<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_24><Z_264><Z_340><Z_157><Z_418><Z_267><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_428><Z_420><Z_185><Z_101><Z_259><Z_131><ANSWER>

Question: There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_369><Z_217><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_367><Z_231><ANSWER>

Question: How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|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
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_369><Z_39><Z_433><Z_502><Z_151><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_166><Z_209><Z_361><Z_85><Z_162><ANSWER>

Question: When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|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
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_24><Z_437><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_74><Z_505><ANSWER>

Question: Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter 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
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_194><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_495><ANSWER>

Question: sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|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
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_477><Z_73><Z_322><Z_433><Z_443><Z_271><Z_430><Z_155><Z_443><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_412><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_395><Z_395><Z_505><Z_47><Z_72><Z_153><Z_344><Z_453><Z_193><ANSWER>

Question: Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|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
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_446><Z_52><Z_107><Z_378><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_171><Z_186><Z_252><Z_155><Z_375><ANSWER>

Question: Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|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 stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_477><Z_351><Z_458><Z_210><Z_400><Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_165><Z_325><Z_405><Z_56><Z_121><Z_479><ANSWER>

Question: A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|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
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_477><Z_232><Z_296><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_366><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_464><Z_22><Z_310><ANSWER>

Question: rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|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 “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_24><Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_494><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_62><Z_308><ANSWER>

Question: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|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
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_477><Z_219><Z_178><Z_219><Z_464><Z_467><Z_157><Z_315><Z_266><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_16><Z_433><Z_437><Z_147><Z_505><Z_485><Z_203><Z_14><Z_365><ANSWER>

Question: Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|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
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|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
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_367><ANSWER>

Question: Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|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 car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_377><Z_393><Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_224><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_167><Z_69><Z_289><Z_416><ANSWER>

Question: a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|im_end|>
<|im_start|>assistant
<Z_369><Z_175><Z_116><Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|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
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|im_end|>
<|im_start|>assistant
<Z_362><Z_370><Z_147><Z_498><ANSWER>

Question: Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|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
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_392><Z_423><Z_77><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_135><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_260><Z_266><Z_338><Z_196><Z_372><ANSWER>

Question: Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|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
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_467><Z_318><Z_465><Z_418><Z_423><Z_443><Z_497><Z_224><Z_321><Z_134><Z_292><Z_98><Z_179><Z_211><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_470><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_149><Z_34><Z_51><Z_20><Z_230><Z_147><Z_152><Z_161><Z_114><Z_263><Z_495><Z_453><Z_168><Z_73><Z_106><ANSWER>

Question: Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|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 an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_369><Z_321><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_8><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_302><Z_101><ANSWER>

Question: In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|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
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_470><Z_87><Z_318><Z_255><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_245><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_16><Z_245><Z_309><Z_295><Z_193><Z_222><ANSWER>

Question: How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_24><Z_465><Z_355><Z_201><Z_387><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_481><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_482><Z_134><Z_39><Z_15><Z_441><ANSWER>

Question: A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|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
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_369><Z_386><Z_378><Z_267><Z_279><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_212><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_113><Z_244><Z_159><Z_123><Z_343><ANSWER>

Question: Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|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 \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_477><Z_335><Z_378><Z_487><Z_375><Z_467><Z_501><Z_247><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_55><Z_328><Z_415><Z_428><Z_66><Z_83><Z_348><Z_390><ANSWER>

Question: Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_24><Z_211><Z_391><Z_217><Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|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
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_274><Z_497><Z_65><Z_338><Z_393><ANSWER>

Question: The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|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 ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_87><Z_330><Z_246><Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_277><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_292><Z_493><Z_316><Z_166><Z_301><ANSWER>

Question: The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|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
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_477><Z_294><Z_362><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_407><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_335><Z_153><Z_140><ANSWER>

Question: Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_477><Z_503><Z_175><Z_458><Z_291><Z_460><Z_396><Z_218><Z_230><Z_206><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_343><Z_120><Z_222><Z_188><Z_503><Z_76><Z_206><Z_74><Z_362><Z_15><ANSWER>

