prompt stringlengths 296 2.22k | answers sequencelengths 4 4 | gt stringlengths 1 260 | rewards sequencelengths 4 4 |
|---|---|---|---|
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Given that $\sin(\frac{\pi}{3} + a) = \frac{5}{12}$, find the value of $\cos(\frac{\pi}{6} - a)$ \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
| [
"<think>\nAlright, let's see. I need to find the value of cos(π/6 - a) given that sin(π/3 + a) = 5/12. Hmm, okay. Let me think about how to connect these two expressions. \n\nFirst, I know that sin and cos are related through complementary angles, right? There's an identity that says sin(θ) = cos(π/2 - θ). Maybe th... | \frac{5}{12} | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Given the product \(\left(\frac{4}{5}\right)\left(\frac{5}{6}\right)\left(\frac{6}{7}\right)\left(\frac{7}{8}\right)\left(\frac{8}{9}\right)\), calculate its value.<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so I need to calculate the value of this product: (4/5)(5/6)(6/7)(7/8)(8/9). Hmm, let's see. I remember that when multiplying fractions, you can multiply the numerators together and the denominators together. But maybe there's a smarter way here because the denominators and numerators seem to follow... | \frac{4}{9} | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Expand $(x-3)(x+3)(x^2+5)$.<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so I need to expand the expression \\((x - 3)(x + 3)(x^2 + 5)\\). Hmm, let's see. I remember that when you have two binomials multiplied together, like \\((a + b)(a - b)\\), the result is \\(a^2 - b^2\\). That's the difference of squares formula. Maybe I can apply that here first with the first two ... | x^4 - 4x^2 - 45 | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Suppose $g(x) = -3$ for all real numbers $x$. What is the value of $g(3x - 5)$?<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so I need to find the value of g(3x - 5) given that the function g(x) is always equal to -3 for any real number x. Hmm, let's break this down step by step. \n\nFirst, I remember that functions like g(x) = -3 are considered constant functions. A constant function has the same output value regardless ... | -3 | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
The areas of two squares are in the ratio $49:64$. What is the ratio of their perimeters? Express your answer in the form $a:b$.<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, let me think. The problem says the areas of two squares are in the ratio 49:64, and we need to find the ratio of their perimeters. Hmm, right. I remember that the area of a square is side length squared, and the perimeter is four times the side length. So maybe I can use the relationship between the... | 7:8 | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Find the remainder when $7 \times 17 \times 27 \times 37 \times \ldots \times 187 \times 197$ is divided by $5$.<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so I need to find the remainder when the product of a bunch of numbers starting at 7 and going up by 10 each time, all the way to 197, is divided by 5. The product is 7 × 17 × 27 × 37 × ... × 187 × 197. Hmm, let me break this down.\n\nFirst, I remember that to find remainders when dealing with produ... | 1 | [
true,
false,
true,
true
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. The question is asking for the constant ter(...TRUNCATED) | 60 | [
true,
true,
true,
true
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nAlright, so I need to figure out the probability that when I randomly pick two numbers fr(...TRUNCATED) | \dfrac{1}{3} | [
true,
true,
true,
true
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nAlright, let's see. The problem is about Konstantin walking from school to home, covering(...TRUNCATED) | a \in \left[60, \frac{18000}{299}\right) | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, so I need to figure out the exact cost of one book when given that nine books cost (...TRUNCATED) | 1 \text{ ruble } 23 \text{ kopeks} | [
false,
false,
false,
false
] |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 5