<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than 20 and the connection between y and some number is equal to 1 / 1. There are 7 possible values of y. What is that number?<|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 “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than 20 and the connection between y and some number is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_94><Z_1><Z_87><Z_40><Z_11><Z_64><Z_83><Z_90><Z_53><Z_28><Z_73><Z_119><Z_52><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than 20 and the connection between y and some number is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than 20 and the connection between y and some number is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_11><Z_35><Z_49><Z_76><Z_10><Z_9><Z_15><Z_126><Z_122><Z_45><Z_96><Z_51><Z_126><Z_13><ANSWER>

Question: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than 20 and the connection between y and some number is equal to 1 / 1. There are 7 possible values of y. What is that number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $3m-4$ and $7-4m$ are two square roots of $N$, then $N=$ ___.<|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
If $3m-4$ and $7-4m$ are two square roots of $N$, then $N=$ ___.<|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
If $3m-4$ and $7-4m$ are two square roots of $N$, then $N=$ ___.<|im_end|>
<|im_start|>assistant
<Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $3m-4$ and $7-4m$ are two square roots of $N$, then $N=$ ___.<|im_end|>
<|im_start|>assistant
<Z_12><ANSWER>

Question: If $3m-4$ and $7-4m$ are two square roots of $N$, then $N=$ ___.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $b^3 \cdot b^6 \div b^2$ if $b = 4$.<|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
Evaluate the expression $b^3 \cdot b^6 \div b^2$ if $b = 4$.<|im_end|>
<|im_start|>assistant
<Z_106><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $b^3 \cdot b^6 \div b^2$ if $b = 4$.<|im_end|>
<|im_start|>assistant
<Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the expression $b^3 \cdot b^6 \div b^2$ if $b = 4$.<|im_end|>
<|im_start|>assistant
<Z_115><Z_102><ANSWER>

Question: Evaluate the expression $b^3 \cdot b^6 \div b^2$ if $b = 4$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A(m,-m+3)$, $B(2,m-1)$, $C(-1,4)$, the slope of line $AC$ is three times the slope of line $BC$. Find the value of the real number $m$.<|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 $A(m,-m+3)$, $B(2,m-1)$, $C(-1,4)$, the slope of line $AC$ is three times the slope of line $BC$. Find the value of the real number $m$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_36><Z_50><Z_72><Z_124><Z_72><Z_121><Z_96><Z_58><Z_10><Z_6><Z_126><Z_55><Z_66><Z_33><Z_72><Z_26><Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A(m,-m+3)$, $B(2,m-1)$, $C(-1,4)$, the slope of line $AC$ is three times the slope of line $BC$. Find the value of the real number $m$.<|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
Let $A(m,-m+3)$, $B(2,m-1)$, $C(-1,4)$, the slope of line $AC$ is three times the slope of line $BC$. Find the value of the real number $m$.<|im_end|>
<|im_start|>assistant
<Z_122><Z_41><Z_20><Z_83><Z_13><Z_68><Z_104><Z_63><Z_96><Z_4><Z_26><Z_23><Z_62><Z_119><Z_47><Z_24><Z_96><Z_98><ANSWER>

Question: Let $A(m,-m+3)$, $B(2,m-1)$, $C(-1,4)$, the slope of line $AC$ is three times the slope of line $BC$. Find the value of the real number $m$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?<|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
There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?<|im_end|>
<|im_start|>assistant
<Z_94><Z_72><Z_119><Z_75><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
There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?<|im_end|>
<|im_start|>assistant
<Z_48><Z_108><Z_12><Z_81><Z_52><Z_93><ANSWER>

Question: There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate: \\((-3)^{2}- \sqrt{4}+ \left( \frac{1}{2} \right)^{-1}\\).<|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
Calculate: \\((-3)^{2}- \sqrt{4}+ \left( \frac{1}{2} \right)^{-1}\\).<|im_end|>
<|im_start|>assistant
<Z_94><Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate: \\((-3)^{2}- \sqrt{4}+ \left( \frac{1}{2} \right)^{-1}\\).<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate: \\((-3)^{2}- \sqrt{4}+ \left( \frac{1}{2} \right)^{-1}\\).<|im_end|>
<|im_start|>assistant
<Z_1><Z_91><ANSWER>

Question: Calculate: \\((-3)^{2}- \sqrt{4}+ \left( \frac{1}{2} \right)^{-1}\\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?<|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
Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?<|im_end|>
<|im_start|>assistant
<Z_113><Z_108><Z_68><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?<|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
Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?<|im_end|>
<|im_start|>assistant
<Z_42><Z_80><Z_121><Z_46><ANSWER>

Question: Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\left(\sqrt{(\sqrt{5})^4}\right)^6$.<|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
Calculate $\left(\sqrt{(\sqrt{5})^4}\right)^6$.<|im_end|>
<|im_start|>assistant
<Z_104><Z_121><Z_4><Z_103><Z_87><Z_61><Z_9><Z_95><Z_45><Z_124><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\left(\sqrt{(\sqrt{5})^4}\right)^6$.<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\left(\sqrt{(\sqrt{5})^4}\right)^6$.<|im_end|>
<|im_start|>assistant
<Z_4><Z_10><Z_116><Z_13><Z_5><Z_117><Z_96><Z_17><Z_33><Z_4><Z_23><ANSWER>

Question: Calculate $\left(\sqrt{(\sqrt{5})^4}\right)^6$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?<|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
What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?<|im_end|>
<|im_start|>assistant
<Z_94><Z_47><Z_33><Z_124><Z_119><Z_80><Z_95><Z_70><Z_93><Z_31><Z_96><Z_78><Z_126><Z_37><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?<|im_end|>
<|im_start|>assistant
<Z_105><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?<|im_end|>
<|im_start|>assistant
<Z_126><Z_98><Z_93><Z_36><Z_7><Z_123><Z_77><Z_62><Z_122><Z_107><Z_89><Z_7><Z_12><Z_119><Z_2><ANSWER>

