problem string | answer string | tokenized_prompt string | responses list | rewards list | mean_reward float64 | sources list | solution string | answer_source string | gemini_solution_reward int64 | gemini_solution list |
|---|---|---|---|---|---|---|---|---|---|---|
A rectangular pyramid has a base length and width of 7 feet and 5 feet, respectively, and a height of 8 feet. One of its edges is perpendicular to the base. What is the surface area of the circumscribed sphere of this pyramid? Express your answer in square feet, including Ο. | 138\pi | <|im_start|>user
A rectangular pyramid has a base length and width of 7 feet and 5 feet, respectively, and a height of 8 feet. One of its edges is perpendicular to the base. What is the surface area of the circumscribed sphere of this pyramid? Express your answer in square feet, including Ο.<|im_end|>
<|im_start|>assis... | [
"We are given a **rectangular pyramid** with:\n\n- Base length = 7 feet \n- Base width = 5 feet \n- Height = 8 feet \n- One edge is perpendicular to the base (this just confirms it's a right rectangular pyramid)\n\nWe are asked to find the **surface area of the circumscribed sphere** of this pyramid β that is, a... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "A rectangular pyramid has a base length and width of 7 feet and 5 feet, respectively, and a height of 8 feet. One of its edges is perpendicular to the base. What is the surface area of the circumscribed sphere of this pyramid? Express your answer in square feet, including Ο.",
"role": "user"
... |
The complex number z satisfies z/(z-i) = i. Determine the quadrant in which the point corresponding to z in the complex plane is located. Express your answer as the quadrant number (I, II, III, or IV). | I | <|im_start|>user
The complex number z satisfies z/(z-i) = i. Determine the quadrant in which the point corresponding to z in the complex plane is located. Express your answer as the quadrant number (I, II, III, or IV).<|im_end|>
<|im_start|>assistant
| [
"We are given the equation involving a complex number $ z $:\n\n$$\n\\frac{z}{z - i} = i\n$$\n\nWe need to solve for $ z $, and then determine which quadrant in the complex plane it lies in.\n\n---\n\n### Step 1: Multiply both sides by $ z - i $\n\n$$\nz = i(z - i)\n$$\n\nDistribute the right-hand side:\n\n$$\nz = ... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "The complex number z satisfies z/(z-i) = i. Determine the quadrant in which the point corresponding to z in the complex plane is located. Express your answer as the quadrant number (I, II, III, or IV).",
"role": "user"
},
{
"content": "To determine the quadrant in which the point corre... |
Given the average of a sample x_1, x_2,..., x_n is \\bar{x} and the average of another sample y_1, y_2,..., y_m is \\bar{y} (\\bar{x} \\neq \\bar{y}), if the average of the combined sample x_1, x_2,..., x_n, y_1, y_2,..., y_m is z = a\\bar{x} + (1-a)\\bar{y}, where 0 < a < \\frac{1}{2}, determine the relationship betwe... | n > m | <|im_start|>user
Given the average of a sample x_1, x_2,..., x_n is \\bar{x} and the average of another sample y_1, y_2,..., y_m is \\bar{y} (\\bar{x} \\neq \\bar{y}), if the average of the combined sample x_1, x_2,..., x_n, y_1, y_2,..., y_m is z = a\\bar{x} + (1-a)\\bar{y}, where 0 < a < \\frac{1}{2}, determine the r... | [
"We are given:\n\n- The average of sample $ x_1, x_2, \\ldots, x_n $ is $ \\bar{x} $.\n- The average of sample $ y_1, y_2, \\ldots, y_m $ is $ \\bar{y} $, with $ \\bar{x} \\ne \\bar{y} $.\n- The average of the **combined** sample (all $ x_i $ and $ y_j $) is:\n\n$$\nz = a\\bar{x} + (1 - a)\\bar{y}\n$$\n\nwhere $ 0 ... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 0 | [
{
"content": "Given the average of a sample x_1, x_2,..., x_n is \\\\bar{x} and the average of another sample y_1, y_2,..., y_m is \\\\bar{y} (\\\\bar{x} \\\\neq \\\\bar{y}), if the average of the combined sample x_1, x_2,..., x_n, y_1, y_2,..., y_m is z = a\\\\bar{x} + (1-a)\\\\bar{y}, where 0 < a < \\\\frac{1... |
In an equilateral triangle ABC with side length β2, let βAB = βc, βBC = βa, and βCA = βb. Calculate the sum of the dot products of vectors a, b, and c, i.e., βa Β· βb + βb Β· βc + βc Β· βa. Express your answer as a single integer. | = -3 | <|im_start|>user
