Search is not available for this dataset
idx int64 0 20.8k | new_prompt stringlengths 4 5.12k | solution stringlengths 17 9.69k | type stringclasses 9
values | my_solu sequencelengths 1 1 | old_prompt stringlengths 104 2.82k | old_solution sequencelengths 1 1 |
|---|---|---|---|---|---|---|
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,417 | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | Mary had 89 stickers.
She used x large stickers on the front page of her journal, which means she used x stickers.
She used 7 stickers each on 6 other pages of her journal, which means she used 7*6 = 42 stickers.
The total number of stickers she used is x + 42.
The number of stickers remaining is 89 - (x + 42).
We are ... | GSM_FOBAR | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... | <bos><start_of_turn>user
Mary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?
If we know the answer to the above question is 44, what is the value of unknown variable x?
Please reason step by st... | [
"<bos><start_of_turn>user\nMary had 89 stickers. She used x large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining?\nIf we know the answer to the above question is 44, what is the value of unknown variable x?\nPlease reason st... |
6,418 | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки
| To find the sum of the six positive integer factors of 18, we first need to list all the factors of 18.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
Now, we add up these six factors: 1 + 2 + 3 + 6 + 9 + 18 = 39.
Next, we find the product of the two smallest factors, which are 1 and 2: 1 × 2 = 2.
Finally, we add th... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... |
6,418 | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки
Step 2: The sum of these factors i... | To find the sum of the six positive integer factors of 18, we first need to list all the factors of 18.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
Now, we add up these six factors: 1 + 2 + 3 + 6 + 9 + 18 = 39.
Next, we find the product of the two smallest factors, which are 1 and 2: 1 × 2 = 2.
Finally, we add th... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... |
6,418 | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки
Step 2: The sum of these factors i... | To find the sum of the six positive integer factors of 18, we first need to list all the factors of 18.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
Now, we add up these six factors: 1 + 2 + 3 + 6 + 9 + 18 = 39.
Next, we find the product of the two smallest factors, which are 1 and 2: 1 × 2 = 2.
Finally, we add th... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... |
6,418 | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки
Step 2: The sum of these factors i... | To find the sum of the six positive integer factors of 18, we first need to list all the factors of 18.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
Now, we add up these six factors: 1 + 2 + 3 + 6 + 9 + 18 = 39.
Next, we find the product of the two smallest factors, which are 1 and 2: 1 × 2 = 2.
Finally, we add th... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... | <bos><start_of_turn>user
If the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf the sum of the six positive integer factors of 18 is added to the product of its two smallest factors, what is the result?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: The positive integer factors of 18 are 1, 2, 3, 6, 9, and 18. ки\nStep 2: The sum of these... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,419 | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the equations as $y = -\frac{1}{2}x + \frac{7t+3}{2}$ and $y = \frac{1}{2}x - t... |
We can solve the given system of equations to find the point of intersection.
First, let's solve for $x$ in terms of $t$ in both equations:
From $x + 2y = 7t + 3$, we have $x = 7t + 3 - 2y$.
From $x - y = 2t - 2$, we have $x = 2t - 2 + y$.
Setting these two expressions for $x$ equal to each other:
$7t + 3 - 2y = ... | MATH_Rephrased | [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... | <bos><start_of_turn>user
Given the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nGiven the lines $x + 2y = 7t + 3$ and $x - y = 2t - 2$, the intersection of these lines forms a line. Find the slope of this line.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the equations as $y = -\\frac{1}{2}x + \\frac{7t+3}{2}$ and $y = \\fra... |
6,420 | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the series as \[\sum_{j=1}^{1000} \left(\frac{1}{j} - \frac{1}{j+1}\right).\] ки
| To find the value of the series, we need to evaluate the sum of the terms from $j=1$ to $j=1000$.
The terms can be written in the form $\frac{1}{j(j+1)}$. Notice that this can be rewritten as $\frac{1}{j} - \frac{1}{j+1}$ using a common denominator.
Now we can rewrite the series as follows:
\begin{align*}
\sum_{j=1}... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Note that the t... | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Using the teles... |
6,420 | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the series as \[\sum_{j=1}^{1000} \left(\frac{1}{j} - \frac{1}{j+1}\right).\] ки
Step 2: Using the telescoping series techniq... | To find the value of the series, we need to evaluate the sum of the terms from $j=1$ to $j=1000$.
The terms can be written in the form $\frac{1}{j(j+1)}$. Notice that this can be rewritten as $\frac{1}{j} - \frac{1}{j+1}$ using a common denominator.
