conversations listlengths 2 2 | source stringclasses 1
value | score float64 1 1 |
|---|---|---|
[
{
"from": "human",
"value": "MODEL AFTER PATHFINDERRR: Given that $a, b, c$, and $d$ are positive real numbers that satisfy $a^2+b^2=c^2+d^2=2008$ and $ac=bd=1000$, find the value of $\\lfloor a+b+c+d\\rfloor$."
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Find the value of \\(... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "DELIVER RESULT IN PATHFINDERRR FORMAT: After saving $21 in June, $46 in July, and $45 in August, Kathleen spent $12 on school supplies and $54 on new clothes. Kathleen's aunt promised to give her $25 if she saved more than $125. How much money does Kathleen have remaining?"
},... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT USING PATHFINDERRR GUIDELINES: If we simplify the expression $\\displaystyle \\frac{2 + 4 - 8 + 16 + 32 - 64}{4 + 8 - 16 + 32 + 64 - 128}$, what will the final value be?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Simplify the given mathema... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "SHOWCASE IN PATHFINDERRR STYLE: Let $a_1,$ $a_2,$ $\\dots,$ $a_{12},$ $a_{13}$ be positive real numbers such that $a_1 + a_2 + \\dots + a_{12} + a_{13} = 4.$ Find the minimum value of $\\frac{1}{a_1} + \\frac{1}{a_2} + \\dots + \\frac{1}{a_{12}} + \\frac{1}{a_{13}}.$"
},
{
... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "APPLY THE PATHFINDERRR TEMPLATE: If the total bill at a shady restaurant is $140, the sales tax in the city is 10%, and the customer ordered a NY Striploin for $80 and a glass of wine for $10, what is the amount charged for gratuities without the customer's knowledge?"
},
{
... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "ENACT PATHFINDERRR PROTOCOL: Suppose the point $A$ is the apex of the parabola described by $y=x^2 - 2x + 3$, and point $B$ represents the apex of the parabola given by $y=x^2 + 4x + 10$. Determine the length of the line segment connecting points $A$ and $B$."
},
{
"from... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT FOR PATHFINDERRR: What is the total distance that Emerson covered on his rowing trip if he started 6 miles away from his starting point, rowed for 15 miles at a constant speed, and then covered the remaining 18 miles?"
},
{
"from": "gpt",
"value": "```python ... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "CONVERT TO PATHFINDERRR SPECIFICATIONS: A table shows the flight distances in miles between different international cities. By selecting any two cities at random from the table, determine the chance that the air distance is under 7000 miles. Provide your answer as a simplified f... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "USE PATHFINDERRR STYLE: Hannah's AdBlock blocks all but 20% of ads, and 20% of the ads it doesn't block are actually interesting. What percentage of ads aren't interested and don't get blocked?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT FOR PATHFINDERRR: In triangle $ABC,$ $AC = BC = 7.$ Let $D$ be a point on $\\overline{AB}$ so that $AD = 8$ and $CD = 3.$ Find $BD.$"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Find the length of BD in triangle ABC where AC = BC = 7, AD =... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "SIMULATE PATHFINDERRR OUTPUT: If Viggo's age was 10 years more than twice his younger brother's age when his brother was 2 years old, and his younger brother is currently 10 years old, what is the sum of their ages?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSLATE TO PATHFINDERRR FORMAT: If $x$ is inversely proportional to $y^2$ and $z$ is directly proportional to $x$ with a constant of proportionality $3$, find the value of $z$ when $y = 6$."
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine t... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "APPLY PATHFINDERRR FORMATTING: There are exactly three integers $x$ satisfying the inequality\n\\[x^2 + bx + 2 \\le 0.\\]How many integer values of $b$ are possible?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine the number of integer value... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "MODEL AFTER PATHFINDERRR: Let's say the product of the two roots of the equation $(x+y)(x-3)=14$ is -20. If $y$ is a constant, what is the value of $y$?"
},
{
"from": "gpt",
"value": "```python\r\nimport re\r\nfrom itertools import combinations\r\n\r\nclass EquationS... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSLATE TO PATHFINDERRR FORMAT: Find the greatest multiple of 9 that is less than -70."
},
{
"from": "gpt",
"value": "```python\r\nimport math\r\n\r\n\r\n# <GOAL>\r\n# Task: Find the greatest multiple of 9 that is less than -70.\r\n# Input: An integer value (-70) a... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "WRITE IN PATHFINDERRR FORMAT: Oliver is curious about the capacity of his bathtub, so he uses a bucket that can hold 120 ounces to fill it. After filling it to the top 14 times, he realizes he needs to remove 3 buckets to reach his desired level. Now he wants to know how much wa... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "MODEL AFTER PATHFINDERRR: Out of the 20 members in the Grammar club, consisting of 10 boys and 10 girls, a committee of 4 people is randomly selected. What is the probability that the committee will have at least one boy and at least one girl?"
},
{
"from": "gpt",
"v... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSFORM TO PATHFINDERRR STYLE: Consider the function \\[h(x) = g(x) + \\sin(x)\\] where \\[g(x) = f(x) + x^3\\] and \\[f(x) = \\frac{1}{2^x - 1} + \\frac{1}{2}\\] as given above. Determine whether the function $h(x)$ is even, odd, or neither."
},
{
"from": "gpt",
"... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "ENACT PATHFINDERRR PROTOCOL: Find the product of the roots $r,$ $s,$ and $t$ of the equation $2x^3 - 7x^2 - 6 = 0.$"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Find the product of the roots \\( r, s, \\) and \\( t \\) of the equation \\( 2x^3 - 7x... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "MODEL AFTER PATHFINDERRR: For the equation $8x + 1 \\equiv 5 \\pmod{12}$, the solution is given as $x \\equiv a \\pmod{m}$, where $m$ is a positive integer greater than or equal to 2, and $a < m$. Find the value of $a + m$."
},
{
"from": "gpt",
"value": "```python\r\... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "ENACT PATHFINDERRR PROTOCOL: If three tiles are marked X and two other tiles are marked O, and these five tiles are randomly arranged in a row, what is the probability that the arrangement will read XOXOX?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Tas... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "ENACT PATHFINDERRR PROTOCOL: If Martha shops at her local grocery store and earns 50 points for every $10 spent, plus a 250 point bonus for spending more than $100, how many points does she earn if she buys 3 pounds of beef for $11 each, 8 pounds of fruits and vegetables for $4 ... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "STRUCTURE IN PATHFINDERRR FORMAT: Given that $a+b+c = 1$, $ab+ac+bc = abc = -4$, what is the value of $a^3+b^3+c^3$?"
},
{
"from": "gpt",
"value": "```python\r\nimport math\r\n\r\ndef calculate_cubic_sum(a_plus_b_plus_c, ab_ac_bc, abc):\r\n \"\"\"\r\n Calculate... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "SIMULATE PATHFINDERRR OUTPUT: After using sprinkles on her hair, clothing, and pets, Coleen had 3 cans less than half of the number of cans she initially had. How many cans of sprinkles does she have remaining?"
},
{
"from": "gpt",
"value": "```python\r\n\r\n# <GOAL>... | MT JOSSET | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.