb971_1_1 | Math_CoT | numglue | 1 | 31.75 | -9.125 | 40.875 | 0 | 31.75 | -9.125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Sara saw 96 birds in a tree. How many dozen birds did Sara see? | 22ddf21c15b40dad32ce8684a7b55da337c3071d27b1a74303bf0f265e2154eb | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSara saw 96 birds in a tree. How many dozen birds did Sara see?",
"role": "user"
},
{
"content": "Step 1: First, I need to calculate how many do... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSara saw 96 birds in a tree. How many dozen birds did Sara see?",
"role": "user"
},
{
"content": "Step 1: Calculate how many hundredths Sara saw... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSara saw 96 birds in a tree. How many dozen birds did Sara see?",
"role": "user"
},
{
"content": "Step 1: First, I need to calculate how many do... | 22ddf21c15b40dad32ce8684a7b55da337c3071d27b1a74303bf0f265e2154eb_1_1 | Math_CoT | numglue | 1 | 16.25 | -24.625 | 40.875 | 0 | 16.25 | -24.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Tom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended? | b6c7af9dcb1307655bc137bdd35668e62d3a73df134a17ec46a4ba794bf6984f | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | b6c7af9dcb1307655bc137bdd35668e62d3a73df134a17ec46a4ba794bf6984f_2_2 | Math_CoT | gsm8k | 3 | 28.75 | -11.9375 | 40.6875 | 0 | 28.75 | -11.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The graph of the function $y=f(x)$ is shown below. For all $x > 4$, it is true that $f(x) > 0.4$. If $f(x) = \frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $C$ are integers, then find... | 061d6e9a8e6bf0de403941fedeca0f0ae8f5b9538813bc793d6e89d506ee738a | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe graph of the function $y=f(x)$ is shown below. For all $x > 4$, it is true that $f(x) > 0.4$. If $f(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe graph of the function $y=f(x)$ is shown below. For all $x > 4$, it is true that $f(x) > 0.4$. If $f(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe graph of the function $y=f(x)$ is shown below. For all $x > 4$, it is true that $f(x) > 0.4$. If $f(x) = \\frac{x^2}{Ax^2 + Bx + C}$, where $A,B,$ and $... | 47856724290b9f55c8c634e49d95e68f48c3bf6c85b0fef617e3aa2dc24fa51b_1_1 | Math_CoT | MATH | 1 | 32.25 | -8.4375 | 40.6875 | 0 | 32.25 | -8.4375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly one of the triplets... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84_5_5 | Math_CoT | MATH | 9 | 19.875 | -20.75 | 40.625 | 0 | 19.875 | -20.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $\alpha$ and $\beta$ be conjugate complex numbers such that $\frac{\alpha}{\beta^2}$ is a real number and $|\alpha - \beta| = 2 \sqrt{3}.$ Find $|\alpha|.$ | 5c38fcff8aa98157ab4764199a57d9c9990923bf5577947373fc0806bb1d8b59 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\alpha$ and $\\beta$ be conjugate complex numbers such that $\\frac{\\alpha}{\\beta^2}$ is a real number and $|\\alpha - \\beta| = 2 \\sqrt{3}.$ Find... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\alpha$ and $\\beta$ be conjugate complex numbers such that $\\frac{\\alpha}{\\beta^2}$ is a real number and $|\\alpha - \\beta| = 2 \\sqrt{3}.$ Find... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\alpha$ and $\\beta$ be conjugate complex numbers such that $\\frac{\\alpha}{\\beta^2}$ is a real number and $|\\alpha - \\beta| = 2 \\sqrt{3}.$ Find... | 5c38fcff8aa98157ab4764199a57d9c9990923bf5577947373fc0806bb1d8b59_5_1 | Math_CoT | MATH | 1 | 33.25 | -7.28125 | 40.53125 | 0 | 33.25 | -7.28125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 5... | deaedd28d6e72d3e0b49f7397deee511523ac05fb1ea6855891cb30f637f3c90 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | deaedd28d6e72d3e0b49f7397deee511523ac05fb1ea6855891cb30f637f3c90_1_1 | Math_CoT | mathqa | 1 | 34.75 | -5.75 | 40.5 | 0 | 34.75 | -5.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
if a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ? | 0a976d9dbc87f535776b0a46188a7388a3f7a1e87ae688b6e786e8596b89b79c | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nif a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ?",
"role": "u... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nif a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ?",
"role": "u... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nif a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ?",
"role": "u... | 0a976d9dbc87f535776b0a46188a7388a3f7a1e87ae688b6e786e8596b89b79c_2_2 | Math_CoT | mathqa | 3 | 26 | -14.4375 | 40.4375 | 0 | 26 | -14.4375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of the middle tree. How tall... | 4e74db38b380da58cba43d1113b43dd9e7447261ca1c0c1c94ad2d789fc98037 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | 4e74db38b380da58cba43d1113b43dd9e7447261ca1c0c1c94ad2d789fc98037_1_1 | Math_CoT | gsm8k | 1 | 25.75 | -14.375 | 40.125 | 0 | 25.75 | -14.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Tim drinks 2 bottles that are each 1.5 quarts and an additional 20 ounces a day. How much water does he drink a week? | 6fdb3c3ec9435ad18ca96611eb5975789d370eba36865b099f44420b666c9688 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTim drinks 2 bottles that are each 1.5 quarts and an additional 20 ounces a day. How much water does he drink a week?",
"role": "user"
},
{
"co... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTim drinks 2 bottles that are each 1.5 quarts and an additional 20 ounces a day. How much water does he drink a week?",
"role": "user"
},
{
"co... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTim drinks 2 bottles that are each 1.5 quarts and an additional 20 ounces a day. How much water does he drink a week?",
"role": "user"
},
{
