<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|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
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_113><Z_77><Z_93><Z_73><Z_114><Z_125><Z_87><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_115><Z_104><Z_60><Z_100><Z_8><Z_27><Z_48><Z_71><ANSWER>

Question: While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|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
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_104><Z_74><Z_58><Z_11><Z_19><Z_19><Z_125><Z_126><Z_88><Z_19><Z_34><Z_98><Z_101><Z_60><Z_53><Z_88><Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_69><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_38><Z_32><Z_15><Z_73><Z_97><Z_37><Z_16><Z_28><Z_13><Z_57><Z_81><Z_52><Z_49><Z_10><Z_94><Z_5><Z_39><ANSWER>

Question: Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|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
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_57><Z_13><Z_115><Z_44><Z_71><Z_121><Z_43><Z_63><Z_82><Z_103><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|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
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_17><Z_54><Z_45><Z_15><Z_122><Z_44><Z_103><Z_71><Z_81><Z_68><Z_15><ANSWER>

Question: In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .<|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
a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .<|im_end|>
<|im_start|>assistant
<Z_104><Z_33><Z_73><Z_51><Z_91><Z_71><Z_67><Z_37><Z_76><Z_66><Z_53><Z_78><Z_47><Z_56><Z_96><Z_107><Z_117><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .<|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
a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .<|im_end|>
<|im_start|>assistant
<Z_4><Z_86><Z_120><Z_43><Z_125><Z_56><Z_12><Z_49><Z_101><Z_65><Z_50><Z_98><Z_28><Z_39><Z_95><Z_103><Z_95><Z_41><ANSWER>

Question: a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the function $f(x)=-\frac{x+a}{bx+1}$ is an odd function in the interval $[-1,1]$, what is its maximum value in this interval?<|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
Given that the function $f(x)=-\frac{x+a}{bx+1}$ is an odd function in the interval $[-1,1]$, what is its maximum value in this interval?<|im_end|>
<|im_start|>assistant
<Z_57><Z_72><Z_91><Z_33><Z_115><Z_78><Z_52><Z_64><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the function $f(x)=-\frac{x+a}{bx+1}$ is an odd function in the interval $[-1,1]$, what is its maximum value in this interval?<|im_end|>
<|im_start|>assistant
<Z_17><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the function $f(x)=-\frac{x+a}{bx+1}$ is an odd function in the interval $[-1,1]$, what is its maximum value in this interval?<|im_end|>
<|im_start|>assistant
<Z_124><Z_46><Z_16><Z_60><Z_82><Z_26><Z_54><Z_3><Z_16><ANSWER>

Question: Given that the function $f(x)=-\frac{x+a}{bx+1}$ is an odd function in the interval $[-1,1]$, what is its maximum value in this interval?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the simple interest if the rate of interest is 12.5%, the principal amount is 400, and the time is 2 years?<|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
What is the simple interest if the rate of interest is 12.5%, the principal amount is 400, and the time is 2 years?<|im_end|>
<|im_start|>assistant
<Z_94><Z_100><Z_105><Z_51><Z_49><Z_72><Z_40><Z_93><Z_64><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the simple interest if the rate of interest is 12.5%, the principal amount is 400, and the time is 2 years?<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the simple interest if the rate of interest is 12.5%, the principal amount is 400, and the time is 2 years?<|im_end|>
<|im_start|>assistant
<Z_5><Z_37><Z_39><Z_89><Z_62><Z_116><Z_121><Z_109><Z_39><Z_83><ANSWER>

Question: What is the simple interest if the rate of interest is 12.5%, the principal amount is 400, and the time is 2 years?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular rug with side lengths of 2 feet and some feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, the fraction of the area of the floor not covered by the rug is 0.78125. What is the length of the longer side of the rug?<|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
A rectangular rug with side lengths of 2 feet and some feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, the fraction of the area of the floor not covered by the rug is 0.78125. What is the length of the longer side of the rug?<|im_end|>
<|im_start|>assistant
<Z_104><Z_99><Z_32><Z_103><Z_82><Z_93><Z_48><Z_101><Z_61><Z_61><Z_61><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular rug with side lengths of 2 feet and some feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, the fraction of the area of the floor not covered by the rug is 0.78125. What is the length of the longer side of the rug?<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular rug with side lengths of 2 feet and some feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, the fraction of the area of the floor not covered by the rug is 0.78125. What is the length of the longer side of the rug?<|im_end|>
<|im_start|>assistant
<Z_11><Z_13><Z_45><Z_81><Z_55><Z_124><Z_103><Z_40><Z_34><Z_93><Z_108><Z_118><ANSWER>

Question: A rectangular rug with side lengths of 2 feet and some feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, the fraction of the area of the floor not covered by the rug is 0.78125. What is the length of the longer side of the rug?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Yesterday, Shelby earned 4 gold stars. Today, she earned 3.5 times more stars than yesterday. How many gold stars did Shelby earn in total?<|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
Yesterday, Shelby earned 4 gold stars. Today, she earned 3.5 times more stars than yesterday. How many gold stars did Shelby earn in total?<|im_end|>
<|im_start|>assistant
<Z_57><Z_79><Z_120><Z_97><Z_91><Z_123><Z_90><Z_53><Z_10><Z_37><Z_75><Z_78><Z_123><Z_82><Z_125><Z_119><Z_80><Z_12><Z_88><Z_12><Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Yesterday, Shelby earned 4 gold stars. Today, she earned 3.5 times more stars than yesterday. How many gold stars did Shelby earn in total?<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Yesterday, Shelby earned 4 gold stars. Today, she earned 3.5 times more stars than yesterday. How many gold stars did Shelby earn in total?<|im_end|>
<|im_start|>assistant
<Z_92><Z_97><Z_100><Z_79><Z_126><Z_65><Z_97><Z_112><Z_43><Z_110><Z_86><Z_115><Z_66><Z_59><Z_13><Z_21><Z_107><Z_34><Z_54><Z_36><Z_102><ANSWER>

Question: Yesterday, Shelby earned 4 gold stars. Today, she earned 3.5 times more stars than yesterday. How many gold stars did Shelby earn in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?<|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
in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_93><Z_59><Z_87><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?<|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
in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?<|im_end|>
<|im_start|>assistant
<Z_96><Z_94><Z_105><Z_85><Z_52><ANSWER>

Question: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?<|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
vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_86><Z_121><Z_34><Z_107><Z_114><Z_49><Z_59><Z_80><Z_90><Z_123><Z_79><Z_72><Z_79><Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?<|im_end|>
<|im_start|>assistant
<Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?<|im_end|>
<|im_start|>assistant
<Z_105><Z_55><Z_49><Z_40><Z_116><Z_127><Z_93><Z_41><Z_97><Z_23><Z_62><Z_18><Z_30><Z_102><Z_46><ANSWER>

Question: vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?<|im_end|>
<|im_start|>assistant
<Z_32><Z_17><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

Question: Two months ago, Wilson had a total of $150 in his bank account. Then last month, he deposited $17. A few days after, he made a withdrawal. This month, he deposited $21 so he has $16 more than what is in his account two months ago. How much did Wilson withdraw last month?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Al, Betty, and Clare split $\$1200$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1800$. Betty and Clare have both tripled their money, whereas Al has managed to lose $\$200$. What was Al's original portion?<|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
Al, Betty, and Clare split $\$1200$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1800$. Betty and Clare have both tripled their money, whereas Al has managed to lose $\$200$. What was Al's original portion?<|im_end|>
<|im_start|>assistant
<Z_57><Z_36><Z_66><Z_65><Z_72><Z_54><Z_61><Z_31><Z_82><Z_31><Z_123><Z_45><Z_31><Z_115><Z_107><Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Al, Betty, and Clare split $\$1200$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1800$. Betty and Clare have both tripled their money, whereas Al has managed to lose $\$200$. What was Al's original portion?<|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
Al, Betty, and Clare split $\$1200$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1800$. Betty and Clare have both tripled their money, whereas Al has managed to lose $\$200$. What was Al's original portion?<|im_end|>
<|im_start|>assistant
<Z_108><Z_59><Z_40><Z_8><Z_1><Z_62><Z_0><Z_48><Z_14><Z_15><Z_71><Z_98><Z_83><Z_75><Z_57><Z_23><ANSWER>

