completion stringlengths 1.63k 38.1k | query stringlengths 1.39k 6.55k |
|---|---|
<think>
Okay, let's tackle this problem step by step. The operation ⊗ is defined as a ⊗ b = a² / b. I need to find the value of [(1 ⊗ 2) ⊗ 3] minus [1 ⊗ (2 ⊗ 3)].
First, I remember from the cheatsheet that when dealing with nonstandard operations like ⊗, I should treat them as functions and apply them consistently. A... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to figure out this problem step by step. So, Doug has made a square window using 8 equal-size panes of glass. Each pane has a height to width ratio of 5:2. The borders around and between the panes are 2 inches wide. We need to find the side length of the square window.
First, I need to visualiz... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to tackle this problem step by step. First, let me make sure I understand the question correctly. We have a polynomial P(x) of degree 3n. The problem gives us specific values of P(x) at various points. Specifically:
- P(0) = P(3) = ... = P(3n) = 2
- P(1) = P(4) = ... = P(3n+1 - 2) = 1
- P(2) = ... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the cheatsheet provided. The function is given as f(x) = a x² - √2, and we need to find the value of a such that f(f(√2)) = -√2. Alright, let's break this down.
First, I need to compute f(√2). Let me substitute x with √2 in the function. So, f(√2) = a*(√... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's see. The problem is asking how many mathematics students at Euclid Middle School are taking the AMC 8 contest this year. The information given is the number of students in each teacher's class: Mrs. Germain has 11, Mr. Newton has 8, and Mrs. Young has 9.
First, I need to figure out if these groups... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's see. I need to find the value of N such that the sum of these numbers 991, 993, 995, 997, 999 equals 5000 minus N. So, the equation is 991 + 993 + 995 + 997 + 999 = 5000 - N. My goal is to solve for N.
First, maybe I should calculate the sum on the left side. Let me add those numbers up. But adding... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's see. The problem is about figuring out how much money you save by buying an appliance from the TV advertiser instead of the in-store price. The in-store price is $99.99. The TV offer has three payments of $29.98 each plus a one-time shipping charge of $9.98. I need to find the difference in cents be... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the given cheatsheet. First, I need to visualize the setup. Points A, B, C, D, E, F are on a straight line AF, each segment between them is length 1. So AF is divided into five equal parts. Then there's a point G not on AF, and points H on GD and J on GF.... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's see. Judy had 35 hits in total. Out of these, there are different types: 1 home run, 1 triple, 5 doubles, and the rest are singles. The question is asking what percent of her hits were singles.
First, I need to figure out how many singles she has. Since the total hits are 35, and the other categori... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the cheatsheet provided. The question is about rotating the graph of y = log₁₀x 90 degrees counter-clockwise around the origin and finding the equation of the new graph G'.
First, I remember from the cheatsheet that a 90° counter-clockwise rotation about... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the given cheatsheet. The problem says that there's a set of consecutive positive integers starting from 1, and one number is erased. The average of the remaining numbers is 35 and 7/17. We need to find out which number was erased.
First, let me recall t... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step. So, the question is about a rectangular yard with two flower beds shaped as congruent isosceles right triangles. The rest of the yard is a trapezoid with parallel sides of 15 and 25 meters. We need to find the fraction of the yard occupied by the flower beds.
... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step. The question is asking for the sum of all possible values of t between 0 and 360 degrees such that the triangle formed by the three points on the unit circle is isosceles. The three points are (cos40°, sin40°), (cos60°, sin60°), and (cos t°, sin t°).
First, ... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 2