"co... | 6fdb3c3ec9435ad18ca96611eb5975789d370eba36865b099f44420b666c9688_2_2 | Math_CoT | gsm8k | 3 | 28.375 | -11.75 | 40.125 | 0 | 28.375 | -11.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
by travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for ... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nby travelling at 70 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what spee... | d1427902ecae6aa74b819a346f2e2043a5f994eb786301bd5bf48d8675f1fff0_5_2 | Math_CoT | mathqa | 3 | 26.75 | -13.3125 | 40.0625 | 0 | 26.75 | -13.3125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Bea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Narra trees that fell. A mo... | 481a7f2d20d5b64567a4cbe098b3ae2dc6969f501964577b274c97a1cf67cfbd | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | 481a7f2d20d5b64567a4cbe098b3ae2dc6969f501964577b274c97a1cf67cfbd_4_3 | Math_CoT | gsm8k | 5 | 29.25 | -10.75 | 40 | 0 | 29.25 | -10.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
An investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the capital within a year. If he... | c4d1c2b8f7da8ffd9c4229e92a38572ce5f296b9c2ab7496f36fb34a2d19f8c3 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAn investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the cap... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAn investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the cap... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAn investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the cap... | c4d1c2b8f7da8ffd9c4229e92a38572ce5f296b9c2ab7496f36fb34a2d19f8c3_3_3 | Math_CoT | gsm8k | 5 | 27.5 | -12.4375 | 39.9375 | 0 | 27.5 | -12.4375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $\star (x)$ be the sum of the digits of a positive integer $x$. $\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\mathcal{S}$, we have that $\sta... | 49731aa0fb5bec86b7cb51c7b8bf10818c7ab58b1083d520f103a891ad0763ba | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | 49731aa0fb5bec86b7cb51c7b8bf10818c7ab58b1083d520f103a891ad0763ba_5_1 | Math_CoT | MATH | 1 | 23 | -16.875 | 39.875 | 0 | 23 | -16.875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Jessie won 3 times as many athletic awards as his buddy Scott, who won 4 awards. The best athlete at the rival high school won twice as many awards as Jessie. How many awards did ... | a085a98ac3d87401c0aa63d20a269306ec6d12914025274aba27b30d8e3181e3 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJessie won 3 times as many athletic awards as his buddy Scott, who won 4 awards. The best athlete at the rival high school won twice as many awards as Jess... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJessie won 3 times as many athletic awards as his buddy Scott, who won 4 awards. The best athlete at the rival high school won twice as many awards as Jess... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJessie won 3 times as many athletic awards as his buddy Scott, who won 4 awards. The best athlete at the rival high school won twice as many awards as Jess... | a085a98ac3d87401c0aa63d20a269306ec6d12914025274aba27b30d8e3181e3_1_1 | Math_CoT | gsm8k | 1 | 32.75 | -7.09375 | 39.84375 | 0 | 32.75 | -7.09375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
If $2x+7$ is a factor of $6x^3+19x^2+cx+35$, find $c$. | ba6e175ab0a524b9468822b595aa96a5c6c03dda8fdcace972a44efc391e0c98 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIf $2x+7$ is a factor of $6x^3+19x^2+cx+35$, find $c$.",
"role": "user"
},
{
"content": "Step 1: To solve this problem, we'll need to apply pol... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIf $2x+7$ is a factor of $6x^3+19x^2+cx+35$, find $c$.",
"role": "user"
},
{
"content": "Step 1: First, let's factorize the given expression. Th... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIf $2x+7$ is a factor of $6x^3+19x^2+cx+35$, find $c$.",
"role": "user"
},
{
"content": "Step 1: To solve this problem, we'll need to apply pol... | ba6e175ab0a524b9468822b595aa96a5c6c03dda8fdcace972a44efc391e0c98_5_1 | Math_CoT | MATH | 1 | 28.875 | -10.9375 | 39.8125 | 0 | 28.875 | -10.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(x,y)$ with $x<y$ is the h... | 77cb57cc16e3595c415ad229f4a65e566cafba91cb2f880da59a7f1005cf03b2 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | 3d12a6f8be4cf3f25eea620aefc79a5ade6791604141b223b5e93a776b375743_1_1 | Math_CoT | MATH | 1 | 33 | -6.78125 | 39.78125 | 0 | 33 | -6.78125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The rim of a standard basketball hoop is 10 feet above the ground. Additionally, most experts will say that a player must be able to reach at least 6 inches above the rim to dunk a... | 94bbb31f79fb6cc080369f6f88c650a8093ec10021b60c87b2a06969d8d3fda5 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe rim of a standard basketball hoop is 10 feet above the ground. Additionally, most experts will say that a player must be able to reach at least 6 inche... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe rim of a standard basketball hoop is 10 feet above the ground. Additionally, most experts will say that a player must be able to reach at least 6 inche... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe rim of a standard basketball hoop is 10 feet above the ground. Additionally, most experts will say that a player must be able to reach at least 6 inche... | 94bbb31f79fb6cc080369f6f88c650a8093ec10021b60c87b2a06969d8d3fda5_2_2 | Math_CoT | gsm8k | 3 | 28.25 | -11.5 | 39.75 | 0 | 28.25 | -11.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Mike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. How much money did he spe... | cb899bcec334d3328c8a0faacaf4756b59a91112bd51dce365a172dcda1ecb6d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | cb899bcec334d3328c8a0faacaf4756b59a91112bd51dce365a172dcda1ecb6d_2_2 | Math_CoT | gsm8k | 3 | 28.5 | -11.25 | 39.75 | 0 | 28.5 | -11.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