Question: Al, Betty, and Clare split $\$1200$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1800$. Betty and Clare have both tripled their money, whereas Al has managed to lose $\$200$. What was Al's original portion?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two regular polygons have the same perimeter. If the first polygon has 24 sides and a side length that is three times as long as the second polygon, how many sides does the second polygon have?<|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
Two regular polygons have the same perimeter. If the first polygon has 24 sides and a side length that is three times as long as the second polygon, how many sides does the second polygon have?<|im_end|>
<|im_start|>assistant
<Z_57><Z_51><Z_86><Z_41><Z_120><Z_81><Z_126><Z_114><Z_55><Z_125><Z_82><Z_118><Z_37><Z_119><Z_6><Z_96><Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two regular polygons have the same perimeter. If the first polygon has 24 sides and a side length that is three times as long as the second polygon, how many sides does the second polygon have?<|im_end|>
<|im_start|>assistant
<Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two regular polygons have the same perimeter. If the first polygon has 24 sides and a side length that is three times as long as the second polygon, how many sides does the second polygon have?<|im_end|>
<|im_start|>assistant
<Z_62><Z_127><Z_32><Z_48><Z_96><Z_123><Z_88><Z_16><Z_75><Z_4><Z_3><Z_108><Z_86><Z_5><Z_125><Z_86><Z_120><ANSWER>

Question: Two regular polygons have the same perimeter. If the first polygon has 24 sides and a side length that is three times as long as the second polygon, how many sides does the second polygon have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples.  For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$  For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,0)}(x)$ is the polynomial of degree at most 9 such that $p(0) = p(2) = p(3) = p(5) = p(7) = p(8) = p(9) = 0$ and $p(1) = p(4) = p(6) = 1.$

Find
\[\sum_{s \in S} p_s(10).\]<|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
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples.  For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$  For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,0)}(x)$ is the polynomial of degree at most 9 such that $p(0) = p(2) = p(3) = p(5) = p(7) = p(8) = p(9) = 0$ and $p(1) = p(4) = p(6) = 1.$

Find
\[\sum_{s \in S} p_s(10).\]<|im_end|>
<|im_start|>assistant
<Z_113><Z_51><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples.  For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$  For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,0)}(x)$ is the polynomial of degree at most 9 such that $p(0) = p(2) = p(3) = p(5) = p(7) = p(8) = p(9) = 0$ and $p(1) = p(4) = p(6) = 1.$

Find
\[\sum_{s \in S} p_s(10).\]<|im_end|>
<|im_start|>assistant
<Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples.  For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$  For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,0)}(x)$ is the polynomial of degree at most 9 such that $p(0) = p(2) = p(3) = p(5) = p(7) = p(8) = p(9) = 0$ and $p(1) = p(4) = p(6) = 1.$

Find
\[\sum_{s \in S} p_s(10).\]<|im_end|>
<|im_start|>assistant
<Z_14><Z_15><Z_0><ANSWER>

Question:
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples.  For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$  For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,0)}(x)$ is the polynomial of degree at most 9 such that $p(0) = p(2) = p(3) = p(5) = p(7) = p(8) = p(9) = 0$ and $p(1) = p(4) = p(6) = 1.$

Find
\[\sum_{s \in S} p_s(10).\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $|a^{3}-27|+\left(b+2\right)^{2}=0$, then $a+b=\_\_\_\_\_\_$.<|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
If $|a^{3}-27|+\left(b+2\right)^{2}=0$, then $a+b=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_81><Z_70><Z_125><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $|a^{3}-27|+\left(b+2\right)^{2}=0$, then $a+b=\_\_\_\_\_\_$.<|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
If $|a^{3}-27|+\left(b+2\right)^{2}=0$, then $a+b=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_15><Z_17><Z_22><Z_38><Z_2><ANSWER>

Question: If $|a^{3}-27|+\left(b+2\right)^{2}=0$, then $a+b=\_\_\_\_\_\_$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 - 3x^3 + 1.8x^2 + 0.35x + 2$ at $x = -1$ using the Horner's method (also known as the Qin Jiushao algorithm). Find the value of $v_2$.<|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
Calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 - 3x^3 + 1.8x^2 + 0.35x + 2$ at $x = -1$ using the Horner's method (also known as the Qin Jiushao algorithm). Find the value of $v_2$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_81><Z_89><Z_89><Z_49><Z_93><Z_125><Z_33><Z_39><Z_58><Z_75><Z_38><Z_91><Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 - 3x^3 + 1.8x^2 + 0.35x + 2$ at $x = -1$ using the Horner's method (also known as the Qin Jiushao algorithm). Find the value of $v_2$.<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 - 3x^3 + 1.8x^2 + 0.35x + 2$ at $x = -1$ using the Horner's method (also known as the Qin Jiushao algorithm). Find the value of $v_2$.<|im_end|>
<|im_start|>assistant
<Z_30><Z_33><Z_122><Z_70><Z_0><Z_99><Z_52><Z_124><Z_78><Z_10><Z_109><Z_85><Z_90><Z_4><ANSWER>

Question: Calculate the value of the polynomial $f(x) = x^6 - 5x^5 + 6x^4 - 3x^3 + 1.8x^2 + 0.35x + 2$ at $x = -1$ using the Horner's method (also known as the Qin Jiushao algorithm). Find the value of $v_2$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76, 65, 82, 67, and 75 marks in mathematics, science, social studies, English, and biology respectively. What are his average marks?<|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
Shekar scored 76, 65, 82, 67, and 75 marks in mathematics, science, social studies, English, and biology respectively. What are his average marks?<|im_end|>
<|im_start|>assistant
<Z_104><Z_120><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76, 65, 82, 67, and 75 marks in mathematics, science, social studies, English, and biology respectively. What are his average marks?<|im_end|>
<|im_start|>assistant
<Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76, 65, 82, 67, and 75 marks in mathematics, science, social studies, English, and biology respectively. What are his average marks?<|im_end|>
<|im_start|>assistant
<Z_60><Z_80><Z_125><ANSWER>

Question: Shekar scored 76, 65, 82, 67, and 75 marks in mathematics, science, social studies, English, and biology respectively. What are his average marks?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. What is the speed of the current in km/h?<|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
A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. What is the speed of the current in km/h?<|im_end|>
<|im_start|>assistant
<Z_57><Z_83><Z_38><Z_108><Z_49><Z_38><Z_121><Z_20><Z_115><Z_75><Z_49><Z_26><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. What is the speed of the current in km/h?<|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
A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. What is the speed of the current in km/h?<|im_end|>
<|im_start|>assistant
<Z_3><Z_18><Z_57><Z_110><Z_119><Z_98><Z_47><Z_104><Z_66><Z_3><Z_19><Z_40><Z_121><ANSWER>

