RaML Data
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"For each value of $x,$ $g(x)$ is defined to be the minimum value of the three numbers $3x + 3,$ $x (...TRUNCATED) |
6
| ["Okay, so I've been given this problem where for each value of x, g(x) is defined as the minimum of(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"Given a square $ABCD$. Let $P\\in{AB},\\ Q\\in{BC},\\ R\\in{CD}\\ S\\in{DA}$ and $PR\\parallel BC,\(...TRUNCATED) |
10
| ["Okay, so I have this geometry problem about a square ABCD. Let me try to visualize it first. A squ(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"In the number $86549.2047$, calculate the ratio of the value of the place occupied by the digit 6 t(...TRUNCATED) |
10,000
| ["Okay, so I have this number: 86549.2047. I need to find the ratio of the value of the place occupi(...TRUNCATED) | [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1(...TRUNCATED) |
"Let $f(x) = x^2 + 6x + c$ for all real numbers $x$, where $c$ is some real number. For what values (...TRUNCATED) |
c = \frac{11 - \sqrt{13}}{2}
| ["Okay, so I have this problem: Given the function f(x) = x² + 6x + c, where c is some real number.(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1(...TRUNCATED) |
"The theme park records the duration of each of the 19 most popular attractions in minutes and secon(...TRUNCATED) |
105
| ["First, I need to list all the durations from the stem-and-leaf plot in order. Each entry consists (...TRUNCATED) | [1,1,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1(...TRUNCATED) |
Let $ABCDEFGH$ denote a cube with a side length of 2. Find the volume of pyramid $ABCG$.
|
\frac{4}{3}
| ["Alright, so I have this problem: there's a cube named ABCDEFGH with each side length being 2. I ne(...TRUNCATED) | [1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"On a table, there are 100 identical-looking coins, of which 85 are counterfeit and 15 are real. You(...TRUNCATED) |
Yes
| ["Okay, so I've got this problem where there are 100 coins on a table, and 85 of them are counterfei(...TRUNCATED) | [0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) |
"In how many ways can the digits of $45,\\!520$ be arranged to form a 5-digit number? (Remember, nu(...TRUNCATED) |
48
| ["Alright, so I have this problem: I need to figure out how many ways the digits of 45,520 can be ar(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"Solve the equation $x(5x - 11) = -2$ and express the solutions in the form $\\frac{m+\\sqrt{n}}{p}$(...TRUNCATED) |
102
| ["Alright, so I have this equation to solve: \\( x(5x - 11) = -2 \\). Hmm, okay. I think I need to s(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"Find all increasing sequences $a_1,a_2,a_3,...$ of natural numbers such that for each $i,j\\in \\ma(...TRUNCATED) |
a_n = n
| ["Alright, so I've come across this interesting problem where I need to find all increasing sequence(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
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