What is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5),$ and the other on the sphere of radius 87 with center $(12,8,-16)$? | d8541af55ac40977d8e51f192f2e78fdcbada0687777af82d1697712d9df6b41 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nWhat is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5),$ and the other on the sphere of radius 87 ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nWhat is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5),$ and the other on the sphere of radius 87 ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nWhat is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5),$ and the other on the sphere of radius 87 ... | d8541af55ac40977d8e51f192f2e78fdcbada0687777af82d1697712d9df6b41_5_1 | Math_CoT | MATH | 1 | 28.125 | -11.625 | 39.75 | 0 | 28.125 | -11.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The bakery has 8 indoor tables and 12 outdoor tables. Each indoor table has 3 chairs and each outdoor table has 3 chairs. How many chairs are there in total? | 5a7b1b4f690bbeb94027ba1cc948910f28f167e5dc2e1c66a173d7aba7db89e6 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe bakery has 8 indoor tables and 12 outdoor tables. Each indoor table has 3 chairs and each outdoor table has 3 chairs. How many chairs are there in total... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe bakery has 8 indoor tables and 12 outdoor tables. Each indoor table has 3 chairs and each outdoor table has 3 chairs. How many chairs are there in total... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe bakery has 8 indoor tables and 12 outdoor tables. Each indoor table has 3 chairs and each outdoor table has 3 chairs. How many chairs are there in total... | 5a7b1b4f690bbeb94027ba1cc948910f28f167e5dc2e1c66a173d7aba7db89e6_1_1 | Math_CoT | gsm8k | 1 | 31.125 | -8.5625 | 39.6875 | 0 | 31.125 | -8.5625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Martin strolled to Lawrence's house. It is 12 miles from Martin's house to Lawrence's house. It took Martin 6 hours to get there. So , Martin went there at _____ miles per hour . | c691408578c4bba83615f3904d4c75310833cb7ead892d16dc19e051877c3ea0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMartin strolled to Lawrence's house. It is 12 miles from Martin's house to Lawrence's house. It took Martin 6 hours to get there. So , Martin went there at ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMartin strolled to Lawrence's house. It is 12 miles from Martin's house to Lawrence's house. It took Martin 6 hours to get there. So , Martin went there at ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMartin strolled to Lawrence's house. It is 12 miles from Martin's house to Lawrence's house. It took Martin 6 hours to get there. So , Martin went there at ... | c691408578c4bba83615f3904d4c75310833cb7ead892d16dc19e051877c3ea0_1_1 | Math_CoT | numglue | 1 | 20 | -19.625 | 39.625 | 0 | 20 | -19.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $k$ be a real number such that $k > 1$ and
\[\sum_{n=1}^{\infty} \frac{5n-1}{k^n} = \frac{13}{4}.\]Find $k.$ | 9089d99ebcc25703b5d92cf908b63ecc594664f899d601eb98304faaec20a1af | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $k$ be a real number such that $k > 1$ and\n\\[\\sum_{n=1}^{\\infty} \\frac{5n-1}{k^n} = \\frac{13}{4}.\\]Find $k.$",
"role": "user"
},
{
"c... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $k$ be a real number such that $k > 1$ and\n\\[\\sum_{n=1}^{\\infty} \\frac{5n-1}{k^n} = \\frac{13}{4}.\\]Find $k.$",
"role": "user"
},
{
"c... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $k$ be a real number such that $k > 1$ and\n\\[\\sum_{n=1}^{\\infty} \\frac{5n-1}{k^n} = \\frac{13}{4}.\\]Find $k.$",
"role": "user"
},
{
"c... | 4f674461d3bf4d809eb8a87bb37cb35c40fad608130463255a671a6b5e3885da_1_1 | Math_CoT | MATH | 1 | 29.25 | -10.25 | 39.5 | 0 | 29.25 | -10.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. What is the length, in units, of the longer diagonal? | 29637be058e54b3eaf26aa19c509320f2350531daf9e782640ee1cffbd425e82 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. What is the length, in units, of the longer diagonal?",
"role": "... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. What is the length, in units, of the longer diagonal?",
"role": "... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. What is the length, in units, of the longer diagonal?",
"role": "... | 29637be058e54b3eaf26aa19c509320f2350531daf9e782640ee1cffbd425e82_5_3 | Math_CoT | MATH | 5 | 30 | -9.5 | 39.5 | 0 | 30 | -9.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Square $ABCD$ has area $200$. Point $E$ lies on side $\overline{BC}$. Points $F$ and $G$ are the midpoints of $\overline{AE}$ and $\overline{DE}$, respectively. Given that quadrilat... | 1c62b7fdd73d8b6bf383e7113e65d63f1004e3d6a5080b098b433961215ff109 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSquare $ABCD$ has area $200$. Point $E$ lies on side $\\overline{BC}$. Points $F$ and $G$ are the midpoints of $\\overline{AE}$ and $\\overline{DE}$, respec... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSquare $ABCD$ has area $200$. Point $E$ lies on side $\\overline{BC}$. Points $F$ and $G$ are the midpoints of $\\overline{AE}$ and $\\overline{DE}$, respec... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nSquare $ABCD$ has area $200$. Point $E$ lies on side $\\overline{BC}$. Points $F$ and $G$ are the midpoints of $\\overline{AE}$ and $\\overline{DE}$, respec... | 1c62b7fdd73d8b6bf383e7113e65d63f1004e3d6a5080b098b433961215ff109_5_2 | Math_CoT | MATH | 3 | 24.25 | -15.25 | 39.5 | 0 | 24.25 | -15.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is... | 7e96aae995bdd6fd18d24887a870041818aeed8601679be8582b3808839fc691 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nthe length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the ar... | 7e96aae995bdd6fd18d24887a870041818aeed8601679be8582b3808839fc691_1_1 | Math_CoT | mathqa | 1 | 26.5 | -12.9375 | 39.4375 | 0 | 26.5 | -12.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)? | 36791a67490510632766068ecb76af9921c3623e30eb1dc4a08d2995eac594f5 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)?",