Question: A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. What is the speed of the current in km/h?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 A pet store had 15 siamese cats and 49 house cats. During a sale they sold 19 cats. How many cats do they have left? <|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
 A pet store had 15 siamese cats and 49 house cats. During a sale they sold 19 cats. How many cats do they have left? <|im_end|>
<|im_start|>assistant
<Z_57><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 A pet store had 15 siamese cats and 49 house cats. During a sale they sold 19 cats. How many cats do they have left? <|im_end|>
<|im_start|>assistant
<Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 A pet store had 15 siamese cats and 49 house cats. During a sale they sold 19 cats. How many cats do they have left? <|im_end|>
<|im_start|>assistant
<Z_94><Z_56><ANSWER>

Question: A pet store had 15 siamese cats and 49 house cats. During a sale they sold 19 cats. How many cats do they have left?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jamie has a jar of coins containing the same number of nickels, dimes, and half-dollars. The total value of the coins in the jar is $\$17.50$. How many dimes does Jamie have?<|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
Jamie has a jar of coins containing the same number of nickels, dimes, and half-dollars. The total value of the coins in the jar is $\$17.50$. How many dimes does Jamie have?<|im_end|>
<|im_start|>assistant
<Z_104><Z_33><Z_124><Z_99><Z_95><Z_87><Z_26><Z_87><Z_96><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jamie has a jar of coins containing the same number of nickels, dimes, and half-dollars. The total value of the coins in the jar is $\$17.50$. How many dimes does Jamie have?<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jamie has a jar of coins containing the same number of nickels, dimes, and half-dollars. The total value of the coins in the jar is $\$17.50$. How many dimes does Jamie have?<|im_end|>
<|im_start|>assistant
<Z_43><Z_85><Z_56><Z_19><Z_24><Z_102><Z_75><Z_41><Z_76><Z_52><ANSWER>

Question: Jamie has a jar of coins containing the same number of nickels, dimes, and half-dollars. The total value of the coins in the jar is $\$17.50$. How many dimes does Jamie have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A chicken weighs 3 kilograms, a duck weighs 6 kilograms, and a cow weighs 624 kilograms. How many times heavier is the cow than the chicken? How many times heavier is the cow than the duck?<|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
A chicken weighs 3 kilograms, a duck weighs 6 kilograms, and a cow weighs 624 kilograms. How many times heavier is the cow than the chicken? How many times heavier is the cow than the duck?<|im_end|>
<|im_start|>assistant
<Z_104><Z_4><Z_13><Z_100><Z_38><Z_89><Z_123><Z_26><Z_90><Z_90><Z_39><Z_117><Z_95><Z_58><Z_98><Z_53><Z_63><Z_67><Z_38><Z_26><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A chicken weighs 3 kilograms, a duck weighs 6 kilograms, and a cow weighs 624 kilograms. How many times heavier is the cow than the chicken? How many times heavier is the cow than the duck?<|im_end|>
<|im_start|>assistant
<Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A chicken weighs 3 kilograms, a duck weighs 6 kilograms, and a cow weighs 624 kilograms. How many times heavier is the cow than the chicken? How many times heavier is the cow than the duck?<|im_end|>
<|im_start|>assistant
<Z_105><Z_121><Z_53><Z_99><Z_38><Z_127><Z_46><Z_59><Z_8><Z_86><Z_54><Z_116><Z_63><Z_56><Z_10><Z_58><Z_33><Z_40><Z_113><Z_88><ANSWER>

Question: A chicken weighs 3 kilograms, a duck weighs 6 kilograms, and a cow weighs 624 kilograms. How many times heavier is the cow than the chicken? How many times heavier is the cow than the duck?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the curve $C_1$: $x + \sqrt{3}y = \sqrt{3}$ and $C_2$: $\begin{cases} x= \sqrt{6}\cos \varphi \\ y= \sqrt{2}\sin \varphi \end{cases}$ (with $\varphi$ as the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, and the same unit of length is taken in both coordinate systems.

$(1)$ Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations;

$(2)$ Suppose $C_1$ intersects the $x$, $y$ axes at points $M$, $N$ respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C_1$, $C_2$ at points $P$, $Q$ respectively, find the distance between points $P$ and $Q$.<|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
Given the curve $C_1$: $x + \sqrt{3}y = \sqrt{3}$ and $C_2$: $\begin{cases} x= \sqrt{6}\cos \varphi \\ y= \sqrt{2}\sin \varphi \end{cases}$ (with $\varphi$ as the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, and the same unit of length is taken in both coordinate systems.

$(1)$ Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations;

$(2)$ Suppose $C_1$ intersects the $x$, $y$ axes at points $M$, $N$ respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C_1$, $C_2$ at points $P$, $Q$ respectively, find the distance between points $P$ and $Q$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_62><Z_119><Z_12><Z_49><Z_76><Z_98><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the curve $C_1$: $x + \sqrt{3}y = \sqrt{3}$ and $C_2$: $\begin{cases} x= \sqrt{6}\cos \varphi \\ y= \sqrt{2}\sin \varphi \end{cases}$ (with $\varphi$ as the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, and the same unit of length is taken in both coordinate systems.

$(1)$ Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations;

$(2)$ Suppose $C_1$ intersects the $x$, $y$ axes at points $M$, $N$ respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C_1$, $C_2$ at points $P$, $Q$ respectively, find the distance between points $P$ and $Q$.<|im_end|>
<|im_start|>assistant
<Z_15><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the curve $C_1$: $x + \sqrt{3}y = \sqrt{3}$ and $C_2$: $\begin{cases} x= \sqrt{6}\cos \varphi \\ y= \sqrt{2}\sin \varphi \end{cases}$ (with $\varphi$ as the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, and the same unit of length is taken in both coordinate systems.

$(1)$ Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations;

$(2)$ Suppose $C_1$ intersects the $x$, $y$ axes at points $M$, $N$ respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C_1$, $C_2$ at points $P$, $Q$ respectively, find the distance between points $P$ and $Q$.<|im_end|>
<|im_start|>assistant
<Z_31><Z_12><Z_88><Z_102><Z_85><Z_29><Z_108><Z_113><ANSWER>

Question:
Given the curve $C_1$: $x + \sqrt{3}y = \sqrt{3}$ and $C_2$: $\begin{cases} x= \sqrt{6}\cos \varphi \\ y= \sqrt{2}\sin \varphi \end{cases}$ (with $\varphi$ as the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, and the same unit of length is taken in both coordinate systems.

$(1)$ Convert the equations of curves $C_1$ and $C_2$ into polar coordinate equations;

$(2)$ Suppose $C_1$ intersects the $x$, $y$ axes at points $M$, $N$ respectively, and the midpoint of segment $MN$ is $P$. If the ray $OP$ intersects $C_1$, $C_2$ at points $P$, $Q$ respectively, find the distance between points $P$ and $Q$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim buys some loaves of bread. Each loaf of bread has 20 slices. He pays for the loaves of bread with 2 $20 bills and gets $16 change. Each slice costs 40 cents. How many loaves of bread did Tim buy?<|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
Tim buys some loaves of bread. Each loaf of bread has 20 slices. He pays for the loaves of bread with 2 $20 bills and gets $16 change. Each slice costs 40 cents. How many loaves of bread did Tim buy?<|im_end|>
<|im_start|>assistant
<Z_94><Z_73><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim buys some loaves of bread. Each loaf of bread has 20 slices. He pays for the loaves of bread with 2 $20 bills and gets $16 change. Each slice costs 40 cents. How many loaves of bread did Tim buy?<|im_end|>
<|im_start|>assistant
<Z_111><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim buys some loaves of bread. Each loaf of bread has 20 slices. He pays for the loaves of bread with 2 $20 bills and gets $16 change. Each slice costs 40 cents. How many loaves of bread did Tim buy?<|im_end|>
<|im_start|>assistant
<Z_17><Z_89><Z_19><ANSWER>

