<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a specific hyperbola, the center is at $(1,-1),$ one focus is at $(1 + \sqrt{45},-1),$ and one vertex is at $(7,-1).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a specific hyperbola, the center is at $(1,-1),$ one focus is at $(1 + \sqrt{45},-1),$ and one vertex is at $(7,-1).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$<|im_end|>
<|im_start|>assistant
<Z_477><Z_242><Z_223><Z_68><Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a specific hyperbola, the center is at $(1,-1),$ one focus is at $(1 + \sqrt{45},-1),$ and one vertex is at $(7,-1).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$<|im_end|>
<|im_start|>assistant
<Z_405><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a specific hyperbola, the center is at $(1,-1),$ one focus is at $(1 + \sqrt{45},-1),$ and one vertex is at $(7,-1).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$<|im_end|>
<|im_start|>assistant
<Z_445><Z_503><Z_334><Z_443><Z_204><ANSWER>

Question:
In a specific hyperbola, the center is at $(1,-1),$ one focus is at $(1 + \sqrt{45},-1),$ and one vertex is at $(7,-1).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]
Find $h + k + a + b.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the units digit of $9 \cdot 19 \cdot 1989 - 9^3$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the units digit of $9 \cdot 19 \cdot 1989 - 9^3$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_393><Z_425><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the units digit of $9 \cdot 19 \cdot 1989 - 9^3$.<|im_end|>
<|im_start|>assistant
<Z_162><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the units digit of $9 \cdot 19 \cdot 1989 - 9^3$.<|im_end|>
<|im_start|>assistant
<Z_463><Z_365><Z_433><ANSWER>

Question: Calculate the units digit of $9 \cdot 19 \cdot 1989 - 9^3$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many pairs of positive integers \( (m, n) \) satisfy \( m^2 + n < 50 \)?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many pairs of positive integers \( (m, n) \) satisfy \( m^2 + n < 50 \)?<|im_end|>
<|im_start|>assistant
<Z_369><Z_82><Z_34><Z_202><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many pairs of positive integers \( (m, n) \) satisfy \( m^2 + n < 50 \)?<|im_end|>
<|im_start|>assistant
<Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many pairs of positive integers \( (m, n) \) satisfy \( m^2 + n < 50 \)?<|im_end|>
<|im_start|>assistant
<Z_70><Z_337><Z_36><Z_52><ANSWER>

Question: How many pairs of positive integers \( (m, n) \) satisfy \( m^2 + n < 50 \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school has a total of 2000 students, with the number of male and female students in each grade shown in the table. It is known that the probability of randomly selecting a female student from the second year of high school from all students in the school is 0.19. Using stratified sampling by grade to select 100 students from the entire school, calculate the number of students that should be selected from the third year of high school.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school has a total of 2000 students, with the number of male and female students in each grade shown in the table. It is known that the probability of randomly selecting a female student from the second year of high school from all students in the school is 0.19. Using stratified sampling by grade to select 100 students from the entire school, calculate the number of students that should be selected from the third year of high school.<|im_end|>
<|im_start|>assistant
<Z_24><Z_494><Z_194><Z_206><Z_469><Z_274><Z_452><Z_317><Z_257><Z_159><Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school has a total of 2000 students, with the number of male and female students in each grade shown in the table. It is known that the probability of randomly selecting a female student from the second year of high school from all students in the school is 0.19. Using stratified sampling by grade to select 100 students from the entire school, calculate the number of students that should be selected from the third year of high school.<|im_end|>
<|im_start|>assistant
<Z_367><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school has a total of 2000 students, with the number of male and female students in each grade shown in the table. It is known that the probability of randomly selecting a female student from the second year of high school from all students in the school is 0.19. Using stratified sampling by grade to select 100 students from the entire school, calculate the number of students that should be selected from the third year of high school.<|im_end|>
<|im_start|>assistant
<Z_366><Z_283><Z_305><Z_243><Z_249><Z_328><Z_182><Z_60><Z_405><Z_394><Z_161><ANSWER>

Question: A school has a total of 2000 students, with the number of male and female students in each grade shown in the table. It is known that the probability of randomly selecting a female student from the second year of high school from all students in the school is 0.19. Using stratified sampling by grade to select 100 students from the entire school, calculate the number of students that should be selected from the third year of high school.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex bakes a total of $36$ pies. Each pie is one of four types: apple, blueberry, cherry, or peach. The ratio of apple to blueberry to cherry to peach pies is $1:4:3:2$. How many peach pies did Alex bake?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex bakes a total of $36$ pies. Each pie is one of four types: apple, blueberry, cherry, or peach. The ratio of apple to blueberry to cherry to peach pies is $1:4:3:2$. How many peach pies did Alex bake?<|im_end|>
<|im_start|>assistant
<Z_24><Z_341><Z_199><Z_184><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex bakes a total of $36$ pies. Each pie is one of four types: apple, blueberry, cherry, or peach. The ratio of apple to blueberry to cherry to peach pies is $1:4:3:2$. How many peach pies did Alex bake?<|im_end|>
<|im_start|>assistant
<Z_496><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex bakes a total of $36$ pies. Each pie is one of four types: apple, blueberry, cherry, or peach. The ratio of apple to blueberry to cherry to peach pies is $1:4:3:2$. How many peach pies did Alex bake?<|im_end|>
<|im_start|>assistant
<Z_81><Z_315><Z_334><Z_81><ANSWER>

Question: Alex bakes a total of $36$ pies. Each pie is one of four types: apple, blueberry, cherry, or peach. The ratio of apple to blueberry to cherry to peach pies is $1:4:3:2$. How many peach pies did Alex bake?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul had some pens and 143 books. After selling some books and pens in a garage sale, he had 113 books and 19 pens left. He sold 23 pens in the garage sale. How many pens did Paul have initially?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul had some pens and 143 books. After selling some books and pens in a garage sale, he had 113 books and 19 pens left. He sold 23 pens in the garage sale. How many pens did Paul have initially?<|im_end|>
<|im_start|>assistant
<Z_477><Z_144><Z_268><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul had some pens and 143 books. After selling some books and pens in a garage sale, he had 113 books and 19 pens left. He sold 23 pens in the garage sale. How many pens did Paul have initially?<|im_end|>
<|im_start|>assistant
<Z_459><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul had some pens and 143 books. After selling some books and pens in a garage sale, he had 113 books and 19 pens left. He sold 23 pens in the garage sale. How many pens did Paul have initially?<|im_end|>
<|im_start|>assistant
<Z_393><Z_347><Z_219><ANSWER>

Question: Paul had some pens and 143 books. After selling some books and pens in a garage sale, he had 113 books and 19 pens left. He sold 23 pens in the garage sale. How many pens did Paul have initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f(x) = \log_{3}(x+6)$, and its inverse function be $f^{-1}(x)$. If $\left[f^{-1}(m)+6\right]\left[f^{-1}(n)+6\right]=27$, then $f(m+n)=$ ?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f(x) = \log_{3}(x+6)$, and its inverse function be $f^{-1}(x)$. If $\left[f^{-1}(m)+6\right]\left[f^{-1}(n)+6\right]=27$, then $f(m+n)=$ ?<|im_end|>
<|im_start|>assistant
<Z_369><Z_199><Z_211><Z_410><Z_151><Z_81><Z_307><Z_115><Z_49><Z_159><Z_454><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f(x) = \log_{3}(x+6)$, and its inverse function be $f^{-1}(x)$. If $\left[f^{-1}(m)+6\right]\left[f^{-1}(n)+6\right]=27$, then $f(m+n)=$ ?<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f(x) = \log_{3}(x+6)$, and its inverse function be $f^{-1}(x)$. If $\left[f^{-1}(m)+6\right]\left[f^{-1}(n)+6\right]=27$, then $f(m+n)=$ ?<|im_end|>
<|im_start|>assistant
<Z_468><Z_76><Z_79><Z_97><Z_46><Z_131><Z_106><Z_16><Z_476><Z_206><Z_262><ANSWER>

Question: Let $f(x) = \log_{3}(x+6)$, and its inverse function be $f^{-1}(x)$. If $\left[f^{-1}(m)+6\right]\left[f^{-1}(n)+6\right]=27$, then $f(m+n)=$ ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A die has the shape of a regular tetrahedron, with the four faces having 1, 2, 3, and 4 pips. The die is placed with 4 pips face down in one corner of the triangular grid, so that the face with 4 pips precisely covers the triangle marked with 4 pips.