"role": "user"
},
{
"co... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)?",
"role": "user"
},
{
"co... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)?",
"role": "user"
},
{
"co... | 36791a67490510632766068ecb76af9921c3623e30eb1dc4a08d2995eac594f5_1_1 | Math_CoT | MATH | 1 | 28.875 | -10.5625 | 39.4375 | 0 | 28.875 | -10.5625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Kiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Kiarra is 30, how old is Harry? | 5c4d52573e70c25b3d6dd3b5f073a0782d50839534c270d5aaf37615a520416e | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nKiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Kiarra is 30, how old is ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nKiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Kiarra is 30, how old is ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nKiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Kiarra is 30, how old is ... | 5c4d52573e70c25b3d6dd3b5f073a0782d50839534c270d5aaf37615a520416e_1_1 | Math_CoT | gsm8k | 1 | 34 | -5.375 | 39.375 | 0 | 34 | -5.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Angela is 4 cm taller than Helen. Helen is 3 cm taller than Amy. If Amy is 150 cm tall, how many centimeters tall is Angela? | 4d5c8224fb3c149720c470eeeac06549a4bf4d2434e7e87248e77a3011f617fa | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAngela is 4 cm taller than Helen. Helen is 3 cm taller than Amy. If Amy is 150 cm tall, how many centimeters tall is Angela?",
"role": "user"
},
{
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAngela is 4 cm taller than Helen. Helen is 3 cm taller than Amy. If Amy is 150 cm tall, how many centimeters tall is Angela?",
"role": "user"
},
{
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAngela is 4 cm taller than Helen. Helen is 3 cm taller than Amy. If Amy is 150 cm tall, how many centimeters tall is Angela?",
"role": "user"
},
{
... | 4d5c8224fb3c149720c470eeeac06549a4bf4d2434e7e87248e77a3011f617fa_1_1 | Math_CoT | gsm8k | 1 | 28.875 | -10.375 | 39.25 | 0 | 28.875 | -10.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A circular sheet of paper with radius of $6$ cm is cut into three congruent sectors. What is the height of the cone in centimeters that can be created by rolling one of the sections... | ad7f36d9842acb01a419112ddd78ee63e77cd10a1f34526fa4faf44959154b8a | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA circular sheet of paper with radius of $6$ cm is cut into three congruent sectors. What is the height of the cone in centimeters that can be created by ro... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA circular sheet of paper with radius of $6$ cm is cut into three congruent sectors. What is the height of the cone in centimeters that can be created by ro... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA circular sheet of paper with radius of $6$ cm is cut into three congruent sectors. What is the height of the cone in centimeters that can be created by ro... | e2ae3084eec33fd923294fde6a65020505ed0aa3ecf6e39a96a3a83e154e1c6c_1_1 | Math_CoT | MATH | 1 | 25.375 | -13.875 | 39.25 | 0 | 25.375 | -13.875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper? | 917b40cd8f36d966fb873d6ee1c371740e14ad40e09b771f7169c631b3f1c9b4 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper?",
"role": ... | 917b40cd8f36d966fb873d6ee1c371740e14ad40e09b771f7169c631b3f1c9b4_1_1 | Math_CoT | gsm8k | 1 | 26.25 | -12.9375 | 39.1875 | 0 | 26.25 | -12.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find his expenditure on food a... | f65dda471df852a9249b611dc769c2013f75c30b8bbee6a6a24e5d948dd3a5ff | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find ... | f65dda471df852a9249b611dc769c2013f75c30b8bbee6a6a24e5d948dd3a5ff_5_4 | Math_CoT | mathqa | 7 | 28.5 | -10.625 | 39.125 | 0 | 28.5 | -10.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Jane's quiz scores were 98, 97, 92, 85 and 93. What was her mean score? | 90bac64994c50951cf93dc741a6f855fc7e4e8b5d16fb87aef585c63ee9e1acb | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJane's quiz scores were 98, 97, 92, 85 and 93. What was her mean score?",
"role": "user"
},
{
"content": "Step 1: Calculate the sum of Jane's qu... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJane's quiz scores were 98, 97, 92, 85 and 93. What was her mean score?",
"role": "user"
},
{
"content": "Step 1: In order to calculate the mea... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJane's quiz scores were 98, 97, 92, 85 and 93. What was her mean score?",
"role": "user"
},
{
"content": "Step 1: Calculate the sum of Jane's qu... | 90bac64994c50951cf93dc741a6f855fc7e4e8b5d16fb87aef585c63ee9e1acb_1_1 | Math_CoT | MATH | 1 | 28.375 | -10.75 | 39.125 | 0 | 28.375 | -10.75 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Annie plants 3 pots of basil, 9 pots of rosemary, and 6 pots of thyme. Each basil plant has 4 leaves, each rosemary plant has 18 leaves, and each thyme plant has 30 leaves. How many... | 12f22e6ead6f5c29ebe7e02dbdcb9a71243737f9421a79d8731a10d5e842805e | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAnnie plants 3 pots of basil, 9 pots of rosemary, and 6 pots of thyme. Each basil plant has 4 leaves, each rosemary plant has 18 leaves, and each thyme plan... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAnnie plants 3 pots of basil, 9 pots of rosemary, and 6 pots of thyme. Each basil plant has 4 leaves, each rosemary plant has 18 leaves, and each thyme plan... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nAnnie plants 3 pots of basil, 9 pots of rosemary, and 6 pots of thyme. Each basil plant has 4 leaves, each rosemary plant has 18 leaves, and each thyme plan... | 12f22e6ead6f5c29ebe7e02dbdcb9a71243737f9421a79d8731a10d5e842805e_1_1 | Math_CoT | gsm8k | 1 | 32 | -7.0625 | 39.0625 | 0 | 32 | -7.0625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ? | 542c1694c738246cdcd84a7a0f7241c7a7bd98be63305ba844eb2571e52719d3 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nin a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?",