Question: It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|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 volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_58><Z_232><Z_240><Z_264><Z_219><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_339><Z_426><Z_491><Z_312><Z_86><Z_449><Z_475><ANSWER>

Question: The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|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
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_477><Z_320><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_431><Z_57><ANSWER>

Question: Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|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 bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|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 bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_133><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_488><ANSWER>

Question: A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.<|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
If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.<|im_end|>
<|im_start|>assistant
<Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.<|im_end|>
<|im_start|>assistant
<Z_216><ANSWER>

Question: If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|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
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|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
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_2><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_130><ANSWER>

Question: Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|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 test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_369><Z_206><Z_378><Z_147><Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_306><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_32><Z_299><Z_354><Z_457><Z_227><ANSWER>

Question: The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|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 greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_406><Z_503><Z_267><Z_464><Z_181><Z_64><Z_240><Z_467><Z_310><Z_488><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_198><Z_219><Z_127><Z_104><Z_170><Z_278><Z_106><Z_316><Z_455><Z_83><Z_172><ANSWER>

Question: Find the greatest common factor (GCF) of $7!$ and $8!$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|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
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_369><Z_393><Z_213><Z_301><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_38><Z_54><Z_221><Z_5><ANSWER>

Question: Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the $100^{\text{th}}$ odd positive integer?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the $100^{\text{th}}$ odd positive integer?<|im_end|>
<|im_start|>assistant
<Z_369><Z_134><Z_213><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the $100^{\text{th}}$ odd positive integer?<|im_end|>
<|im_start|>assistant
<Z_330><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the $100^{\text{th}}$ odd positive integer?<|im_end|>
<|im_start|>assistant
<Z_16><Z_367><Z_426><ANSWER>

Question: What is the $100^{\text{th}}$ odd positive integer?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( n \) is a positive integer not greater than 2021, and satisfies
\[ \left(\lfloor \sqrt{n} \rfloor^2 + 1\right) \mid \left(n^2 + 1\right), \]
find the number of such \( n \).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( n \) is a positive integer not greater than 2021, and satisfies
\[ \left(\lfloor \sqrt{n} \rfloor^2 + 1\right) \mid \left(n^2 + 1\right), \]
find the number of such \( n \).<|im_end|>
<|im_start|>assistant
<Z_369><Z_463><Z_400><Z_498><Z_378><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( n \) is a positive integer not greater than 2021, and satisfies
\[ \left(\lfloor \sqrt{n} \rfloor^2 + 1\right) \mid \left(n^2 + 1\right), \]
find the number of such \( n \).<|im_end|>
<|im_start|>assistant
<Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \( n \) is a positive integer not greater than 2021, and satisfies
\[ \left(\lfloor \sqrt{n} \rfloor^2 + 1\right) \mid \left(n^2 + 1\right), \]
find the number of such \( n \).<|im_end|>
<|im_start|>assistant
<Z_155><Z_222><Z_215><Z_31><Z_19><ANSWER>

Question:
Given that \( n \) is a positive integer not greater than 2021, and satisfies
\[ \left(\lfloor \sqrt{n} \rfloor^2 + 1\right) \mid \left(n^2 + 1\right), \]
find the number of such \( n \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are three numbers 10, 11, and 12. What is the value of the multiplication of the largest number and the smallest 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
There are three numbers 10, 11, and 12. What is the value of the multiplication of the largest number and the smallest number?<|im_end|>
<|im_start|>assistant
<Z_24><Z_361><Z_460><Z_52><Z_446><Z_418><Z_309><Z_146><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are three numbers 10, 11, and 12. What is the value of the multiplication of the largest number and the smallest number?<|im_end|>
<|im_start|>assistant
<Z_218><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are three numbers 10, 11, and 12. What is the value of the multiplication of the largest number and the smallest number?<|im_end|>
<|im_start|>assistant
<Z_399><Z_417><Z_289><Z_464><Z_486><Z_38><Z_16><Z_11><ANSWER>