In an equilateral triangle ABC with side length β2, let βAB = βc, βBC = βa, and βCA = βb. Calculate the sum of the dot products of vectors a, b, and c, i.e., βa Β· βb + βb Β· βc + βc Β· βa. Express your answer as a single integer.<|im_end|>
<|im_start|>assistant
| [
"We are given an **equilateral triangle ABC** with side length $ \\sqrt{2} $, and vectors defined as:\n\n- $ \\vec{AB} = \\vec{c} $\n- $ \\vec{BC} = \\vec{a} $\n- $ \\vec{CA} = \\vec{b} $\n\nWe are to compute the sum of dot products:\n\n$$\n\\vec{a} \\cdot \\vec{b} + \\vec{b} \\cdot \\vec{c} + \\vec{c} \\cdot \\vec... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "In an equilateral triangle ABC with side length β2, let βAB = βc, βBC = βa, and βCA = βb. Calculate the sum of the dot products of vectors a, b, and c, i.e., βa Β· βb + βb Β· βc + βc Β· βa. Express your answer as a single integer.",
"role": "user"
},
{
"content": "Here is the step-by-step... |
Ten people are each waiting for a 45-minute operation. The first operation starts at 8:00 a.m., the second at 8:15 a.m., and each of the other operations starts at 15-minute intervals thereafter. What is the end time of the last operation? Express your answer in 12-hour clock format (e.g., 11:00 a.m.). | 11:00 a.m. | <|im_start|>user
Ten people are each waiting for a 45-minute operation. The first operation starts at 8:00 a.m., the second at 8:15 a.m., and each of the other operations starts at 15-minute intervals thereafter. What is the end time of the last operation? Express your answer in 12-hour clock format (e.g., 11:00 a.m.).... | [
"We are given:\n\n- 10 people are each waiting for a 45-minute operation.\n- Operations start at 8:00 a.m., then every 15 minutes after that.\n- The first operation starts at 8:00 a.m., the second at 8:15 a.m., and so on.\n- Each operation lasts 45 minutes.\n- We are to find the **end time of the last operation** (... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "Ten people are each waiting for a 45-minute operation. The first operation starts at 8:00 a.m., the second at 8:15 a.m., and each of the other operations starts at 15-minute intervals thereafter. What is the end time of the last operation? Express your answer in 12-hour clock format (e.g., 11:00 a... |
Today is Wednesday. What day of the week will it be 100 days from now? Express your answer as the name of a day of the week. | Friday | <|im_start|>user
Today is Wednesday. What day of the week will it be 100 days from now? Express your answer as the name of a day of the week.<|im_end|>
<|im_start|>assistant
| [
"We are given that **today is Wednesday**, and we want to find out what day of the week it will be **100 days from now**.\n\n---\n\n### Step 1: Understand the cycle of days\nThe days of the week repeat every **7 days**. So, to find the day of the week 100 days from now, we can compute the **remainder when 100 is di... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "Today is Wednesday. What day of the week will it be 100 days from now? Express your answer as the name of a day of the week.",
"role": "user"
},
{
"content": "Here's how to solve it:\n\n1. There are 7 days in a week.\n2. Divide 100 by 7: 100 Γ· 7 = 14 with a remainder of 2.\n3. This ... |
The second class starts at 9:25, and each class lasts for 35 minutes. Find the time when the second class ends. Express your answer in 12-hour clock format (HH:MM). | 10:00 | <|im_start|>user
The second class starts at 9:25, and each class lasts for 35 minutes. Find the time when the second class ends. Express your answer in 12-hour clock format (HH:MM).<|im_end|>
<|im_start|>assistant
| [
"The second class starts at **9:25** and lasts for **35 minutes**.\n\nTo find the end time:\n\nAdd 35 minutes to 9:25.\n\n- 9:25 + 35 minutes = 10:00\n\nβ
So, the second class ends at **10:00**.\n\nIn **12-hour clock format**, that is:\n\n**10:00** β
\n\nπ Final answer: **10:00**",
"The second class starts at **9... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "The second class starts at 9:25, and each class lasts for 35 minutes. Find the time when the second class ends. Express your answer in 12-hour clock format (HH:MM).",
"role": "user"
},
{
"content": "To find the end time of the second class, you need to add the duration of the class to ... |
Given the function f(x) = 1/2 * x^2 - ln(x), find the interval on which the function is monotonically decreasing. Express your answer as an interval, e.g., (a, b]. | (0, 1] | <|im_start|>user