"role": "user"
},
{
"content": "Step 1: F... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nin a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?",
"role": "user"
},
{
"content": "Step 1: F... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nin a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?",
"role": "user"
},
{
"content": "Step 1: F... | 542c1694c738246cdcd84a7a0f7241c7a7bd98be63305ba844eb2571e52719d3_5_3 | Math_CoT | mathqa | 5 | 25.25 | -13.8125 | 39.0625 | 0 | 25.25 | -13.8125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Four days' temperatures were recorded for Wayupnorth, Canada. The temperatures were: -36 degrees Fahrenheit, +13 degrees Fahrenheit, -15 degrees Fahrenheit, and -10 degrees Fahrenhe... | 1aff45ad04c7cc4e27d494058b5af9b6d9135a425d5854e6d1815a18570cf6bb | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFour days' temperatures were recorded for Wayupnorth, Canada. The temperatures were: -36 degrees Fahrenheit, +13 degrees Fahrenheit, -15 degrees Fahrenheit,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFour days' temperatures were recorded for Wayupnorth, Canada. The temperatures were: -36 degrees Fahrenheit, +13 degrees Fahrenheit, -15 degrees Fahrenheit,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFour days' temperatures were recorded for Wayupnorth, Canada. The temperatures were: -36 degrees Fahrenheit, +13 degrees Fahrenheit, -15 degrees Fahrenheit,... | 1aff45ad04c7cc4e27d494058b5af9b6d9135a425d5854e6d1815a18570cf6bb_2_2 | Math_CoT | gsm8k | 3 | 21.625 | -17.375 | 39 | 0 | 21.625 | -17.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Michelangelo has 28 ceilings to paint. This week, he paints 12 of them. Next week, he will paint 1/4 the number of ceilings he did this week. How many ceilings will be left to paint... | 2e7a55215574de9ab1b7f1c25f2a2c5dbe98bcb9ebb55deacc117a457dc5d1e4 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMichelangelo has 28 ceilings to paint. This week, he paints 12 of them. Next week, he will paint 1/4 the number of ceilings he did this week. How many ceili... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMichelangelo has 28 ceilings to paint. This week, he paints 12 of them. Next week, he will paint 1/4 the number of ceilings he did this week. How many ceili... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMichelangelo has 28 ceilings to paint. This week, he paints 12 of them. Next week, he will paint 1/4 the number of ceilings he did this week. How many ceili... | 2e7a55215574de9ab1b7f1c25f2a2c5dbe98bcb9ebb55deacc117a457dc5d1e4_2_2 | Math_CoT | gsm8k | 3 | 16.75 | -22.25 | 39 | 0 | 16.75 | -22.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle? | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65_5_2 | Math_CoT | MATH | 3 | 29.125 | -9.8125 | 38.9375 | 0 | 29.125 | -9.8125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Charles is jogging while listening to his favorite album. He runs at 6 MPH when he's got music on and 4 MPH when he doesn't. His album is 40 minutes long. How many minutes will it t... | db01f52644610dfcc7d8e4891c6f703d201ad4b54356d980d45387bd175cbf27 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCharles is jogging while listening to his favorite album. He runs at 6 MPH when he's got music on and 4 MPH when he doesn't. His album is 40 minutes long. H... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCharles is jogging while listening to his favorite album. He runs at 6 MPH when he's got music on and 4 MPH when he doesn't. His album is 40 minutes long. H... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCharles is jogging while listening to his favorite album. He runs at 6 MPH when he's got music on and 4 MPH when he doesn't. His album is 40 minutes long. H... | db01f52644610dfcc7d8e4891c6f703d201ad4b54356d980d45387bd175cbf27_3_3 | Math_CoT | gsm8k | 5 | 17.625 | -21.25 | 38.875 | 0 | 17.625 | -21.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Monica and Michelle are combining their money to throw a party. Monica brings $15. Michelle brings $12. The cake costs 15 dollars, and soda is $3 a bottle. Each bottle of soda has 1... | baa9331165ee2fa0311d9ce574922023047cb8dea3cf287d82a48af2b3cb42bf | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMonica and Michelle are combining their money to throw a party. Monica brings $15. Michelle brings $12. The cake costs 15 dollars, and soda is $3 a bottle. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMonica and Michelle are combining their money to throw a party. Monica brings $15. Michelle brings $12. The cake costs 15 dollars, and soda is $3 a bottle. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMonica and Michelle are combining their money to throw a party. Monica brings $15. Michelle brings $12. The cake costs 15 dollars, and soda is $3 a bottle. ... | baa9331165ee2fa0311d9ce574922023047cb8dea3cf287d82a48af2b3cb42bf_2_2 | Math_CoT | gsm8k | 3 | 30 | -8.8125 | 38.8125 | 0 | 30 | -8.8125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
jennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have ... | 43277b5a2ebd470bc354448fe730119241dc629c5d4dbf400cf2e47f4d8b193a | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\njennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\njennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\njennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much ... | 43277b5a2ebd470bc354448fe730119241dc629c5d4dbf400cf2e47f4d8b193a_1_1 | Math_CoT | mathqa | 1 | 23.5 | -15.25 | 38.75 | 0 | 23.5 | -15.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In triangle $ABC$, we have $AB=1$ and $AC=2$. Side $\overline{BC}$ and the median from $A$ to $\overline{BC}$ have the same length. What is $BC$? Express your answer in simplest rad... | 0f9cac0fdda8aa4f905d4e19d97c7921cea5b7d00c7574fb22823bfeb043117d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, we have $AB=1$ and $AC=2$. Side $\\overline{BC}$ and the median from $A$ to $\\overline{BC}$ have the same length. What is $BC$? Express ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, we have $AB=1$ and $AC=2$. Side $\\overline{BC}$ and the median from $A$ to $\\overline{BC}$ have the same length. What is $BC$? Express ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, we have $AB=1$ and $AC=2$. Side $\\overline{BC}$ and the median from $A$ to $\\overline{BC}$ have the same length. What is $BC$? Express ... | 0f9cac0fdda8aa4f905d4e19d97c7921cea5b7d00c7574fb22823bfeb043117d_5_5 | Math_CoT | MATH | 9 | 22.75 | -15.9375 | 38.6875 | 0 | 22.75 | -15.9375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Find the least odd prime factor of $2019^8+1$. | 090f55ed2eeab5771c5f3cfe7424e6397a03a01a0681cc8af4b75dd9302e0bf7 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the least odd prime factor of $2019^8+1$.",
"role": "user"
},
{
"content": "Step 1: To solve this problem, we need to find the least odd p... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the least odd prime factor of $2019^8+1$.",
"role": "user"
},
{
"content": "Step 1: To solve this problem, let's first find the prime fact... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the least odd prime factor of $2019^8+1$.",
"role": "user"
},
{
"content": "Step 1: To solve this problem, we need to find the least odd p... | 71390e2f5ddd8fcf2a6acbe6ff12735ec564878287001b49ebd28a151b39acfc_1_1 | Math_CoT | MATH | 1 | 30.625 | -8 | 38.625 | 0 | 30.625 | -8 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the tr... | a1d52f42fc2672a2e925f2832e9191c965f130191c4ae49b41e2123bac717e15 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest pos... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest pos... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest pos... | a1d52f42fc2672a2e925f2832e9191c965f130191c4ae49b41e2123bac717e15_3_3 | Math_CoT | MATH | 5 | 20.375 | -18.25 | 38.625 | 0 | 20.375 | -18.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(x,y)$ with $x<y$ is the h... | 77cb57cc16e3595c415ad229f4a65e566cafba91cb2f880da59a7f1005cf03b2 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | b9e37685633a0b55beaca15ad8d34d7e1211a47fe37ffc7f9e1717d8c042ba72_1_1 | Math_CoT | MATH | 1 | 29.75 | -8.8125 | 38.5625 | 0 | 29.75 | -8.8125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A gasoline tank is $\frac78$ full. After $12$ gallons have been used, it is half full. How many gallons does this tank hold when it is full? | 5248efd30bf07fa0d33be2b2b8bd0c9851cff5eddaa96537aa3b3e75085a7d7e | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA gasoline tank is $\\frac78$ full. After $12$ gallons have been used, it is half full. How many gallons does this tank hold when it is full?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA gasoline tank is $\\frac78$ full. After $12$ gallons have been used, it is half full. How many gallons does this tank hold when it is full?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA gasoline tank is $\\frac78$ full. After $12$ gallons have been used, it is half full. How many gallons does this tank hold when it is full?",
"role": ... | bde2c0a78c016b84edcbb31f26e37d937084e569d150263b65787d3f9dd4c165_1_1 | Math_CoT | MATH | 1 | 34.5 | -4.03125 | 38.53125 | 0 | 34.5 | -4.03125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle? | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65_5_3 | Math_CoT | MATH | 5 | 28.125 | -10.375 | 38.5 | 0 | 28.125 | -10.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In triangle $ABC$, $\cos(2A-B)+\sin(A+B)=2$ and $AB=4$. What is $BC$? | 26d71ef0486474fd4cffdc30e59b472e195a88b8e299e169086243db963de7c6 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, $\\cos(2A-B)+\\sin(A+B)=2$ and $AB=4$. What is $BC$?",
"role": "user"
},
{
"content": "Step 1: Let's start by using the given... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, $\\cos(2A-B)+\\sin(A+B)=2$ and $AB=4$. What is $BC$?",
"role": "user"
},
{
"content": "Step 1: Let's start by using the given... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn triangle $ABC$, $\\cos(2A-B)+\\sin(A+B)=2$ and $AB=4$. What is $BC$?",
"role": "user"
},
{