Question: What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the beach, Janet, her sister, and their two friends built sandcastles and then measured their heights. Janet's sandcastle was 3 5/6 feet tall, her sister's was 2 7/12 feet tall, their friend Tom's sandcastle was 1 11/20 feet tall, and their friend Lucy's sandcastle was 2 13/24 feet tall. What was the total height of all four sandcastles combined?<|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
At the beach, Janet, her sister, and their two friends built sandcastles and then measured their heights. Janet's sandcastle was 3 5/6 feet tall, her sister's was 2 7/12 feet tall, their friend Tom's sandcastle was 1 11/20 feet tall, and their friend Lucy's sandcastle was 2 13/24 feet tall. What was the total height of all four sandcastles combined?<|im_end|>
<|im_start|>assistant
<Z_57><Z_65><Z_121><Z_87><Z_87><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the beach, Janet, her sister, and their two friends built sandcastles and then measured their heights. Janet's sandcastle was 3 5/6 feet tall, her sister's was 2 7/12 feet tall, their friend Tom's sandcastle was 1 11/20 feet tall, and their friend Lucy's sandcastle was 2 13/24 feet tall. What was the total height of all four sandcastles combined?<|im_end|>
<|im_start|>assistant
<Z_9><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the beach, Janet, her sister, and their two friends built sandcastles and then measured their heights. Janet's sandcastle was 3 5/6 feet tall, her sister's was 2 7/12 feet tall, their friend Tom's sandcastle was 1 11/20 feet tall, and their friend Lucy's sandcastle was 2 13/24 feet tall. What was the total height of all four sandcastles combined?<|im_end|>
<|im_start|>assistant
<Z_124><Z_105><Z_19><Z_41><Z_125><Z_72><ANSWER>

Question: At the beach, Janet, her sister, and their two friends built sandcastles and then measured their heights. Janet's sandcastle was 3 5/6 feet tall, her sister's was 2 7/12 feet tall, their friend Tom's sandcastle was 1 11/20 feet tall, and their friend Lucy's sandcastle was 2 13/24 feet tall. What was the total height of all four sandcastles combined?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $g$ defined by $g(x)= \frac{px+q}{rx+s}$, where $p$, $q$, $r$, and $s$ are nonzero real numbers, satisfies $g(23)=23$, $g(101)=101$, and $g(g(x))=x$ for all values except $\frac{-s}{r}$. Find the unique number that is not in the range of $g$.<|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 function $g$ defined by $g(x)= \frac{px+q}{rx+s}$, where $p$, $q$, $r$, and $s$ are nonzero real numbers, satisfies $g(23)=23$, $g(101)=101$, and $g(g(x))=x$ for all values except $\frac{-s}{r}$. Find the unique number that is not in the range of $g$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_125><Z_1><Z_1><Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $g$ defined by $g(x)= \frac{px+q}{rx+s}$, where $p$, $q$, $r$, and $s$ are nonzero real numbers, satisfies $g(23)=23$, $g(101)=101$, and $g(g(x))=x$ for all values except $\frac{-s}{r}$. Find the unique number that is not in the range of $g$.<|im_end|>
<|im_start|>assistant
<Z_44><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $g$ defined by $g(x)= \frac{px+q}{rx+s}$, where $p$, $q$, $r$, and $s$ are nonzero real numbers, satisfies $g(23)=23$, $g(101)=101$, and $g(g(x))=x$ for all values except $\frac{-s}{r}$. Find the unique number that is not in the range of $g$.<|im_end|>
<|im_start|>assistant
<Z_78><Z_34><Z_31><Z_101><Z_88><ANSWER>

Question: A function $g$ defined by $g(x)= \frac{px+q}{rx+s}$, where $p$, $q$, $r$, and $s$ are nonzero real numbers, satisfies $g(23)=23$, $g(101)=101$, and $g(g(x))=x$ for all values except $\frac{-s}{r}$. Find the unique number that is not in the range of $g$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The h.c.f. of two numbers is 42, and the other two factors of their l.c.m. are 12 and 14. What is the larger of the two numbers?<|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 h.c.f. of two numbers is 42, and the other two factors of their l.c.m. are 12 and 14. What is the larger of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_104><Z_47><Z_89><Z_123><Z_41><Z_39><Z_99><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The h.c.f. of two numbers is 42, and the other two factors of their l.c.m. are 12 and 14. What is the larger of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_42><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The h.c.f. of two numbers is 42, and the other two factors of their l.c.m. are 12 and 14. What is the larger of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_92><Z_9><Z_46><Z_120><Z_23><Z_111><Z_70><Z_123><ANSWER>

Question: The h.c.f. of two numbers is 42, and the other two factors of their l.c.m. are 12 and 14. What is the larger of the two numbers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?<|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
how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_104><Z_74><Z_13><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_77><Z_57><Z_55><Z_45><ANSWER>

Question: how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A book has some chapters. Each chapter is 61 pages long. The book has altogether 1891 pages. How many chapters does the book 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
A book has some chapters. Each chapter is 61 pages long. The book has altogether 1891 pages. How many chapters does the book have?<|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 book has some chapters. Each chapter is 61 pages long. The book has altogether 1891 pages. How many chapters does the book have?<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A book has some chapters. Each chapter is 61 pages long. The book has altogether 1891 pages. How many chapters does the book have?<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

Question: A book has some chapters. Each chapter is 61 pages long. The book has altogether 1891 pages. How many chapters does the book have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number $0.375$ can be written as a fraction $\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$?<|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 number $0.375$ can be written as a fraction $\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_79><Z_83><Z_107><Z_63><Z_45><Z_54><Z_90><Z_22><Z_16><Z_10><Z_39><Z_59><Z_71><Z_55><Z_75><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number $0.375$ can be written as a fraction $\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$?<|im_end|>
<|im_start|>assistant
<Z_46><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number $0.375$ can be written as a fraction $\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$?<|im_end|>
<|im_start|>assistant
<Z_118><Z_13><Z_44><Z_35><Z_30><Z_11><Z_102><Z_42><Z_75><Z_95><Z_19><Z_99><Z_4><Z_115><Z_117><Z_6><Z_46><ANSWER>