Question: There are three numbers 10, 11, and 12. What is the value of the multiplication of the largest number and the smallest number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $g(x) = x^2 - 4x$. How many distinct real numbers $c$ satisfy $g(g(g(g(c)))) = 5$?<|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 $g(x) = x^2 - 4x$. How many distinct real numbers $c$ satisfy $g(g(g(g(c)))) = 5$?<|im_end|>
<|im_start|>assistant
<Z_369><Z_187><Z_283><Z_254><Z_473><Z_269><Z_494><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $g(x) = x^2 - 4x$. How many distinct real numbers $c$ satisfy $g(g(g(g(c)))) = 5$?<|im_end|>
<|im_start|>assistant
<Z_277><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $g(x) = x^2 - 4x$. How many distinct real numbers $c$ satisfy $g(g(g(g(c)))) = 5$?<|im_end|>
<|im_start|>assistant
<Z_181><Z_121><Z_176><Z_246><Z_371><Z_178><Z_7><ANSWER>

Question: Let $g(x) = x^2 - 4x$. How many distinct real numbers $c$ satisfy $g(g(g(g(c)))) = 5$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jessica figured it would take a certain number of bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of colors in each bag. She bought one bag of jellybeans and separated them by color. She had 24 red, 13 black, 36 green, 28 purple, 32 yellow and 18 white. Jessica's guess as to how many red and white jelly beans were in the fishbowl was 126. How many bags of jelly beans did she think it would take to fill the fishbowl?<|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
Jessica figured it would take a certain number of bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of colors in each bag. She bought one bag of jellybeans and separated them by color. She had 24 red, 13 black, 36 green, 28 purple, 32 yellow and 18 white. Jessica's guess as to how many red and white jelly beans were in the fishbowl was 126. How many bags of jelly beans did she think it would take to fill the fishbowl?<|im_end|>
<|im_start|>assistant
<Z_24><Z_505><Z_101><Z_320><Z_123><Z_256><Z_267><Z_176><Z_467><Z_467><Z_494><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jessica figured it would take a certain number of bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of colors in each bag. She bought one bag of jellybeans and separated them by color. She had 24 red, 13 black, 36 green, 28 purple, 32 yellow and 18 white. Jessica's guess as to how many red and white jelly beans were in the fishbowl was 126. How many bags of jelly beans did she think it would take to fill the fishbowl?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jessica figured it would take a certain number of bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of colors in each bag. She bought one bag of jellybeans and separated them by color. She had 24 red, 13 black, 36 green, 28 purple, 32 yellow and 18 white. Jessica's guess as to how many red and white jelly beans were in the fishbowl was 126. How many bags of jelly beans did she think it would take to fill the fishbowl?<|im_end|>
<|im_start|>assistant
<Z_399><Z_72><Z_316><Z_10><Z_369><Z_350><Z_232><Z_19><Z_502><Z_231><Z_451><ANSWER>

Question: Jessica figured it would take a certain number of bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of colors in each bag. She bought one bag of jellybeans and separated them by color. She had 24 red, 13 black, 36 green, 28 purple, 32 yellow and 18 white. Jessica's guess as to how many red and white jelly beans were in the fishbowl was 126. How many bags of jelly beans did she think it would take to fill the fishbowl?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of all integers from $-50$ to $100$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of all integers from $-50$ to $100$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_177><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of all integers from $-50$ to $100$.<|im_end|>
<|im_start|>assistant
<Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of all integers from $-50$ to $100$.<|im_end|>
<|im_start|>assistant
<Z_368><Z_121><ANSWER>

Question: Calculate the sum of all integers from $-50$ to $100$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n\ge 3$ . Suppose  $a_1, a_2, ... , a_n$  are  $n$   distinct in pairs real numbers.
In terms of  $n$ , find the smallest possible number of different assumed values by the following  $n$  numbers:  $$ a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1 $$  <|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
Let  $n\ge 3$ . Suppose  $a_1, a_2, ... , a_n$  are  $n$   distinct in pairs real numbers.
In terms of  $n$ , find the smallest possible number of different assumed values by the following  $n$  numbers:  $$ a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1 $$  <|im_end|>
<|im_start|>assistant
<Z_477><Z_263><Z_100><Z_429><Z_497><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n\ge 3$ . Suppose  $a_1, a_2, ... , a_n$  are  $n$   distinct in pairs real numbers.
In terms of  $n$ , find the smallest possible number of different assumed values by the following  $n$  numbers:  $$ a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1 $$  <|im_end|>
<|im_start|>assistant
<Z_505><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n\ge 3$ . Suppose  $a_1, a_2, ... , a_n$  are  $n$   distinct in pairs real numbers.
In terms of  $n$ , find the smallest possible number of different assumed values by the following  $n$  numbers:  $$ a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1 $$  <|im_end|>
<|im_start|>assistant
<Z_410><Z_230><Z_424><Z_471><Z_54><ANSWER>

