instruction_seed string | response_seed string | reasoning string | deepseek_solution string | __original_row_idx int64 | source string | final_reasoning_trace string | conversations list | text string | difficulty float64 | topic string | r1_solution_1 string | r1_solution_2 string | r1_solution_3 string | generated_solution string | problem_source string | solution string | is_correct bool | solution_steps sequence | rtg sequence | undiscounted_rtg sequence | target_answer string | completion int64 | trajectory int64 | reference_answer string | responses list | input string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the distance on a Cartesian coordinate plane from $(1, -1)$ to $(7, 7)?$ | Using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
In this case, $(x_1, y_1) = (1, -1)$ and $(x_2, y_2) = (7, 7)$.
Plugging these values into the distance formula, we have
$\sqrt{(7 - 1)^2 + (7 - (-1))^2} = \sqrt{6^2 + 8^2} = \sq... | Okay, let's see. I need to find the distance between the points (1, -1) and (7, 7) on a Cartesian coordinate plane. Hmm, I remember there's a formula for calculating the distance between two points. Is it the Pythagorean Theorem or something like that? Yeah, I think it is. Let me recall. If you have two points, (x1, y1... | To find the distance between the points \((1, -1)\) and \((7, 7)\) on a Cartesian coordinate plane, we use the distance formula:
\[
\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the given coordinates \((x_1, y_1) = (1, -1)\) and \((x_2, y_2) = (7, 7)\):
1. Calculate the differences in the x ... | 4,748 | TIGER-Lab/MATH-plus | <think>
Okay, let's see. I need to find the distance between the points (1, -1) and (7, 7) on a Cartesian coordinate plane. Hmm, I remember there's a formula for calculating the distance between two points. Is it the Pythagorean Theorem or something like that? Yeah, I think it is. Let me recall. If you have two points,... | [
{
"from": "human",
"value": "What is the distance on a Cartesian coordinate plane from $(1, -1)$ to $(7, 7)?$"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the distance between the points (1, -1) and (7, 7) on a Cartesian coordinate plane. Hmm, I remember there's a for... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
b"What is the lth term of 105502, 105659, 105816, 105973?\n" | 157*l + 105345\n | Okay, let's see. The user is asking for the lth term of the sequence: 105502, 105659, 105816, 105973. Hmm, first I need to figure out the pattern here. Let me write down the numbers to see the differences between consecutive terms.
So, starting with 105502. The next term is 105659. Let's subtract the first term from t... | The sequence provided is an arithmetic sequence where each term increases by a common difference of 157.
**Step-by-Step Explanation:**
1. **Identify the common difference:**
- \(105659 - 105502 = 157\)
- \(105816 - 105659 = 157\)
- \(105973 - 105816 = 157\)
2. **General formula for the \(l\)-th term... | 7,667 | ibivibiv/math_instruct | <think>
Okay, let's see. The user is asking for the lth term of the sequence: 105502, 105659, 105816, 105973. Hmm, first I need to figure out the pattern here. Let me write down the numbers to see the differences between consecutive terms.
So, starting with 105502. The next term is 105659. Let's subtract the first ter... | [
{
"from": "human",
"value": "b\"What is the lth term of 105502, 105659, 105816, 105973?\\n\""
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The user is asking for the lth term of the sequence: 105502, 105659, 105816, 105973. Hmm, first I need to figure out the pattern here. Let me writ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | |
In X days, Tom swims one hour daily. He starts with a pace of $z$ minutes per mile, increasing the swim time by $7$ minutes each day. How many total miles does he swim over the four days? If we know the answer to the above question is 24, what is the value of unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of days Tom swims, and how many total miles he swims over those days based on his swimming pace and duration.
Let's break down the information given:
- Tom swims for 1 hour daily, which is 60 minutes.
- He starts with a pace of z m... | Okay, let's try to figure out this problem. So, Tom swims for X days, one hour each day. He starts with a pace of z minutes per mile and increases his swim time by 7 minutes each day. We need to find the total miles he swims over four days, and given that the answer is 24, find X. Wait, hold on. Wait, the problem says ... | Tom swims for \( X \) days, one hour each day, starting with a pace of \( z \) minutes per mile and increasing his swim time by 7 minutes each day. We need to determine the value of \( X \) given that the total miles he swims over four days is 24.