The die is now 'rolled' by rotating about an edge without slipping, so that 1 pip is face down. It is rolled again, so that 2 pips are face down, as indicated. The rolling continues until the die rests on the shaded triangle in the opposite corner of the grid.

How many pips are now face down?
A 1
B 2
C 3
D 4
E it depends on the route taken<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A die has the shape of a regular tetrahedron, with the four faces having 1, 2, 3, and 4 pips. The die is placed with 4 pips face down in one corner of the triangular grid, so that the face with 4 pips precisely covers the triangle marked with 4 pips.

The die is now 'rolled' by rotating about an edge without slipping, so that 1 pip is face down. It is rolled again, so that 2 pips are face down, as indicated. The rolling continues until the die rests on the shaded triangle in the opposite corner of the grid.

How many pips are now face down?
A 1
B 2
C 3
D 4
E it depends on the route taken<|im_end|>
<|im_start|>assistant
<Z_369><Z_64><Z_352><Z_503><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A die has the shape of a regular tetrahedron, with the four faces having 1, 2, 3, and 4 pips. The die is placed with 4 pips face down in one corner of the triangular grid, so that the face with 4 pips precisely covers the triangle marked with 4 pips.

The die is now 'rolled' by rotating about an edge without slipping, so that 1 pip is face down. It is rolled again, so that 2 pips are face down, as indicated. The rolling continues until the die rests on the shaded triangle in the opposite corner of the grid.

How many pips are now face down?
A 1
B 2
C 3
D 4
E it depends on the route taken<|im_end|>
<|im_start|>assistant
<Z_384><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A die has the shape of a regular tetrahedron, with the four faces having 1, 2, 3, and 4 pips. The die is placed with 4 pips face down in one corner of the triangular grid, so that the face with 4 pips precisely covers the triangle marked with 4 pips.

The die is now 'rolled' by rotating about an edge without slipping, so that 1 pip is face down. It is rolled again, so that 2 pips are face down, as indicated. The rolling continues until the die rests on the shaded triangle in the opposite corner of the grid.

How many pips are now face down?
A 1
B 2
C 3
D 4
E it depends on the route taken<|im_end|>
<|im_start|>assistant
<Z_341><Z_210><Z_142><Z_18><ANSWER>

Question:
A die has the shape of a regular tetrahedron, with the four faces having 1, 2, 3, and 4 pips. The die is placed with 4 pips face down in one corner of the triangular grid, so that the face with 4 pips precisely covers the triangle marked with 4 pips.

The die is now 'rolled' by rotating about an edge without slipping, so that 1 pip is face down. It is rolled again, so that 2 pips are face down, as indicated. The rolling continues until the die rests on the shaded triangle in the opposite corner of the grid.

How many pips are now face down?
A 1
B 2
C 3
D 4
E it depends on the route taken


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence of integers \(a_0, a_1, \cdots\) and a sequence of positive integers \(b_0, b_1, \cdots\), such that \(a_0 = 0\) and \(a_1 = 1\), for any positive integer \(n\), we have
\[
a_{n+1} =
\begin{cases}
a_n b_n + a_{n-1}, & b_{n-1} = 1; \\
a_n b_n - a_{n-1}, & b_{n-1} > 1.
\end{cases}
\]

Prove: Among \(a_{2017}\) and \(a_{2018}\), at least one of them is not less than 2017.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence of integers \(a_0, a_1, \cdots\) and a sequence of positive integers \(b_0, b_1, \cdots\), such that \(a_0 = 0\) and \(a_1 = 1\), for any positive integer \(n\), we have
\[
a_{n+1} =
\begin{cases}
a_n b_n + a_{n-1}, & b_{n-1} = 1; \\
a_n b_n - a_{n-1}, & b_{n-1} > 1.
\end{cases}
\]

Prove: Among \(a_{2017}\) and \(a_{2018}\), at least one of them is not less than 2017.<|im_end|>
<|im_start|>assistant
<Z_24><Z_159><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence of integers \(a_0, a_1, \cdots\) and a sequence of positive integers \(b_0, b_1, \cdots\), such that \(a_0 = 0\) and \(a_1 = 1\), for any positive integer \(n\), we have
\[
a_{n+1} =
\begin{cases}
a_n b_n + a_{n-1}, & b_{n-1} = 1; \\
a_n b_n - a_{n-1}, & b_{n-1} > 1.
\end{cases}
\]

Prove: Among \(a_{2017}\) and \(a_{2018}\), at least one of them is not less than 2017.<|im_end|>
<|im_start|>assistant
<Z_452><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence of integers \(a_0, a_1, \cdots\) and a sequence of positive integers \(b_0, b_1, \cdots\), such that \(a_0 = 0\) and \(a_1 = 1\), for any positive integer \(n\), we have
\[
a_{n+1} =
\begin{cases}
a_n b_n + a_{n-1}, & b_{n-1} = 1; \\
a_n b_n - a_{n-1}, & b_{n-1} > 1.
\end{cases}
\]

Prove: Among \(a_{2017}\) and \(a_{2018}\), at least one of them is not less than 2017.<|im_end|>
<|im_start|>assistant
<Z_139><Z_35><Z_28><ANSWER>

Question:
Given a sequence of integers \(a_0, a_1, \cdots\) and a sequence of positive integers \(b_0, b_1, \cdots\), such that \(a_0 = 0\) and \(a_1 = 1\), for any positive integer \(n\), we have
\[
a_{n+1} =
\begin{cases}
a_n b_n + a_{n-1}, & b_{n-1} = 1; \\
a_n b_n - a_{n-1}, & b_{n-1} > 1.
\end{cases}
\]

Prove: Among \(a_{2017}\) and \(a_{2018}\), at least one of them is not less than 2017.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the odd function $f(x)$ is an increasing function defined on $\mathbb{R}$, and the sequence $\{x_n\}$ is an arithmetic sequence with a common difference of 2, satisfying $f(x_8)+f(x_9)+f(x_{10})+f(x_{11})=0$, then the value of $x_{2012}$ is.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the odd function $f(x)$ is an increasing function defined on $\mathbb{R}$, and the sequence $\{x_n\}$ is an arithmetic sequence with a common difference of 2, satisfying $f(x_8)+f(x_9)+f(x_{10})+f(x_{11})=0$, then the value of $x_{2012}$ is.<|im_end|>
<|im_start|>assistant
<Z_369><Z_87><Z_140><Z_87><Z_228><Z_200><Z_116><Z_181><Z_181><Z_483><Z_276><Z_321><Z_163><Z_372><Z_194><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the odd function $f(x)$ is an increasing function defined on $\mathbb{R}$, and the sequence $\{x_n\}$ is an arithmetic sequence with a common difference of 2, satisfying $f(x_8)+f(x_9)+f(x_{10})+f(x_{11})=0$, then the value of $x_{2012}$ is.<|im_end|>
<|im_start|>assistant
<Z_478><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the odd function $f(x)$ is an increasing function defined on $\mathbb{R}$, and the sequence $\{x_n\}$ is an arithmetic sequence with a common difference of 2, satisfying $f(x_8)+f(x_9)+f(x_{10})+f(x_{11})=0$, then the value of $x_{2012}$ is.<|im_end|>
<|im_start|>assistant
<Z_419><Z_150><Z_188><Z_130><Z_5><Z_80><Z_365><Z_155><Z_137><Z_506><Z_396><Z_375><Z_99><Z_147><Z_168><ANSWER>

