<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?<|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 man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_450><Z_453><Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?<|im_end|>
<|im_start|>assistant
<Z_160><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?<|im_end|>
<|im_start|>assistant
<Z_401><Z_380><Z_309><Z_220><ANSWER>

Question: a man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?<|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 tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?<|im_end|>
<|im_start|>assistant
<Z_369><Z_509><Z_288><Z_111><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?<|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 tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?<|im_end|>
<|im_start|>assistant
<Z_142><Z_243><Z_411><Z_263><ANSWER>

Question: a tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Thomas made some stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, and the fourth stack was 10 blocks taller than the third stack. The fifth stack has twice as many blocks as the second stack. How many blocks did Thomas use in all?<|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
Thomas made some stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, and the fourth stack was 10 blocks taller than the third stack. The fifth stack has twice as many blocks as the second stack. How many blocks did Thomas use in all?<|im_end|>
<|im_start|>assistant
<Z_369><Z_458><Z_236><Z_413><Z_453><Z_149><Z_77><Z_276><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Thomas made some stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, and the fourth stack was 10 blocks taller than the third stack. The fifth stack has twice as many blocks as the second stack. How many blocks did Thomas use in all?<|im_end|>
<|im_start|>assistant
<Z_442><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Thomas made some stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, and the fourth stack was 10 blocks taller than the third stack. The fifth stack has twice as many blocks as the second stack. How many blocks did Thomas use in all?<|im_end|>
<|im_start|>assistant
<Z_202><Z_269><Z_63><Z_42><Z_151><Z_100><Z_451><Z_279><ANSWER>

Question: Thomas made some stacks of wooden blocks. The first stack was 7 blocks tall. The second stack was 3 blocks taller than the first. The third stack was 6 blocks shorter than the second stack, and the fourth stack was 10 blocks taller than the third stack. The fifth stack has twice as many blocks as the second stack. How many blocks did Thomas use in all?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh had 7 marbles in his collection. He lost 8 marbles and found 10 new ones.. How many more marbles did he find than those he lost?<|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
Josh had 7 marbles in his collection. He lost 8 marbles and found 10 new ones.. How many more marbles did he find than those he lost?<|im_end|>
<|im_start|>assistant
<Z_24><Z_53><Z_363><Z_330><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh had 7 marbles in his collection. He lost 8 marbles and found 10 new ones.. How many more marbles did he find than those he lost?<|im_end|>
<|im_start|>assistant
<Z_333><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh had 7 marbles in his collection. He lost 8 marbles and found 10 new ones.. How many more marbles did he find than those he lost?<|im_end|>
<|im_start|>assistant
<Z_21><Z_465><Z_70><Z_55><ANSWER>

Question: Josh had 7 marbles in his collection. He lost 8 marbles and found 10 new ones.. How many more marbles did he find than those he lost?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train 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
two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_153><Z_434><Z_63><Z_146><Z_279><Z_349><Z_425><Z_278><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?<|im_end|>
<|im_start|>assistant
<Z_439><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?<|im_end|>
<|im_start|>assistant
<Z_295><Z_60><Z_338><Z_219><Z_266><Z_178><Z_305><Z_77><Z_488><ANSWER>

Question: two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even four-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5$?<|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
How many even four-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5$?<|im_end|>
<|im_start|>assistant
<Z_369><Z_140><Z_274><Z_482><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even four-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5$?<|im_end|>
<|im_start|>assistant
<Z_474><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many even four-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5$?<|im_end|>
<|im_start|>assistant
<Z_202><Z_144><Z_445><Z_450><ANSWER>

Question: How many even four-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.<|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
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.<|im_end|>
<|im_start|>assistant
<Z_369><Z_386><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.<|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
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.<|im_end|>
<|im_start|>assistant
<Z_448><Z_125><ANSWER>

Question:
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain company, there are some female managers. If 2/5 of all the employees are managers and 2/5 of all male employees are managers, the total number of female employees in the company is 750. How many female managers are there in the company?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain company, there are some female managers. If 2/5 of all the employees are managers and 2/5 of all male employees are managers, the total number of female employees in the company is 750. How many female managers are there in the company?<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain company, there are some female managers. If 2/5 of all the employees are managers and 2/5 of all male employees are managers, the total number of female employees in the company is 750. How many female managers are there in the company?<|im_end|>
<|im_start|>assistant
<Z_100><ANSWER>

Question: In a certain company, there are some female managers. If 2/5 of all the employees are managers and 2/5 of all male employees are managers, the total number of female employees in the company is 750. How many female managers are there in the company?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $g(x) = x^4 + ax^3 + bx^2 + cx + d$ has real coefficients, and $g(3i) = g(1+i) = 0$, find the value of $a + b + c + d$.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $g(x) = x^4 + ax^3 + bx^2 + cx + d$ has real coefficients, and $g(3i) = g(1+i) = 0$, find the value of $a + b + c + d$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_157><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $g(x) = x^4 + ax^3 + bx^2 + cx + d$ has real coefficients, and $g(3i) = g(1+i) = 0$, find the value of $a + b + c + d$.<|im_end|>
<|im_start|>assistant
<Z_501><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $g(x) = x^4 + ax^3 + bx^2 + cx + d$ has real coefficients, and $g(3i) = g(1+i) = 0$, find the value of $a + b + c + d$.<|im_end|>
<|im_start|>assistant
<Z_465><Z_312><ANSWER>

Question: If the polynomial $g(x) = x^4 + ax^3 + bx^2 + cx + d$ has real coefficients, and $g(3i) = g(1+i) = 0$, find the value of $a + b + c + d$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f\left(\frac{1}{x}+1\right)=\frac{1}{{x^2}}+\frac{1}{x}+\frac{1}{4}$, find the value of $f\left(\frac{3}{2}\right)$.<|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
Given the function $f\left(\frac{1}{x}+1\right)=\frac{1}{{x^2}}+\frac{1}{x}+\frac{1}{4}$, find the value of $f\left(\frac{3}{2}\right)$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_470><Z_238><Z_232><Z_510><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f\left(\frac{1}{x}+1\right)=\frac{1}{{x^2}}+\frac{1}{x}+\frac{1}{4}$, find the value of $f\left(\frac{3}{2}\right)$.<|im_end|>
<|im_start|>assistant
<Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f\left(\frac{1}{x}+1\right)=\frac{1}{{x^2}}+\frac{1}{x}+\frac{1}{4}$, find the value of $f\left(\frac{3}{2}\right)$.<|im_end|>
<|im_start|>assistant
<Z_164><Z_298><Z_213><Z_423><Z_281><ANSWER>

Question: Given the function $f\left(\frac{1}{x}+1\right)=\frac{1}{{x^2}}+\frac{1}{x}+\frac{1}{4}$, find the value of $f\left(\frac{3}{2}\right)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A collection of 8 cubes consists of one cube with edge-length  $k$  for each integer  $k,\thinspace 1 \le k \le 8.$   A tower is to be built using all 8 cubes according to the rules:

 $\bullet$  Any cube may be the bottom cube in the tower.
 $\bullet$  The cube immediately on top of a cube with edge-length  $k$  must have edge-length at most  $k+2.$