Question:
Let  $n\ge 3$ . Suppose  $a_1, a_2, ... , a_n$  are  $n$   distinct in pairs real numbers.
In terms of  $n$ , find the smallest possible number of different assumed values by the following  $n$  numbers:  $$ a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1 $$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dana earns $13 per hour. She worked some hours on Friday, 10 hours on Saturday, and 3 hours on Sunday. In all, Dana earned $286. How many hours did Dana work on Friday?<|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
Dana earns $13 per hour. She worked some hours on Friday, 10 hours on Saturday, and 3 hours on Sunday. In all, Dana earned $286. How many hours did Dana work on Friday?<|im_end|>
<|im_start|>assistant
<Z_24><Z_144><Z_269><Z_202><Z_262><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dana earns $13 per hour. She worked some hours on Friday, 10 hours on Saturday, and 3 hours on Sunday. In all, Dana earned $286. How many hours did Dana work on Friday?<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dana earns $13 per hour. She worked some hours on Friday, 10 hours on Saturday, and 3 hours on Sunday. In all, Dana earned $286. How many hours did Dana work on Friday?<|im_end|>
<|im_start|>assistant
<Z_510><Z_218><Z_490><Z_127><Z_110><ANSWER>

Question: Dana earns $13 per hour. She worked some hours on Friday, 10 hours on Saturday, and 3 hours on Sunday. In all, Dana earned $286. How many hours did Dana work on Friday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many four-digit numbers contain at least one even digit?<|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 four-digit numbers contain at least one even digit?<|im_end|>
<|im_start|>assistant
<Z_24><Z_286><Z_106><Z_297><Z_118><Z_175><Z_306><Z_287><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many four-digit numbers contain at least one even digit?<|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
How many four-digit numbers contain at least one even digit?<|im_end|>
<|im_start|>assistant
<Z_242><Z_198><Z_26><Z_312><Z_322><Z_222><Z_24><Z_350><ANSWER>

Question: How many four-digit numbers contain at least one even digit?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 20 feet and bounces back up to three-quarters of the height it fell from each time. After how many bounces will the ball first reach a maximum height of less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 20 feet and bounces back up to three-quarters of the height it fell from each time. After how many bounces will the ball first reach a maximum height of less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_24><Z_253><Z_330><Z_250><Z_246><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 20 feet and bounces back up to three-quarters of the height it fell from each time. After how many bounces will the ball first reach a maximum height of less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_323><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 20 feet and bounces back up to three-quarters of the height it fell from each time. After how many bounces will the ball first reach a maximum height of less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_408><Z_428><Z_117><Z_169><Z_398><ANSWER>

Question: A ball is dropped from 20 feet and bounces back up to three-quarters of the height it fell from each time. After how many bounces will the ball first reach a maximum height of less than 2 feet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive multiple of $31$ that is $7$ more than a multiple of $103$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive multiple of $31$ that is $7$ more than a multiple of $103$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_134><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive multiple of $31$ that is $7$ more than a multiple of $103$?<|im_end|>
<|im_start|>assistant
<Z_352><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive multiple of $31$ that is $7$ more than a multiple of $103$?<|im_end|>
<|im_start|>assistant
<Z_95><Z_461><Z_397><ANSWER>