Question: Tim buys some loaves of bread. Each loaf of bread has 20 slices. He pays for the loaves of bread with 2 $20 bills and gets $16 change. Each slice costs 40 cents. How many loaves of bread did Tim buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the volume of the region in space defined by
\[|x + y + z| + |x + y - z| \le 12\]
and \(x, y, z \ge 0.\)<|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
Determine the volume of the region in space defined by
\[|x + y + z| + |x + y - z| \le 12\]
and \(x, y, z \ge 0.\)<|im_end|>
<|im_start|>assistant
<Z_94><Z_97><Z_120><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the volume of the region in space defined by
\[|x + y + z| + |x + y - z| \le 12\]
and \(x, y, z \ge 0.\)<|im_end|>
<|im_start|>assistant
<Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the volume of the region in space defined by
\[|x + y + z| + |x + y - z| \le 12\]
and \(x, y, z \ge 0.\)<|im_end|>
<|im_start|>assistant
<Z_14><Z_4><Z_47><Z_41><ANSWER>

Question:
Determine the volume of the region in space defined by
\[|x + y + z| + |x + y - z| \le 12\]
and \(x, y, z \ge 0.\)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when the sum of the first seven primes is divided by the eighth prime?<|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
What is the remainder when the sum of the first seven primes is divided by the eighth prime?<|im_end|>
<|im_start|>assistant
<Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when the sum of the first seven primes is divided by the eighth prime?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

Question: What is the remainder when the sum of the first seven primes is divided by the eighth prime?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A national team needs to select 4 out of 6 sprinters to participate in the 4×100 m relay at the Asian Games. If sprinter A cannot run the first leg and sprinter B cannot run the fourth leg, there are a total of ______ ways to participate.<|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
A national team needs to select 4 out of 6 sprinters to participate in the 4×100 m relay at the Asian Games. If sprinter A cannot run the first leg and sprinter B cannot run the fourth leg, there are a total of ______ ways to participate.<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><Z_38><Z_49><Z_121><Z_20><Z_108><Z_98><Z_125><Z_75><Z_53><Z_39><Z_9><Z_90><Z_83><Z_53><Z_71><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A national team needs to select 4 out of 6 sprinters to participate in the 4×100 m relay at the Asian Games. If sprinter A cannot run the first leg and sprinter B cannot run the fourth leg, there are a total of ______ ways to participate.<|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
A national team needs to select 4 out of 6 sprinters to participate in the 4×100 m relay at the Asian Games. If sprinter A cannot run the first leg and sprinter B cannot run the fourth leg, there are a total of ______ ways to participate.<|im_end|>
<|im_start|>assistant
<Z_83><Z_71><Z_87><Z_96><Z_57><Z_59><Z_91><Z_68><Z_46><Z_62><Z_103><Z_117><Z_120><Z_87><Z_57><Z_87><Z_75><Z_41><ANSWER>

Question: A national team needs to select 4 out of 6 sprinters to participate in the 4×100 m relay at the Asian Games. If sprinter A cannot run the first leg and sprinter B cannot run the fourth leg, there are a total of ______ ways to participate.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Winnie now has 32 cherry lollipops, 150 wintergreen lollipops, 7 grape lollipops, and 280 shrimp cocktail lollipops. She wants to distribute these lollipops equally among her 14 friends, with each friend receiving the same number of lollipops. How many lollipops will Winnie have left after distributing as many as she can to her friends?<|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
Winnie now has 32 cherry lollipops, 150 wintergreen lollipops, 7 grape lollipops, and 280 shrimp cocktail lollipops. She wants to distribute these lollipops equally among her 14 friends, with each friend receiving the same number of lollipops. How many lollipops will Winnie have left after distributing as many as she can to her friends?<|im_end|>
<|im_start|>assistant
<Z_94><Z_121><Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Winnie now has 32 cherry lollipops, 150 wintergreen lollipops, 7 grape lollipops, and 280 shrimp cocktail lollipops. She wants to distribute these lollipops equally among her 14 friends, with each friend receiving the same number of lollipops. How many lollipops will Winnie have left after distributing as many as she can to her friends?<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Winnie now has 32 cherry lollipops, 150 wintergreen lollipops, 7 grape lollipops, and 280 shrimp cocktail lollipops. She wants to distribute these lollipops equally among her 14 friends, with each friend receiving the same number of lollipops. How many lollipops will Winnie have left after distributing as many as she can to her friends?<|im_end|>
<|im_start|>assistant
<Z_56><Z_30><Z_83><ANSWER>

Question: Winnie now has 32 cherry lollipops, 150 wintergreen lollipops, 7 grape lollipops, and 280 shrimp cocktail lollipops. She wants to distribute these lollipops equally among her 14 friends, with each friend receiving the same number of lollipops. How many lollipops will Winnie have left after distributing as many as she can to her friends?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that:
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by reversing the digits of $x$;
3. $z = |x - y|$;
4. $z$ is divisible by 33.

How many distinct values of $z$ are possible under these conditions?<|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
Given that:
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by reversing the digits of $x$;
3. $z = |x - y|$;
4. $z$ is divisible by 33.

How many distinct values of $z$ are possible under these conditions?<|im_end|>
<|im_start|>assistant
<Z_104><Z_62><Z_114><Z_72><Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that:
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by reversing the digits of $x$;
3. $z = |x - y|$;
4. $z$ is divisible by 33.

How many distinct values of $z$ are possible under these conditions?<|im_end|>
<|im_start|>assistant
<Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that:
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by reversing the digits of $x$;
3. $z = |x - y|$;
4. $z$ is divisible by 33.

How many distinct values of $z$ are possible under these conditions?<|im_end|>
<|im_start|>assistant
<Z_70><Z_127><Z_42><Z_89><Z_87><ANSWER>

Question:
Given that:
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by reversing the digits of $x$;
3. $z = |x - y|$;
4. $z$ is divisible by 33.

How many distinct values of $z$ are possible under these conditions?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be real numbers such that $x^2 + y^2 + xy = 1.$ Find the maximum value of $3x - 2y.$<|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
Let $x$ and $y$ be real numbers such that $x^2 + y^2 + xy = 1.$ Find the maximum value of $3x - 2y.$<|im_end|>
<|im_start|>assistant
<Z_104><Z_1><Z_40><Z_87><Z_121><Z_93><Z_124><Z_107><Z_87><Z_83><Z_8><Z_118><Z_66><Z_47><Z_123><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be real numbers such that $x^2 + y^2 + xy = 1.$ Find the maximum value of $3x - 2y.$<|im_end|>
<|im_start|>assistant
<Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be real numbers such that $x^2 + y^2 + xy = 1.$ Find the maximum value of $3x - 2y.$<|im_end|>
<|im_start|>assistant
<Z_8><Z_29><Z_67><Z_27><Z_104><Z_124><Z_29><Z_75><Z_83><Z_25><Z_117><Z_76><Z_34><Z_57><Z_109><Z_9><ANSWER>

Question: Let $x$ and $y$ be real numbers such that $x^2 + y^2 + xy = 1.$ Find the maximum value of $3x - 2y.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the digits of the number $\underbrace{44 \ldots 4}_{2012 \text { times}} \cdot \underbrace{99 \ldots 9}_{2012 \text { times}}$.<|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 sum of the digits of the number $\underbrace{44 \ldots 4}_{2012 \text { times}} \cdot \underbrace{99 \ldots 9}_{2012 \text { times}}$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_41><Z_80><Z_103><Z_91><Z_124><Z_117><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the digits of the number $\underbrace{44 \ldots 4}_{2012 \text { times}} \cdot \underbrace{99 \ldots 9}_{2012 \text { times}}$.<|im_end|>
<|im_start|>assistant
<Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the digits of the number $\underbrace{44 \ldots 4}_{2012 \text { times}} \cdot \underbrace{99 \ldots 9}_{2012 \text { times}}$.<|im_end|>
<|im_start|>assistant
<Z_36><Z_30><Z_45><Z_39><Z_17><Z_107><Z_57><Z_41><ANSWER>