1. **Understanding the problem**:
- Tom swims one hour (60 minutes) ... | 24,995 | MetaMath-AIME | <think>
Okay, let's try to figure out this problem. So, Tom swims for X days, one hour each day. He starts with a pace of z minutes per mile and increases his swim time by 7 minutes each day. We need to find the total miles he swims over four days, and given that the answer is 24, find X. Wait, hold on. Wait, the probl... | [
{
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"Initially, the men, women, children, and elderly in a room were in the ratio of 4 : 5 : 3 : 2. Then(...TRUNCATED) | "Let's denote the initial number of men, women, children, and elderly as M, W, C, and E respectively(...TRUNCATED) | "Okay, so let's see. There's this problem about ratios and changes in the number of people in a room(...TRUNCATED) | "Initially, the men, women, children, and elderly in a room were in the ratio of \\(4:5:3:2\\). Let (...TRUNCATED) | 7,961 | TIGER-Lab/MATH-plus | "<think>\nOkay, so let's see. There's this problem about ratios and changes in the number of people (...TRUNCATED) | [{"from":"human","value":"Initially, the men, women, children, and elderly in a room were in the rat(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"Given two differentiable functions \\( u(x) \\) and \\( v(x) \\), if the product of these functions(...TRUNCATED) | "Okay, so I need to figure out the derivative of the product of two functions, u(x) and v(x). The pr(...TRUNCATED) | "Given two differentiable functions \\( u(x) \\) and \\( v(x) \\), the derivative of their product \(...TRUNCATED) | 11,687 | ddrg/named_math_formulas | "<think>\nOkay, so I need to figure out the derivative of the product of two functions, u(x) and v(x(...TRUNCATED) | [{"from":"human","value":"Given two differentiable functions \\( u(x) \\) and \\( v(x) \\), if the p(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | |
"# Question\n\nA $\\textit{palindrome}$ is a positive integer which reads the same forward and backw(...TRUNCATED) | null | "Okay, so I need to figure out how many 4-digit palindromes are divisible by 3. Hmm, let's start by (...TRUNCATED) | "A 4-digit palindrome has the form \\( abba \\), where \\( a \\) and \\( b \\) are digits, with \\( (...TRUNCATED) | 28,399 | Asap7772/hendrycks-math-mc-llama-sft-intermediate-parallel | "<think>\nOkay, so I need to figure out how many 4-digit palindromes are divisible by 3. Hmm, let's (...TRUNCATED) | [{"from":"human","value":"# Question\n\nA $\\textit{palindrome}$ is a positive integer which reads t(...TRUNCATED) | null | null | null | null | null | null | null | null | "# Question\n\nA $\\textit{palindrome}$ is a positive integer which reads the same forward and backw(...TRUNCATED) | false | ["# Question\n\nA $\\textit{palindrome}$ is a positive integer which reads the same forward and back(...TRUNCATED) | [0.0036397168941875234,0.004564311264492365,0.008037104041075015,0.002821327731146601,0.002616028501(...TRUNCATED) | [0.033264033264033266,0.03754266211604096,0.059496567505720827,0.018796992481203006,0.01568627450980(...TRUNCATED) | 30 | 6 | 1,398 | null | null | null |
"Given the equations \\( x + 2i - y = yi - 3xi \\) and \\( x = y \\), solve for the real values of \(...TRUNCATED) | "Okay, so I need to solve these equations: \\( x + 2i - y = yi - 3xi \\) and \\( x = y \\). The prob(...TRUNCATED) | "Given the equations \\( x + 2i - y = yi - 3xi \\) and \\( x = y \\), we need to solve for the real (...TRUNCATED) | 19,507 | math-ai/AutoMathText | "<think>\nOkay, so I need to solve these equations: \\( x + 2i - y = yi - 3xi \\) and \\( x = y \\).(...TRUNCATED) | [{"from":"human","value":"Given the equations \\( x + 2i - y = yi - 3xi \\) and \\( x = y \\), solve(...TRUNCATED) | "+0\n\n# Determine x and y\n\n0\n263\n2\n+606\n\nHi friends,\n\nx + 2i - y = yi - 3xi\n\nthank you!!(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | |
"Given a random variable \\( B \\) with mean \\( \\mathbb{E}(B) \\) and variance \\( \\text{VAR}(B) (...TRUNCATED) | "Okay, so I have this problem here about a random variable B. The question is asking for the expecte(...TRUNCATED) | "Given a random variable \\( B \\) with mean \\( \\mathbb{E}(B) = 5 \\) and variance \\( \\text{VAR}(...TRUNCATED) | 1,479 | ddrg/named_math_formulas | "<think>\nOkay, so I have this problem here about a random variable B. The question is asking for th(...TRUNCATED) | [{"from":"human","value":"Given a random variable \\( B \\) with mean \\( \\mathbb{E}(B) \\) and var(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | |
"Given an ellipse with a center at the origin, a major axis of length 18, and a minor axis of length(...TRUNCATED) | "Alright, so I need to find the equations of an ellipse in standard form for both orientations of th(...TRUNCATED) | "Given an ellipse with a center at the origin, a major axis of length 18, and a minor axis of length(...TRUNCATED) | 18,194 | math-ai/AutoMathText | "<think>\nAlright, so I need to find the equations of an ellipse in standard form for both orientati(...TRUNCATED) | [{"from":"human","value":"Given an ellipse with a center at the origin, a major axis of length 18, a(...TRUNCATED) | "# How do you write an equation of an ellipse in standard form given center is at origin, major axis(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | |
"A particle starts at the 0.5 meter mark and moves towards the 4 meter mark at a constant speed of 0(...TRUNCATED) | "Okay, so there's this particle that starts at the 0.5 meter mark and moves towards the 4 meter mark(...TRUNCATED) | "The particle starts at the 0.5 meter mark and moves towards the 4 meter mark at a constant speed of(...TRUNCATED) | 22,173 | math-ai/AutoMathText | "<think>\nOkay, so there's this particle that starts at the 0.5 meter mark and moves towards the 4 m(...TRUNCATED) | [{"from":"human","value":"A particle starts at the 0.5 meter mark and moves towards the 4 meter mark(...TRUNCATED) | "## calculusxy one year ago MEDAL!!! Start at the 0.5 meter mark and walk towards the 4 meter mark a(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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