Let  $T$  be the number of different towers than can be constructed.  What is the remainder when  $T$  is divided by 1000?<|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 collection of 8 cubes consists of one cube with edge-length  $k$  for each integer  $k,\thinspace 1 \le k \le 8.$   A tower is to be built using all 8 cubes according to the rules:

 $\bullet$  Any cube may be the bottom cube in the tower.
 $\bullet$  The cube immediately on top of a cube with edge-length  $k$  must have edge-length at most  $k+2.$

Let  $T$  be the number of different towers than can be constructed.  What is the remainder when  $T$  is divided by 1000?<|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 collection of 8 cubes consists of one cube with edge-length  $k$  for each integer  $k,\thinspace 1 \le k \le 8.$   A tower is to be built using all 8 cubes according to the rules:

 $\bullet$  Any cube may be the bottom cube in the tower.
 $\bullet$  The cube immediately on top of a cube with edge-length  $k$  must have edge-length at most  $k+2.$

Let  $T$  be the number of different towers than can be constructed.  What is the remainder when  $T$  is divided by 1000?<|im_end|>
<|im_start|>assistant
<Z_396><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A collection of 8 cubes consists of one cube with edge-length  $k$  for each integer  $k,\thinspace 1 \le k \le 8.$   A tower is to be built using all 8 cubes according to the rules:

 $\bullet$  Any cube may be the bottom cube in the tower.
 $\bullet$  The cube immediately on top of a cube with edge-length  $k$  must have edge-length at most  $k+2.$

Let  $T$  be the number of different towers than can be constructed.  What is the remainder when  $T$  is divided by 1000?<|im_end|>
<|im_start|>assistant
<Z_456><ANSWER>

Question:
A collection of 8 cubes consists of one cube with edge-length  $k$  for each integer  $k,\thinspace 1 \le k \le 8.$   A tower is to be built using all 8 cubes according to the rules:

 $\bullet$  Any cube may be the bottom cube in the tower.
 $\bullet$  The cube immediately on top of a cube with edge-length  $k$  must have edge-length at most  $k+2.$

Let  $T$  be the number of different towers than can be constructed.  What is the remainder when  $T$  is divided by 1000?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are some red peaches, 90 yellow peaches, and 16 green peaches in the basket. There are 22 red and green peaches in the basket. How many red peaches are in the basket?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are some red peaches, 90 yellow peaches, and 16 green peaches in the basket. There are 22 red and green peaches in the basket. How many red peaches are in the basket?<|im_end|>
<|im_start|>assistant
<Z_24><Z_146><Z_181><Z_70><Z_446><Z_412><Z_373><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are some red peaches, 90 yellow peaches, and 16 green peaches in the basket. There are 22 red and green peaches in the basket. How many red peaches are in the basket?<|im_end|>
<|im_start|>assistant
<Z_253><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are some red peaches, 90 yellow peaches, and 16 green peaches in the basket. There are 22 red and green peaches in the basket. How many red peaches are in the basket?<|im_end|>
<|im_start|>assistant
<Z_56><Z_358><Z_277><Z_373><Z_363><Z_482><Z_224><ANSWER>

Question: There are some red peaches, 90 yellow peaches, and 16 green peaches in the basket. There are 22 red and green peaches in the basket. How many red peaches are in the basket?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of 17 persons in an office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. What is the age of the 15th person?<|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 average age of 17 persons in an office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. What is the age of the 15th person?<|im_end|>
<|im_start|>assistant
<Z_369><Z_35><Z_470><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of 17 persons in an office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. What is the age of the 15th person?<|im_end|>
<|im_start|>assistant
<Z_201><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of 17 persons in an office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. What is the age of the 15th person?<|im_end|>
<|im_start|>assistant
<Z_216><Z_3><Z_433><ANSWER>

Question: The average age of 17 persons in an office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. What is the age of the 15th person?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. He has 3 hours of free time available, and he uses this time to clean his apartment. How many minutes of free time will he have left after he cleans the apartment?<|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
Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. He has 3 hours of free time available, and he uses this time to clean his apartment. How many minutes of free time will he have left after he cleans the apartment?<|im_end|>
<|im_start|>assistant
<Z_477><Z_75><Z_73><Z_196><Z_34><Z_63><Z_59><Z_250><Z_445><Z_92><Z_273><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. He has 3 hours of free time available, and he uses this time to clean his apartment. How many minutes of free time will he have left after he cleans the apartment?<|im_end|>
<|im_start|>assistant
<Z_221><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. He has 3 hours of free time available, and he uses this time to clean his apartment. How many minutes of free time will he have left after he cleans the apartment?<|im_end|>
<|im_start|>assistant
<Z_161><Z_460><Z_162><Z_383><Z_398><Z_463><Z_113><Z_184><Z_506><Z_109><Z_486><ANSWER>

Question: Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. He has 3 hours of free time available, and he uses this time to clean his apartment. How many minutes of free time will he have left after he cleans the apartment?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the remainder when $5^{5^{5^5}}$ is divided by 500.<|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 remainder when $5^{5^{5^5}}$ is divided by 500.<|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 remainder when $5^{5^{5^5}}$ is divided by 500.<|im_end|>
<|im_start|>assistant
<Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the remainder when $5^{5^{5^5}}$ is divided by 500.<|im_end|>
<|im_start|>assistant
<Z_197><ANSWER>

Question: Find the remainder when $5^{5^{5^5}}$ is divided by 500.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers, not exceeding 150, are multiples of 3 or 4 but not 6?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers, not exceeding 150, are multiples of 3 or 4 but not 6?<|im_end|>
<|im_start|>assistant
<Z_24><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers, not exceeding 150, are multiples of 3 or 4 but not 6?<|im_end|>
<|im_start|>assistant
<Z_252><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive integers, not exceeding 150, are multiples of 3 or 4 but not 6?<|im_end|>
<|im_start|>assistant
<Z_395><Z_297><ANSWER>

Question: How many positive integers, not exceeding 150, are multiples of 3 or 4 but not 6?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If you cut and used 105 millimeters (mm) from a 23.3 centimeter (cm) wire and another 4.6 centimeters (cm) the next day, how many millimeters (mm) of wire are left?<|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 you cut and used 105 millimeters (mm) from a 23.3 centimeter (cm) wire and another 4.6 centimeters (cm) the next day, how many millimeters (mm) of wire are left?<|im_end|>
<|im_start|>assistant
<Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If you cut and used 105 millimeters (mm) from a 23.3 centimeter (cm) wire and another 4.6 centimeters (cm) the next day, how many millimeters (mm) of wire are left?<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

Question: If you cut and used 105 millimeters (mm) from a 23.3 centimeter (cm) wire and another 4.6 centimeters (cm) the next day, how many millimeters (mm) of wire are left?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If m = 3^some exponent, what is the greatest value of the exponent for which m is a factor of 25!?<|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 m = 3^some exponent, what is the greatest value of the exponent for which m is a factor of 25!?<|im_end|>
<|im_start|>assistant
<Z_477><Z_304><Z_447><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If m = 3^some exponent, what is the greatest value of the exponent for which m is a factor of 25!?<|im_end|>
<|im_start|>assistant
<Z_293><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If m = 3^some exponent, what is the greatest value of the exponent for which m is a factor of 25!?<|im_end|>
<|im_start|>assistant
<Z_505><Z_476><Z_418><ANSWER>