Question: What is the smallest positive multiple of $31$ that is $7$ more than a multiple of $103$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lila rode 50 miles at 20 miles per hour and 20 miles at 40 miles per hour. During the transition between the two segments, she took a half-hour break. What was her average speed, in miles per hour, for the entire ride?<|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
Lila rode 50 miles at 20 miles per hour and 20 miles at 40 miles per hour. During the transition between the two segments, she took a half-hour break. What was her average speed, in miles per hour, for the entire ride?<|im_end|>
<|im_start|>assistant
<Z_477><Z_314><Z_432><Z_140><Z_319><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lila rode 50 miles at 20 miles per hour and 20 miles at 40 miles per hour. During the transition between the two segments, she took a half-hour break. What was her average speed, in miles per hour, for the entire ride?<|im_end|>
<|im_start|>assistant
<Z_275><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lila rode 50 miles at 20 miles per hour and 20 miles at 40 miles per hour. During the transition between the two segments, she took a half-hour break. What was her average speed, in miles per hour, for the entire ride?<|im_end|>
<|im_start|>assistant
<Z_278><Z_62><Z_333><Z_284><Z_366><ANSWER>

Question: Lila rode 50 miles at 20 miles per hour and 20 miles at 40 miles per hour. During the transition between the two segments, she took a half-hour break. What was her average speed, in miles per hour, for the entire ride?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( g \) be the function defined by \( g(x) = -3 \cos(\pi x / 2) \). How many values of \( x \) such that \( -1 \leq x \leq 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?<|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
Let \( g \) be the function defined by \( g(x) = -3 \cos(\pi x / 2) \). How many values of \( x \) such that \( -1 \leq x \leq 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?<|im_end|>
<|im_start|>assistant
<Z_369><Z_330><Z_177><Z_187><Z_264><Z_228><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( g \) be the function defined by \( g(x) = -3 \cos(\pi x / 2) \). How many values of \( x \) such that \( -1 \leq x \leq 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?<|im_end|>
<|im_start|>assistant
<Z_387><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( g \) be the function defined by \( g(x) = -3 \cos(\pi x / 2) \). How many values of \( x \) such that \( -1 \leq x \leq 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?<|im_end|>
<|im_start|>assistant
<Z_219><Z_344><Z_319><Z_480><Z_393><Z_177><ANSWER>

Question: Let \( g \) be the function defined by \( g(x) = -3 \cos(\pi x / 2) \). How many values of \( x \) such that \( -1 \leq x \leq 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $\left(\frac{4}{9}\right)^{\frac{1}{2}}-\left(\frac{\sqrt{2}}{2}\right)^{0}+\left(\frac{27}{64}\right)^{-\frac{1}{3}}$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $\left(\frac{4}{9}\right)^{\frac{1}{2}}-\left(\frac{\sqrt{2}}{2}\right)^{0}+\left(\frac{27}{64}\right)^{-\frac{1}{3}}$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_55><Z_344><Z_254><Z_376><Z_378><Z_267><Z_310><Z_472><Z_478><Z_264><Z_261><Z_391><Z_294><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $\left(\frac{4}{9}\right)^{\frac{1}{2}}-\left(\frac{\sqrt{2}}{2}\right)^{0}+\left(\frac{27}{64}\right)^{-\frac{1}{3}}$.<|im_end|>
<|im_start|>assistant
<Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $\left(\frac{4}{9}\right)^{\frac{1}{2}}-\left(\frac{\sqrt{2}}{2}\right)^{0}+\left(\frac{27}{64}\right)^{-\frac{1}{3}}$.<|im_end|>
<|im_start|>assistant
<Z_372><Z_91><Z_257><Z_103><Z_487><Z_462><Z_314><Z_277><Z_485><Z_280><Z_215><Z_304><Z_268><Z_135><ANSWER>