Question: Given that the odd function $f(x)$ is an increasing function defined on $\mathbb{R}$, and the sequence $\{x_n\}$ is an arithmetic sequence with a common difference of 2, satisfying $f(x_8)+f(x_9)+f(x_{10})+f(x_{11})=0$, then the value of $x_{2012}$ is.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers less than 500 are congruent to 3 (mod 7)?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers less than 500 are congruent to 3 (mod 7)?<|im_end|>
<|im_start|>assistant
<Z_477><Z_47><Z_140><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers less than 500 are congruent to 3 (mod 7)?<|im_end|>
<|im_start|>assistant
<Z_415><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers less than 500 are congruent to 3 (mod 7)?<|im_end|>
<|im_start|>assistant
<Z_395><Z_286><Z_150><ANSWER>

Question: How many positive integers less than 500 are congruent to 3 (mod 7)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 20 cars lined up at a race. Each of the cars have 2 passengers and a driver, then when the cars go past the race’s halfway point, each car gains a certain number of passengers. By the end of the race, there are 80 people in the cars. How many passengers do the cars gain at the halfway point?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 20 cars lined up at a race. Each of the cars have 2 passengers and a driver, then when the cars go past the race’s halfway point, each car gains a certain number of passengers. By the end of the race, there are 80 people in the cars. How many passengers do the cars gain at the halfway point?<|im_end|>
<|im_start|>assistant
<Z_24><Z_99><Z_219><Z_37><Z_185><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 20 cars lined up at a race. Each of the cars have 2 passengers and a driver, then when the cars go past the race’s halfway point, each car gains a certain number of passengers. By the end of the race, there are 80 people in the cars. How many passengers do the cars gain at the halfway point?<|im_end|>
<|im_start|>assistant
<Z_354><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 20 cars lined up at a race. Each of the cars have 2 passengers and a driver, then when the cars go past the race’s halfway point, each car gains a certain number of passengers. By the end of the race, there are 80 people in the cars. How many passengers do the cars gain at the halfway point?<|im_end|>
<|im_start|>assistant
<Z_479><Z_137><Z_76><Z_281><Z_476><Z_204><ANSWER>

Question: There are 20 cars lined up at a race. Each of the cars have 2 passengers and a driver, then when the cars go past the race’s halfway point, each car gains a certain number of passengers. By the end of the race, there are 80 people in the cars. How many passengers do the cars gain at the halfway point?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding a certain number of rackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets, and 24 cartons of the other type were used. How many rackets does the other type of carton hold?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding a certain number of rackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets, and 24 cartons of the other type were used. How many rackets does the other type of carton hold?<|im_end|>
<|im_start|>assistant
<Z_477><Z_155><Z_430><Z_494><Z_364><Z_375><Z_250><Z_382><Z_219><Z_279><Z_353><Z_364><Z_309><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding a certain number of rackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets, and 24 cartons of the other type were used. How many rackets does the other type of carton hold?<|im_end|>
<|im_start|>assistant
<Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding a certain number of rackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets, and 24 cartons of the other type were used. How many rackets does the other type of carton hold?<|im_end|>
<|im_start|>assistant
<Z_83><Z_501><Z_248><Z_23><Z_268><Z_198><Z_197><Z_305><Z_88><Z_12><Z_188><Z_65><Z_347><ANSWER>

Question: Tennis rackets can be packaged in cartons holding 2 rackets each or in cartons holding a certain number of rackets each. Yesterday's packing slip showed that 38 cartons were used to pack a total of 100 rackets, and 24 cartons of the other type were used. How many rackets does the other type of carton hold?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even integers are in the top 15 rows of Pascal's Triangle?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even integers are in the top 15 rows of Pascal's Triangle?<|im_end|>
<|im_start|>assistant
<Z_24><Z_348><Z_267><Z_53><Z_507><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even integers are in the top 15 rows of Pascal's Triangle?<|im_end|>
<|im_start|>assistant
<Z_217><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even integers are in the top 15 rows of Pascal's Triangle?<|im_end|>
<|im_start|>assistant
<Z_236><Z_367><Z_211><Z_379><Z_32><Z_40><ANSWER>

Question: How many even integers are in the top 15 rows of Pascal's Triangle?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=m+\log_{a}x$ ($a > 0$ and $a \neq 1$) whose graph passes through the point $(8,2)$, and the point $P(3,-1)$ is symmetric to the point $Q$ with respect to the line $x=2$ on the graph of $f(x)$.
(Ⅰ) Find the expression of the function $f(x)$.
(Ⅱ) Let $g(x)=2f(x)-f(x-1)$, find the minimum value of $g(x)$ and the value of $x$ at which the minimum is attained.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=m+\log_{a}x$ ($a > 0$ and $a \neq 1$) whose graph passes through the point $(8,2)$, and the point $P(3,-1)$ is symmetric to the point $Q$ with respect to the line $x=2$ on the graph of $f(x)$.
(Ⅰ) Find the expression of the function $f(x)$.
(Ⅱ) Let $g(x)=2f(x)-f(x-1)$, find the minimum value of $g(x)$ and the value of $x$ at which the minimum is attained.<|im_end|>
<|im_start|>assistant
<Z_369><Z_463><Z_418><Z_63><Z_118><Z_361><Z_358><Z_102><Z_267><Z_286><Z_233><Z_264><Z_434><Z_447><Z_414><Z_211><Z_219><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=m+\log_{a}x$ ($a > 0$ and $a \neq 1$) whose graph passes through the point $(8,2)$, and the point $P(3,-1)$ is symmetric to the point $Q$ with respect to the line $x=2$ on the graph of $f(x)$.
(Ⅰ) Find the expression of the function $f(x)$.
(Ⅱ) Let $g(x)=2f(x)-f(x-1)$, find the minimum value of $g(x)$ and the value of $x$ at which the minimum is attained.<|im_end|>
<|im_start|>assistant
<Z_441><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=m+\log_{a}x$ ($a > 0$ and $a \neq 1$) whose graph passes through the point $(8,2)$, and the point $P(3,-1)$ is symmetric to the point $Q$ with respect to the line $x=2$ on the graph of $f(x)$.
(Ⅰ) Find the expression of the function $f(x)$.
(Ⅱ) Let $g(x)=2f(x)-f(x-1)$, find the minimum value of $g(x)$ and the value of $x$ at which the minimum is attained.<|im_end|>
<|im_start|>assistant
<Z_477><Z_93><Z_444><Z_261><Z_507><Z_148><Z_136><Z_9><Z_264><Z_225><Z_324><Z_295><Z_185><Z_438><Z_275><Z_345><Z_284><ANSWER>

Question:
Given the function $f(x)=m+\log_{a}x$ ($a > 0$ and $a \neq 1$) whose graph passes through the point $(8,2)$, and the point $P(3,-1)$ is symmetric to the point $Q$ with respect to the line $x=2$ on the graph of $f(x)$.
(Ⅰ) Find the expression of the function $f(x)$.
(Ⅱ) Let $g(x)=2f(x)-f(x-1)$, find the minimum value of $g(x)$ and the value of $x$ at which the minimum is attained.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some identical printing presses 12 hours to print 500,000 papers. It would take 30 of these printing presses 15.999999999999998 hours to print 500,000 papers. How many printing presses were used in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some identical printing presses 12 hours to print 500,000 papers. It would take 30 of these printing presses 15.999999999999998 hours to print 500,000 papers. How many printing presses were used in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_477><Z_240><Z_219><Z_63><Z_485><Z_293><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some identical printing presses 12 hours to print 500,000 papers. It would take 30 of these printing presses 15.999999999999998 hours to print 500,000 papers. How many printing presses were used in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some identical printing presses 12 hours to print 500,000 papers. It would take 30 of these printing presses 15.999999999999998 hours to print 500,000 papers. How many printing presses were used in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_140><Z_201><Z_325><Z_115><Z_159><Z_492><Z_399><ANSWER>