Question: If m = 3^some exponent, what is the greatest value of the exponent for which m is a factor of 25!?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?<|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 factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_158><Z_450><Z_458><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?<|im_end|>
<|im_start|>assistant
<Z_166><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?<|im_end|>
<|im_start|>assistant
<Z_508><Z_390><Z_15><Z_226><ANSWER>

Question: a factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the 25% of a certain amount which is Rs. 200. What is the amount?<|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 25% of a certain amount which is Rs. 200. What is the amount?<|im_end|>
<|im_start|>assistant
<Z_24><Z_262><Z_264><Z_184><Z_443><Z_463><Z_445><Z_404><Z_348><Z_176><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the 25% of a certain amount which is Rs. 200. What is the amount?<|im_end|>
<|im_start|>assistant
<Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the 25% of a certain amount which is Rs. 200. What is the amount?<|im_end|>
<|im_start|>assistant
<Z_90><Z_192><Z_439><Z_17><Z_113><Z_424><Z_11><Z_34><Z_501><Z_181><Z_303><ANSWER>

Question: Find the 25% of a certain amount which is Rs. 200. What is the amount?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the smallest possible product of two distinct prime numbers, each greater than 50.<|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
Determine the smallest possible product of two distinct prime numbers, each greater than 50.<|im_end|>
<|im_start|>assistant
<Z_477><Z_416><Z_149><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the smallest possible product of two distinct prime numbers, each greater than 50.<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the smallest possible product of two distinct prime numbers, each greater than 50.<|im_end|>
<|im_start|>assistant
<Z_353><Z_29><Z_467><ANSWER>

Question: Determine the smallest possible product of two distinct prime numbers, each greater than 50.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A family buys 5 black pencils, 3 blue pens, 1 red pen, and 1 green pen. How many ways are there to arrange these writing utensils in a circular holder if the 2 blue pens are not to be adjacent?<|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 family buys 5 black pencils, 3 blue pens, 1 red pen, and 1 green pen. How many ways are there to arrange these writing utensils in a circular holder if the 2 blue pens are not to be adjacent?<|im_end|>
<|im_start|>assistant
<Z_369><Z_219><Z_71><Z_497><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A family buys 5 black pencils, 3 blue pens, 1 red pen, and 1 green pen. How many ways are there to arrange these writing utensils in a circular holder if the 2 blue pens are not to be adjacent?<|im_end|>
<|im_start|>assistant
<Z_508><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A family buys 5 black pencils, 3 blue pens, 1 red pen, and 1 green pen. How many ways are there to arrange these writing utensils in a circular holder if the 2 blue pens are not to be adjacent?<|im_end|>
<|im_start|>assistant
<Z_147><Z_125><Z_330><Z_57><ANSWER>

Question: A family buys 5 black pencils, 3 blue pens, 1 red pen, and 1 green pen. How many ways are there to arrange these writing utensils in a circular holder if the 2 blue pens are not to be adjacent?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 34 pencils and 49 crayons in the drawer. Dan took 22 pencils from the drawer and then returned 5 of them. After that, he took 11 crayons out of the drawer. How many pencils are now in the drawer?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 34 pencils and 49 crayons in the drawer. Dan took 22 pencils from the drawer and then returned 5 of them. After that, he took 11 crayons out of the drawer. How many pencils are now in the drawer?<|im_end|>
<|im_start|>assistant
<Z_477><Z_85><Z_463><Z_33><Z_210><Z_352><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 34 pencils and 49 crayons in the drawer. Dan took 22 pencils from the drawer and then returned 5 of them. After that, he took 11 crayons out of the drawer. How many pencils are now in the drawer?<|im_end|>
<|im_start|>assistant
<Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 34 pencils and 49 crayons in the drawer. Dan took 22 pencils from the drawer and then returned 5 of them. After that, he took 11 crayons out of the drawer. How many pencils are now in the drawer?<|im_end|>
<|im_start|>assistant
<Z_386><Z_222><Z_83><Z_110><Z_101><Z_337><ANSWER>

Question: There are 34 pencils and 49 crayons in the drawer. Dan took 22 pencils from the drawer and then returned 5 of them. After that, he took 11 crayons out of the drawer. How many pencils are now in the drawer?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a castle, there are 25 identical square rooms forming a $5 \times 5$ square. Each of the 25 rooms is occupied by one person - either a liar or a knight (liars always lie, knights always tell the truth). Each of these 25 people said, "In at least one of the rooms adjacent to mine, there lives a liar." Rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 25 people?<|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 a castle, there are 25 identical square rooms forming a $5 \times 5$ square. Each of the 25 rooms is occupied by one person - either a liar or a knight (liars always lie, knights always tell the truth). Each of these 25 people said, "In at least one of the rooms adjacent to mine, there lives a liar." Rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 25 people?<|im_end|>
<|im_start|>assistant
<Z_477><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a castle, there are 25 identical square rooms forming a $5 \times 5$ square. Each of the 25 rooms is occupied by one person - either a liar or a knight (liars always lie, knights always tell the truth). Each of these 25 people said, "In at least one of the rooms adjacent to mine, there lives a liar." Rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 25 people?<|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
In a castle, there are 25 identical square rooms forming a $5 \times 5$ square. Each of the 25 rooms is occupied by one person - either a liar or a knight (liars always lie, knights always tell the truth). Each of these 25 people said, "In at least one of the rooms adjacent to mine, there lives a liar." Rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 25 people?<|im_end|>
<|im_start|>assistant
<Z_429><Z_488><ANSWER>

Question: In a castle, there are 25 identical square rooms forming a $5 \times 5$ square. Each of the 25 rooms is occupied by one person - either a liar or a knight (liars always lie, knights always tell the truth). Each of these 25 people said, "In at least one of the rooms adjacent to mine, there lives a liar." Rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 25 people?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The light glows for some seconds. It glowed 292.29411764705884 times between 1:57:58 and 3:20:47 am. How many seconds does the light glow for?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The light glows for some seconds. It glowed 292.29411764705884 times between 1:57:58 and 3:20:47 am. How many seconds does the light glow for?<|im_end|>
<|im_start|>assistant
<Z_24><Z_403><Z_199><Z_488><Z_470><Z_123><Z_116><Z_200><Z_186><Z_274><Z_478><Z_451><Z_115><Z_294><Z_403><Z_368><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The light glows for some seconds. It glowed 292.29411764705884 times between 1:57:58 and 3:20:47 am. How many seconds does the light glow for?<|im_end|>
<|im_start|>assistant
<Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The light glows for some seconds. It glowed 292.29411764705884 times between 1:57:58 and 3:20:47 am. How many seconds does the light glow for?<|im_end|>
<|im_start|>assistant
<Z_452><Z_373><Z_402><Z_422><Z_36><Z_107><Z_30><Z_303><Z_36><Z_174><Z_184><Z_410><Z_133><Z_337><Z_287><Z_434><ANSWER>