Question: The number $0.375$ can be written as a fraction $\frac{a}{b}$ for positive integers $a$ and $b$. When this fraction is in simplest terms, what is $a+b$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $x > 0$, $y > 0$, if ${2}^{x}\cdot {8}^{y}=16$, then ${2}^{-1+{\mathrm{log}}_{}\left(2x\right)}+{\mathrm{log}}_{}^{27y}=\_\_\_\_\_\mathrm{.}$<|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 $x > 0$, $y > 0$, if ${2}^{x}\cdot {8}^{y}=16$, then ${2}^{-1+{\mathrm{log}}_{}\left(2x\right)}+{\mathrm{log}}_{}^{27y}=\_\_\_\_\_\mathrm{.}$<|im_end|>
<|im_start|>assistant
<Z_57><Z_47><Z_59><Z_66><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $x > 0$, $y > 0$, if ${2}^{x}\cdot {8}^{y}=16$, then ${2}^{-1+{\mathrm{log}}_{}\left(2x\right)}+{\mathrm{log}}_{}^{27y}=\_\_\_\_\_\mathrm{.}$<|im_end|>
<|im_start|>assistant
<Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $x > 0$, $y > 0$, if ${2}^{x}\cdot {8}^{y}=16$, then ${2}^{-1+{\mathrm{log}}_{}\left(2x\right)}+{\mathrm{log}}_{}^{27y}=\_\_\_\_\_\mathrm{.}$<|im_end|>
<|im_start|>assistant
<Z_32><Z_5><Z_57><Z_36><Z_101><ANSWER>

Question: Given that $x > 0$, $y > 0$, if ${2}^{x}\cdot {8}^{y}=16$, then ${2}^{-1+{\mathrm{log}}_{}\left(2x\right)}+{\mathrm{log}}_{}^{27y}=\_\_\_\_\_\mathrm{.}$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
\(1.25 \times 67.875 + 125 \times 6.7875 + 1250 \times 0.053375\).<|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
\(1.25 \times 67.875 + 125 \times 6.7875 + 1250 \times 0.053375\).<|im_end|>
<|im_start|>assistant
<Z_104><Z_77><Z_44><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
\(1.25 \times 67.875 + 125 \times 6.7875 + 1250 \times 0.053375\).<|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
\(1.25 \times 67.875 + 125 \times 6.7875 + 1250 \times 0.053375\).<|im_end|>
<|im_start|>assistant
<Z_127><Z_9><Z_116><ANSWER>

Question: \(1.25 \times 67.875 + 125 \times 6.7875 + 1250 \times 0.053375\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The height of a right cone C is some value, and the diameter of the base of C is 8. The distance from the apex of C to any point on the circumference of the base of C is 5. What is the height of the cone?<|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 height of a right cone C is some value, and the diameter of the base of C is 8. The distance from the apex of C to any point on the circumference of the base of C is 5. What is the height of the cone?<|im_end|>
<|im_start|>assistant
<Z_57><Z_81><Z_82><Z_47><Z_64><Z_56><Z_95><Z_37><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The height of a right cone C is some value, and the diameter of the base of C is 8. The distance from the apex of C to any point on the circumference of the base of C is 5. What is the height of the cone?<|im_end|>
<|im_start|>assistant
<Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The height of a right cone C is some value, and the diameter of the base of C is 8. The distance from the apex of C to any point on the circumference of the base of C is 5. What is the height of the cone?<|im_end|>
<|im_start|>assistant
<Z_121><Z_116><Z_79><Z_117><Z_3><Z_123><Z_48><Z_112><Z_33><ANSWER>

Question: The height of a right cone C is some value, and the diameter of the base of C is 8. The distance from the apex of C to any point on the circumference of the base of C is 5. What is the height of the cone?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a point $M(a,b)$ on the line $3x+4y-15=0$, find the minimum value of $\sqrt{(a-1)^{2}+(b+2)^{2}}$.<|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
Given a point $M(a,b)$ on the line $3x+4y-15=0$, find the minimum value of $\sqrt{(a-1)^{2}+(b+2)^{2}}$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_33><Z_103><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a point $M(a,b)$ on the line $3x+4y-15=0$, find the minimum value of $\sqrt{(a-1)^{2}+(b+2)^{2}}$.<|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
Given a point $M(a,b)$ on the line $3x+4y-15=0$, find the minimum value of $\sqrt{(a-1)^{2}+(b+2)^{2}}$.<|im_end|>
<|im_start|>assistant
<Z_37><Z_76><Z_110><Z_37><ANSWER>

Question: Given a point $M(a,b)$ on the line $3x+4y-15=0$, find the minimum value of $\sqrt{(a-1)^{2}+(b+2)^{2}}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob is tilling a plot of his garden. The plot is 110 feet wide by 120 feet long. His tiller digs a swath two feet wide, and he can till 1 foot of ground in about 2 seconds. How long will it take him to till this plot of land, in minutes?<|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
Bob is tilling a plot of his garden. The plot is 110 feet wide by 120 feet long. His tiller digs a swath two feet wide, and he can till 1 foot of ground in about 2 seconds. How long will it take him to till this plot of land, in minutes?<|im_end|>
<|im_start|>assistant
<Z_113><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob is tilling a plot of his garden. The plot is 110 feet wide by 120 feet long. His tiller digs a swath two feet wide, and he can till 1 foot of ground in about 2 seconds. How long will it take him to till this plot of land, in minutes?<|im_end|>
<|im_start|>assistant
<Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob is tilling a plot of his garden. The plot is 110 feet wide by 120 feet long. His tiller digs a swath two feet wide, and he can till 1 foot of ground in about 2 seconds. How long will it take him to till this plot of land, in minutes?<|im_end|>
<|im_start|>assistant
<Z_92><Z_87><ANSWER>

Question: Bob is tilling a plot of his garden. The plot is 110 feet wide by 120 feet long. His tiller digs a swath two feet wide, and he can till 1 foot of ground in about 2 seconds. How long will it take him to till this plot of land, in minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $1010^2 - 990^2 - 1005^2 + 995^2$ without using a calculator.<|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 $1010^2 - 990^2 - 1005^2 + 995^2$ without using a calculator.<|im_end|>
<|im_start|>assistant
<Z_57><Z_38><Z_79><Z_120><Z_103><Z_124><Z_80><Z_16><Z_91><Z_78><Z_80><Z_107><Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $1010^2 - 990^2 - 1005^2 + 995^2$ without using a calculator.<|im_end|>
<|im_start|>assistant
<Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $1010^2 - 990^2 - 1005^2 + 995^2$ without using a calculator.<|im_end|>
<|im_start|>assistant
<Z_126><Z_121><Z_102><Z_43><Z_52><Z_101><Z_74><Z_119><Z_79><Z_106><Z_70><Z_35><Z_95><ANSWER>