"content": "Step 1: Let's start by using the given... | 26d71ef0486474fd4cffdc30e59b472e195a88b8e299e169086243db963de7c6_5_2 | Math_CoT | MATH | 3 | 21.25 | -17.25 | 38.5 | 0 | 21.25 | -17.25 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Josh went to the shopping center. He bought 9 films and 4 books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. How much did Josh spend in all? | d552f1272b46726c6c55b6629e84178ae375ddda396d9da6c7a49978af7227d7 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJosh went to the shopping center. He bought 9 films and 4 books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. How much di... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJosh went to the shopping center. He bought 9 films and 4 books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. How much di... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJosh went to the shopping center. He bought 9 films and 4 books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. How much di... | d552f1272b46726c6c55b6629e84178ae375ddda396d9da6c7a49978af7227d7_1_1 | Math_CoT | gsm8k | 1 | 28.625 | -9.8125 | 38.4375 | 0 | 28.625 | -9.8125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Eve wants to buy her 3 nieces cooking gear that's made for kids. The hand mitts cost $14.00 and the apron is $16.00. A set of 3 cooking utensils is $10.00 and a small knife is twi... | 3f57f8d79e8888d7955625b239b04d55caafbd34801b977e987c71deb8a0eb19 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEve wants to buy her 3 nieces cooking gear that's made for kids. The hand mitts cost $14.00 and the apron is $16.00. A set of 3 cooking utensils is $10.00... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEve wants to buy her 3 nieces cooking gear that's made for kids. The hand mitts cost $14.00 and the apron is $16.00. A set of 3 cooking utensils is $10.00... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEve wants to buy her 3 nieces cooking gear that's made for kids. The hand mitts cost $14.00 and the apron is $16.00. A set of 3 cooking utensils is $10.00... | 3f57f8d79e8888d7955625b239b04d55caafbd34801b977e987c71deb8a0eb19_2_2 | Math_CoT | gsm8k | 3 | 29.125 | -9.3125 | 38.4375 | 0 | 29.125 | -9.3125 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The coefficients of the polynomial
\[a_{10} x^{10} + a_9 x^9 + a_8 x^8 + \dots + a_2 x^2 + a_1 x + a_0 = 0\]are all integers, and its roots $r_1,$ $r_2,$ $\dots,$ $r_{10}$ are all i... | 57ce671e04c8c67bd75a40ba46d72efed04e739e6094529a8afbd6aa03f23d77 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe coefficients of the polynomial\n\\[a_{10} x^{10} + a_9 x^9 + a_8 x^8 + \\dots + a_2 x^2 + a_1 x + a_0 = 0\\]are all integers, and its roots $r_1,$ $r_2,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe coefficients of the polynomial\n\\[a_{10} x^{10} + a_9 x^9 + a_8 x^8 + \\dots + a_2 x^2 + a_1 x + a_0 = 0\\]are all integers, and its roots $r_1,$ $r_2,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe coefficients of the polynomial\n\\[a_{10} x^{10} + a_9 x^9 + a_8 x^8 + \\dots + a_2 x^2 + a_1 x + a_0 = 0\\]are all integers, and its roots $r_1,$ $r_2,... | 7f2e4a72610472f7bd89d91b070357610b6a89f99100e8282c1e49921235e26f_1_1 | Math_CoT | MATH | 1 | 28 | -10.4375 | 38.4375 | 0 | 28 | -10.4375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The area of this region formed by six congruent squares is 294 square centimeters. What is the perimeter of the region, in centimeters?
[asy]
draw((0,0)--(-10,0)--(-10,10)--(0,10)-... | 84f99de94c0a64c13107b28c4e880382091c72eea1e571e54230021edf26ba4a | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe area of this region formed by six congruent squares is 294 square centimeters. What is the perimeter of the region, in centimeters?\n\n[asy]\ndraw((0,0)... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe area of this region formed by six congruent squares is 294 square centimeters. What is the perimeter of the region, in centimeters?\n\n[asy]\ndraw((0,0)... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe area of this region formed by six congruent squares is 294 square centimeters. What is the perimeter of the region, in centimeters?\n\n[asy]\ndraw((0,0)... | b3945e935469714630f33ffb77e7223cc4fd7b1c5a5de8ab8a1c5973e4908e4b_1_1 | Math_CoT | MATH | 1 | 25.375 | -13.0625 | 38.4375 | 0 | 25.375 | -13.0625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
James gets paid $0.50/mile to drive a truck carrying hazardous waste. He has to pay $4.00/gallon for gas and his truck gets 20 miles per gallon. How much profit does he make from a ... | 30bfad7bdd0af8525549089963908b019c31bc09852a2a98c6d54b8c8a71fb80 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJames gets paid $0.50/mile to drive a truck carrying hazardous waste. He has to pay $4.00/gallon for gas and his truck gets 20 miles per gallon. How much pr... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJames gets paid $0.50/mile to drive a truck carrying hazardous waste. He has to pay $4.00/gallon for gas and his truck gets 20 miles per gallon. How much pr... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJames gets paid $0.50/mile to drive a truck carrying hazardous waste. He has to pay $4.00/gallon for gas and his truck gets 20 miles per gallon. How much pr... | 30bfad7bdd0af8525549089963908b019c31bc09852a2a98c6d54b8c8a71fb80_2_2 | Math_CoT | gsm8k | 3 | 22.75 | -15.625 | 38.375 | 0 | 22.75 | -15.625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Compute $\cos \left( \arcsin \frac{5}{13} \right).$ | 9ba68c9b7e9939e98cad4f4b913fcaf60841747b5c7a8db6e72cdee6531f2911 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCompute $\\cos \\left( \\arcsin \\frac{5}{13} \\right).$",
"role": "user"
},
{
"content": "Step 1: We are given the expression $\\cos \\left( \\... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCompute $\\cos \\left( \\arcsin \\frac{5}{13} \\right).$",
"role": "user"
},
{
"content": "Step 1: In this problem, we are required to find the... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCompute $\\cos \\left( \\arcsin \\frac{5}{13} \\right).$",
"role": "user"
},
{