Question: The light glows for some seconds. It glowed 292.29411764705884 times between 1:57:58 and 3:20:47 am. How many seconds does the light glow for?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the square root of a positive number $x$ is $3a-4$ and $1-6a$, then $a=$______, $x=______.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the square root of a positive number $x$ is $3a-4$ and $1-6a$, then $a=$______, $x=______.<|im_end|>
<|im_start|>assistant
<Z_369><Z_49><Z_86><Z_31><Z_227><Z_145><Z_266><Z_406><Z_467><Z_118><Z_211><Z_410><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the square root of a positive number $x$ is $3a-4$ and $1-6a$, then $a=$______, $x=______.<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the square root of a positive number $x$ is $3a-4$ and $1-6a$, then $a=$______, $x=______.<|im_end|>
<|im_start|>assistant
<Z_171><Z_432><Z_93><Z_130><Z_71><Z_300><Z_86><Z_383><Z_41><Z_257><Z_423><Z_273><ANSWER>

Question: If the square root of a positive number $x$ is $3a-4$ and $1-6a$, then $a=$______, $x=______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the number of intersection points between the graphs of $r = 3 \cos \theta$ and $r = 6 \sin \theta$.<|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
Determine the number of intersection points between the graphs of $r = 3 \cos \theta$ and $r = 6 \sin \theta$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_403><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the number of intersection points between the graphs of $r = 3 \cos \theta$ and $r = 6 \sin \theta$.<|im_end|>
<|im_start|>assistant
<Z_139><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the number of intersection points between the graphs of $r = 3 \cos \theta$ and $r = 6 \sin \theta$.<|im_end|>
<|im_start|>assistant
<Z_206><Z_407><ANSWER>

Question: Determine the number of intersection points between the graphs of $r = 3 \cos \theta$ and $r = 6 \sin \theta$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Is there a positive integer $m$, such that for any positive integer $n$, $f(n)={3}^{n}(2n+7)+m$ is divisible by $36$? If it exists, find the minimum value of $m$ and prove your conclusion using mathematical induction; if it does not exist, please explain why.<|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
Is there a positive integer $m$, such that for any positive integer $n$, $f(n)={3}^{n}(2n+7)+m$ is divisible by $36$? If it exists, find the minimum value of $m$ and prove your conclusion using mathematical induction; if it does not exist, please explain why.<|im_end|>
<|im_start|>assistant
<Z_477><Z_273><Z_71><Z_83><Z_219><Z_372><Z_166><Z_67><Z_109><Z_403><Z_272><Z_254><Z_300><Z_472><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Is there a positive integer $m$, such that for any positive integer $n$, $f(n)={3}^{n}(2n+7)+m$ is divisible by $36$? If it exists, find the minimum value of $m$ and prove your conclusion using mathematical induction; if it does not exist, please explain why.<|im_end|>
<|im_start|>assistant
<Z_147><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Is there a positive integer $m$, such that for any positive integer $n$, $f(n)={3}^{n}(2n+7)+m$ is divisible by $36$? If it exists, find the minimum value of $m$ and prove your conclusion using mathematical induction; if it does not exist, please explain why.<|im_end|>
<|im_start|>assistant
<Z_315><Z_345><Z_349><Z_386><Z_125><Z_231><Z_380><Z_492><Z_91><Z_154><Z_342><Z_475><Z_218><Z_204><ANSWER>

Question: Is there a positive integer $m$, such that for any positive integer $n$, $f(n)={3}^{n}(2n+7)+m$ is divisible by $36$? If it exists, find the minimum value of $m$ and prove your conclusion using mathematical induction; if it does not exist, please explain why.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school arranges Chinese, Mathematics, English, Physics, Chemistry, elective courses, and 2 self-study periods within 8 class periods in one day. The first period can only be one of Chinese, Mathematics, or English. The eighth period can only be an elective course or a self-study period. Elective courses and self-study periods, as well as self-study periods with each other, cannot be adjacent. The total number of different arrangements is \_\_\_\_\_\_ (The result should be expressed in numbers).<|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 school arranges Chinese, Mathematics, English, Physics, Chemistry, elective courses, and 2 self-study periods within 8 class periods in one day. The first period can only be one of Chinese, Mathematics, or English. The eighth period can only be an elective course or a self-study period. Elective courses and self-study periods, as well as self-study periods with each other, cannot be adjacent. The total number of different arrangements is \_\_\_\_\_\_ (The result should be expressed in numbers).<|im_end|>
<|im_start|>assistant
<Z_369><Z_488><Z_114><Z_245><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school arranges Chinese, Mathematics, English, Physics, Chemistry, elective courses, and 2 self-study periods within 8 class periods in one day. The first period can only be one of Chinese, Mathematics, or English. The eighth period can only be an elective course or a self-study period. Elective courses and self-study periods, as well as self-study periods with each other, cannot be adjacent. The total number of different arrangements is \_\_\_\_\_\_ (The result should be expressed in numbers).<|im_end|>
<|im_start|>assistant
<Z_137><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A school arranges Chinese, Mathematics, English, Physics, Chemistry, elective courses, and 2 self-study periods within 8 class periods in one day. The first period can only be one of Chinese, Mathematics, or English. The eighth period can only be an elective course or a self-study period. Elective courses and self-study periods, as well as self-study periods with each other, cannot be adjacent. The total number of different arrangements is \_\_\_\_\_\_ (The result should be expressed in numbers).<|im_end|>
<|im_start|>assistant
<Z_194><Z_220><Z_278><Z_225><ANSWER>

Question: A school arranges Chinese, Mathematics, English, Physics, Chemistry, elective courses, and 2 self-study periods within 8 class periods in one day. The first period can only be one of Chinese, Mathematics, or English. The eighth period can only be an elective course or a self-study period. Elective courses and self-study periods, as well as self-study periods with each other, cannot be adjacent. The total number of different arrangements is \_\_\_\_\_\_ (The result should be expressed in numbers).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 7 points) A store is having a seasonal sale on its merchandise. If the merchandise is sold at 60% of its original price, the store will lose 20 yuan. If it is sold at 80% of its original price, the store will gain 15 yuan. The question is: What is the original price of this merchandise?<|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
(This question is worth 7 points) A store is having a seasonal sale on its merchandise. If the merchandise is sold at 60% of its original price, the store will lose 20 yuan. If it is sold at 80% of its original price, the store will gain 15 yuan. The question is: What is the original price of this merchandise?<|im_end|>
<|im_start|>assistant
<Z_24><Z_274><Z_195><Z_99><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 7 points) A store is having a seasonal sale on its merchandise. If the merchandise is sold at 60% of its original price, the store will lose 20 yuan. If it is sold at 80% of its original price, the store will gain 15 yuan. The question is: What is the original price of this merchandise?<|im_end|>
<|im_start|>assistant
<Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 7 points) A store is having a seasonal sale on its merchandise. If the merchandise is sold at 60% of its original price, the store will lose 20 yuan. If it is sold at 80% of its original price, the store will gain 15 yuan. The question is: What is the original price of this merchandise?<|im_end|>
<|im_start|>assistant
<Z_83><Z_140><Z_322><Z_494><Z_477><ANSWER>