Now we can rewrite the series as follows:
\begin{align*}
\sum_{j=1}... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Using the teles... | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Using the teles... |
6,420 | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the series as \[\sum_{j=1}^{1000} \left(\frac{1}{j} - \frac{1}{j+1}\right).\] ки
Step 2: Using the telescoping series techniq... | To find the value of the series, we need to evaluate the sum of the terms from $j=1$ to $j=1000$.
The terms can be written in the form $\frac{1}{j(j+1)}$. Notice that this can be rewritten as $\frac{1}{j} - \frac{1}{j+1}$ using a common denominator.
Now we can rewrite the series as follows:
\begin{align*}
\sum_{j=1}... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Using the teles... | <bos><start_of_turn>user
Determine the value of the series given by \[\sum_{j=1}^{1000} \frac{1}{j(j + 1)}.\]
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nDetermine the value of the series given by \\[\\sum_{j=1}^{1000} \\frac{1}{j(j + 1)}.\\]\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the series as \\[\\sum_{j=1}^{1000} \\left(\\frac{1}{j} - \\frac{1}{j+1}\\right).\\] ки\nStep 2: Using the teles... |
6,421 | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We start from the inside and work our way out. We have $f(2) = 2^2 - 1 = 3$. ки
| To compute $f(f(f(2)))$, we first need to find $f(2)$.
Since $2 < 4$, we use the first case of the definition of $f(v)$, which gives us $f(2) = 2^2 - 1 = 3$.
Now, we need to compute $f(f(3))$.
Since $3 < 4$, we again use the first case of the definition of $f(v)$, which gives us $f(3) = 3^2 - 1 = 8$.
Finally, we ne... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... |
6,421 | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We start from the inside and work our way out. We have $f(2) = 2^2 - 1 = 3$. ки
St... | To compute $f(f(f(2)))$, we first need to find $f(2)$.
Since $2 < 4$, we use the first case of the definition of $f(v)$, which gives us $f(2) = 2^2 - 1 = 3$.
Now, we need to compute $f(f(3))$.
Since $3 < 4$, we again use the first case of the definition of $f(v)$, which gives us $f(3) = 3^2 - 1 = 8$.
Finally, we ne... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... |
6,421 | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We start from the inside and work our way out. We have $f(2) = 2^2 - 1 = 3$. ки
St... | To compute $f(f(f(2)))$, we first need to find $f(2)$.
Since $2 < 4$, we use the first case of the definition of $f(v)$, which gives us $f(2) = 2^2 - 1 = 3$.
Now, we need to compute $f(f(3))$.
Since $3 < 4$, we again use the first case of the definition of $f(v)$, which gives us $f(3) = 3^2 - 1 = 8$.
Finally, we ne... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... |
6,421 | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We start from the inside and work our way out. We have $f(2) = 2^2 - 1 = 3$. ки
St... | To compute $f(f(f(2)))$, we first need to find $f(2)$.
Since $2 < 4$, we use the first case of the definition of $f(v)$, which gives us $f(2) = 2^2 - 1 = 3$.
Now, we need to compute $f(f(3))$.
Since $3 < 4$, we again use the first case of the definition of $f(v)$, which gives us $f(3) = 3^2 - 1 = 8$.
Finally, we ne... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... |
6,421 | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We start from the inside and work our way out. We have $f(2) = 2^2 - 1 = 3$. ки
St... | To compute $f(f(f(2)))$, we first need to find $f(2)$.
Since $2 < 4$, we use the first case of the definition of $f(v)$, which gives us $f(2) = 2^2 - 1 = 3$.
Now, we need to compute $f(f(3))$.
Since $3 < 4$, we again use the first case of the definition of $f(v)$, which gives us $f(3) = 3^2 - 1 = 8$.
Finally, we ne... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... | <bos><start_of_turn>user
The function \[f(v) =
\begin{cases}
v^2 - 1 & \text{ if }v < 4,
\\ 3v - 2 & \text{ if }v \geq 4.
\end{cases}
\]is given. Compute $f(f(f(2)))$.
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe function \\[f(v) =\n\\begin{cases}\nv^2 - 1 & \\text{ if }v < 4,\n\\\\ 3v - 2 & \\text{ if }v \\geq 4.\n\\end{cases}\n\\]is given. Compute $f(f(f(2)))$.\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We start from the inside and work our way out. We have $f(2... |
6,422 | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can simplify $\dfrac{x^2}{x^3}$ as follows: ки
| To solve this problem, we need to evaluate the expression $\frac{x^2}{x^3}$ using the given value of $x$.