Question: Calculate $1010^2 - 990^2 - 1005^2 + 995^2$ without using a calculator.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 7 ^ (x - y) equals a certain number and 7 ^ (x + y) equals 16807, what is the value of x when the certain number is 343?<|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 7 ^ (x - y) equals a certain number and 7 ^ (x + y) equals 16807, what is the value of x when the certain number is 343?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><Z_115><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 7 ^ (x - y) equals a certain number and 7 ^ (x + y) equals 16807, what is the value of x when the certain number is 343?<|im_end|>
<|im_start|>assistant
<Z_32><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 7 ^ (x - y) equals a certain number and 7 ^ (x + y) equals 16807, what is the value of x when the certain number is 343?<|im_end|>
<|im_start|>assistant
<Z_124><Z_127><Z_49><Z_11><ANSWER>

Question: If 7 ^ (x - y) equals a certain number and 7 ^ (x + y) equals 16807, what is the value of x when the certain number is 343?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sammy has 2 more bottle caps than Janine. Janine has 3 times as many bottle caps as Billie, but Billie gifted 4 bottle caps to Tommy, who now has twice as many bottle caps as Billie. If Billie started with an unknown number of bottle caps and Tommy initially had no bottle caps, how many bottle caps does Sammy have now?<|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
Sammy has 2 more bottle caps than Janine. Janine has 3 times as many bottle caps as Billie, but Billie gifted 4 bottle caps to Tommy, who now has twice as many bottle caps as Billie. If Billie started with an unknown number of bottle caps and Tommy initially had no bottle caps, how many bottle caps does Sammy have now?<|im_end|>
<|im_start|>assistant
<Z_94><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sammy has 2 more bottle caps than Janine. Janine has 3 times as many bottle caps as Billie, but Billie gifted 4 bottle caps to Tommy, who now has twice as many bottle caps as Billie. If Billie started with an unknown number of bottle caps and Tommy initially had no bottle caps, how many bottle caps does Sammy have now?<|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
Sammy has 2 more bottle caps than Janine. Janine has 3 times as many bottle caps as Billie, but Billie gifted 4 bottle caps to Tommy, who now has twice as many bottle caps as Billie. If Billie started with an unknown number of bottle caps and Tommy initially had no bottle caps, how many bottle caps does Sammy have now?<|im_end|>
<|im_start|>assistant
<Z_76><Z_30><ANSWER>

Question: Sammy has 2 more bottle caps than Janine. Janine has 3 times as many bottle caps as Billie, but Billie gifted 4 bottle caps to Tommy, who now has twice as many bottle caps as Billie. If Billie started with an unknown number of bottle caps and Tommy initially had no bottle caps, how many bottle caps does Sammy have now?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many digits $D$ is the positive three-digit number $4D5$ a multiple of 7?<|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
For how many digits $D$ is the positive three-digit number $4D5$ a multiple of 7?<|im_end|>
<|im_start|>assistant
<Z_113><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many digits $D$ is the positive three-digit number $4D5$ a multiple of 7?<|im_end|>
<|im_start|>assistant
<Z_46><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many digits $D$ is the positive three-digit number $4D5$ a multiple of 7?<|im_end|>
<|im_start|>assistant
<Z_96><Z_66><ANSWER>

Question: For how many digits $D$ is the positive three-digit number $4D5$ a multiple of 7?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A portion of the graph of $g(x)=px^4+qx^3+rx^2+sx+t$ is shown below. Determine the value of $12p - 6q + 3r - 2s + t$ given that $g(-1) = 4$.

[asy]
import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=4.25,ymin=-5.25,ymax=5.25;

pen cqcqcq=rgb(0.75,0.75,0.75);

/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10);

xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);
real g1(real x){return 0.5*x*(x+1)*(x-1)*(x-2)/8;} draw(graph(g1,-3.25,4.25),linewidth(0.75));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]<|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 portion of the graph of $g(x)=px^4+qx^3+rx^2+sx+t$ is shown below. Determine the value of $12p - 6q + 3r - 2s + t$ given that $g(-1) = 4$.

[asy]
import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=4.25,ymin=-5.25,ymax=5.25;

pen cqcqcq=rgb(0.75,0.75,0.75);

/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10);

xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);
real g1(real x){return 0.5*x*(x+1)*(x-1)*(x-2)/8;} draw(graph(g1,-3.25,4.25),linewidth(0.75));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]<|im_end|>
<|im_start|>assistant
<Z_94><Z_31><Z_100><Z_123><Z_36><Z_45><Z_88><Z_37><Z_61><Z_90><Z_90><Z_126><Z_52><Z_38><Z_98><Z_28><Z_117><Z_8><Z_39><Z_28><Z_9><Z_103><Z_71><Z_125><Z_91><Z_78><Z_54><Z_59><Z_88><Z_63><Z_76><Z_103><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A portion of the graph of $g(x)=px^4+qx^3+rx^2+sx+t$ is shown below. Determine the value of $12p - 6q + 3r - 2s + t$ given that $g(-1) = 4$.

[asy]
import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=4.25,ymin=-5.25,ymax=5.25;

pen cqcqcq=rgb(0.75,0.75,0.75);

/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10);

xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);
real g1(real x){return 0.5*x*(x+1)*(x-1)*(x-2)/8;} draw(graph(g1,-3.25,4.25),linewidth(0.75));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]<|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
A portion of the graph of $g(x)=px^4+qx^3+rx^2+sx+t$ is shown below. Determine the value of $12p - 6q + 3r - 2s + t$ given that $g(-1) = 4$.

[asy]
import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=4.25,ymin=-5.25,ymax=5.25;

pen cqcqcq=rgb(0.75,0.75,0.75);

/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10);

xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);
real g1(real x){return 0.5*x*(x+1)*(x-1)*(x-2)/8;} draw(graph(g1,-3.25,4.25),linewidth(0.75));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]<|im_end|>
<|im_start|>assistant
<Z_76><Z_3><Z_80><Z_29><Z_84><Z_40><Z_80><Z_110><Z_95><Z_26><Z_26><Z_88><Z_35><Z_36><Z_82><Z_56><Z_0><Z_42><Z_55><Z_58><Z_16><Z_19><Z_22><Z_42><Z_33><Z_17><Z_117><Z_37><Z_49><Z_39><Z_54><Z_33><Z_32><ANSWER>

Question:
A portion of the graph of $g(x)=px^4+qx^3+rx^2+sx+t$ is shown below. Determine the value of $12p - 6q + 3r - 2s + t$ given that $g(-1) = 4$.