Question: It takes some identical printing presses 12 hours to print 500,000 papers. It would take 30 of these printing presses 15.999999999999998 hours to print 500,000 papers. How many printing presses were used in the first scenario?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Joyce, Michael, Nikki, and Ryn have a favorite movie. Joyce's favorite movie is 2 hours longer than Michael's movie. Nikki's movie is three times as long as Michael's movie, and Ryn's favorite movie is 4/5 times as long as Nikki's favorite movie. If Nikki's favorite movie is 30 hours long, calculate the total number of hours of their favorite movies together.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Joyce, Michael, Nikki, and Ryn have a favorite movie. Joyce's favorite movie is 2 hours longer than Michael's movie. Nikki's movie is three times as long as Michael's movie, and Ryn's favorite movie is 4/5 times as long as Nikki's favorite movie. If Nikki's favorite movie is 30 hours long, calculate the total number of hours of their favorite movies together.<|im_end|>
<|im_start|>assistant
<Z_477><Z_157><Z_388><Z_209><Z_430><Z_425><Z_171><Z_81><Z_181><Z_313><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Joyce, Michael, Nikki, and Ryn have a favorite movie. Joyce's favorite movie is 2 hours longer than Michael's movie. Nikki's movie is three times as long as Michael's movie, and Ryn's favorite movie is 4/5 times as long as Nikki's favorite movie. If Nikki's favorite movie is 30 hours long, calculate the total number of hours of their favorite movies together.<|im_end|>
<|im_start|>assistant
<Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Joyce, Michael, Nikki, and Ryn have a favorite movie. Joyce's favorite movie is 2 hours longer than Michael's movie. Nikki's movie is three times as long as Michael's movie, and Ryn's favorite movie is 4/5 times as long as Nikki's favorite movie. If Nikki's favorite movie is 30 hours long, calculate the total number of hours of their favorite movies together.<|im_end|>
<|im_start|>assistant
<Z_89><Z_510><Z_98><Z_284><Z_481><Z_159><Z_210><Z_246><Z_245><Z_181><ANSWER>

Question: Joyce, Michael, Nikki, and Ryn have a favorite movie. Joyce's favorite movie is 2 hours longer than Michael's movie. Nikki's movie is three times as long as Michael's movie, and Ryn's favorite movie is 4/5 times as long as Nikki's favorite movie. If Nikki's favorite movie is 30 hours long, calculate the total number of hours of their favorite movies together.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The bacteria in a lab dish double in number every three hours. Initially, there are 800 bacteria cells. How many hours will it take for the bacteria to reach 102,400 cells?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The bacteria in a lab dish double in number every three hours. Initially, there are 800 bacteria cells. How many hours will it take for the bacteria to reach 102,400 cells?<|im_end|>
<|im_start|>assistant
<Z_477><Z_485><Z_220><Z_159><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The bacteria in a lab dish double in number every three hours. Initially, there are 800 bacteria cells. How many hours will it take for the bacteria to reach 102,400 cells?<|im_end|>
<|im_start|>assistant
<Z_504><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The bacteria in a lab dish double in number every three hours. Initially, there are 800 bacteria cells. How many hours will it take for the bacteria to reach 102,400 cells?<|im_end|>
<|im_start|>assistant
<Z_432><Z_221><Z_213><Z_358><ANSWER>

Question: The bacteria in a lab dish double in number every three hours. Initially, there are 800 bacteria cells. How many hours will it take for the bacteria to reach 102,400 cells?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the term $x^4y^3$ in the expansion of $(1+x)^{6}(2+y)^{4}$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the term $x^4y^3$ in the expansion of $(1+x)^{6}(2+y)^{4}$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_450><Z_456><Z_129><Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the term $x^4y^3$ in the expansion of $(1+x)^{6}(2+y)^{4}$.<|im_end|>
<|im_start|>assistant
<Z_468><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the term $x^4y^3$ in the expansion of $(1+x)^{6}(2+y)^{4}$.<|im_end|>
<|im_start|>assistant
<Z_234><Z_265><Z_349><Z_61><Z_418><ANSWER>

Question: Find the coefficient of the term $x^4y^3$ in the expansion of $(1+x)^{6}(2+y)^{4}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The square root of $x$ is greater than 3 and less than 5. How many integer values of $x$ satisfy this condition?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The square root of $x$ is greater than 3 and less than 5. How many integer values of $x$ satisfy this condition?<|im_end|>
<|im_start|>assistant
<Z_24><Z_280><Z_485><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The square root of $x$ is greater than 3 and less than 5. How many integer values of $x$ satisfy this condition?<|im_end|>
<|im_start|>assistant
<Z_130><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The square root of $x$ is greater than 3 and less than 5. How many integer values of $x$ satisfy this condition?<|im_end|>
<|im_start|>assistant
<Z_414><Z_8><Z_276><ANSWER>

Question: The square root of $x$ is greater than 3 and less than 5. How many integer values of $x$ satisfy this condition?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Aubriella is pouring water into a 50-gallon fish tank at the rate of 1 gallon every 20 seconds. How many more gallons will she have to pour into the tank to fill the tank if she poured water into the fish tank for 6 minutes?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Aubriella is pouring water into a 50-gallon fish tank at the rate of 1 gallon every 20 seconds. How many more gallons will she have to pour into the tank to fill the tank if she poured water into the fish tank for 6 minutes?<|im_end|>
<|im_start|>assistant
<Z_477><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Aubriella is pouring water into a 50-gallon fish tank at the rate of 1 gallon every 20 seconds. How many more gallons will she have to pour into the tank to fill the tank if she poured water into the fish tank for 6 minutes?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Aubriella is pouring water into a 50-gallon fish tank at the rate of 1 gallon every 20 seconds. How many more gallons will she have to pour into the tank to fill the tank if she poured water into the fish tank for 6 minutes?<|im_end|>
<|im_start|>assistant
<Z_311><Z_455><ANSWER>

Question: Aubriella is pouring water into a 50-gallon fish tank at the rate of 1 gallon every 20 seconds. How many more gallons will she have to pour into the tank to fill the tank if she poured water into the fish tank for 6 minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of seven consecutive positive integers all of which are nonprime?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of seven consecutive positive integers all of which are nonprime?<|im_end|>
<|im_start|>assistant
<Z_24><Z_362><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of seven consecutive positive integers all of which are nonprime?<|im_end|>
<|im_start|>assistant
<Z_497><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of seven consecutive positive integers all of which are nonprime?<|im_end|>
<|im_start|>assistant
<Z_315><Z_434><ANSWER>

Question: When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of seven consecutive positive integers all of which are nonprime?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the equation, $\frac{1}{7} + \frac{7}{x} = \frac{15}{x} + \frac{1}{15}$, find the value of $x$.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the equation, $\frac{1}{7} + \frac{7}{x} = \frac{15}{x} + \frac{1}{15}$, find the value of $x$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_94><Z_139><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the equation, $\frac{1}{7} + \frac{7}{x} = \frac{15}{x} + \frac{1}{15}$, find the value of $x$.<|im_end|>
<|im_start|>assistant
<Z_305><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the equation, $\frac{1}{7} + \frac{7}{x} = \frac{15}{x} + \frac{1}{15}$, find the value of $x$.<|im_end|>
<|im_start|>assistant
<Z_51><Z_452><Z_510><ANSWER>