"content": "Step 1: We are given the expression $\\cos \\left( \\... | 9ba68c9b7e9939e98cad4f4b913fcaf60841747b5c7a8db6e72cdee6531f2911_1_1 | Math_CoT | MATH | 1 | 22 | -16.375 | 38.375 | 0 | 22 | -16.375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures $3$ by $4$ by $5$ units. Given that the volume of this set is $\fra... | 078960f709b77b95222309c98b9a04cac992f8e3f3d2a69fbe594b3d59f74d21 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nConsider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures $3$ by $4$ by $5$ units. Given that the vo... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nConsider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures $3$ by $4$ by $5$ units. Given that the vo... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nConsider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures $3$ by $4$ by $5$ units. Given that the vo... | 0d3a6a90559f60d233c19ace087209e83e957c1371c779631ae4f46ea495bbe8_1_1 | Math_CoT | MATH | 1 | 31.25 | -7.09375 | 38.34375 | 0 | 31.25 | -7.09375 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Each vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. What is the value of the sum $p + a$... | be978b7c66dd6ac14669dd9e41663d7995df74a2839b2c111a508f7a325c7992 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEach vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. What is the... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEach vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. What is the... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nEach vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. What is the... | 49ee41d7dea831ba28be156ae030afc50b7df1c9e7d57587717e429247ded08b_1_1 | Math_CoT | MATH | 1 | 27.75 | -10.5625 | 38.3125 | 0 | 27.75 | -10.5625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the tria... | 9ecc5b46b721c40239ec249b93b3bcb2bf72f08faf357c57142236f13a5e2692 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls... | 9ecc5b46b721c40239ec249b93b3bcb2bf72f08faf357c57142236f13a5e2692_5_3 | Math_CoT | MATH | 5 | 31.75 | -6.5625 | 38.3125 | 0 | 31.75 | -6.5625 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The city is holding its annual rubber duck race for charity. The regular size rubber ducks are $3.00 each and the large size rubber duck is $5.00 each. All of the rubber ducks wil... | fcef6ad1be692606253a57a533543ad860385cc45bac462ab0bba8df31a48a50 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe city is holding its annual rubber duck race for charity. The regular size rubber ducks are $3.00 each and the large size rubber duck is $5.00 each. Al... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe city is holding its annual rubber duck race for charity. The regular size rubber ducks are $3.00 each and the large size rubber duck is $5.00 each. Al... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe city is holding its annual rubber duck race for charity. The regular size rubber ducks are $3.00 each and the large size rubber duck is $5.00 each. Al... | fcef6ad1be692606253a57a533543ad860385cc45bac462ab0bba8df31a48a50_1_1 | Math_CoT | gsm8k | 1 | 22.75 | -15.5 | 38.25 | 0 | 22.75 | -15.5 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find the area of the polygon.
[... | 4043c6cffff07ca7c40cb5a9c7d42b49ad451c9dbc08ad9025a021ee4b08dcd0 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find th... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find th... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find th... | a84dc3bab4b1c94c29ac6009e76691b6d2170c3e1b98a4973d9b4dda14c861a4_1_1 | Math_CoT | MATH | 1 | 26.375 | -11.875 | 38.25 | 0 | 26.375 | -11.875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located at $(1, 14)$. They agree t... | a616c9d5798b2b938ff8349de2558128bae7d174d909488f071ff5b4404e21e8 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located a... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located a... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located a... | a616c9d5798b2b938ff8349de2558128bae7d174d909488f071ff5b4404e21e8_2_1 | Math_CoT | MATH | 1 | 24.375 | -13.875 | 38.25 | 0 | 24.375 | -13.875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Mikaela earns $10 an hour tutoring. For the first month, she tutored for 35 hours and in the second month, she tutored 5 hours more than the first month. She spent 4/5 of her total... | 5b37f583c9be08e04f052e4a61cd1dc6024a072cafcc9af5aef88a8b48a64eea | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMikaela earns $10 an hour tutoring. For the first month, she tutored for 35 hours and in the second month, she tutored 5 hours more than the first month. S... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMikaela earns $10 an hour tutoring. For the first month, she tutored for 35 hours and in the second month, she tutored 5 hours more than the first month. S... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMikaela earns $10 an hour tutoring. For the first month, she tutored for 35 hours and in the second month, she tutored 5 hours more than the first month. S... | 5b37f583c9be08e04f052e4a61cd1dc6024a072cafcc9af5aef88a8b48a64eea_1_1 | Math_CoT | gsm8k | 1 | 31.5 | -6.6875 | 38.1875 | 0 | 31.5 | -6.6875 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Find the largest positive integer $n$ such that
\[\sin^n x + \cos^n x \ge \frac{1}{n}\]for all real numbers $x.$ | a795da56b35ff44d6092dcd9d2e8abef4108ee157bad2fe2002f3520a5a7fa55 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the largest positive integer $n$ such that\n\\[\\sin^n x + \\cos^n x \\ge \\frac{1}{n}\\]for all real numbers $x.$",
"role": "user"
},
{
"c... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the largest positive integer $n$ such that\n\\[\\sin^n x + \\cos^n x \\ge \\frac{1}{n}\\]for all real numbers $x.$",
"role": "user"
},
{
"c... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFind the largest positive integer $n$ such that\n\\[\\sin^n x + \\cos^n x \\ge \\frac{1}{n}\\]for all real numbers $x.$",
"role": "user"
},
{
"c... | a795da56b35ff44d6092dcd9d2e8abef4108ee157bad2fe2002f3520a5a7fa55_5_1 | Math_CoT | MATH | 1 | 24.875 | -13.3125 | 38.1875 | 0 | 24.875 | -13.3125 |
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