[asy]
import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=4.25,ymin=-5.25,ymax=5.25;

pen cqcqcq=rgb(0.75,0.75,0.75);

/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10);

xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true);
real g1(real x){return 0.5*x*(x+1)*(x-1)*(x-2)/8;} draw(graph(g1,-3.25,4.25),linewidth(0.75));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Arrange the numbers 1 to 8 in a row, requiring that each pair of adjacent numbers be coprime. There can be $\boxed{1728}$ ways to arrange them.<|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
Arrange the numbers 1 to 8 in a row, requiring that each pair of adjacent numbers be coprime. There can be $\boxed{1728}$ ways to arrange them.<|im_end|>
<|im_start|>assistant
<Z_94><Z_64><Z_77><Z_103><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Arrange the numbers 1 to 8 in a row, requiring that each pair of adjacent numbers be coprime. There can be $\boxed{1728}$ ways to arrange them.<|im_end|>
<|im_start|>assistant
<Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Arrange the numbers 1 to 8 in a row, requiring that each pair of adjacent numbers be coprime. There can be $\boxed{1728}$ ways to arrange them.<|im_end|>
<|im_start|>assistant
<Z_8><Z_42><Z_37><Z_91><Z_69><ANSWER>

Question: Arrange the numbers 1 to 8 in a row, requiring that each pair of adjacent numbers be coprime. There can be $\boxed{1728}$ ways to arrange them.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.<|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 \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.<|im_end|>
<|im_start|>assistant
<Z_94><Z_32><Z_86><Z_124><Z_107><Z_65><Z_62><Z_63><Z_11><Z_123><Z_114><Z_76><Z_73><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.<|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
Let \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.<|im_end|>
<|im_start|>assistant
<Z_74><Z_4><Z_70><Z_6><Z_25><Z_40><Z_99><Z_47><Z_36><Z_50><Z_93><Z_39><Z_10><Z_106><ANSWER>

Question: Let \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?<|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 length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?<|im_end|>
<|im_start|>assistant
<Z_113><Z_78><Z_49><Z_110><Z_86><Z_126><Z_70><Z_107><Z_114><Z_39><Z_72><Z_126><Z_96><Z_117><Z_47><Z_16><Z_76><Z_73><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?<|im_end|>
<|im_start|>assistant
<Z_26><Z_123><Z_79><Z_74><Z_3><Z_97><Z_95><Z_29><Z_99><Z_109><Z_124><Z_87><Z_104><Z_49><Z_116><Z_0><Z_32><Z_111><Z_17><ANSWER>

Question: The length of the bridge, which a train 200 m long and traveling at 32 km/hr can cross in 20 seconds is?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take some bottles of water from Samira's box, and at the end of the game, take one more bottle each. There are 15 bottles of water remaining in Samira's box. How many bottles of water did each player take during the first break?<|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
Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take some bottles of water from Samira's box, and at the end of the game, take one more bottle each. There are 15 bottles of water remaining in Samira's box. How many bottles of water did each player take during the first break?<|im_end|>
<|im_start|>assistant
<Z_94><Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take some bottles of water from Samira's box, and at the end of the game, take one more bottle each. There are 15 bottles of water remaining in Samira's box. How many bottles of water did each player take during the first break?<|im_end|>
<|im_start|>assistant
<Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take some bottles of water from Samira's box, and at the end of the game, take one more bottle each. There are 15 bottles of water remaining in Samira's box. How many bottles of water did each player take during the first break?<|im_end|>
<|im_start|>assistant
<Z_10><Z_13><ANSWER>

Question: Samira is the assistant coach of a soccer team playing against one of the best teams in their league. She has four dozen water bottles filled with water in a box. In the first break of the match, the 11 players on the field each take some bottles of water from Samira's box, and at the end of the game, take one more bottle each. There are 15 bottles of water remaining in Samira's box. How many bottles of water did each player take during the first break?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that 268 x a certain number = 19832, and the value of 2.68 x that number is 1.9832, what is the original number?<|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
Given that 268 x a certain number = 19832, and the value of 2.68 x that number is 1.9832, what is the original number?<|im_end|>
<|im_start|>assistant
<Z_94><Z_73><Z_97><Z_43><Z_41><Z_64><Z_31><Z_98><Z_34><Z_16><Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that 268 x a certain number = 19832, and the value of 2.68 x that number is 1.9832, what is the original number?<|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
Given that 268 x a certain number = 19832, and the value of 2.68 x that number is 1.9832, what is the original number?<|im_end|>
<|im_start|>assistant
<Z_18><Z_115><Z_6><Z_45><Z_8><Z_123><Z_98><Z_119><Z_115><Z_99><Z_18><ANSWER>

Question: Given that 268 x a certain number = 19832, and the value of 2.68 x that number is 1.9832, what is the original number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $3^{2x} = 13$, evaluate $27^{x+1}$.<|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 $3^{2x} = 13$, evaluate $27^{x+1}$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_72><Z_66><Z_12><Z_99><Z_71><Z_114><Z_99><Z_47><Z_54><Z_36><Z_58><Z_114><Z_39><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $3^{2x} = 13$, evaluate $27^{x+1}$.<|im_end|>
<|im_start|>assistant
<Z_6><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $3^{2x} = 13$, evaluate $27^{x+1}$.<|im_end|>
<|im_start|>assistant
<Z_109><Z_28><Z_125><Z_90><Z_45><Z_103><Z_46><Z_9><Z_42><Z_29><Z_116><Z_15><Z_84><Z_51><Z_20><ANSWER>

Question: If $3^{2x} = 13$, evaluate $27^{x+1}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $\textit{composite number}$ is a number that has two or more prime factors. The number 91 can be expressed as the sum of two composite numbers. What is the minimum positive difference between two such numbers?<|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 $\textit{composite number}$ is a number that has two or more prime factors. The number 91 can be expressed as the sum of two composite numbers. What is the minimum positive difference between two such numbers?<|im_end|>
<|im_start|>assistant
<Z_57><Z_125><Z_43><Z_64><Z_120><Z_58><Z_117><Z_11><Z_22><Z_124><Z_118><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $\textit{composite number}$ is a number that has two or more prime factors. The number 91 can be expressed as the sum of two composite numbers. What is the minimum positive difference between two such numbers?<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $\textit{composite number}$ is a number that has two or more prime factors. The number 91 can be expressed as the sum of two composite numbers. What is the minimum positive difference between two such numbers?<|im_end|>
<|im_start|>assistant
<Z_23><Z_110><Z_26><Z_4><Z_92><Z_27><Z_96><Z_2><Z_106><Z_96><Z_16><Z_106><ANSWER>

