<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|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 prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_24><Z_485><Z_165><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_374><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_441><Z_158><Z_125><ANSWER>

Question: The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|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 a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_477><Z_493><Z_393><Z_92><Z_505><Z_252><Z_468><Z_273><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|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 a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_342><Z_231><Z_86><Z_240><Z_360><Z_169><Z_12><Z_416><ANSWER>

Question: Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|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
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_477><Z_141><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_282><Z_20><ANSWER>

Question:
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|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
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_477><Z_98><Z_200><Z_296><Z_376><Z_305><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_13><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_490><Z_374><Z_266><Z_468><Z_356><Z_461><ANSWER>

Question: If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|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 four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_369><Z_209><Z_431><Z_274><Z_213><Z_280><Z_390><Z_445><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_291><Z_482><Z_313><Z_203><Z_506><Z_470><Z_86><Z_160><ANSWER>

Question: A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|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 starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_377><Z_443><Z_321><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_134><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_50><Z_248><Z_421><Z_364><ANSWER>

Question: a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|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 worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_24><Z_320><Z_144><Z_372><Z_485><Z_470><Z_427><Z_321><Z_30><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_36><Z_191><Z_340><Z_13><Z_407><Z_247><Z_473><Z_389><Z_427><ANSWER>

Question: A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|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 exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_24><Z_253><Z_368><Z_125><Z_332><Z_497><Z_313><Z_450><Z_194><Z_335><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_383><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_146><Z_485><Z_449><Z_296><Z_73><Z_206><Z_232><Z_294><Z_488><Z_482><ANSWER>

Question: There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|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 modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_24><Z_168><Z_181><Z_296><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_483><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_239><Z_310><Z_239><Z_82><ANSWER>

Question: Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|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
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_265><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_407><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_370><Z_207><ANSWER>

Question: What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|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 maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_477><Z_424><Z_111><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_319><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_395><Z_267><Z_89><ANSWER>

Question:
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|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
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_369><Z_295><Z_366><Z_470><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_330><Z_411><Z_104><Z_294><Z_220><ANSWER>

Question: Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|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
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_369><Z_248><Z_349><Z_468><Z_335><Z_373><Z_186><Z_200><Z_453><Z_98><Z_132><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_104><Z_396><Z_296><Z_507><Z_205><Z_318><Z_312><Z_270><Z_443><Z_123><Z_156><ANSWER>

Question: In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|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 largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_24><Z_377><Z_441><Z_276><Z_148><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_488><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_349><Z_463><Z_451><Z_478><Z_289><ANSWER>

Question: Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|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
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_24><Z_343><Z_46><Z_406><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_204><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_170><Z_235><Z_104><Z_107><ANSWER>

Question: Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|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
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_477><Z_465><Z_48><Z_414><Z_272><Z_265><Z_378><Z_80><Z_116><Z_42><Z_273><Z_425><Z_116><Z_58><Z_246><Z_267><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_341><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_458><Z_107><Z_59><Z_481><Z_256><Z_331><Z_44><Z_350><Z_426><Z_119><Z_5><Z_21><Z_122><Z_447><Z_232><Z_75><ANSWER>

Question: Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|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
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_150><Z_181><Z_64><Z_381><Z_445><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_429><Z_429><Z_391><Z_321><Z_66><Z_144><ANSWER>

Question: What is the greatest prime factor of $2^8 + 5^5$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|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
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_24><Z_443><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_264><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_286><Z_389><ANSWER>

Question: Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|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 third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_369><Z_357><Z_377><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_342><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_230><Z_456><Z_325><ANSWER>

Question: The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|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
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_24><Z_439><Z_155><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_284><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_3><Z_63><Z_217><ANSWER>

Question: What is the value of \(635^2 - 615^2\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|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
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_369><Z_264><Z_186><Z_388><Z_89><Z_465><Z_89><Z_38><Z_104><Z_64><Z_170><Z_363><Z_48><Z_420><Z_490><Z_53><Z_175><Z_244><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_198><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_355><Z_145><Z_235><Z_194><Z_117><Z_424><Z_318><Z_467><Z_89><Z_374><Z_64><Z_149><Z_440><Z_3><Z_105><Z_435><Z_246><Z_236><ANSWER>

Question: John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|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 company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_477><Z_245><Z_279><Z_395><Z_211><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_495><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_32><Z_118><Z_434><Z_332><Z_447><ANSWER>

Question: The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|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
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_477><Z_174><Z_456><Z_413><Z_116><Z_43><Z_68><Z_88><Z_463><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_472><Z_288><Z_160><Z_271><Z_273><Z_282><Z_44><Z_154><Z_487><ANSWER>

Question: In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|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 dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|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
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|im_end|>
<|im_start|>assistant
<Z_502><ANSWER>

Question: A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|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
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_369><Z_187><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|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
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_251><Z_218><ANSWER>

Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|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
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_24><Z_288><Z_440><Z_437><Z_462><Z_144><Z_84><Z_159><Z_388><Z_502><Z_205><Z_470><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_193><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_502><Z_41><Z_161><Z_13><Z_509><Z_373><Z_278><Z_218><Z_81><Z_347><Z_509><Z_207><Z_429><ANSWER>

Question: What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|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 certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_369><Z_109><Z_443><Z_227><Z_373><Z_451><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_457><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_325><Z_110><Z_30><Z_262><Z_173><Z_18><ANSWER>