Question: Find the sum of the digits of the number $\underbrace{44 \ldots 4}_{2012 \text { times}} \cdot \underbrace{99 \ldots 9}_{2012 \text { times}}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The newly constructed sports stadium is 61 yards in length. Genesis has a measurement device that measures only in feet. Find the length reported by Genesis.<|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 newly constructed sports stadium is 61 yards in length. Genesis has a measurement device that measures only in feet. Find the length reported by Genesis.<|im_end|>
<|im_start|>assistant
<Z_105><Z_49><Z_49><Z_47><Z_59><Z_125><Z_38><Z_22><Z_26><Z_96><Z_10><Z_54><Z_124><Z_67><Z_5><Z_70><Z_71><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The newly constructed sports stadium is 61 yards in length. Genesis has a measurement device that measures only in feet. Find the length reported by Genesis.<|im_end|>
<|im_start|>assistant
<Z_85><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The newly constructed sports stadium is 61 yards in length. Genesis has a measurement device that measures only in feet. Find the length reported by Genesis.<|im_end|>
<|im_start|>assistant
<Z_58><Z_108><Z_14><Z_78><Z_42><Z_48><Z_65><Z_73><Z_68><Z_43><Z_36><Z_43><Z_24><Z_44><Z_103><Z_65><Z_19><Z_62><ANSWER>

Question: The newly constructed sports stadium is 61 yards in length. Genesis has a measurement device that measures only in feet. Find the length reported by Genesis.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $98\times 98$ in your head.<|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
Evaluate $98\times 98$ in your head.<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $98\times 98$ in your head.<|im_end|>
<|im_start|>assistant
<Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $98\times 98$ in your head.<|im_end|>
<|im_start|>assistant
<Z_56><Z_29><ANSWER>

Question: Evaluate $98\times 98$ in your head.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom, and Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. Susan is 15 years old, and the total age of all four family members is 51 years. How old is Bob?<|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
Susan, Arthur, Tom, and Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. Susan is 15 years old, and the total age of all four family members is 51 years. How old is Bob?<|im_end|>
<|im_start|>assistant
<Z_113><Z_27><Z_114><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom, and Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. Susan is 15 years old, and the total age of all four family members is 51 years. How old is Bob?<|im_end|>
<|im_start|>assistant
<Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom, and Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. Susan is 15 years old, and the total age of all four family members is 51 years. How old is Bob?<|im_end|>
<|im_start|>assistant
<Z_114><Z_122><Z_80><Z_97><ANSWER>

Question: Susan, Arthur, Tom, and Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. Susan is 15 years old, and the total age of all four family members is 51 years. How old is Bob?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_114><Z_43><Z_43><Z_49><Z_40><Z_58><Z_121><Z_34><Z_37><Z_88><Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.<|im_end|>
<|im_start|>assistant
<Z_6><Z_42><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.<|im_end|>
<|im_start|>assistant
<Z_88><Z_38><Z_90><Z_80><Z_94><Z_6><Z_45><Z_83><Z_16><Z_22><Z_100><Z_8><ANSWER>

Question: Given the function $y=f(x)$ which passes through the points $(1,3), (2,1),$ and $(3,5)$, find two points that must be on the graph of $y = f(f(x))$. Let's denote these points as $(a, b)$ and $(c, d)$. Calculate $ab + cd$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( x + \frac{1}{x} = 3 \), compute the value of
\[
(x - 3)^2 + \frac{16}{(x - 3)^2}.
\]<|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
If \( x + \frac{1}{x} = 3 \), compute the value of
\[
(x - 3)^2 + \frac{16}{(x - 3)^2}.
\]<|im_end|>
<|im_start|>assistant
<Z_16><ANSWER>

Question:
If \( x + \frac{1}{x} = 3 \), compute the value of
\[
(x - 3)^2 + \frac{16}{(x - 3)^2}.
\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A horse 36 feet from the center of a merry-go-round makes 40 revolutions. In order to travel the same distance, how many revolutions would a horse 12 feet from the center have to make?<|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
A horse 36 feet from the center of a merry-go-round makes 40 revolutions. In order to travel the same distance, how many revolutions would a horse 12 feet from the center have to make?<|im_end|>
<|im_start|>assistant
<Z_57><Z_33><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A horse 36 feet from the center of a merry-go-round makes 40 revolutions. In order to travel the same distance, how many revolutions would a horse 12 feet from the center have to make?<|im_end|>
<|im_start|>assistant
<Z_86><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A horse 36 feet from the center of a merry-go-round makes 40 revolutions. In order to travel the same distance, how many revolutions would a horse 12 feet from the center have to make?<|im_end|>
<|im_start|>assistant
<Z_102><Z_87><Z_66><ANSWER>

Question: A horse 36 feet from the center of a merry-go-round makes 40 revolutions. In order to travel the same distance, how many revolutions would a horse 12 feet from the center have to make?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa had 32 music files and 96 video files on her flash drive. If she deleted 60 of the files, how many files were still on her flash drive?<|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
Vanessa had 32 music files and 96 video files on her flash drive. If she deleted 60 of the files, how many files were still on her flash drive?<|im_end|>
<|im_start|>assistant
<Z_104><Z_64><Z_36><Z_58><Z_63><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa had 32 music files and 96 video files on her flash drive. If she deleted 60 of the files, how many files were still on her flash drive?<|im_end|>
<|im_start|>assistant
<Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Vanessa had 32 music files and 96 video files on her flash drive. If she deleted 60 of the files, how many files were still on her flash drive?<|im_end|>
<|im_start|>assistant
<Z_122><Z_4><Z_16><Z_33><Z_83><Z_32><ANSWER>

Question: Vanessa had 32 music files and 96 video files on her flash drive. If she deleted 60 of the files, how many files were still on her flash drive?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The chess club at my school consists of 8 boys and 10 girls. We need to send a team of 8 members to a regional competition. The team must consist of 5 boys and 3 girls. How many ways can we select this team?<|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
The chess club at my school consists of 8 boys and 10 girls. We need to send a team of 8 members to a regional competition. The team must consist of 5 boys and 3 girls. How many ways can we select this team?<|im_end|>
<|im_start|>assistant
<Z_104><Z_97><Z_78><Z_81><Z_48><Z_43><Z_61><Z_125><Z_65><Z_70><Z_121><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The chess club at my school consists of 8 boys and 10 girls. We need to send a team of 8 members to a regional competition. The team must consist of 5 boys and 3 girls. How many ways can we select this team?<|im_end|>
<|im_start|>assistant
<Z_11><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The chess club at my school consists of 8 boys and 10 girls. We need to send a team of 8 members to a regional competition. The team must consist of 5 boys and 3 girls. How many ways can we select this team?<|im_end|>
<|im_start|>assistant
<Z_91><Z_125><Z_99><Z_44><Z_31><Z_117><Z_125><Z_102><Z_53><Z_119><Z_63><Z_73><ANSWER>

Question: The chess club at my school consists of 8 boys and 10 girls. We need to send a team of 8 members to a regional competition. The team must consist of 5 boys and 3 girls. How many ways can we select this team?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if x, y, z, and w are positive integers, and 2x² = 5y³ = 8z⁴ = 3w, then find the least possible value of x + y + z + w.<|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
if x, y, z, and w are positive integers, and 2x² = 5y³ = 8z⁴ = 3w, then find the least possible value of x + y + z + w.<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><Z_30><Z_120><Z_33><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if x, y, z, and w are positive integers, and 2x² = 5y³ = 8z⁴ = 3w, then find the least possible value of x + y + z + w.<|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
if x, y, z, and w are positive integers, and 2x² = 5y³ = 8z⁴ = 3w, then find the least possible value of x + y + z + w.<|im_end|>
<|im_start|>assistant
<Z_41><Z_43><Z_16><Z_54><Z_20><Z_72><ANSWER>