Question: In the equation, $\frac{1}{7} + \frac{7}{x} = \frac{15}{x} + \frac{1}{15}$, find the value of $x$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 $1+2+3+4+5+6=6+7+8$ .
What is the smallest number  $k$  greater than  $6$  for which: $1 + 2 +...+ k = k + (k+1) +...+ n$ , with  $n$  an integer greater than  $k$  ?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 $1+2+3+4+5+6=6+7+8$ .
What is the smallest number  $k$  greater than  $6$  for which: $1 + 2 +...+ k = k + (k+1) +...+ n$ , with  $n$  an integer greater than  $k$  ?<|im_end|>
<|im_start|>assistant
<Z_369><Z_112><Z_386><Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 $1+2+3+4+5+6=6+7+8$ .
What is the smallest number  $k$  greater than  $6$  for which: $1 + 2 +...+ k = k + (k+1) +...+ n$ , with  $n$  an integer greater than  $k$  ?<|im_end|>
<|im_start|>assistant
<Z_231><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 $1+2+3+4+5+6=6+7+8$ .
What is the smallest number  $k$  greater than  $6$  for which: $1 + 2 +...+ k = k + (k+1) +...+ n$ , with  $n$  an integer greater than  $k$  ?<|im_end|>
<|im_start|>assistant
<Z_42><Z_51><Z_287><Z_142><ANSWER>

Question:
 $1+2+3+4+5+6=6+7+8$ .
What is the smallest number  $k$  greater than  $6$  for which: $1 + 2 +...+ k = k + (k+1) +...+ n$ , with  $n$  an integer greater than  $k$  ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two different unit vectors in a plane $\overrightarrow{m}=({x}_{1},{y}_{1})$, $\overrightarrow{n}=({x}_{2},{y}_{2})$, and $\overrightarrow{p}=(1,1)$, where the angles formed by $\overrightarrow{m}$ and $\overrightarrow{p}$, and $\overrightarrow{n}$ and $\overrightarrow{p}$ are both $\frac{π}{6}$, find $\overrightarrow{m} \cdot \overrightarrow{n}=$______; $\frac{{y}_{1}{y}_{2}}{{x}_{1}{x}_{2}}=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two different unit vectors in a plane $\overrightarrow{m}=({x}_{1},{y}_{1})$, $\overrightarrow{n}=({x}_{2},{y}_{2})$, and $\overrightarrow{p}=(1,1)$, where the angles formed by $\overrightarrow{m}$ and $\overrightarrow{p}$, and $\overrightarrow{n}$ and $\overrightarrow{p}$ are both $\frac{π}{6}$, find $\overrightarrow{m} \cdot \overrightarrow{n}=$______; $\frac{{y}_{1}{y}_{2}}{{x}_{1}{x}_{2}}=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_172><Z_501><Z_279><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two different unit vectors in a plane $\overrightarrow{m}=({x}_{1},{y}_{1})$, $\overrightarrow{n}=({x}_{2},{y}_{2})$, and $\overrightarrow{p}=(1,1)$, where the angles formed by $\overrightarrow{m}$ and $\overrightarrow{p}$, and $\overrightarrow{n}$ and $\overrightarrow{p}$ are both $\frac{π}{6}$, find $\overrightarrow{m} \cdot \overrightarrow{n}=$______; $\frac{{y}_{1}{y}_{2}}{{x}_{1}{x}_{2}}=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_344><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two different unit vectors in a plane $\overrightarrow{m}=({x}_{1},{y}_{1})$, $\overrightarrow{n}=({x}_{2},{y}_{2})$, and $\overrightarrow{p}=(1,1)$, where the angles formed by $\overrightarrow{m}$ and $\overrightarrow{p}$, and $\overrightarrow{n}$ and $\overrightarrow{p}$ are both $\frac{π}{6}$, find $\overrightarrow{m} \cdot \overrightarrow{n}=$______; $\frac{{y}_{1}{y}_{2}}{{x}_{1}{x}_{2}}=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_302><Z_101><Z_420><Z_386><ANSWER>

Question: Given two different unit vectors in a plane $\overrightarrow{m}=({x}_{1},{y}_{1})$, $\overrightarrow{n}=({x}_{2},{y}_{2})$, and $\overrightarrow{p}=(1,1)$, where the angles formed by $\overrightarrow{m}$ and $\overrightarrow{p}$, and $\overrightarrow{n}$ and $\overrightarrow{p}$ are both $\frac{π}{6}$, find $\overrightarrow{m} \cdot \overrightarrow{n}=$______; $\frac{{y}_{1}{y}_{2}}{{x}_{1}{x}_{2}}=\_\_\_\_\_\_$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An optometrist charges $175 per pair for soft contact lenses and $95 per pair for hard contact lenses. Last week, she sold 7 more pairs of soft lenses than hard lenses. She also offered a 10% discount on the total amount for customers who purchased both types of lenses. If her total sales for pairs of contact lenses last week were $2469, what was the total number of pairs of contact lenses that she sold?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An optometrist charges $175 per pair for soft contact lenses and $95 per pair for hard contact lenses. Last week, she sold 7 more pairs of soft lenses than hard lenses. She also offered a 10% discount on the total amount for customers who purchased both types of lenses. If her total sales for pairs of contact lenses last week were $2469, what was the total number of pairs of contact lenses that she sold?<|im_end|>
<|im_start|>assistant
<Z_24><Z_400><Z_175><Z_83><Z_255><Z_272><Z_63><Z_193><Z_211><Z_432><Z_169><Z_183><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An optometrist charges $175 per pair for soft contact lenses and $95 per pair for hard contact lenses. Last week, she sold 7 more pairs of soft lenses than hard lenses. She also offered a 10% discount on the total amount for customers who purchased both types of lenses. If her total sales for pairs of contact lenses last week were $2469, what was the total number of pairs of contact lenses that she sold?<|im_end|>
<|im_start|>assistant
<Z_140><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An optometrist charges $175 per pair for soft contact lenses and $95 per pair for hard contact lenses. Last week, she sold 7 more pairs of soft lenses than hard lenses. She also offered a 10% discount on the total amount for customers who purchased both types of lenses. If her total sales for pairs of contact lenses last week were $2469, what was the total number of pairs of contact lenses that she sold?<|im_end|>
<|im_start|>assistant
<Z_320><Z_393><Z_365><Z_385><Z_161><Z_114><Z_417><Z_168><Z_261><Z_423><Z_243><Z_389><ANSWER>

Question: An optometrist charges $175 per pair for soft contact lenses and $95 per pair for hard contact lenses. Last week, she sold 7 more pairs of soft lenses than hard lenses. She also offered a 10% discount on the total amount for customers who purchased both types of lenses. If her total sales for pairs of contact lenses last week were $2469, what was the total number of pairs of contact lenses that she sold?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many numbers are in the list $ -33, -26, -19, \ldots, 65, 72?$<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many numbers are in the list $ -33, -26, -19, \ldots, 65, 72?$<|im_end|>
<|im_start|>assistant
<Z_369><Z_266><Z_152><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many numbers are in the list $ -33, -26, -19, \ldots, 65, 72?$<|im_end|>
<|im_start|>assistant
<Z_333><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many numbers are in the list $ -33, -26, -19, \ldots, 65, 72?$<|im_end|>
<|im_start|>assistant
<Z_457><Z_326><Z_275><ANSWER>

Question: How many numbers are in the list $ -33, -26, -19, \ldots, 65, 72?$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We have a  $100\times100$  garden and we’ve plant  $10000$  trees in the  $1\times1$  squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We have a  $100\times100$  garden and we’ve plant  $10000$  trees in the  $1\times1$  squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree.<|im_end|>
<|im_start|>assistant
<Z_24><Z_273><Z_382><Z_420><Z_183><Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We have a  $100\times100$  garden and we’ve plant  $10000$  trees in the  $1\times1$  squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree.<|im_end|>
<|im_start|>assistant
<Z_206><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We have a  $100\times100$  garden and we’ve plant  $10000$  trees in the  $1\times1$  squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree.<|im_end|>
<|im_start|>assistant
<Z_119><Z_257><Z_161><Z_104><Z_4><Z_61><ANSWER>