Given the function f(x) = 1/2 * x^2 - ln(x), find the interval on which the function is monotonically decreasing. Express your answer as an interval, e.g., (a, b].<|im_end|>
<|im_start|>assistant
| [
"We are given the function:\n\n$$\nf(x) = \\frac{1}{2}x^2 - \\ln(x)\n$$\n\nWe are to find the interval on which the function is **monotonically decreasing**.\n\n---\n\n### Step 1: Determine the domain\n\nSince $\\ln(x)$ is only defined for $x > 0$, the **domain** of $f(x)$ is:\n\n$$\n(0, \\infty)\n$$\n\n---\n\n### ... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "Given the function f(x) = 1/2 * x^2 - ln(x), find the interval on which the function is monotonically decreasing. Express your answer as an interval, e.g., (a, b].",
"role": "user"
},
{
"content": "To find the interval on which the function is monotonically decreasing, we need to find ... |
Find the instantaneous rate of change of the curve $y=xe^{x}$ at the point $(1,1)$. Express your answer as a numerical value. | 2e | <|im_start|>user
Find the instantaneous rate of change of the curve $y=xe^{x}$ at the point $(1,1)$. Express your answer as a numerical value.<|im_end|>
<|im_start|>assistant
| [
"We are given the function:\n\n$$\ny = x e^x\n$$\n\nand asked to find the **instantaneous rate of change** at the point $(1, 1)$.\n\n---\n\n### Step 1: Find the derivative\n\nThe instantaneous rate of change is given by the derivative $ \\frac{dy}{dx} $.\n\nUse the **product rule**:\n\n$$\n\\frac{d}{dx}(x e^x) = \\... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "Find the instantaneous rate of change of the curve $y=xe^{x}$ at the point $(1,1)$. Express your answer as a numerical value.",
"role": "user"
},
{
"content": "Of course. Here is the step-by-step solution.\n\nThe instantaneous rate of change of a curve at a specific point is given by t... |
There are four balls that look the same but have different weights, denoted as $a$, $b$, $c$, and $d$. Given the inequalities $a+b=c+d$, $a+d>b+c$, and $a+c<b$, find the order of these four balls from heaviest to lightest. Express your answer as a sequence of variables, using '>' to denote 'heavier than' (e.g., d>b>a>c... | d>b>a>c | <|im_start|>user
There are four balls that look the same but have different weights, denoted as $a$, $b$, $c$, and $d$. Given the inequalities $a+b=c+d$, $a+d>b+c$, and $a+c<b$, find the order of these four balls from heaviest to lightest. Express your answer as a sequence of variables, using '>' to denote 'heavier tha... | [
"We are given four balls with different weights $ a, b, c, d $, and three inequalities:\n\n1. $ a + b = c + d $ \n2. $ a + d > b + c $ \n3. $ a + c < b $\n\nWe are to determine the order of the balls from **heaviest to lightest**.\n\n---\n\n### Step 1: Use the first equation: $ a + b = c + d $\n\nThis tells us th... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 1 | [
{
"content": "There are four balls that look the same but have different weights, denoted as $a$, $b$, $c$, and $d$. Given the inequalities $a+b=c+d$, $a+d>b+c$, and $a+c<b$, find the order of these four balls from heaviest to lightest. Express your answer as a sequence of variables, using '>' to denote 'heavie... |
What is the output of the given program when the input is 6? Express your answer as a numerical value. | 720 | <|im_start|>user
What is the output of the given program when the input is 6? Express your answer as a numerical value.<|im_end|>
<|im_start|>assistant
| [
"It seems that your question refers to \"the given program,\" but no program was actually provided in your message. Could you please share the program or code you're referring to so I can determine the output when the input is 6?\n\nOnce I have the program, Iβll be able to simulate its behavior with input 6 and giv... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0... | 0 | [
"nvidia/AceReason-Math"
] | null | null | 0 | [
{
"content": "What is the output of the given program when the input is 6? Express your answer as a numerical value.",
"role": "user"
},
{
"content": "Here is a step-by-step analysis of the program's execution with the input `6`.\n\n### Program Logic\n\n1. **Initialization**: An integer variable `c... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.