Question: A $\textit{composite number}$ is a number that has two or more prime factors. The number 91 can be expressed as the sum of two composite numbers. What is the minimum positive difference between two such numbers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $ a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .<|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  $ a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .<|im_end|>
<|im_start|>assistant
<Z_104><Z_29><Z_65><Z_59><Z_11><Z_48><Z_60><Z_118><Z_66><Z_96><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $ a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .<|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
Let  $ a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .<|im_end|>
<|im_start|>assistant
<Z_56><Z_1><Z_44><Z_85><Z_19><Z_50><Z_117><Z_57><Z_107><Z_93><Z_64><ANSWER>

Question: Let  $ a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The greatest common divisor of 8251 and 6105 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
The greatest common divisor of 8251 and 6105 is __________.<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_66><Z_75><Z_126><Z_33><Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The greatest common divisor of 8251 and 6105 is __________.<|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
The greatest common divisor of 8251 and 6105 is __________.<|im_end|>
<|im_start|>assistant
<Z_75><Z_3><Z_116><Z_113><Z_108><Z_114><Z_104><ANSWER>

Question: The greatest common divisor of 8251 and 6105 is __________.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To make sure that the cake is sweet, he needs 450 lbs. of sugar. If he has 287 lbs. of sugar stored in his house, how much additional sugar will he need?<|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
To make sure that the cake is sweet, he needs 450 lbs. of sugar. If he has 287 lbs. of sugar stored in his house, how much additional sugar will he need?<|im_end|>
<|im_start|>assistant
<Z_57><Z_74><Z_86><Z_73><Z_65><Z_99><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To make sure that the cake is sweet, he needs 450 lbs. of sugar. If he has 287 lbs. of sugar stored in his house, how much additional sugar will he need?<|im_end|>
<|im_start|>assistant
<Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To make sure that the cake is sweet, he needs 450 lbs. of sugar. If he has 287 lbs. of sugar stored in his house, how much additional sugar will he need?<|im_end|>
<|im_start|>assistant
<Z_73><Z_58><Z_116><Z_99><Z_87><Z_119><Z_18><ANSWER>

Question: To make sure that the cake is sweet, he needs 450 lbs. of sugar. If he has 287 lbs. of sugar stored in his house, how much additional sugar will he need?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For his long distance phone calls, John pays a 5 dollars monthly fee plus 25 cents per minute. Last month, John's long distance bill was 12.02 dollars. For how many minutes was John billed?<|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
For his long distance phone calls, John pays a 5 dollars monthly fee plus 25 cents per minute. Last month, John's long distance bill was 12.02 dollars. For how many minutes was John billed?<|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
For his long distance phone calls, John pays a 5 dollars monthly fee plus 25 cents per minute. Last month, John's long distance bill was 12.02 dollars. For how many minutes was John billed?<|im_end|>
<|im_start|>assistant
<Z_42><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For his long distance phone calls, John pays a 5 dollars monthly fee plus 25 cents per minute. Last month, John's long distance bill was 12.02 dollars. For how many minutes was John billed?<|im_end|>
<|im_start|>assistant
<Z_84><ANSWER>

Question: For his long distance phone calls, John pays a 5 dollars monthly fee plus 25 cents per minute. Last month, John's long distance bill was 12.02 dollars. For how many minutes was John billed?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark started the day with 14 buttons. His friend Shane gave him 3.5 times that amount of buttons. Then, he lent 7 buttons to his friend Anna who needed them for her project, but she accidentally lost half of them and returned only half of the borrowed amount. Later, his other friend Sam asked if he could have 2/3 of Mark's buttons. After all these exchanges, how many buttons did Mark end up with?<|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
Mark started the day with 14 buttons. His friend Shane gave him 3.5 times that amount of buttons. Then, he lent 7 buttons to his friend Anna who needed them for her project, but she accidentally lost half of them and returned only half of the borrowed amount. Later, his other friend Sam asked if he could have 2/3 of Mark's buttons. After all these exchanges, how many buttons did Mark end up with?<|im_end|>
<|im_start|>assistant
<Z_104><Z_87><Z_115><Z_36><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark started the day with 14 buttons. His friend Shane gave him 3.5 times that amount of buttons. Then, he lent 7 buttons to his friend Anna who needed them for her project, but she accidentally lost half of them and returned only half of the borrowed amount. Later, his other friend Sam asked if he could have 2/3 of Mark's buttons. After all these exchanges, how many buttons did Mark end up with?<|im_end|>
<|im_start|>assistant
<Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark started the day with 14 buttons. His friend Shane gave him 3.5 times that amount of buttons. Then, he lent 7 buttons to his friend Anna who needed them for her project, but she accidentally lost half of them and returned only half of the borrowed amount. Later, his other friend Sam asked if he could have 2/3 of Mark's buttons. After all these exchanges, how many buttons did Mark end up with?<|im_end|>
<|im_start|>assistant
<Z_7><Z_5><Z_16><Z_75><Z_115><ANSWER>

Question: Mark started the day with 14 buttons. His friend Shane gave him 3.5 times that amount of buttons. Then, he lent 7 buttons to his friend Anna who needed them for her project, but she accidentally lost half of them and returned only half of the borrowed amount. Later, his other friend Sam asked if he could have 2/3 of Mark's buttons. After all these exchanges, how many buttons did Mark end up with?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose $p(x), q(x), r(x)$ are linear functions, and $s(x)$ and $t(x)$ are defined by
$$s(x) = \max\{p(x), q(x), r(x)\},$$
$$t(x) = \min\{p(x), q(x), r(x)\}.$$
For each $x$, $s(x)$ is the greatest and $t(x)$ is the least of these three values.