Question: Evaluate the expression $\left(\frac{4}{9}\right)^{\frac{1}{2}}-\left(\frac{\sqrt{2}}{2}\right)^{0}+\left(\frac{27}{64}\right)^{-\frac{1}{3}}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the x-coordinates of all the points of intersection of the two circles defined by \(x^2 - 6x + y^2 - 8y + 24 = 0\) and \(x^2 - 4x + y^2 - 8y + 16 = 0\)?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the x-coordinates of all the points of intersection of the two circles defined by \(x^2 - 6x + y^2 - 8y + 24 = 0\) and \(x^2 - 4x + y^2 - 8y + 16 = 0\)?<|im_end|>
<|im_start|>assistant
<Z_369><Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the x-coordinates of all the points of intersection of the two circles defined by \(x^2 - 6x + y^2 - 8y + 24 = 0\) and \(x^2 - 4x + y^2 - 8y + 16 = 0\)?<|im_end|>
<|im_start|>assistant
<Z_433><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the x-coordinates of all the points of intersection of the two circles defined by \(x^2 - 6x + y^2 - 8y + 24 = 0\) and \(x^2 - 4x + y^2 - 8y + 16 = 0\)?<|im_end|>
<|im_start|>assistant
<Z_115><Z_18><ANSWER>

Question: What is the sum of the x-coordinates of all the points of intersection of the two circles defined by \(x^2 - 6x + y^2 - 8y + 24 = 0\) and \(x^2 - 4x + y^2 - 8y + 16 = 0\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 26 and 26.5.<|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 a positive integer that is divisible by 18 and has a square root between 26 and 26.5.<|im_end|>
<|im_start|>assistant
<Z_477><Z_199><Z_114><Z_413><Z_484><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 26 and 26.5.<|im_end|>
<|im_start|>assistant
<Z_375><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 26 and 26.5.<|im_end|>
<|im_start|>assistant
<Z_230><Z_114><Z_418><Z_414><Z_383><ANSWER>

Question: Find a positive integer that is divisible by 18 and has a square root between 26 and 26.5.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are there between \( (9.8)^3 \) and \( (9.9)^3 \)?<|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
How many integers are there between \( (9.8)^3 \) and \( (9.9)^3 \)?<|im_end|>
<|im_start|>assistant
<Z_369><Z_236><Z_333><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are there between \( (9.8)^3 \) and \( (9.9)^3 \)?<|im_end|>
<|im_start|>assistant
<Z_457><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are there between \( (9.8)^3 \) and \( (9.9)^3 \)?<|im_end|>
<|im_start|>assistant
<Z_467><Z_507><Z_397><ANSWER>

Question: How many integers are there between \( (9.8)^3 \) and \( (9.9)^3 \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine how many numbers are in the list $$3.25, 7.25, 11.25, 15.25, \ldots, 51.25, 55.25.$$<|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
Determine how many numbers are in the list $$3.25, 7.25, 11.25, 15.25, \ldots, 51.25, 55.25.$$<|im_end|>
<|im_start|>assistant
<Z_477><Z_320><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine how many numbers are in the list $$3.25, 7.25, 11.25, 15.25, \ldots, 51.25, 55.25.$$<|im_end|>
<|im_start|>assistant
<Z_453><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine how many numbers are in the list $$3.25, 7.25, 11.25, 15.25, \ldots, 51.25, 55.25.$$<|im_end|>
<|im_start|>assistant
<Z_18><Z_71><ANSWER>

Question: Determine how many numbers are in the list $$3.25, 7.25, 11.25, 15.25, \ldots, 51.25, 55.25.$$


<|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 $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. Consider the graph of $$2x\equiv 3y + 1 \pmod{37}$$ which has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<37$.

What is the value of $x_0+y_0$?<|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 $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. Consider the graph of $$2x\equiv 3y + 1 \pmod{37}$$ which has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<37$.

What is the value of $x_0+y_0$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_114><Z_264><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 $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. Consider the graph of $$2x\equiv 3y + 1 \pmod{37}$$ which has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<37$.

What is the value of $x_0+y_0$?<|im_end|>
<|im_start|>assistant
<Z_254><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 $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. Consider the graph of $$2x\equiv 3y + 1 \pmod{37}$$ which has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<37$.

What is the value of $x_0+y_0$?<|im_end|>
<|im_start|>assistant
<Z_102><Z_350><Z_42><ANSWER>

Question:
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. To graph a congruence on modulo $m$ graph paper, we mark every point $(x,y)$ that satisfies the congruence. Consider the graph of $$2x\equiv 3y + 1 \pmod{37}$$ which has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0,y_0<37$.