Question: if x, y, z, and w are positive integers, and 2x² = 5y³ = 8z⁴ = 3w, then find the least possible value of x + y + z + w.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a four-digit number that is a perfect square, where the first two digits are the same and the last two digits are also the same.<|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
Find a four-digit number that is a perfect square, where the first two digits are the same and the last two digits are also the same.<|im_end|>
<|im_start|>assistant
<Z_104><Z_82><Z_120><Z_37><Z_80><Z_64><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a four-digit number that is a perfect square, where the first two digits are the same and the last two digits are also the same.<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a four-digit number that is a perfect square, where the first two digits are the same and the last two digits are also the same.<|im_end|>
<|im_start|>assistant
<Z_23><Z_55><Z_58><Z_86><Z_10><Z_107><Z_117><ANSWER>

Question: Find a four-digit number that is a perfect square, where the first two digits are the same and the last two digits are also the same.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bangladesh National Mathematical Olympiad 2016 Higher Secondary

<u>**Problem 2:**</u>
(a) How many positive integer factors does  $6000$  have?

(b) How many positive integer factors of  $6000$  are not perfect squares?<|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
Bangladesh National Mathematical Olympiad 2016 Higher Secondary

<u>**Problem 2:**</u>
(a) How many positive integer factors does  $6000$  have?

(b) How many positive integer factors of  $6000$  are not perfect squares?<|im_end|>
<|im_start|>assistant
<Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bangladesh National Mathematical Olympiad 2016 Higher Secondary

<u>**Problem 2:**</u>
(a) How many positive integer factors does  $6000$  have?

(b) How many positive integer factors of  $6000$  are not perfect squares?<|im_end|>
<|im_start|>assistant
<Z_56><ANSWER>

Question:
Bangladesh National Mathematical Olympiad 2016 Higher Secondary

<u>**Problem 2:**</u>
(a) How many positive integer factors does  $6000$  have?

(b) How many positive integer factors of  $6000$  are not perfect squares?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the speed of a bus is 54 km/hr, and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?<|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
Excluding stoppages, the speed of a bus is 54 km/hr, and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?<|im_end|>
<|im_start|>assistant
<Z_94><Z_68><Z_93><Z_103><Z_68><Z_59><Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the speed of a bus is 54 km/hr, and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?<|im_end|>
<|im_start|>assistant
<Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the speed of a bus is 54 km/hr, and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?<|im_end|>
<|im_start|>assistant
<Z_64><Z_77><Z_37><Z_56><Z_74><Z_117><Z_55><ANSWER>

Question: Excluding stoppages, the speed of a bus is 54 km/hr, and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $f(x) = x^2$ and $g(x) = 2x^2 + 3x + 1$, what is $f(g(2))$?<|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
Given that $f(x) = x^2$ and $g(x) = 2x^2 + 3x + 1$, what is $f(g(2))$?<|im_end|>
<|im_start|>assistant
<Z_105><Z_110><Z_58><Z_79><Z_100><Z_36><Z_80><Z_75><Z_53><Z_37><Z_76><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $f(x) = x^2$ and $g(x) = 2x^2 + 3x + 1$, what is $f(g(2))$?<|im_end|>
<|im_start|>assistant
<Z_7><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $f(x) = x^2$ and $g(x) = 2x^2 + 3x + 1$, what is $f(g(2))$?<|im_end|>
<|im_start|>assistant
<Z_29><Z_26><Z_15><Z_61><Z_4><Z_14><Z_86><Z_6><Z_51><Z_114><Z_116><Z_69><ANSWER>

Question: Given that $f(x) = x^2$ and $g(x) = 2x^2 + 3x + 1$, what is $f(g(2))$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, what is his highest score?<|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
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, what is his highest score?<|im_end|>
<|im_start|>assistant
<Z_57><Z_115><Z_47><Z_99><Z_47><Z_47><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, what is his highest score?<|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
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, what is his highest score?<|im_end|>
<|im_start|>assistant
<Z_109><Z_106><Z_72><Z_92><Z_40><Z_13><Z_42><ANSWER>

Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, what is his highest score?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In decimal representation, the natural number
$$
n = \frac{99 \cdots 9}{100 \uparrow}
$$

How many 9s are there in the representation of \(n^3\)?
(Dutch Mathematical Olympiad, 1983)<|im_end|>
<|im_start|>assistant
<Z_104><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In decimal representation, the natural number
$$
n = \frac{99 \cdots 9}{100 \uparrow}
$$

How many 9s are there in the representation of \(n^3\)?
(Dutch Mathematical Olympiad, 1983)<|im_end|>
<|im_start|>assistant
<Z_104><Z_59><Z_92><Z_79><Z_117><Z_124><Z_107><Z_75><Z_88><Z_8><Z_75><Z_87><Z_76><Z_63><Z_39><Z_79><Z_119><Z_90><Z_31><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In decimal representation, the natural number
$$
n = \frac{99 \cdots 9}{100 \uparrow}
$$

How many 9s are there in the representation of \(n^3\)?
(Dutch Mathematical Olympiad, 1983)<|im_end|>
<|im_start|>assistant
<Z_125><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In decimal representation, the natural number
$$
n = \frac{99 \cdots 9}{100 \uparrow}
$$

How many 9s are there in the representation of \(n^3\)?
(Dutch Mathematical Olympiad, 1983)<|im_end|>
<|im_start|>assistant
<Z_107><Z_79><Z_44><Z_117><Z_59><Z_48><Z_115><Z_27><Z_28><Z_24><Z_63><Z_59><Z_27><Z_80><Z_97><Z_10><Z_114><Z_125><Z_115><Z_3><ANSWER>

Question:
In decimal representation, the natural number
$$
n = \frac{99 \cdots 9}{100 \uparrow}
$$

How many 9s are there in the representation of \(n^3\)?
(Dutch Mathematical Olympiad, 1983)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy’s car can drive 19 miles per gallon of gas. She was able to drive 15 miles to school, some miles to the softball park, 2 miles to a burger restaurant, 4 miles to her friend’s house, and 11 miles home before she ran out of gas. She started with 2 gallons of gas. How many miles did she drive to the softball park?<|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
Kennedy’s car can drive 19 miles per gallon of gas. She was able to drive 15 miles to school, some miles to the softball park, 2 miles to a burger restaurant, 4 miles to her friend’s house, and 11 miles home before she ran out of gas. She started with 2 gallons of gas. How many miles did she drive to the softball park?<|im_end|>
<|im_start|>assistant
<Z_94><Z_108><Z_38><Z_89><Z_32><Z_89><Z_49><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy’s car can drive 19 miles per gallon of gas. She was able to drive 15 miles to school, some miles to the softball park, 2 miles to a burger restaurant, 4 miles to her friend’s house, and 11 miles home before she ran out of gas. She started with 2 gallons of gas. How many miles did she drive to the softball park?<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy’s car can drive 19 miles per gallon of gas. She was able to drive 15 miles to school, some miles to the softball park, 2 miles to a burger restaurant, 4 miles to her friend’s house, and 11 miles home before she ran out of gas. She started with 2 gallons of gas. How many miles did she drive to the softball park?<|im_end|>
<|im_start|>assistant
<Z_46><Z_71><Z_0><Z_106><Z_84><Z_121><Z_25><Z_54><ANSWER>