Question: We have a  $100\times100$  garden and we’ve plant  $10000$  trees in the  $1\times1$  squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 5 out of 9 volleyballs are lent to other schools, what is the number of volleyballs left?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 5 out of 9 volleyballs are lent to other schools, what is the number of volleyballs left?<|im_end|>
<|im_start|>assistant
<Z_477><Z_449><Z_445><Z_148><Z_432><Z_490><Z_250><Z_448><Z_351><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 5 out of 9 volleyballs are lent to other schools, what is the number of volleyballs left?<|im_end|>
<|im_start|>assistant
<Z_149><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 5 out of 9 volleyballs are lent to other schools, what is the number of volleyballs left?<|im_end|>
<|im_start|>assistant
<Z_107><Z_454><Z_2><Z_457><Z_171><Z_157><Z_109><Z_277><Z_216><ANSWER>

Question: If 5 out of 9 volleyballs are lent to other schools, what is the number of volleyballs left?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the smallest base-10 positive integer greater than 10 that is a palindrome when written in both base 2 and base 4.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the smallest base-10 positive integer greater than 10 that is a palindrome when written in both base 2 and base 4.<|im_end|>
<|im_start|>assistant
<Z_369><Z_260><Z_232><Z_183><Z_276><Z_453><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the smallest base-10 positive integer greater than 10 that is a palindrome when written in both base 2 and base 4.<|im_end|>
<|im_start|>assistant
<Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the smallest base-10 positive integer greater than 10 that is a palindrome when written in both base 2 and base 4.<|im_end|>
<|im_start|>assistant
<Z_212><Z_330><Z_73><Z_88><Z_311><Z_508><Z_428><ANSWER>

Question: Compute the smallest base-10 positive integer greater than 10 that is a palindrome when written in both base 2 and base 4.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exists a constant $d,$ such that among all chords $\overline{AB}$ of the cubic curve $y = x^3$ passing through $C = (0,d),$
\[t = \frac{1}{AC^2} + \frac{1}{BC^2}\] is a fixed constant. Find the constant $t.$<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exists a constant $d,$ such that among all chords $\overline{AB}$ of the cubic curve $y = x^3$ passing through $C = (0,d),$
\[t = \frac{1}{AC^2} + \frac{1}{BC^2}\] is a fixed constant. Find the constant $t.$<|im_end|>
<|im_start|>assistant
<Z_24><Z_209><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exists a constant $d,$ such that among all chords $\overline{AB}$ of the cubic curve $y = x^3$ passing through $C = (0,d),$
\[t = \frac{1}{AC^2} + \frac{1}{BC^2}\] is a fixed constant. Find the constant $t.$<|im_end|>
<|im_start|>assistant
<Z_3><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exists a constant $d,$ such that among all chords $\overline{AB}$ of the cubic curve $y = x^3$ passing through $C = (0,d),$
\[t = \frac{1}{AC^2} + \frac{1}{BC^2}\] is a fixed constant. Find the constant $t.$<|im_end|>
<|im_start|>assistant
<Z_48><Z_484><ANSWER>

Question:
There exists a constant $d,$ such that among all chords $\overline{AB}$ of the cubic curve $y = x^3$ passing through $C = (0,d),$
\[t = \frac{1}{AC^2} + \frac{1}{BC^2}\] is a fixed constant. Find the constant $t.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $S$  be a square formed by the four vertices  $(1,1),(1.-1),(-1,1)$  and  $(-1,-1)$ . Let the region  $R$  be the set of points inside  $S$  which are closer to the center than any of the four sides. Find the area of the region  $R$ .<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $S$  be a square formed by the four vertices  $(1,1),(1.-1),(-1,1)$  and  $(-1,-1)$ . Let the region  $R$  be the set of points inside  $S$  which are closer to the center than any of the four sides. Find the area of the region  $R$ .<|im_end|>
<|im_start|>assistant
<Z_477><Z_421><Z_219><Z_159><Z_35><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $S$  be a square formed by the four vertices  $(1,1),(1.-1),(-1,1)$  and  $(-1,-1)$ . Let the region  $R$  be the set of points inside  $S$  which are closer to the center than any of the four sides. Find the area of the region  $R$ .<|im_end|>
<|im_start|>assistant
<Z_318><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $S$  be a square formed by the four vertices  $(1,1),(1.-1),(-1,1)$  and  $(-1,-1)$ . Let the region  $R$  be the set of points inside  $S$  which are closer to the center than any of the four sides. Find the area of the region  $R$ .<|im_end|>
<|im_start|>assistant
<Z_290><Z_80><Z_62><Z_261><Z_37><ANSWER>

Question: Let  $S$  be a square formed by the four vertices  $(1,1),(1.-1),(-1,1)$  and  $(-1,-1)$ . Let the region  $R$  be the set of points inside  $S$  which are closer to the center than any of the four sides. Find the area of the region  $R$ .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of \(\log _{2}\left[2^{3} 4^{4} 8^{5} \cdots\left(2^{20}\right)^{22}\right]\).
Choose one of the following options:
(a) 3290
(b) 3500
(c) 3710
(d) 4172<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of \(\log _{2}\left[2^{3} 4^{4} 8^{5} \cdots\left(2^{20}\right)^{22}\right]\).
Choose one of the following options:
(a) 3290
(b) 3500
(c) 3710
(d) 4172<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of \(\log _{2}\left[2^{3} 4^{4} 8^{5} \cdots\left(2^{20}\right)^{22}\right]\).
Choose one of the following options:
(a) 3290
(b) 3500
(c) 3710
(d) 4172<|im_end|>
<|im_start|>assistant
<Z_172><ANSWER>

Question:
Find the value of \(\log _{2}\left[2^{3} 4^{4} 8^{5} \cdots\left(2^{20}\right)^{22}\right]\).
Choose one of the following options:
(a) 3290
(b) 3500
(c) 3710
(d) 4172


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marion received some more turtles than Martha at the animal rescue center where they had gone to take part in the animal saving day event. Martha received 40 turtles. They received 100 turtles together. How many more turtles did Marion receive than Martha?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marion received some more turtles than Martha at the animal rescue center where they had gone to take part in the animal saving day event. Martha received 40 turtles. They received 100 turtles together. How many more turtles did Marion receive than Martha?<|im_end|>
<|im_start|>assistant
<Z_24><Z_426><Z_30><Z_148><Z_232><Z_143><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marion received some more turtles than Martha at the animal rescue center where they had gone to take part in the animal saving day event. Martha received 40 turtles. They received 100 turtles together. How many more turtles did Marion receive than Martha?<|im_end|>
<|im_start|>assistant
<Z_441><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marion received some more turtles than Martha at the animal rescue center where they had gone to take part in the animal saving day event. Martha received 40 turtles. They received 100 turtles together. How many more turtles did Marion receive than Martha?<|im_end|>
<|im_start|>assistant
<Z_375><Z_237><Z_260><Z_179><Z_208><Z_264><ANSWER>