Question: (This question is worth 7 points) A store is having a seasonal sale on its merchandise. If the merchandise is sold at 60% of its original price, the store will lose 20 yuan. If it is sold at 80% of its original price, the store will gain 15 yuan. The question is: What is the original price of this merchandise?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a\ast b = 4a + 5b - 2ab$, what is the value of $6\ast3$?<|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 $a\ast b = 4a + 5b - 2ab$, what is the value of $6\ast3$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_373><Z_382><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a\ast b = 4a + 5b - 2ab$, what is the value of $6\ast3$?<|im_end|>
<|im_start|>assistant
<Z_239><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a\ast b = 4a + 5b - 2ab$, what is the value of $6\ast3$?<|im_end|>
<|im_start|>assistant
<Z_376><Z_464><Z_240><ANSWER>

Question: If $a\ast b = 4a + 5b - 2ab$, what is the value of $6\ast3$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
One day Max says to Liz, "Out of the 25 people taking either English or French, you and I are the only two taking both.'' Liz, being mathematically inclined, responds by pointing out that there are exactly twice as many people in the English class as there are in the French class. How many people are taking English but not French?<|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
One day Max says to Liz, "Out of the 25 people taking either English or French, you and I are the only two taking both.'' Liz, being mathematically inclined, responds by pointing out that there are exactly twice as many people in the English class as there are in the French class. How many people are taking English but not French?<|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
One day Max says to Liz, "Out of the 25 people taking either English or French, you and I are the only two taking both.'' Liz, being mathematically inclined, responds by pointing out that there are exactly twice as many people in the English class as there are in the French class. How many people are taking English but not French?<|im_end|>
<|im_start|>assistant
<Z_266><ANSWER>

Question: One day Max says to Liz, "Out of the 25 people taking either English or French, you and I are the only two taking both.'' Liz, being mathematically inclined, responds by pointing out that there are exactly twice as many people in the English class as there are in the French class. How many people are taking English but not French?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a triangle, there are generally nine altitudes, angle bisectors, and medians. Investigate cases when there are fewer.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a triangle, there are generally nine altitudes, angle bisectors, and medians. Investigate cases when there are fewer.<|im_end|>
<|im_start|>assistant
<Z_24><Z_485><Z_208><Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a triangle, there are generally nine altitudes, angle bisectors, and medians. Investigate cases when there are fewer.<|im_end|>
<|im_start|>assistant
<Z_156><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a triangle, there are generally nine altitudes, angle bisectors, and medians. Investigate cases when there are fewer.<|im_end|>
<|im_start|>assistant
<Z_508><Z_299><Z_220><Z_273><ANSWER>

Question: In a triangle, there are generally nine altitudes, angle bisectors, and medians. Investigate cases when there are fewer.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man purchased 4 cotton blankets @ Rs. 100 each, 3 woolen blankets @ Rs. 150 each, and 2 silk blankets at a certain rate which is now slipped off from his memory. In addition, there was a discount on the cotton and woolen blankets: the cotton blankets had a 10% discount, and the woolen blankets had a 5% discount. He also remembers that the average price of all the blankets, after applying the discounts but before adding any taxes, was Rs. 130. Find the original price of the two silk blankets before any discounts or taxes were applied.<|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 man purchased 4 cotton blankets @ Rs. 100 each, 3 woolen blankets @ Rs. 150 each, and 2 silk blankets at a certain rate which is now slipped off from his memory. In addition, there was a discount on the cotton and woolen blankets: the cotton blankets had a 10% discount, and the woolen blankets had a 5% discount. He also remembers that the average price of all the blankets, after applying the discounts but before adding any taxes, was Rs. 130. Find the original price of the two silk blankets before any discounts or taxes were applied.<|im_end|>
<|im_start|>assistant
<Z_477><Z_240><Z_161><Z_304><Z_450><Z_391><Z_375><Z_400><Z_143><Z_64><Z_173><Z_286><Z_499><Z_135><Z_450><Z_330><Z_264><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man purchased 4 cotton blankets @ Rs. 100 each, 3 woolen blankets @ Rs. 150 each, and 2 silk blankets at a certain rate which is now slipped off from his memory. In addition, there was a discount on the cotton and woolen blankets: the cotton blankets had a 10% discount, and the woolen blankets had a 5% discount. He also remembers that the average price of all the blankets, after applying the discounts but before adding any taxes, was Rs. 130. Find the original price of the two silk blankets before any discounts or taxes were applied.<|im_end|>
<|im_start|>assistant
<Z_281><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man purchased 4 cotton blankets @ Rs. 100 each, 3 woolen blankets @ Rs. 150 each, and 2 silk blankets at a certain rate which is now slipped off from his memory. In addition, there was a discount on the cotton and woolen blankets: the cotton blankets had a 10% discount, and the woolen blankets had a 5% discount. He also remembers that the average price of all the blankets, after applying the discounts but before adding any taxes, was Rs. 130. Find the original price of the two silk blankets before any discounts or taxes were applied.<|im_end|>
<|im_start|>assistant
<Z_501><Z_505><Z_435><Z_227><Z_451><Z_12><Z_106><Z_412><Z_377><Z_386><Z_390><Z_348><Z_362><Z_501><Z_177><Z_178><Z_335><ANSWER>

Question: A man purchased 4 cotton blankets @ Rs. 100 each, 3 woolen blankets @ Rs. 150 each, and 2 silk blankets at a certain rate which is now slipped off from his memory. In addition, there was a discount on the cotton and woolen blankets: the cotton blankets had a 10% discount, and the woolen blankets had a 5% discount. He also remembers that the average price of all the blankets, after applying the discounts but before adding any taxes, was Rs. 130. Find the original price of the two silk blankets before any discounts or taxes were applied.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?<|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
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?<|im_end|>
<|im_start|>assistant
<Z_24><Z_227><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?<|im_end|>
<|im_start|>assistant
<Z_249><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?<|im_end|>
<|im_start|>assistant
<Z_38><Z_136><ANSWER>

Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
One hundred bricks, each measuring $3''\times11''\times18''$, are to be stacked one on top of another in a tower. Each brick can be oriented to contribute $3''$, $11''$, or $18''$ to the tower height. Determine how many different tower heights can be achieved using all one hundred bricks.<|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
One hundred bricks, each measuring $3''\times11''\times18''$, are to be stacked one on top of another in a tower. Each brick can be oriented to contribute $3''$, $11''$, or $18''$ to the tower height. Determine how many different tower heights can be achieved using all one hundred bricks.<|im_end|>
<|im_start|>assistant
<Z_477><Z_290><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
One hundred bricks, each measuring $3''\times11''\times18''$, are to be stacked one on top of another in a tower. Each brick can be oriented to contribute $3''$, $11''$, or $18''$ to the tower height. Determine how many different tower heights can be achieved using all one hundred bricks.<|im_end|>
<|im_start|>assistant
<Z_0><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
One hundred bricks, each measuring $3''\times11''\times18''$, are to be stacked one on top of another in a tower. Each brick can be oriented to contribute $3''$, $11''$, or $18''$ to the tower height. Determine how many different tower heights can be achieved using all one hundred bricks.<|im_end|>
<|im_start|>assistant
<Z_411><Z_14><ANSWER>