Question: Kennedy’s car can drive 19 miles per gallon of gas. She was able to drive 15 miles to school, some miles to the softball park, 2 miles to a burger restaurant, 4 miles to her friend’s house, and 11 miles home before she ran out of gas. She started with 2 gallons of gas. How many miles did she drive to the softball park?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :<|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
a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :<|im_end|>
<|im_start|>assistant
<Z_94><Z_43><Z_82><Z_70><Z_76><Z_119><Z_47><Z_22><Z_80><Z_45><Z_34><Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :<|im_end|>
<|im_start|>assistant
<Z_13><Z_126><Z_40><Z_51><Z_122><Z_13><Z_104><Z_74><Z_28><Z_20><Z_82><Z_89><ANSWER>

Question: a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different values can be obtained by placing parentheses in all possible ways in the expression 2:3:5:7:11:13:17:19:23:29?<|im_end|>
<|im_start|>assistant
<Z_104><Z_50><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different values can be obtained by placing parentheses in all possible ways in the expression 2:3:5:7:11:13:17:19:23:29?<|im_end|>
<|im_start|>assistant
<Z_94><Z_78><Z_32><Z_125><Z_59><Z_103><Z_66><Z_28><Z_28><Z_22><Z_124><Z_26><Z_124><Z_126><Z_83><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different values can be obtained by placing parentheses in all possible ways in the expression 2:3:5:7:11:13:17:19:23:29?<|im_end|>
<|im_start|>assistant
<Z_88><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 different values can be obtained by placing parentheses in all possible ways in the expression 2:3:5:7:11:13:17:19:23:29?<|im_end|>
<|im_start|>assistant
<Z_21><Z_1><Z_110><Z_13><Z_91><Z_54><Z_22><Z_102><Z_117><Z_70><Z_51><Z_102><Z_66><Z_7><Z_103><Z_5><ANSWER>

Question: How many different values can be obtained by placing parentheses in all possible ways in the expression 2:3:5:7:11:13:17:19:23:29?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box is 8 inches in height, 10 inches in width, and 12 inches in length. A wooden building block is 3 inches in height, has a certain width, and 4 inches in length. 40 building blocks can fit into the box. What is the width of the building block?<|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
A box is 8 inches in height, 10 inches in width, and 12 inches in length. A wooden building block is 3 inches in height, has a certain width, and 4 inches in length. 40 building blocks can fit into the box. What is the width of the building block?<|im_end|>
<|im_start|>assistant
<Z_94><Z_27><Z_29><Z_32><Z_64><Z_100><Z_47><Z_54><Z_66><Z_125><Z_96><Z_37><Z_41><Z_126><Z_67><Z_45><Z_91><Z_72><Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box is 8 inches in height, 10 inches in width, and 12 inches in length. A wooden building block is 3 inches in height, has a certain width, and 4 inches in length. 40 building blocks can fit into the box. What is the width of the building block?<|im_end|>
<|im_start|>assistant
<Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box is 8 inches in height, 10 inches in width, and 12 inches in length. A wooden building block is 3 inches in height, has a certain width, and 4 inches in length. 40 building blocks can fit into the box. What is the width of the building block?<|im_end|>
<|im_start|>assistant
<Z_82><Z_51><Z_102><Z_7><Z_113><Z_82><Z_10><Z_11><Z_120><Z_25><Z_74><Z_36><Z_33><Z_13><Z_8><Z_94><Z_0><Z_103><Z_81><ANSWER>

Question: A box is 8 inches in height, 10 inches in width, and 12 inches in length. A wooden building block is 3 inches in height, has a certain width, and 4 inches in length. 40 building blocks can fit into the box. What is the width of the building block?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon  $ANDD'Y$  has  $AN \parallel DY$  and  $AY \parallel D'N$  with  $AN = D'Y$  and  $AY = DN$ . If the area of  $ANDY$  is 20, the area of  $AND'Y$  is 24, and the area of  $ADD'$  is 26, the area of  $ANDD'Y$  can be expressed in the form  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $m+n$ .

*Proposed by Andy Xu*<|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
Pentagon  $ANDD'Y$  has  $AN \parallel DY$  and  $AY \parallel D'N$  with  $AN = D'Y$  and  $AY = DN$ . If the area of  $ANDY$  is 20, the area of  $AND'Y$  is 24, and the area of  $ADD'$  is 26, the area of  $ANDD'Y$  can be expressed in the form  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $m+n$ .

*Proposed by Andy Xu*<|im_end|>
<|im_start|>assistant
<Z_57><Z_34><Z_47><Z_89><Z_78><Z_119><Z_40><Z_76><Z_82><Z_48><Z_26><Z_60><Z_92><Z_82><Z_31><Z_41><Z_82><Z_80><Z_60><Z_75><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon  $ANDD'Y$  has  $AN \parallel DY$  and  $AY \parallel D'N$  with  $AN = D'Y$  and  $AY = DN$ . If the area of  $ANDY$  is 20, the area of  $AND'Y$  is 24, and the area of  $ADD'$  is 26, the area of  $ANDD'Y$  can be expressed in the form  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $m+n$ .

*Proposed by Andy Xu*<|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
Pentagon  $ANDD'Y$  has  $AN \parallel DY$  and  $AY \parallel D'N$  with  $AN = D'Y$  and  $AY = DN$ . If the area of  $ANDY$  is 20, the area of  $AND'Y$  is 24, and the area of  $ADD'$  is 26, the area of  $ANDD'Y$  can be expressed in the form  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $m+n$ .

*Proposed by Andy Xu*<|im_end|>
<|im_start|>assistant
<Z_7><Z_0><Z_26><Z_26><Z_34><Z_34><Z_89><Z_2><Z_73><Z_16><Z_69><Z_69><Z_101><Z_122><Z_81><Z_67><Z_31><Z_67><Z_66><Z_19><ANSWER>

Question:
Pentagon  $ANDD'Y$  has  $AN \parallel DY$  and  $AY \parallel D'N$  with  $AN = D'Y$  and  $AY = DN$ . If the area of  $ANDY$  is 20, the area of  $AND'Y$  is 24, and the area of  $ADD'$  is 26, the area of  $ANDD'Y$  can be expressed in the form  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Find  $m+n$ .

*Proposed by Andy Xu*


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mcdonald is planning to open up a farm that provides eggs to the community. In his local community, Saly needs 10 eggs, Ben needs 14 eggs, and Ked needs half of the number of eggs needed by Ben per week. In a month which has 4 weeks, how many eggs should Mcdonald's farm produce?<|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
Mcdonald is planning to open up a farm that provides eggs to the community. In his local community, Saly needs 10 eggs, Ben needs 14 eggs, and Ked needs half of the number of eggs needed by Ben per week. In a month which has 4 weeks, how many eggs should Mcdonald's farm produce?<|im_end|>
<|im_start|>assistant
<Z_94><Z_13><Z_4><Z_37><Z_51><Z_66><Z_37><Z_115><Z_66><Z_87><Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mcdonald is planning to open up a farm that provides eggs to the community. In his local community, Saly needs 10 eggs, Ben needs 14 eggs, and Ked needs half of the number of eggs needed by Ben per week. In a month which has 4 weeks, how many eggs should Mcdonald's farm produce?<|im_end|>
<|im_start|>assistant
<Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mcdonald is planning to open up a farm that provides eggs to the community. In his local community, Saly needs 10 eggs, Ben needs 14 eggs, and Ked needs half of the number of eggs needed by Ben per week. In a month which has 4 weeks, how many eggs should Mcdonald's farm produce?<|im_end|>
<|im_start|>assistant
<Z_69><Z_124><Z_2><Z_112><Z_2><Z_62><Z_116><Z_36><Z_38><Z_48><Z_2><ANSWER>