Question:
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|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
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_369><Z_175><Z_433><Z_140><Z_379><Z_267><Z_77><Z_123><Z_176><Z_200><Z_123><Z_390><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_64><Z_485><Z_403><Z_495><Z_228><Z_227><Z_350><Z_103><Z_333><Z_156><Z_240><Z_496><ANSWER>

Question: If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|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 cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_24><Z_342><Z_338><Z_295><Z_181><Z_202><Z_318><Z_322><Z_247><Z_211><Z_358><Z_300><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_316><Z_379><Z_87><Z_97><Z_398><Z_187><Z_301><Z_493><Z_103><Z_100><Z_499><Z_40><ANSWER>

Question: A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|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
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_369><Z_507><Z_450><Z_146><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_348><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_391><Z_485><Z_290><Z_277><ANSWER>

Question: Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|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 natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_477><Z_209><Z_449><Z_378><Z_377><Z_54><Z_252><Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_190><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_43><Z_225><Z_7><Z_250><Z_68><Z_209><Z_55><Z_283><ANSWER>

Question:
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|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 numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_369><Z_362><Z_75><Z_378><Z_181><Z_484><Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_29><Z_18><Z_486><Z_113><Z_285><Z_336><Z_228><ANSWER>

Question:
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|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
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|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
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|im_end|>
<|im_start|>assistant
<Z_274><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|im_end|>
<|im_start|>assistant
<Z_295><ANSWER>

Question: Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|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 that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_369><Z_362><Z_344><Z_374><Z_286><Z_159><Z_344><Z_344><Z_94><Z_279><Z_98><Z_247><Z_470><Z_118><Z_56><Z_135><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_177><Z_84><Z_397><Z_355><Z_300><Z_348><Z_150><Z_432><Z_407><Z_200><Z_156><Z_296><Z_254><Z_470><Z_68><Z_304><Z_454><ANSWER>

Question:
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|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
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|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
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|im_end|>
<|im_start|>assistant
<Z_343><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|im_end|>
<|im_start|>assistant
<Z_362><ANSWER>

Question:
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|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
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_477><Z_443><Z_466><Z_173><Z_313><Z_128><Z_413><Z_220><Z_92><Z_144><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_150><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_47><Z_89><Z_511><Z_504><Z_237><Z_238><Z_479><Z_240><Z_506><Z_327><ANSWER>

Question: Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|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
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_369><Z_161><Z_253><Z_346><Z_214><Z_199><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_193><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_37><Z_214><Z_29><Z_437><Z_125><Z_73><Z_303><ANSWER>

Question: Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|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 certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|im_end|>
<|im_start|>assistant
<Z_24><Z_360><Z_181><Z_194><Z_252><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|im_end|>
<|im_start|>assistant
<Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|im_end|>
<|im_start|>assistant
<Z_31><Z_94><Z_188><Z_499><Z_88><ANSWER>

Question: A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|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
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|im_end|>
<|im_start|>assistant
<Z_24><Z_181><Z_453><Z_469><Z_223><Z_446><Z_149><Z_214><Z_465><Z_439><Z_37><Z_89><Z_313><Z_291><Z_301><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|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
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|im_end|>
<|im_start|>assistant
<Z_79><Z_460><Z_374><Z_310><Z_6><Z_164><Z_159><Z_339><Z_351><Z_348><Z_336><Z_167><Z_457><Z_144><Z_87><ANSWER>

Question: In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|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 metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_477><Z_175><Z_181><Z_274><Z_305><Z_118><Z_157><Z_155><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_211><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_60><Z_142><Z_252><Z_268><Z_96><Z_238><Z_83><Z_29><Z_470><ANSWER>

Question: A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|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 box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_24><Z_274><Z_152><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_205><Z_347><Z_419><ANSWER>

Question: A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|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
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_477><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_207><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_184><Z_130><ANSWER>

Question: Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|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
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_369><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_251><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_106><Z_495><ANSWER>

Question: In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|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
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|im_end|>
<|im_start|>assistant
<Z_477><Z_219><Z_185><Z_195><Z_205><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|im_end|>
<|im_start|>assistant
<Z_285><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|im_end|>
<|im_start|>assistant
<Z_173><Z_185><Z_317><Z_276><Z_162><ANSWER>

Question: To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|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 does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|im_end|>
<|im_start|>assistant
<Z_477><Z_112><Z_157><Z_334><Z_118><Z_414><Z_400><Z_248><Z_57><Z_338><Z_322><Z_343><Z_439><Z_386><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|im_end|>
<|im_start|>assistant
<Z_150><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|im_end|>
<|im_start|>assistant
<Z_51><Z_137><Z_39><Z_327><Z_114><Z_151><Z_416><Z_36><Z_486><Z_510><Z_112><Z_205><Z_293><Z_307><ANSWER>

Question: Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|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 integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_332><Z_98><Z_173><Z_80><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_417><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_263><Z_36><Z_255><Z_67><Z_376><Z_31><ANSWER>

Question:
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|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 certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_24><Z_140><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_395><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_386><Z_400><ANSWER>

Question: A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|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 bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_369><Z_140><Z_382><Z_194><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_372><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_328><Z_139><Z_183><Z_414><Z_502><ANSWER>

Question: A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|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 Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_24><Z_187><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_330><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_508><Z_422><Z_149><ANSWER>

Question: In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?