Given the graph of $y=s(x)$ for $-4 \le x \le 4$ as follows, where $p(x), q(x), r(x)$ intersect at different points creating segments with different slopes:

[asy]
size(150);
real ticklen=3;
real tickspace=2;

real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i<xright; i+=xstep) {
if(abs(i) >0.1) {TicksArrx.push(i);}
}
for(i=ybottom+ystep; i<ytop; i+=ystep) {
if(abs(i) >0.1) {TicksArry.push(i);}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,5);
draw((-4,6)--(-2,2)--(2,2)--(4,6),red+1.25);
dot((-2,2),red);
dot((2,2),red);
[/asy]

Determine the length of the graph of $y=t(x)$ for the interval $-4 \le x \le 4$ and find the value of this length squared.<|im_end|>
<|im_start|>assistant
<Z_104><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose $p(x), q(x), r(x)$ are linear functions, and $s(x)$ and $t(x)$ are defined by
$$s(x) = \max\{p(x), q(x), r(x)\},$$
$$t(x) = \min\{p(x), q(x), r(x)\}.$$
For each $x$, $s(x)$ is the greatest and $t(x)$ is the least of these three values.

Given the graph of $y=s(x)$ for $-4 \le x \le 4$ as follows, where $p(x), q(x), r(x)$ intersect at different points creating segments with different slopes:

[asy]
size(150);
real ticklen=3;
real tickspace=2;

real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i<xright; i+=xstep) {
if(abs(i) >0.1) {TicksArrx.push(i);}
}
for(i=ybottom+ystep; i<ytop; i+=ystep) {
if(abs(i) >0.1) {TicksArry.push(i);}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,5);
draw((-4,6)--(-2,2)--(2,2)--(4,6),red+1.25);
dot((-2,2),red);
dot((2,2),red);
[/asy]

Determine the length of the graph of $y=t(x)$ for the interval $-4 \le x \le 4$ and find the value of this length squared.<|im_end|>
<|im_start|>assistant
<Z_94><Z_65><Z_73><Z_28><Z_82><Z_49><Z_47><Z_61><Z_49><Z_32><Z_39><Z_39><Z_60><Z_37><Z_28><Z_56><Z_38><Z_60><Z_75><Z_78><Z_83><Z_60><Z_59><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose $p(x), q(x), r(x)$ are linear functions, and $s(x)$ and $t(x)$ are defined by
$$s(x) = \max\{p(x), q(x), r(x)\},$$
$$t(x) = \min\{p(x), q(x), r(x)\}.$$
For each $x$, $s(x)$ is the greatest and $t(x)$ is the least of these three values.

Given the graph of $y=s(x)$ for $-4 \le x \le 4$ as follows, where $p(x), q(x), r(x)$ intersect at different points creating segments with different slopes:

[asy]
size(150);
real ticklen=3;
real tickspace=2;

real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i<xright; i+=xstep) {
if(abs(i) >0.1) {TicksArrx.push(i);}
}
for(i=ybottom+ystep; i<ytop; i+=ystep) {
if(abs(i) >0.1) {TicksArry.push(i);}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,5);
draw((-4,6)--(-2,2)--(2,2)--(4,6),red+1.25);
dot((-2,2),red);
dot((2,2),red);
[/asy]

Determine the length of the graph of $y=t(x)$ for the interval $-4 \le x \le 4$ and find the value of this length squared.<|im_end|>
<|im_start|>assistant
<Z_15><Z_97><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose $p(x), q(x), r(x)$ are linear functions, and $s(x)$ and $t(x)$ are defined by
$$s(x) = \max\{p(x), q(x), r(x)\},$$
$$t(x) = \min\{p(x), q(x), r(x)\}.$$
For each $x$, $s(x)$ is the greatest and $t(x)$ is the least of these three values.

Given the graph of $y=s(x)$ for $-4 \le x \le 4$ as follows, where $p(x), q(x), r(x)$ intersect at different points creating segments with different slopes:

[asy]
size(150);
real ticklen=3;
real tickspace=2;

real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i<xright; i+=xstep) {
if(abs(i) >0.1) {TicksArrx.push(i);}
}
for(i=ybottom+ystep; i<ytop; i+=ystep) {
if(abs(i) >0.1) {TicksArry.push(i);}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,5);
draw((-4,6)--(-2,2)--(2,2)--(4,6),red+1.25);
dot((-2,2),red);
dot((2,2),red);
[/asy]

Determine the length of the graph of $y=t(x)$ for the interval $-4 \le x \le 4$ and find the value of this length squared.<|im_end|>
<|im_start|>assistant
<Z_60><Z_34><Z_84><Z_50><Z_14><Z_51><Z_70><Z_108><Z_4><Z_20><Z_25><Z_85><Z_106><Z_41><Z_87><Z_101><Z_0><Z_50><Z_58><Z_20><Z_34><Z_103><Z_26><Z_96><ANSWER>

Question:
Suppose $p(x), q(x), r(x)$ are linear functions, and $s(x)$ and $t(x)$ are defined by
$$s(x) = \max\{p(x), q(x), r(x)\},$$
$$t(x) = \min\{p(x), q(x), r(x)\}.$$
For each $x$, $s(x)$ is the greatest and $t(x)$ is the least of these three values.

Given the graph of $y=s(x)$ for $-4 \le x \le 4$ as follows, where $p(x), q(x), r(x)$ intersect at different points creating segments with different slopes:

[asy]
size(150);
real ticklen=3;
real tickspace=2;

real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i<xright; i+=xstep) {
if(abs(i) >0.1) {TicksArrx.push(i);}
}
for(i=ybottom+ystep; i<ytop; i+=ystep) {
if(abs(i) >0.1) {TicksArry.push(i);}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,5);
draw((-4,6)--(-2,2)--(2,2)--(4,6),red+1.25);
dot((-2,2),red);
dot((2,2),red);
[/asy]

Determine the length of the graph of $y=t(x)$ for the interval $-4 \le x \le 4$ and find the value of this length squared.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jackson wants to improve his endurance running. He starts by running some miles a day the first week, then spends the next four weeks running one additional mile/day each week. At the end of this exercise program, Jackson is running 7 miles each day. How many miles did he start running each day in the first week?<|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
Jackson wants to improve his endurance running. He starts by running some miles a day the first week, then spends the next four weeks running one additional mile/day each week. At the end of this exercise program, Jackson is running 7 miles each day. How many miles did he start running each day in the first week?<|im_end|>
<|im_start|>assistant
<Z_113><Z_38><Z_77><Z_59><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jackson wants to improve his endurance running. He starts by running some miles a day the first week, then spends the next four weeks running one additional mile/day each week. At the end of this exercise program, Jackson is running 7 miles each day. How many miles did he start running each day in the first week?<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jackson wants to improve his endurance running. He starts by running some miles a day the first week, then spends the next four weeks running one additional mile/day each week. At the end of this exercise program, Jackson is running 7 miles each day. How many miles did he start running each day in the first week?<|im_end|>
<|im_start|>assistant
<Z_83><Z_115><Z_56><Z_65><Z_125><ANSWER>