Question: Marion received some more turtles than Martha at the animal rescue center where they had gone to take part in the animal saving day event. Martha received 40 turtles. They received 100 turtles together. How many more turtles did Marion receive than Martha?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mary was working on a research paper and initially borrowed 15 books from the library. After 6 days, she found that 40% of the books weren't helpful, so she returned those and checked out 8 more books. A week later, she evaluated that 25% of her remaining books were not relevant; she returned them and checked out 6 more books. In the following 5 days, she determined that 30% of the books she currently had were irrelevant to her research, so she returned those and checked out 12 additional books. After 3 more days, she discovered that 50% of her checked-out books were helpful, so she returned the unhelpful ones and checked out another 10 books. How many books does Mary currently have checked out of the library?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mary was working on a research paper and initially borrowed 15 books from the library. After 6 days, she found that 40% of the books weren't helpful, so she returned those and checked out 8 more books. A week later, she evaluated that 25% of her remaining books were not relevant; she returned them and checked out 6 more books. In the following 5 days, she determined that 30% of the books she currently had were irrelevant to her research, so she returned those and checked out 12 additional books. After 3 more days, she discovered that 50% of her checked-out books were helpful, so she returned the unhelpful ones and checked out another 10 books. How many books does Mary currently have checked out of the library?<|im_end|>
<|im_start|>assistant
<Z_369><Z_321><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mary was working on a research paper and initially borrowed 15 books from the library. After 6 days, she found that 40% of the books weren't helpful, so she returned those and checked out 8 more books. A week later, she evaluated that 25% of her remaining books were not relevant; she returned them and checked out 6 more books. In the following 5 days, she determined that 30% of the books she currently had were irrelevant to her research, so she returned those and checked out 12 additional books. After 3 more days, she discovered that 50% of her checked-out books were helpful, so she returned the unhelpful ones and checked out another 10 books. How many books does Mary currently have checked out of the library?<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mary was working on a research paper and initially borrowed 15 books from the library. After 6 days, she found that 40% of the books weren't helpful, so she returned those and checked out 8 more books. A week later, she evaluated that 25% of her remaining books were not relevant; she returned them and checked out 6 more books. In the following 5 days, she determined that 30% of the books she currently had were irrelevant to her research, so she returned those and checked out 12 additional books. After 3 more days, she discovered that 50% of her checked-out books were helpful, so she returned the unhelpful ones and checked out another 10 books. How many books does Mary currently have checked out of the library?<|im_end|>
<|im_start|>assistant
<Z_272><Z_117><ANSWER>

Question: Mary was working on a research paper and initially borrowed 15 books from the library. After 6 days, she found that 40% of the books weren't helpful, so she returned those and checked out 8 more books. A week later, she evaluated that 25% of her remaining books were not relevant; she returned them and checked out 6 more books. In the following 5 days, she determined that 30% of the books she currently had were irrelevant to her research, so she returned those and checked out 12 additional books. After 3 more days, she discovered that 50% of her checked-out books were helpful, so she returned the unhelpful ones and checked out another 10 books. How many books does Mary currently have checked out of the library?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Indicate the integer closest to the number: \(\sqrt{2012-\sqrt{2013 \cdot 2011}}+\sqrt{2010-\sqrt{2011 \cdot 2009}}+\ldots+\sqrt{2-\sqrt{3 \cdot 1}}\).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Indicate the integer closest to the number: \(\sqrt{2012-\sqrt{2013 \cdot 2011}}+\sqrt{2010-\sqrt{2011 \cdot 2009}}+\ldots+\sqrt{2-\sqrt{3 \cdot 1}}\).<|im_end|>
<|im_start|>assistant
<Z_477><Z_433><Z_346><Z_286><Z_254><Z_41><Z_387><Z_343><Z_396><Z_49><Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Indicate the integer closest to the number: \(\sqrt{2012-\sqrt{2013 \cdot 2011}}+\sqrt{2010-\sqrt{2011 \cdot 2009}}+\ldots+\sqrt{2-\sqrt{3 \cdot 1}}\).<|im_end|>
<|im_start|>assistant
<Z_139><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Indicate the integer closest to the number: \(\sqrt{2012-\sqrt{2013 \cdot 2011}}+\sqrt{2010-\sqrt{2011 \cdot 2009}}+\ldots+\sqrt{2-\sqrt{3 \cdot 1}}\).<|im_end|>
<|im_start|>assistant
<Z_419><Z_164><Z_27><Z_220><Z_176><Z_455><Z_273><Z_396><Z_215><Z_389><Z_340><ANSWER>

Question: Indicate the integer closest to the number: \(\sqrt{2012-\sqrt{2013 \cdot 2011}}+\sqrt{2010-\sqrt{2011 \cdot 2009}}+\ldots+\sqrt{2-\sqrt{3 \cdot 1}}\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A floor 10 feet by 15 feet is to be tiled with 6-inch by 9-inch tiles. How many tiles are needed to cover the floor?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A floor 10 feet by 15 feet is to be tiled with 6-inch by 9-inch tiles. How many tiles are needed to cover the floor?<|im_end|>
<|im_start|>assistant
<Z_24><Z_87><Z_343><Z_228><Z_208><Z_91><Z_288><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A floor 10 feet by 15 feet is to be tiled with 6-inch by 9-inch tiles. How many tiles are needed to cover the floor?<|im_end|>
<|im_start|>assistant
<Z_250><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A floor 10 feet by 15 feet is to be tiled with 6-inch by 9-inch tiles. How many tiles are needed to cover the floor?<|im_end|>
<|im_start|>assistant
<Z_55><Z_346><Z_168><Z_199><Z_390><Z_117><Z_358><ANSWER>

Question: A floor 10 feet by 15 feet is to be tiled with 6-inch by 9-inch tiles. How many tiles are needed to cover the floor?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man can row upstream at a certain speed and downstream at 31 kmph. The speed of the man in still water is 28 kmph. What is the speed of the man rowing upstream?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man can row upstream at a certain speed and downstream at 31 kmph. The speed of the man in still water is 28 kmph. What is the speed of the man rowing upstream?<|im_end|>
<|im_start|>assistant
<Z_24><Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man can row upstream at a certain speed and downstream at 31 kmph. The speed of the man in still water is 28 kmph. What is the speed of the man rowing upstream?<|im_end|>
<|im_start|>assistant
<Z_403><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man can row upstream at a certain speed and downstream at 31 kmph. The speed of the man in still water is 28 kmph. What is the speed of the man rowing upstream?<|im_end|>
<|im_start|>assistant
<Z_208><Z_168><ANSWER>

Question: A man can row upstream at a certain speed and downstream at 31 kmph. The speed of the man in still water is 28 kmph. What is the speed of the man rowing upstream?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake has 36 comic books. His brother has 15 more comic books than Jake. How many comic books do they have altogether?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake has 36 comic books. His brother has 15 more comic books than Jake. How many comic books do they have altogether?<|im_end|>
<|im_start|>assistant
<Z_24><Z_428><Z_269><Z_250><Z_416><Z_340><Z_483><Z_470><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake has 36 comic books. His brother has 15 more comic books than Jake. How many comic books do they have altogether?<|im_end|>
<|im_start|>assistant
<Z_505><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake has 36 comic books. His brother has 15 more comic books than Jake. How many comic books do they have altogether?<|im_end|>
<|im_start|>assistant
<Z_188><Z_81><Z_125><Z_306><Z_399><Z_414><Z_175><Z_360><ANSWER>

Question: Jake has 36 comic books. His brother has 15 more comic books than Jake. How many comic books do they have altogether?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( 4 ) ^ 14 x ( 37 ) ^ 7 x ( 2 ) ^ 13 x ( 19 ) ^ 3.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( 4 ) ^ 14 x ( 37 ) ^ 7 x ( 2 ) ^ 13 x ( 19 ) ^ 3.<|im_end|>
<|im_start|>assistant
<Z_24><Z_450><Z_94><Z_501><Z_245><Z_472><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( 4 ) ^ 14 x ( 37 ) ^ 7 x ( 2 ) ^ 13 x ( 19 ) ^ 3.<|im_end|>
<|im_start|>assistant
<Z_84><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( 4 ) ^ 14 x ( 37 ) ^ 7 x ( 2 ) ^ 13 x ( 19 ) ^ 3.<|im_end|>
<|im_start|>assistant
<Z_205><Z_175><Z_240><Z_317><Z_290><Z_509><ANSWER>