What is the value of $x_0+y_0$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A farmer has rice weighing 49 and 3/4 pounds. He decides to divide the rice equally and place them in 7 containers. How many ounces of rice are in each container? (Note that 1 pound = 16 ounces, and 1 ounce = 28.35 grams)<|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 farmer has rice weighing 49 and 3/4 pounds. He decides to divide the rice equally and place them in 7 containers. How many ounces of rice are in each container? (Note that 1 pound = 16 ounces, and 1 ounce = 28.35 grams)<|im_end|>
<|im_start|>assistant
<Z_24><Z_109><Z_224><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A farmer has rice weighing 49 and 3/4 pounds. He decides to divide the rice equally and place them in 7 containers. How many ounces of rice are in each container? (Note that 1 pound = 16 ounces, and 1 ounce = 28.35 grams)<|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
A farmer has rice weighing 49 and 3/4 pounds. He decides to divide the rice equally and place them in 7 containers. How many ounces of rice are in each container? (Note that 1 pound = 16 ounces, and 1 ounce = 28.35 grams)<|im_end|>
<|im_start|>assistant
<Z_189><Z_123><Z_215><ANSWER>

Question: A farmer has rice weighing 49 and 3/4 pounds. He decides to divide the rice equally and place them in 7 containers. How many ounces of rice are in each container? (Note that 1 pound = 16 ounces, and 1 ounce = 28.35 grams)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Machine A produces 100 parts twice as fast as Machine B. Machine B produces 100 parts in 20 minutes. Machine C produces the same 100 parts in 15 minutes, and Machine D produces them in 10 minutes. If each machine produces parts at a constant rate, how many parts does each machine produce collectively in 45 minutes?<|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
Machine A produces 100 parts twice as fast as Machine B. Machine B produces 100 parts in 20 minutes. Machine C produces the same 100 parts in 15 minutes, and Machine D produces them in 10 minutes. If each machine produces parts at a constant rate, how many parts does each machine produce collectively in 45 minutes?<|im_end|>
<|im_start|>assistant
<Z_369><Z_159><Z_225><Z_206><Z_116><Z_54><Z_152><Z_190><Z_56><Z_420><Z_494><Z_52><Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Machine A produces 100 parts twice as fast as Machine B. Machine B produces 100 parts in 20 minutes. Machine C produces the same 100 parts in 15 minutes, and Machine D produces them in 10 minutes. If each machine produces parts at a constant rate, how many parts does each machine produce collectively in 45 minutes?<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Machine A produces 100 parts twice as fast as Machine B. Machine B produces 100 parts in 20 minutes. Machine C produces the same 100 parts in 15 minutes, and Machine D produces them in 10 minutes. If each machine produces parts at a constant rate, how many parts does each machine produce collectively in 45 minutes?<|im_end|>
<|im_start|>assistant
<Z_205><Z_203><Z_453><Z_204><Z_221><Z_91><Z_215><Z_274><Z_295><Z_223><Z_18><Z_5><Z_248><ANSWER>

Question: Machine A produces 100 parts twice as fast as Machine B. Machine B produces 100 parts in 20 minutes. Machine C produces the same 100 parts in 15 minutes, and Machine D produces them in 10 minutes. If each machine produces parts at a constant rate, how many parts does each machine produce collectively in 45 minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Roger's age is 5 more than twice Jill's age. In 15 years, their age difference will be 30 years less than Finley's age. Jill is 20 years old now. How old is Finley?<|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
Roger's age is 5 more than twice Jill's age. In 15 years, their age difference will be 30 years less than Finley's age. Jill is 20 years old now. How old is Finley?<|im_end|>
<|im_start|>assistant
<Z_477><Z_253><Z_437><Z_318><Z_196><Z_206><Z_357><Z_214><Z_330><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Roger's age is 5 more than twice Jill's age. In 15 years, their age difference will be 30 years less than Finley's age. Jill is 20 years old now. How old is Finley?<|im_end|>
<|im_start|>assistant
<Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Roger's age is 5 more than twice Jill's age. In 15 years, their age difference will be 30 years less than Finley's age. Jill is 20 years old now. How old is Finley?<|im_end|>
<|im_start|>assistant
<Z_225><Z_43><Z_422><Z_214><Z_456><Z_181><Z_241><Z_85><Z_369><ANSWER>