First, let's simplify $x^2$ and $x^3$.
We have $x^2 = \left(7^{\frac{1}{6}}\right)^2 = 7^{\frac{1}{3}}$.
Similarly, $x^3 = \left(7^{\frac{1}{6}}\right)^3 = 7^{\frac{1}{2}}$.
Now, let's substitute these values b... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: \\[\\dfrac{x^2}{x^3} = x^{2-3} = x^{-1}.\\] ки\nStep 3: Since $x = 7^{\\frac{1}{6}}$, w... | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... |
6,422 | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can simplify $\dfrac{x^2}{x^3}$ as follows: ки
Step 2: $\dfrac{x^2}{x^3} = \dfrac{(7^{\frac{1}{6}})^2}{(7^{\frac{1}{6}})^3}$ ки
| To solve this problem, we need to evaluate the expression $\frac{x^2}{x^3}$ using the given value of $x$.
First, let's simplify $x^2$ and $x^3$.
We have $x^2 = \left(7^{\frac{1}{6}}\right)^2 = 7^{\frac{1}{3}}$.
Similarly, $x^3 = \left(7^{\frac{1}{6}}\right)^3 = 7^{\frac{1}{2}}$.
Now, let's substitute these values b... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: U... | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... |
6,422 | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can simplify $\dfrac{x^2}{x^3}$ as follows: ки
Step 2: $\dfrac{x^2}{x^3} = \dfrac{(7^{\frac{1}{6}})^2}{(7^{\frac{1}{6}})^3}$ ки
Step 3: $= \dfrac{7^{\frac{... | To solve this problem, we need to evaluate the expression $\frac{x^2}{x^3}$ using the given value of $x$.
First, let's simplify $x^2$ and $x^3$.
We have $x^2 = \left(7^{\frac{1}{6}}\right)^2 = 7^{\frac{1}{3}}$.
Similarly, $x^3 = \left(7^{\frac{1}{6}}\right)^3 = 7^{\frac{1}{2}}$.
Now, let's substitute these values b... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... |
6,422 | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can simplify $\dfrac{x^2}{x^3}$ as follows: ки
Step 2: $\dfrac{x^2}{x^3} = \dfrac{(7^{\frac{1}{6}})^2}{(7^{\frac{1}{6}})^3}$ ки
Step 3: $= \dfrac{7^{\frac{... | To solve this problem, we need to evaluate the expression $\frac{x^2}{x^3}$ using the given value of $x$.
First, let's simplify $x^2$ and $x^3$.
We have $x^2 = \left(7^{\frac{1}{6}}\right)^2 = 7^{\frac{1}{3}}$.
Similarly, $x^3 = \left(7^{\frac{1}{6}}\right)^3 = 7^{\frac{1}{2}}$.
Now, let's substitute these values b... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... |
6,422 | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can simplify $\dfrac{x^2}{x^3}$ as follows: ки
Step 2: $\dfrac{x^2}{x^3} = \dfrac{(7^{\frac{1}{6}})^2}{(7^{\frac{1}{6}})^3}$ ки
Step 3: $= \dfrac{7^{\frac{... | To solve this problem, we need to evaluate the expression $\frac{x^2}{x^3}$ using the given value of $x$.
First, let's simplify $x^2$ and $x^3$.
We have $x^2 = \left(7^{\frac{1}{6}}\right)^2 = 7^{\frac{1}{3}}$.
Similarly, $x^3 = \left(7^{\frac{1}{6}}\right)^3 = 7^{\frac{1}{2}}$.
