prompt stringlengths 20 1.73k | answers sequencelengths 1.02k 1.02k | label sequencelengths 1.02k 1.02k | step_scores sequencelengths 1.02k 1.02k |
|---|---|---|---|
"Convert the point $(0,3)$ in rectangular coordinates to polar coordinates. Enter your answer in th(...TRUNCATED) | [" Step 1: To convert from rectangular coordinates to polar coordinates, we use the formulas $r = \\(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,1(...TRUNCATED) | [[0.9875683188438416,0.9986749291419983,0.9525741338729858,0.9947799444198608,0.9940890073776245],[0(...TRUNCATED) |
"Define\n\\[p = \\sum_{k = 1}^\\infty \\frac{1}{k^2} \\quad \\text{and} \\quad q = \\sum_{k = 1}^\\i(...TRUNCATED) | [" Step 1: We can rewrite the sum as 泻懈\nStep 2: \\begin{align*}\n\\sum_{j = 1}^\\infty \\sum_{k =(...TRUNCATED) | [1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0(...TRUNCATED) | [[0.10669060051441193,0.06008664518594742],[0.09534946084022522,0.005911068990826607],[0.09534946084(...TRUNCATED) |
"If $f(x) = \\frac{3x-2}{x-2}$, what is the value of $f(-2) +f(-1)+f(0)$? Express your answer as a c(...TRUNCATED) | [" Step 1: To find $f(-2)$, we substitute $x=-2$ into the expression for $f(x)$:\n\\[f(-2) = \\frac{(...TRUNCATED) | [0,0,0,0,0,1,0,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0(...TRUNCATED) | [[0.8807970285415649,0.2689414322376251,0.6791787147521973,0.2689414322376251],[0.6513549089431763,0(...TRUNCATED) |
How many positive whole-number divisors does 196 have? | [" Step 1: To find the number of divisors of 196, we prime factorize it as $196=2^6\\cdot7^1$. 泻懈\(...TRUNCATED) | [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [[0.7981867790222168,0.977022647857666,0.18242551386356354],[0.8807970285415649,0.562176525592804,0.(...TRUNCATED) |
"The results of a cross-country team's training run are graphed below. Which student has the greates(...TRUNCATED) | [" Step 1: To find the average speed, we need to find the distance traveled and the time taken. 泻懈(...TRUNCATED) | [0,0,0,1,0,1,0,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0(...TRUNCATED) | [[0.9046505093574524,0.7549149990081787,0.7772998809814453],[0.9399133324623108,0.851952850818634,0.(...TRUNCATED) |
"A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the tri(...TRUNCATED) | [" Step 1: Each side of the equilateral triangle has length $21/3 = 7$ inches. 泻懈\nStep 2: Since t(...TRUNCATED) | [1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,1,1,0,1(...TRUNCATED) | [[0.9840936064720154,0.9947799444198608,0.562176525592804],[0.9820137619972229,0.9046505093574524],[(...TRUNCATED) |
"What is the smallest positive perfect cube that can be written as the sum of three consecutive inte(...TRUNCATED) | [" Step 1: Let the three consecutive integers be $n-1,$ $n,$ and $n+1.$ 泻懈\nStep 2: We want $(n-1)(...TRUNCATED) | [0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0,1,1,1,1,1,1,1,0,0,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,1(...TRUNCATED) | [[0.6791787147521973,0.5926666259765625,0.622459352016449,0.01590639166533947],[0.531209409236908,0.(...TRUNCATED) |
"The set of points $(x,y,z)$ that satisfy\n\\[2x = 3y = -z\\]is a line.\n\nThe set of points $(x,y,z(...TRUNCATED) | [" Step 1: The first line is parameterized by $x = \\frac{3}{2} t$ and $y = t$, so it lies in the pl(...TRUNCATED) | [1,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0(...TRUNCATED) | [[0.3486451506614685,0.43782350420951843,0.29421496391296387],[0.3208213150501251,0.2942149639129638(...TRUNCATED) |
"What is the distance, in units, between the points $(2, -6)$ and $(-4, 3)$? Express your answer in (...TRUNCATED) | [" Step 1: Using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$(...TRUNCATED) | [1,1,0,0,0,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,1,1,0(...TRUNCATED) | [[0.9740425944328308,0.9980732202529907,0.9989677667617798,0.9978172779083252,0.9840936064720154,0.9(...TRUNCATED) |
"The expression $2\\cdot 3 \\cdot 4\\cdot 5+1$ is equal to 121, since multiplication is carried out (...TRUNCATED) | [" Step 1: To obtain a different value, we need to change the order of operations, which means we ne(...TRUNCATED) | [0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [[0.2689414322376251,0.531209409236908,0.531209409236908,0.7549149990081787,0.6791787147521973],[0.2(...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 8