Question: Mcdonald is planning to open up a farm that provides eggs to the community. In his local community, Saly needs 10 eggs, Ben needs 14 eggs, and Ked needs half of the number of eggs needed by Ben per week. In a month which has 4 weeks, how many eggs should Mcdonald's farm produce?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Simplify: $|{-5^2 + 7 - 3}|$<|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
Simplify: $|{-5^2 + 7 - 3}|$<|im_end|>
<|im_start|>assistant
<Z_20><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Simplify: $|{-5^2 + 7 - 3}|$<|im_end|>
<|im_start|>assistant
<Z_32><ANSWER>

Question: Simplify: $|{-5^2 + 7 - 3}|$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the integer formed by the rightmost two digits of the integer equal to \(4^{127} + 5^{129} + 7^{131}\)?<|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
What is the integer formed by the rightmost two digits of the integer equal to \(4^{127} + 5^{129} + 7^{131}\)?<|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
What is the integer formed by the rightmost two digits of the integer equal to \(4^{127} + 5^{129} + 7^{131}\)?<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the integer formed by the rightmost two digits of the integer equal to \(4^{127} + 5^{129} + 7^{131}\)?<|im_end|>
<|im_start|>assistant
<Z_125><ANSWER>

Question: What is the integer formed by the rightmost two digits of the integer equal to \(4^{127} + 5^{129} + 7^{131}\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jason bought a new bookcase that can hold a maximum of 80 pounds of weight. He has a certain number of hardcover books that each weigh half a pound, 30 textbooks that each weigh 2 pounds, and 3 knick-knacks that each weight 6 pounds. The total collection of items is 33 pounds over the bookcase's weight limit. How many hardcover books does Jason have?<|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
Jason bought a new bookcase that can hold a maximum of 80 pounds of weight. He has a certain number of hardcover books that each weigh half a pound, 30 textbooks that each weigh 2 pounds, and 3 knick-knacks that each weight 6 pounds. The total collection of items is 33 pounds over the bookcase's weight limit. How many hardcover books does Jason have?<|im_end|>
<|im_start|>assistant
<Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jason bought a new bookcase that can hold a maximum of 80 pounds of weight. He has a certain number of hardcover books that each weigh half a pound, 30 textbooks that each weigh 2 pounds, and 3 knick-knacks that each weight 6 pounds. The total collection of items is 33 pounds over the bookcase's weight limit. How many hardcover books does Jason have?<|im_end|>
<|im_start|>assistant
<Z_50><ANSWER>

Question: Jason bought a new bookcase that can hold a maximum of 80 pounds of weight. He has a certain number of hardcover books that each weigh half a pound, 30 textbooks that each weigh 2 pounds, and 3 knick-knacks that each weight 6 pounds. The total collection of items is 33 pounds over the bookcase's weight limit. How many hardcover books does Jason have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x + y + z = 14\) and \(xy + xz + yz = 32,\) then find
\[
x^3 + y^3 + z^3 - 3xyz.
\]<|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
If \(x + y + z = 14\) and \(xy + xz + yz = 32,\) then find
\[
x^3 + y^3 + z^3 - 3xyz.
\]<|im_end|>
<|im_start|>assistant
<Z_104><Z_78><Z_121><Z_77><Z_11><Z_126><Z_79><Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x + y + z = 14\) and \(xy + xz + yz = 32,\) then find
\[
x^3 + y^3 + z^3 - 3xyz.
\]<|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
If \(x + y + z = 14\) and \(xy + xz + yz = 32,\) then find
\[
x^3 + y^3 + z^3 - 3xyz.
\]<|im_end|>
<|im_start|>assistant
<Z_120><Z_30><Z_9><Z_92><Z_117><Z_62><Z_91><Z_62><ANSWER>

Question:
If \(x + y + z = 14\) and \(xy + xz + yz = 32,\) then find
\[
x^3 + y^3 + z^3 - 3xyz.
\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If Ken's house is twice as far from Dawn's house as Mary's house along a certain road, and Ken's house is 4 miles away from Dawn's house along this same road. Jack's house is 3 miles further down the road from Mary's house. How much distance (in miles) will Ken cover if he goes from his house to Dawn's house, then Mary's, then Jack's before going back to Mary's, Dawn's and finally his own house? Also, if Ken had to detour through a longer route that added an extra two miles each time he traveled from Dawn's to Jack's house and back, how much extra distance would he travel in total?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If Ken's house is twice as far from Dawn's house as Mary's house along a certain road, and Ken's house is 4 miles away from Dawn's house along this same road. Jack's house is 3 miles further down the road from Mary's house. How much distance (in miles) will Ken cover if he goes from his house to Dawn's house, then Mary's, then Jack's before going back to Mary's, Dawn's and finally his own house? Also, if Ken had to detour through a longer route that added an extra two miles each time he traveled from Dawn's to Jack's house and back, how much extra distance would he travel in total?<|im_end|>
<|im_start|>assistant
<Z_113><Z_100><Z_51><Z_51><Z_119><Z_121><Z_126><Z_28><Z_114><Z_123><Z_80><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If Ken's house is twice as far from Dawn's house as Mary's house along a certain road, and Ken's house is 4 miles away from Dawn's house along this same road. Jack's house is 3 miles further down the road from Mary's house. How much distance (in miles) will Ken cover if he goes from his house to Dawn's house, then Mary's, then Jack's before going back to Mary's, Dawn's and finally his own house? Also, if Ken had to detour through a longer route that added an extra two miles each time he traveled from Dawn's to Jack's house and back, how much extra distance would he travel in total?<|im_end|>
<|im_start|>assistant
<Z_89><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If Ken's house is twice as far from Dawn's house as Mary's house along a certain road, and Ken's house is 4 miles away from Dawn's house along this same road. Jack's house is 3 miles further down the road from Mary's house. How much distance (in miles) will Ken cover if he goes from his house to Dawn's house, then Mary's, then Jack's before going back to Mary's, Dawn's and finally his own house? Also, if Ken had to detour through a longer route that added an extra two miles each time he traveled from Dawn's to Jack's house and back, how much extra distance would he travel in total?<|im_end|>
<|im_start|>assistant
<Z_15><Z_94><Z_114><Z_126><Z_111><Z_108><Z_56><Z_26><Z_42><Z_48><Z_20><Z_91><ANSWER>

Question: If Ken's house is twice as far from Dawn's house as Mary's house along a certain road, and Ken's house is 4 miles away from Dawn's house along this same road. Jack's house is 3 miles further down the road from Mary's house. How much distance (in miles) will Ken cover if he goes from his house to Dawn's house, then Mary's, then Jack's before going back to Mary's, Dawn's and finally his own house? Also, if Ken had to detour through a longer route that added an extra two miles each time he traveled from Dawn's to Jack's house and back, how much extra distance would he travel in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Without using a calculator, compute $1010^2 - 990^2 - 1005^2 + 995^2 + 1012^2 - 988^2$.<|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
Without using a calculator, compute $1010^2 - 990^2 - 1005^2 + 995^2 + 1012^2 - 988^2$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_27><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Without using a calculator, compute $1010^2 - 990^2 - 1005^2 + 995^2 + 1012^2 - 988^2$.<|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
Without using a calculator, compute $1010^2 - 990^2 - 1005^2 + 995^2 + 1012^2 - 988^2$.<|im_end|>
<|im_start|>assistant
<Z_117><Z_31><Z_6><ANSWER>

Question: Without using a calculator, compute $1010^2 - 990^2 - 1005^2 + 995^2 + 1012^2 - 988^2$.