Now, let's substitute these values b... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... | <bos><start_of_turn>user
If $x = 7^{\frac{1}{6}}$, what is the value of $\dfrac{x^2}{x^3}$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf $x = 7^{\\frac{1}{6}}$, what is the value of $\\dfrac{x^2}{x^3}$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can simplify $\\dfrac{x^2}{x^3}$ as follows: ки\nStep 2: $\\dfrac{x^2}{x^3} = \\dfrac{(7^{\\frac{1}{6}})^2}{(7^{\\frac{1}{6}})^3}$ ки\nStep 3: $... |
6,423 | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We know that the medians of a triangle intersect at a point, so we can draw a diagram with the... | Let us draw our triangle and medians and label our points of interest: [asy]
pair A, B, C, D, E, F;
A = (0, 8);
B = (-6, 0);
C = (6, 0);
D = (0, 0);
E = (3, 4);
F = (-3, 4);
draw(A--B--C--cycle);
draw(A--D);
draw(B--E);
draw(C--F);
label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, S);
label(... | math | [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... |
6,423 | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We know that the medians of a triangle intersect at a point, so we can draw a diagram with the... | Let us draw our triangle and medians and label our points of interest: [asy]
pair A, B, C, D, E, F;
A = (0, 8);
B = (-6, 0);
C = (6, 0);
D = (0, 0);
E = (3, 4);
F = (-3, 4);
draw(A--B--C--cycle);
draw(A--D);
draw(B--E);
draw(C--F);
label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, S);
label(... | math | [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... |
6,423 | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We know that the medians of a triangle intersect at a point, so we can draw a diagram with the... | Let us draw our triangle and medians and label our points of interest: [asy]
pair A, B, C, D, E, F;
A = (0, 8);
B = (-6, 0);
C = (6, 0);
D = (0, 0);
E = (3, 4);
F = (-3, 4);
draw(A--B--C--cycle);
draw(A--D);
draw(B--E);
draw(C--F);
label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, S);
label(... | math | [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... | <bos><start_of_turn>user
What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nWhat is the sum of the squares of the lengths of the $\\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We know that the medians of a triangle intersect at a point, so we can draw a diagra... |
6,424 | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | We first assume a population of $100$ to facilitate solving. Then we simply organize the statistics given into a Venn diagram.
[asy] pair A,B,C,D,E,F,G; A=(0,55); B=(60,55); C=(60,0); D=(0,0); draw(A--B--C--D--A); E=(30,35); F=(20,20); G=(40,20); draw(circle(E,15)); draw(circle(F,15)); draw(circle(G,15)); draw("$A$",... | math | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... |
6,424 | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | We first assume a population of $100$ to facilitate solving. Then we simply organize the statistics given into a Venn diagram.
[asy] pair A,B,C,D,E,F,G; A=(0,55); B=(60,55); C=(60,0); D=(0,0); draw(A--B--C--D--A); E=(30,35); F=(20,20); G=(40,20); draw(circle(E,15)); draw(circle(F,15)); draw(circle(G,15)); draw("$A$",... | math | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... |
6,424 | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | We first assume a population of $100$ to facilitate solving. Then we simply organize the statistics given into a Venn diagram.
[asy] pair A,B,C,D,E,F,G; A=(0,55); B=(60,55); C=(60,0); D=(0,0); draw(A--B--C--D--A); E=(30,35); F=(20,20); G=(40,20); draw(circle(E,15)); draw(circle(F,15)); draw(circle(G,15)); draw("$A$",... | math | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... |
6,424 | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | We first assume a population of $100$ to facilitate solving. Then we simply organize the statistics given into a Venn diagram.
[asy] pair A,B,C,D,E,F,G; A=(0,55); B=(60,55); C=(60,0); D=(0,0); draw(A--B--C--D--A); E=(30,35); F=(20,20); G=(40,20); draw(circle(E,15)); draw(circle(F,15)); draw(circle(G,15)); draw("$A$",... | math | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... |
6,424 | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | We first assume a population of $100$ to facilitate solving. Then we simply organize the statistics given into a Venn diagram.