Question: One hundred bricks, each measuring $3''\times11''\times18''$, are to be stacked one on top of another in a tower. Each brick can be oriented to contribute $3''$, $11''$, or $18''$ to the tower height. Determine how many different tower heights can be achieved using all one hundred bricks.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given positive integers $x$ and $y$ such that $\frac{1}{x} + \frac{1}{3y} = \frac{1}{8}$, find the least possible value of $xy$.<|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 positive integers $x$ and $y$ such that $\frac{1}{x} + \frac{1}{3y} = \frac{1}{8}$, find the least possible value of $xy$.<|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 positive integers $x$ and $y$ such that $\frac{1}{x} + \frac{1}{3y} = \frac{1}{8}$, find the least possible value of $xy$.<|im_end|>
<|im_start|>assistant
<Z_188><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given positive integers $x$ and $y$ such that $\frac{1}{x} + \frac{1}{3y} = \frac{1}{8}$, find the least possible value of $xy$.<|im_end|>
<|im_start|>assistant
<Z_456><ANSWER>

Question: Given positive integers $x$ and $y$ such that $\frac{1}{x} + \frac{1}{3y} = \frac{1}{8}$, find the least possible value of $xy$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given: $x : y : z = 1 : 2 : 7$ and $2x - y + 3z = 105$, find the value of $xyz$.<|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: $x : y : z = 1 : 2 : 7$ and $2x - y + 3z = 105$, find the value of $xyz$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_31><Z_30><Z_420><Z_71><Z_127><Z_392><Z_263><Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given: $x : y : z = 1 : 2 : 7$ and $2x - y + 3z = 105$, find the value of $xyz$.<|im_end|>
<|im_start|>assistant
<Z_402><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given: $x : y : z = 1 : 2 : 7$ and $2x - y + 3z = 105$, find the value of $xyz$.<|im_end|>
<|im_start|>assistant
<Z_238><Z_471><Z_103><Z_280><Z_215><Z_489><Z_383><Z_307><Z_200><ANSWER>

Question: Given: $x : y : z = 1 : 2 : 7$ and $2x - y + 3z = 105$, find the value of $xyz$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He plans to buy at least 150 jellybeans. He wants to buy the minimum amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He plans to buy at least 150 jellybeans. He wants to buy the minimum amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_24><Z_214><Z_485><Z_114><Z_63><Z_501><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He plans to buy at least 150 jellybeans. He wants to buy the minimum amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_288><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He plans to buy at least 150 jellybeans. He wants to buy the minimum amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_358><Z_115><Z_11><Z_212><Z_97><Z_81><ANSWER>

Question: Alex is at the candy store buying jellybeans. He plans to buy at least 150 jellybeans. He wants to buy the minimum amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $g(x) = x^3$ and $f(x) = 3x^2 - 2x + 1$, find the value of $f(g(3))$.<|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
If $g(x) = x^3$ and $f(x) = 3x^2 - 2x + 1$, find the value of $f(g(3))$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_217><Z_279><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $g(x) = x^3$ and $f(x) = 3x^2 - 2x + 1$, find the value of $f(g(3))$.<|im_end|>
<|im_start|>assistant
<Z_509><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $g(x) = x^3$ and $f(x) = 3x^2 - 2x + 1$, find the value of $f(g(3))$.<|im_end|>
<|im_start|>assistant
<Z_158><Z_100><Z_481><ANSWER>

Question: If $g(x) = x^3$ and $f(x) = 3x^2 - 2x + 1$, find the value of $f(g(3))$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $(-64)^{4/3}$.<|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
Evaluate $(-64)^{4/3}$.<|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
Evaluate $(-64)^{4/3}$.<|im_end|>
<|im_start|>assistant
<Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $(-64)^{4/3}$.<|im_end|>
<|im_start|>assistant
<Z_486><ANSWER>

Question: Evaluate $(-64)^{4/3}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the speed of the bus is some kmph, and including stoppages, it is 36 kmph. The bus stops for 20 minutes per hour. What is the speed of the bus excluding stoppages?<|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
Excluding stoppages, the speed of the bus is some kmph, and including stoppages, it is 36 kmph. The bus stops for 20 minutes per hour. What is the speed of the bus excluding stoppages?<|im_end|>
<|im_start|>assistant
<Z_326><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the speed of the bus is some kmph, and including stoppages, it is 36 kmph. The bus stops for 20 minutes per hour. What is the speed of the bus excluding stoppages?<|im_end|>
<|im_start|>assistant
<Z_56><ANSWER>

Question: Excluding stoppages, the speed of the bus is some kmph, and including stoppages, it is 36 kmph. The bus stops for 20 minutes per hour. What is the speed of the bus excluding stoppages?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^2f'(1) - 3x$, find the value of $f'(2)$.<|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
Given the function $f(x) = x^2f'(1) - 3x$, find the value of $f'(2)$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_193><Z_485><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^2f'(1) - 3x$, find the value of $f'(2)$.<|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
Given the function $f(x) = x^2f'(1) - 3x$, find the value of $f'(2)$.<|im_end|>
<|im_start|>assistant
<Z_459><Z_148><Z_7><ANSWER>

Question: Given the function $f(x) = x^2f'(1) - 3x$, find the value of $f'(2)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On an east-west shipping lane are ten ships sailing individually.  The first five from the west are sailing eastwards while the other five ships are sailing westwards.  They sail at the same constant speed at all times.  Whenever two ships meet, each turns around and sails in the opposite direction.  When all ships have returned to port, how many meetings of two ships have taken place?<|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
On an east-west shipping lane are ten ships sailing individually.  The first five from the west are sailing eastwards while the other five ships are sailing westwards.  They sail at the same constant speed at all times.  Whenever two ships meet, each turns around and sails in the opposite direction.  When all ships have returned to port, how many meetings of two ships have taken place?<|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
On an east-west shipping lane are ten ships sailing individually.  The first five from the west are sailing eastwards while the other five ships are sailing westwards.  They sail at the same constant speed at all times.  Whenever two ships meet, each turns around and sails in the opposite direction.  When all ships have returned to port, how many meetings of two ships have taken place?<|im_end|>
<|im_start|>assistant
<Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On an east-west shipping lane are ten ships sailing individually.  The first five from the west are sailing eastwards while the other five ships are sailing westwards.  They sail at the same constant speed at all times.  Whenever two ships meet, each turns around and sails in the opposite direction.  When all ships have returned to port, how many meetings of two ships have taken place?<|im_end|>
<|im_start|>assistant
<Z_242><ANSWER>

Question: On an east-west shipping lane are ten ships sailing individually.  The first five from the west are sailing eastwards while the other five ships are sailing westwards.  They sail at the same constant speed at all times.  Whenever two ships meet, each turns around and sails in the opposite direction.  When all ships have returned to port, how many meetings of two ships have taken place?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A line has a slope of $5$ and passes through the point $(-2, 4)$. Determine the expression for this line in the form $y = mx + b$ and calculate the value of $m + b$.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A line has a slope of $5$ and passes through the point $(-2, 4)$. Determine the expression for this line in the form $y = mx + b$ and calculate the value of $m + b$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_89><Z_298><Z_149><Z_265><Z_436><Z_510><Z_278><Z_68><Z_382><Z_256><Z_465><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A line has a slope of $5$ and passes through the point $(-2, 4)$. Determine the expression for this line in the form $y = mx + b$ and calculate the value of $m + b$.<|im_end|>
<|im_start|>assistant
<Z_173><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A line has a slope of $5$ and passes through the point $(-2, 4)$. Determine the expression for this line in the form $y = mx + b$ and calculate the value of $m + b$.<|im_end|>
<|im_start|>assistant
<Z_484><Z_44><Z_490><Z_199><Z_271><Z_265><Z_246><Z_505><Z_122><Z_300><Z_241><Z_511><ANSWER>