Question: Find the total number of prime factors in the expression ( 4 ) ^ 14 x ( 37 ) ^ 7 x ( 2 ) ^ 13 x ( 19 ) ^ 3.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold a different number of people. There is room for 72 people altogether, and there are 9 four-passenger cars. How many people can the other type of car hold?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold a different number of people. There is room for 72 people altogether, and there are 9 four-passenger cars. How many people can the other type of car hold?<|im_end|>
<|im_start|>assistant
<Z_369><Z_223><Z_487><Z_199><Z_50><Z_377><Z_99><Z_63><Z_382><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold a different number of people. There is room for 72 people altogether, and there are 9 four-passenger cars. How many people can the other type of car hold?<|im_end|>
<|im_start|>assistant
<Z_147><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold a different number of people. There is room for 72 people altogether, and there are 9 four-passenger cars. How many people can the other type of car hold?<|im_end|>
<|im_start|>assistant
<Z_239><Z_400><Z_149><Z_189><Z_109><Z_272><Z_412><Z_225><Z_223><ANSWER>

Question: The Rocket Coaster has 15 cars, some that hold 4 people and some that hold a different number of people. There is room for 72 people altogether, and there are 9 four-passenger cars. How many people can the other type of car hold?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_148><Z_187><Z_425><Z_188><Z_320><Z_157><Z_432><Z_404><Z_498><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?<|im_end|>
<|im_start|>assistant
<Z_421><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?<|im_end|>
<|im_start|>assistant
<Z_432><Z_44><Z_372><Z_211><Z_346><Z_336><Z_87><Z_368><Z_280><Z_438><Z_445><ANSWER>

Question: the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney follows a pattern in doing jumping jacks: on Monday, he does 20, on Tuesday he does 36, and he continues to add an increasing even number of jumping jacks each day for the next five days. Brooke does four times as many jumping jacks as Sidney each day. How many jumping jacks did Brooke do during the entire eight-day period?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney follows a pattern in doing jumping jacks: on Monday, he does 20, on Tuesday he does 36, and he continues to add an increasing even number of jumping jacks each day for the next five days. Brooke does four times as many jumping jacks as Sidney each day. How many jumping jacks did Brooke do during the entire eight-day period?<|im_end|>
<|im_start|>assistant
<Z_477><Z_28><Z_274><Z_253><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney follows a pattern in doing jumping jacks: on Monday, he does 20, on Tuesday he does 36, and he continues to add an increasing even number of jumping jacks each day for the next five days. Brooke does four times as many jumping jacks as Sidney each day. How many jumping jacks did Brooke do during the entire eight-day period?<|im_end|>
<|im_start|>assistant
<Z_129><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney follows a pattern in doing jumping jacks: on Monday, he does 20, on Tuesday he does 36, and he continues to add an increasing even number of jumping jacks each day for the next five days. Brooke does four times as many jumping jacks as Sidney each day. How many jumping jacks did Brooke do during the entire eight-day period?<|im_end|>
<|im_start|>assistant
<Z_220><Z_132><Z_204><Z_105><ANSWER>

Question: Sidney follows a pattern in doing jumping jacks: on Monday, he does 20, on Tuesday he does 36, and he continues to add an increasing even number of jumping jacks each day for the next five days. Brooke does four times as many jumping jacks as Sidney each day. How many jumping jacks did Brooke do during the entire eight-day period?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.<|im_end|>
<|im_start|>assistant
<Z_477><Z_373><Z_470><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.<|im_end|>
<|im_start|>assistant
<Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.<|im_end|>
<|im_start|>assistant
<Z_213><Z_177><Z_58><ANSWER>

Question:
Given an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike has some baseball cards. Sam gave Mike 13 more baseball cards, and now Mike has 100 baseball cards. How many baseball cards did Mike have initially?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike has some baseball cards. Sam gave Mike 13 more baseball cards, and now Mike has 100 baseball cards. How many baseball cards did Mike have initially?<|im_end|>
<|im_start|>assistant
<Z_24><Z_343><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike has some baseball cards. Sam gave Mike 13 more baseball cards, and now Mike has 100 baseball cards. How many baseball cards did Mike have initially?<|im_end|>
<|im_start|>assistant
<Z_178><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike has some baseball cards. Sam gave Mike 13 more baseball cards, and now Mike has 100 baseball cards. How many baseball cards did Mike have initially?<|im_end|>
<|im_start|>assistant
<Z_145><Z_145><ANSWER>

Question: Mike has some baseball cards. Sam gave Mike 13 more baseball cards, and now Mike has 100 baseball cards. How many baseball cards did Mike have initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A list of seven positive integers has a median of 4 and a mean of 10. What is the maximum possible value of the list's largest element?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A list of seven positive integers has a median of 4 and a mean of 10. What is the maximum possible value of the list's largest element?<|im_end|>
<|im_start|>assistant
<Z_24><Z_162><Z_440><Z_64><Z_502><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A list of seven positive integers has a median of 4 and a mean of 10. What is the maximum possible value of the list's largest element?<|im_end|>
<|im_start|>assistant
<Z_239><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A list of seven positive integers has a median of 4 and a mean of 10. What is the maximum possible value of the list's largest element?<|im_end|>
<|im_start|>assistant
<Z_356><Z_230><Z_17><Z_9><Z_235><ANSWER>

Question: A list of seven positive integers has a median of 4 and a mean of 10. What is the maximum possible value of the list's largest element?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).<|im_end|>
<|im_start|>assistant
<Z_24><Z_77><Z_173><Z_149><Z_237><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).<|im_end|>
<|im_start|>assistant
<Z_389><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).<|im_end|>
<|im_start|>assistant
<Z_430><Z_319><Z_443><Z_145><Z_296><ANSWER>

Question: Given that \( a_{0} = 0 \), \( a_{1} = a_{2} = 1 \), \( a_{3n} = a_{n} \), and \( a_{3n+1} = a_{3n+2} = a_{n}+1 \) for \( n \geq 1 \), find the value of \( a_{2021} \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa set a school record for most points in a single basketball game when her team scored 48 points. The six other players on her team averaged 3.5 points each. How many points did Vanessa score to set her school record?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa set a school record for most points in a single basketball game when her team scored 48 points. The six other players on her team averaged 3.5 points each. How many points did Vanessa score to set her school record?<|im_end|>
<|im_start|>assistant
<Z_477><Z_247><Z_152><Z_137><Z_219><Z_488><Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa set a school record for most points in a single basketball game when her team scored 48 points. The six other players on her team averaged 3.5 points each. How many points did Vanessa score to set her school record?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa set a school record for most points in a single basketball game when her team scored 48 points. The six other players on her team averaged 3.5 points each. How many points did Vanessa score to set her school record?<|im_end|>
<|im_start|>assistant
<Z_234><Z_167><Z_71><Z_486><Z_272><Z_489><Z_66><ANSWER>

Question: Vanessa set a school record for most points in a single basketball game when her team scored 48 points. The six other players on her team averaged 3.5 points each. How many points did Vanessa score to set her school record?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_477><Z_99><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_461><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_92><Z_318><Z_169><ANSWER>

Question: The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_24><Z_437><Z_377><Z_476><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_424><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_284><Z_289><Z_147><Z_458><ANSWER>

Question:
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_469><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_281><ANSWER>

Question: Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_477><Z_181><Z_250><Z_465><Z_446><Z_125><Z_232><Z_463><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_371><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_231><Z_20><Z_299><Z_388><Z_417><Z_34><Z_282><Z_502><ANSWER>

Question: Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_267><Z_393><Z_97><Z_330><Z_434><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_378><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_255><Z_223><Z_80><Z_238><Z_226><Z_175><ANSWER>

Question: Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?