Question: Roger's age is 5 more than twice Jill's age. In 15 years, their age difference will be 30 years less than Finley's age. Jill is 20 years old now. How old is Finley?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An Italian sausage is 34.29 centimeters long. How many pieces of sausage can be cut from the 34.29-centimeter piece of sausage if each piece is to be cut in alternating sizes of 3/5 of a centimeter and 7/8 of a centimeter?<|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 Italian sausage is 34.29 centimeters long. How many pieces of sausage can be cut from the 34.29-centimeter piece of sausage if each piece is to be cut in alternating sizes of 3/5 of a centimeter and 7/8 of a centimeter?<|im_end|>
<|im_start|>assistant
<Z_477><Z_236><Z_252><Z_464><Z_465><Z_146><Z_330><Z_141><Z_113><Z_32><Z_443><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An Italian sausage is 34.29 centimeters long. How many pieces of sausage can be cut from the 34.29-centimeter piece of sausage if each piece is to be cut in alternating sizes of 3/5 of a centimeter and 7/8 of a centimeter?<|im_end|>
<|im_start|>assistant
<Z_306><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An Italian sausage is 34.29 centimeters long. How many pieces of sausage can be cut from the 34.29-centimeter piece of sausage if each piece is to be cut in alternating sizes of 3/5 of a centimeter and 7/8 of a centimeter?<|im_end|>
<|im_start|>assistant
<Z_100><Z_132><Z_455><Z_370><Z_200><Z_362><Z_364><Z_409><Z_407><Z_335><Z_422><ANSWER>

Question: An Italian sausage is 34.29 centimeters long. How many pieces of sausage can be cut from the 34.29-centimeter piece of sausage if each piece is to be cut in alternating sizes of 3/5 of a centimeter and 7/8 of a centimeter?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine a base in which the number $729_{10}$ is expressed having the form XYXY, where X and Y are distinct digits. Identify the base.<|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 a base in which the number $729_{10}$ is expressed having the form XYXY, where X and Y are distinct digits. Identify the base.<|im_end|>
<|im_start|>assistant
<Z_477><Z_224><Z_111><Z_343><Z_230><Z_469><Z_349><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine a base in which the number $729_{10}$ is expressed having the form XYXY, where X and Y are distinct digits. Identify the base.<|im_end|>
<|im_start|>assistant
<Z_275><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine a base in which the number $729_{10}$ is expressed having the form XYXY, where X and Y are distinct digits. Identify the base.<|im_end|>
<|im_start|>assistant
<Z_347><Z_218><Z_242><Z_64><Z_66><Z_186><Z_8><ANSWER>

Question: Determine a base in which the number $729_{10}$ is expressed having the form XYXY, where X and Y are distinct digits. Identify the base.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $8! - 7 \cdot 7! - 7!$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $8! - 7 \cdot 7! - 7!$.<|im_end|>
<|im_start|>assistant
<Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $8! - 7 \cdot 7! - 7!$.<|im_end|>
<|im_start|>assistant
<Z_284><ANSWER>

Question: Calculate $8! - 7 \cdot 7! - 7!$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If we divide  $2020$  by a prime  $p$ , the remainder is  $6$ . Determine the largest
possible value of  $p$ .<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If we divide  $2020$  by a prime  $p$ , the remainder is  $6$ . Determine the largest
possible value of  $p$ .<|im_end|>
<|im_start|>assistant
<Z_24><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If we divide  $2020$  by a prime  $p$ , the remainder is  $6$ . Determine the largest
possible value of  $p$ .<|im_end|>
<|im_start|>assistant
<Z_415><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If we divide  $2020$  by a prime  $p$ , the remainder is  $6$ . Determine the largest
possible value of  $p$ .<|im_end|>
<|im_start|>assistant
<Z_21><Z_319><ANSWER>

Question:
If we divide  $2020$  by a prime  $p$ , the remainder is  $6$ . Determine the largest
possible value of  $p$ .