Question: A line has a slope of $5$ and passes through the point $(-2, 4)$. Determine the expression for this line in the form $y = mx + b$ and calculate the value of $m + b$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point a. Finally, he repeats this entire process, this time plotting the result as the point b. What is the probability that the distance between a and b is greater than the value of b?<|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
Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point a. Finally, he repeats this entire process, this time plotting the result as the point b. What is the probability that the distance between a and b is greater than the value of b?<|im_end|>
<|im_start|>assistant
<Z_477><Z_267><Z_510><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point a. Finally, he repeats this entire process, this time plotting the result as the point b. What is the probability that the distance between a and b is greater than the value of b?<|im_end|>
<|im_start|>assistant
<Z_499><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point a. Finally, he repeats this entire process, this time plotting the result as the point b. What is the probability that the distance between a and b is greater than the value of b?<|im_end|>
<|im_start|>assistant
<Z_463><Z_363><Z_255><Z_339><ANSWER>

Question: Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point a. Finally, he repeats this entire process, this time plotting the result as the point b. What is the probability that the distance between a and b is greater than the value of b?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An infinite geometric series has a common ratio of \( \frac{1}{4} \) and a sum of 80. What is the first term of the series?<|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
An infinite geometric series has a common ratio of \( \frac{1}{4} \) and a sum of 80. What is the first term of the series?<|im_end|>
<|im_start|>assistant
<Z_369><Z_310><Z_469><Z_357><Z_430><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An infinite geometric series has a common ratio of \( \frac{1}{4} \) and a sum of 80. What is the first term of the series?<|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
An infinite geometric series has a common ratio of \( \frac{1}{4} \) and a sum of 80. What is the first term of the series?<|im_end|>
<|im_start|>assistant
<Z_105><Z_434><Z_136><Z_395><Z_319><ANSWER>

Question: An infinite geometric series has a common ratio of \( \frac{1}{4} \) and a sum of 80. What is the first term of the series?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f_{1}(x) = \sqrt{2 - x}$, and for integers $n \geq 2$, let \[f_{n}(x) = f_{n-1}\left(\sqrt{(n+1)^2 - x}\right).\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N$, the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f_{1}(x) = \sqrt{2 - x}$, and for integers $n \geq 2$, let \[f_{n}(x) = f_{n-1}\left(\sqrt{(n+1)^2 - x}\right).\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N$, the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$<|im_end|>
<|im_start|>assistant
<Z_477><Z_372><Z_100><Z_420><Z_313><Z_376><Z_493><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f_{1}(x) = \sqrt{2 - x}$, and for integers $n \geq 2$, let \[f_{n}(x) = f_{n-1}\left(\sqrt{(n+1)^2 - x}\right).\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N$, the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$<|im_end|>
<|im_start|>assistant
<Z_289><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f_{1}(x) = \sqrt{2 - x}$, and for integers $n \geq 2$, let \[f_{n}(x) = f_{n-1}\left(\sqrt{(n+1)^2 - x}\right).\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N$, the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$<|im_end|>
<|im_start|>assistant
<Z_148><Z_428><Z_158><Z_182><Z_146><Z_477><Z_258><ANSWER>

Question: Let $f_{1}(x) = \sqrt{2 - x}$, and for integers $n \geq 2$, let \[f_{n}(x) = f_{n-1}\left(\sqrt{(n+1)^2 - x}\right).\]Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N$, the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Petya wrote the natural numbers 1, 2, ..., 20 on the board. Vasya first erased all even numbers and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board?<|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
Petya wrote the natural numbers 1, 2, ..., 20 on the board. Vasya first erased all even numbers and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board?<|im_end|>
<|im_start|>assistant
<Z_477><Z_382><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Petya wrote the natural numbers 1, 2, ..., 20 on the board. Vasya first erased all even numbers and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Petya wrote the natural numbers 1, 2, ..., 20 on the board. Vasya first erased all even numbers and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board?<|im_end|>
<|im_start|>assistant
<Z_276><Z_71><ANSWER>

Question: Petya wrote the natural numbers 1, 2, ..., 20 on the board. Vasya first erased all even numbers and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
10.25 people are lined up in a row, each of whom either tells the truth or lies.
The person at the front of the line says: "Everyone behind me is lying."
Everyone else says: "The person in front of me (the one directly next to the speaker) is lying."
Among these 25 people, there are ___ people who are lying.<|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
10.25 people are lined up in a row, each of whom either tells the truth or lies.
The person at the front of the line says: "Everyone behind me is lying."
Everyone else says: "The person in front of me (the one directly next to the speaker) is lying."
Among these 25 people, there are ___ people who are lying.<|im_end|>
<|im_start|>assistant
<Z_24><Z_425><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
10.25 people are lined up in a row, each of whom either tells the truth or lies.
The person at the front of the line says: "Everyone behind me is lying."
Everyone else says: "The person in front of me (the one directly next to the speaker) is lying."
Among these 25 people, there are ___ people who are lying.<|im_end|>
<|im_start|>assistant
<Z_294><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
10.25 people are lined up in a row, each of whom either tells the truth or lies.
The person at the front of the line says: "Everyone behind me is lying."
Everyone else says: "The person in front of me (the one directly next to the speaker) is lying."
Among these 25 people, there are ___ people who are lying.<|im_end|>
<|im_start|>assistant
<Z_428><Z_437><ANSWER>

Question:
10.25 people are lined up in a row, each of whom either tells the truth or lies.
The person at the front of the line says: "Everyone behind me is lying."
Everyone else says: "The person in front of me (the one directly next to the speaker) is lying."
Among these 25 people, there are ___ people who are lying.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the numerical value of $k$ for which
\[\frac{9}{x + y} = \frac{k}{x + z} = \frac{15}{z - y}.\]<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the numerical value of $k$ for which
\[\frac{9}{x + y} = \frac{k}{x + z} = \frac{15}{z - y}.\]<|im_end|>
<|im_start|>assistant
<Z_477><Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the numerical value of $k$ for which
\[\frac{9}{x + y} = \frac{k}{x + z} = \frac{15}{z - y}.\]<|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
Find the numerical value of $k$ for which
\[\frac{9}{x + y} = \frac{k}{x + z} = \frac{15}{z - y}.\]<|im_end|>
<|im_start|>assistant
<Z_53><Z_285><ANSWER>

Question:
Find the numerical value of $k$ for which
\[\frac{9}{x + y} = \frac{k}{x + z} = \frac{15}{z - y}.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pete's memory card can hold 3,000 pictures of 8 megabytes each. How many pictures can it hold of 6 megabytes each?<|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
Pete's memory card can hold 3,000 pictures of 8 megabytes each. How many pictures can it hold of 6 megabytes each?<|im_end|>
<|im_start|>assistant
<Z_24><Z_263><Z_97><Z_287><Z_94><Z_264><Z_487><Z_253><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pete's memory card can hold 3,000 pictures of 8 megabytes each. How many pictures can it hold of 6 megabytes each?<|im_end|>
<|im_start|>assistant
<Z_131><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pete's memory card can hold 3,000 pictures of 8 megabytes each. How many pictures can it hold of 6 megabytes each?<|im_end|>
<|im_start|>assistant
<Z_234><Z_1><Z_22><Z_75><Z_98><Z_186><Z_165><Z_387><ANSWER>