[asy] pair A,B,C,D,E,F,G; A=(0,55); B=(60,55); C=(60,0); D=(0,0); draw(A--B--C--D--A); E=(30,35); F=(20,20); G=(40,20); draw(circle(E,15)); draw(circle(F,15)); draw(circle(G,15)); draw("$A$",... | math | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... | <bos><start_of_turn>user
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three f... | [
"<bos><start_of_turn>user\nArnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the t... |
6,425 | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the expression as \[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \] ки
| Let's start by expanding the given expression:
\[ (u^2+v)^2 - (u^2-v)^2 = (u^4 + 2u^2 v + v^2) - (u^4 - 2u^2 v + v^2) \]
Notice that all the terms involving $v^2$ cancel out, leaving us with:
\[ 2u^2 v - (-2u^2 v) = 4u^2 v \]
Now, we can substitute $u=4$ into the expression:
\[ 4u^2 v = 4 \cdot 4^2 v = 64v \]
We ... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... |
6,425 | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the expression as \[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \] ки
Step 2: Substituting $u=4$, ... | Let's start by expanding the given expression:
\[ (u^2+v)^2 - (u^2-v)^2 = (u^4 + 2u^2 v + v^2) - (u^4 - 2u^2 v + v^2) \]
Notice that all the terms involving $v^2$ cancel out, leaving us with:
\[ 2u^2 v - (-2u^2 v) = 4u^2 v \]
Now, we can substitute $u=4$ into the expression:
\[ 4u^2 v = 4 \cdot 4^2 v = 64v \]
We ... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... |
6,425 | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the expression as \[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \] ки
Step 2: Substituting $u=4$, ... | Let's start by expanding the given expression:
\[ (u^2+v)^2 - (u^2-v)^2 = (u^4 + 2u^2 v + v^2) - (u^4 - 2u^2 v + v^2) \]
Notice that all the terms involving $v^2$ cancel out, leaving us with:
\[ 2u^2 v - (-2u^2 v) = 4u^2 v \]
Now, we can substitute $u=4$ into the expression:
\[ 4u^2 v = 4 \cdot 4^2 v = 64v \]
We ... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... |
6,425 | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: We can rewrite the expression as \[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \] ки
Step 2: Substituting $u=4$, ... | Let's start by expanding the given expression:
\[ (u^2+v)^2 - (u^2-v)^2 = (u^4 + 2u^2 v + v^2) - (u^4 - 2u^2 v + v^2) \]
Notice that all the terms involving $v^2$ cancel out, leaving us with:
\[ 2u^2 v - (-2u^2 v) = 4u^2 v \]
Now, we can substitute $u=4$ into the expression:
\[ 4u^2 v = 4 \cdot 4^2 v = 64v \]
We ... | gpt-3.5-turbo | [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... | <bos><start_of_turn>user
The expression \[ (u^2+v)^2 - (u^2-v)^2 \] equals 64 when $u=4$. What is the value of $v$?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nThe expression \\[ (u^2+v)^2 - (u^2-v)^2 \\] equals 64 when $u=4$. What is the value of $v$?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: We can rewrite the expression as \\[(u^2+v)^2 - (u^2-v)^2 = (u^2+v+u^2-v)(u^2+v-u^2+v) = 2(u^4-v^2). \\] ки\nStep 2: Substi... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,426 | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | Tracy feeds each of her two dogs 1.5 cups of food per meal, so each dog consumes 1.5 * 3 = 4.5 cups of food per day.
We know that 1 pound is equal to 2.25 cups of food.
Let's find out how many pounds of food Tracy's x dogs consume. Each dog consumes 4.5 cups of food per day, so x dogs consume 4.5 * x cups of food per d... | GSM_FOBAR | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... | <bos><start_of_turn>user
Tracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?
If we know the answer to the above question is 4, what is the value of unknown variable x?
Please reason step by step.<end... | [
"<bos><start_of_turn>user\nTracy feeds each of her two dogs 1.5 cups of food per meal. She feeds her dogs thrice a day. How many pounds of food do her x dogs consume if 1 pound is equal to 2.25 cups?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?\nPlease reason step by s... |
6,427 | <bos><start_of_turn>user
If Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: If Robi saves $2 in January, $... | Robi saves $2 in January, $4 in February, and $8 in March.
To find out his total savings after 6 months, we need to continue this saving pattern for the next 3 months (April, May, June).
In April, he will save $8 x 2 = $16.
In May, he will save $16 x 2 = $32.
In June, he will save $32 x 2 = $64.
Adding up all the savin... | GSM_Rephrased | [
"<bos><start_of_turn>user\nIf Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: If Robi saves $2 in J... | <bos><start_of_turn>user
If Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: If Robi saves $2 in J... |
6,427 | <bos><start_of_turn>user
If Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?
Please reason step by step.<end_of_turn>
<start_of_turn>model
Step 1: If Robi saves $2 in January, $... | Robi saves $2 in January, $4 in February, and $8 in March.
To find out his total savings after 6 months, we need to continue this saving pattern for the next 3 months (April, May, June).
In April, he will save $8 x 2 = $16.
In May, he will save $16 x 2 = $32.
In June, he will save $32 x 2 = $64.
Adding up all the savin... | GSM_Rephrased | [
"<bos><start_of_turn>user\nIf Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: If Robi saves $2 in J... | <bos><start_of_turn>user
If Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?
Please reason step by step.<end_of_turn>
<start_of_turn>model
| [
"<bos><start_of_turn>user\nIf Robi's new year's resolution is to start saving and he saves $2 in January, $4 in February, and $8 in March, what will be his total savings after 6 months if he continues this saving pattern?\nPlease reason step by step.<end_of_turn>\n<start_of_turn>model\nStep 1: If Robi saves $2 in J... |
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