Question: Pete's memory card can hold 3,000 pictures of 8 megabytes each. How many pictures can it hold of 6 megabytes each?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the areas of two squares with side lengths of 8 and 10 respectively.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the areas of two squares with side lengths of 8 and 10 respectively.<|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 sum of the areas of two squares with side lengths of 8 and 10 respectively.<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the areas of two squares with side lengths of 8 and 10 respectively.<|im_end|>
<|im_start|>assistant
<Z_274><ANSWER>

Question: Find the sum of the areas of two squares with side lengths of 8 and 10 respectively.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tracy set up a booth at an art fair. 20 people came to look at her art. Four of those customers bought two paintings each. The next 12 of those customers bought one painting each. The last 4 customers bought four paintings each.  How many paintings did Tracy sell at the art fair?<|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
Tracy set up a booth at an art fair. 20 people came to look at her art. Four of those customers bought two paintings each. The next 12 of those customers bought one painting each. The last 4 customers bought four paintings each.  How many paintings did Tracy sell at the art fair?<|im_end|>
<|im_start|>assistant
<Z_24><Z_403><Z_220><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tracy set up a booth at an art fair. 20 people came to look at her art. Four of those customers bought two paintings each. The next 12 of those customers bought one painting each. The last 4 customers bought four paintings each.  How many paintings did Tracy sell at the art fair?<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tracy set up a booth at an art fair. 20 people came to look at her art. Four of those customers bought two paintings each. The next 12 of those customers bought one painting each. The last 4 customers bought four paintings each.  How many paintings did Tracy sell at the art fair?<|im_end|>
<|im_start|>assistant
<Z_73><Z_343><Z_433><ANSWER>

Question: Tracy set up a booth at an art fair. 20 people came to look at her art. Four of those customers bought two paintings each. The next 12 of those customers bought one painting each. The last 4 customers bought four paintings each.  How many paintings did Tracy sell at the art fair?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?<|im_end|>
<|im_start|>assistant
<Z_369><Z_102><Z_81><Z_490><Z_378><Z_346><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?<|im_end|>
<|im_start|>assistant
<Z_492><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?<|im_end|>
<|im_start|>assistant
<Z_502><Z_262><Z_501><Z_393><Z_361><Z_141><Z_140><ANSWER>

Question: An event has some adults and 20 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. The greatest number of tables the planner can set up is 4. How many adults are at the event?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \(\mathbf{Z}\) is the set of integers, and sets \(A\), \(B\), and \(C\) are defined as follows:

\[A = \left\{ x \mid | x - 3 | < \pi, x \in \mathbf{Z} \right\} \]

\[B = \left\{ x \mid x^2 - 11x + 5 < 0, x \in \mathbf{Z} \right\} \]

\[C = \left\{ x \mid |2x^2 - 11x + 10| \geq |3x - 2|, x \in \mathbf{Z} \right\} \]

Let \(\bar{C}\) be the complement of \(C\) in \(\mathbf{Z}\). The number of elements in \(A \cap B \cap \bar{C}\) is ( ).

A. 7

B. 8

C. 15

D. 16<|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 \(\mathbf{Z}\) is the set of integers, and sets \(A\), \(B\), and \(C\) are defined as follows:

\[A = \left\{ x \mid | x - 3 | < \pi, x \in \mathbf{Z} \right\} \]

\[B = \left\{ x \mid x^2 - 11x + 5 < 0, x \in \mathbf{Z} \right\} \]

\[C = \left\{ x \mid |2x^2 - 11x + 10| \geq |3x - 2|, x \in \mathbf{Z} \right\} \]

Let \(\bar{C}\) be the complement of \(C\) in \(\mathbf{Z}\). The number of elements in \(A \cap B \cap \bar{C}\) is ( ).

A. 7

B. 8

C. 15

D. 16<|im_end|>
<|im_start|>assistant
<Z_369><Z_134><Z_293><Z_494><Z_210><Z_345><Z_274><Z_163><Z_118><Z_434><Z_420><Z_441><Z_418><Z_386><Z_151><Z_237><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \(\mathbf{Z}\) is the set of integers, and sets \(A\), \(B\), and \(C\) are defined as follows:

\[A = \left\{ x \mid | x - 3 | < \pi, x \in \mathbf{Z} \right\} \]

\[B = \left\{ x \mid x^2 - 11x + 5 < 0, x \in \mathbf{Z} \right\} \]

\[C = \left\{ x \mid |2x^2 - 11x + 10| \geq |3x - 2|, x \in \mathbf{Z} \right\} \]

Let \(\bar{C}\) be the complement of \(C\) in \(\mathbf{Z}\). The number of elements in \(A \cap B \cap \bar{C}\) is ( ).

A. 7

B. 8

C. 15

D. 16<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \(\mathbf{Z}\) is the set of integers, and sets \(A\), \(B\), and \(C\) are defined as follows:

\[A = \left\{ x \mid | x - 3 | < \pi, x \in \mathbf{Z} \right\} \]

\[B = \left\{ x \mid x^2 - 11x + 5 < 0, x \in \mathbf{Z} \right\} \]

\[C = \left\{ x \mid |2x^2 - 11x + 10| \geq |3x - 2|, x \in \mathbf{Z} \right\} \]

Let \(\bar{C}\) be the complement of \(C\) in \(\mathbf{Z}\). The number of elements in \(A \cap B \cap \bar{C}\) is ( ).

A. 7

B. 8

C. 15

D. 16<|im_end|>
<|im_start|>assistant
<Z_35><Z_315><Z_458><Z_276><Z_365><Z_171><Z_79><Z_206><Z_24><Z_428><Z_313><Z_471><Z_294><Z_96><Z_79><Z_288><ANSWER>

Question:
Given that \(\mathbf{Z}\) is the set of integers, and sets \(A\), \(B\), and \(C\) are defined as follows:

\[A = \left\{ x \mid | x - 3 | < \pi, x \in \mathbf{Z} \right\} \]

\[B = \left\{ x \mid x^2 - 11x + 5 < 0, x \in \mathbf{Z} \right\} \]

\[C = \left\{ x \mid |2x^2 - 11x + 10| \geq |3x - 2|, x \in \mathbf{Z} \right\} \]

Let \(\bar{C}\) be the complement of \(C\) in \(\mathbf{Z}\). The number of elements in \(A \cap B \cap \bar{C}\) is ( ).

A. 7

B. 8

C. 15

D. 16


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the first 5 multiples of a certain number is 27. What is the number?<|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 average of the first 5 multiples of a certain number is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_24><Z_501><Z_263><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the first 5 multiples of a certain number is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_437><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the first 5 multiples of a certain number is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_435><Z_203><Z_47><ANSWER>

Question: The average of the first 5 multiples of a certain number is 27. What is the number?