Question: Jackson wants to improve his endurance running. He starts by running some miles a day the first week, then spends the next four weeks running one additional mile/day each week. At the end of this exercise program, Jackson is running 7 miles each day. How many miles did he start running each day in the first week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?<|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
how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_113><Z_13><Z_47><Z_49><Z_65><Z_114><Z_80><Z_22><Z_11><Z_58><Z_125><Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?<|im_end|>
<|im_start|>assistant
<Z_15><Z_6><Z_111><Z_84><Z_89><Z_76><Z_48><Z_41><Z_123><Z_93><Z_29><Z_93><ANSWER>

Question: how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On her 10th birthday in 2006, Lucy's mother said, "My age is now five times your age." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?<|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
On her 10th birthday in 2006, Lucy's mother said, "My age is now five times your age." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><Z_59><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On her 10th birthday in 2006, Lucy's mother said, "My age is now five times your age." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?<|im_end|>
<|im_start|>assistant
<Z_30><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On her 10th birthday in 2006, Lucy's mother said, "My age is now five times your age." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?<|im_end|>
<|im_start|>assistant
<Z_5><Z_101><Z_77><Z_21><ANSWER>

Question: On her 10th birthday in 2006, Lucy's mother said, "My age is now five times your age." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the even numbers between 1 and n is 85 * 86, where n is an odd number. What is the value of n?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the even numbers between 1 and n is 85 * 86, where n is an odd number. What is the value of n?<|im_end|>
<|im_start|>assistant
<Z_104><Z_72><Z_82><Z_32><Z_49><Z_39><Z_117><Z_88><Z_8><Z_41><Z_60><Z_55><Z_125><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the even numbers between 1 and n is 85 * 86, where n is an odd number. What is the value of n?<|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
The sum of the even numbers between 1 and n is 85 * 86, where n is an odd number. What is the value of n?<|im_end|>
<|im_start|>assistant
<Z_103><Z_82><Z_61><Z_84><Z_20><Z_51><Z_35><Z_32><Z_37><Z_106><Z_115><Z_75><Z_112><Z_2><ANSWER>

Question: The sum of the even numbers between 1 and n is 85 * 86, where n is an odd number. What is the value of n?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest prime divisor of $3^{15} + 11^9$?<|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 smallest prime divisor of $3^{15} + 11^9$?<|im_end|>
<|im_start|>assistant
<Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest prime divisor of $3^{15} + 11^9$?<|im_end|>
<|im_start|>assistant
<Z_31><Z_18><Z_13><Z_49><Z_120><Z_79><Z_19><Z_37><Z_14><Z_7><Z_94><Z_106><Z_11><Z_109><Z_8><Z_32><Z_13><Z_49><Z_46><Z_35><Z_1><Z_33><Z_26><ANSWER>

Question: What is the smallest prime divisor of $3^{15} + 11^9$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many years was the money lent if the simple interest on rs. 4000 amounts to rs. 640 at an interest rate of 8%?<|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
For how many years was the money lent if the simple interest on rs. 4000 amounts to rs. 640 at an interest rate of 8%?<|im_end|>
<|im_start|>assistant
<Z_104><Z_78><Z_62><Z_66><Z_16><Z_73><Z_73><Z_70><Z_118><Z_96><Z_101><Z_61><Z_55><Z_76><Z_60><Z_82><Z_63><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many years was the money lent if the simple interest on rs. 4000 amounts to rs. 640 at an interest rate of 8%?<|im_end|>
<|im_start|>assistant
<Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many years was the money lent if the simple interest on rs. 4000 amounts to rs. 640 at an interest rate of 8%?<|im_end|>
<|im_start|>assistant
<Z_49><Z_51><Z_13><Z_114><Z_26><Z_125><Z_109><Z_74><Z_101><Z_28><Z_77><Z_14><Z_53><Z_6><Z_61><Z_96><Z_96><Z_10><ANSWER>

Question: For how many years was the money lent if the simple interest on rs. 4000 amounts to rs. 640 at an interest rate of 8%?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( some number ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2. The total number of prime factors is 27. What is the number?<|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
Find the total number of prime factors in the expression ( some number ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2. The total number of prime factors is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_104><Z_77><Z_100><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( some number ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2. The total number of prime factors is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the total number of prime factors in the expression ( some number ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2. The total number of prime factors is 27. What is the number?<|im_end|>
<|im_start|>assistant
<Z_41><Z_24><Z_40><Z_127><ANSWER>

Question: Find the total number of prime factors in the expression ( some number ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2. The total number of prime factors is 27. What is the number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In $\triangle ABC$, $AC=5 \sqrt {2}$, $\cos C= \frac {3}{5}$, $B= \frac {\pi}{4}$.
(1) Find the length of $AB$;
(2) Find the area of $\triangle ABC$, denoted as $S_{\triangle ABC}$.<|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
In $\triangle ABC$, $AC=5 \sqrt {2}$, $\cos C= \frac {3}{5}$, $B= \frac {\pi}{4}$.
(1) Find the length of $AB$;
(2) Find the area of $\triangle ABC$, denoted as $S_{\triangle ABC}$.<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In $\triangle ABC$, $AC=5 \sqrt {2}$, $\cos C= \frac {3}{5}$, $B= \frac {\pi}{4}$.
(1) Find the length of $AB$;
(2) Find the area of $\triangle ABC$, denoted as $S_{\triangle ABC}$.<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

Question:
In $\triangle ABC$, $AC=5 \sqrt {2}$, $\cos C= \frac {3}{5}$, $B= \frac {\pi}{4}$.
(1) Find the length of $AB$;
(2) Find the area of $\triangle ABC$, denoted as $S_{\triangle ABC}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all of the solutions of the equation $\frac{6x}{30}=\frac{8}{x}$?<|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
What is the sum of all of the solutions of the equation $\frac{6x}{30}=\frac{8}{x}$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_43><Z_50><Z_39><Z_71><Z_33><Z_70><Z_59><Z_75><Z_45><Z_26><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all of the solutions of the equation $\frac{6x}{30}=\frac{8}{x}$?<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all of the solutions of the equation $\frac{6x}{30}=\frac{8}{x}$?<|im_end|>
<|im_start|>assistant
<Z_92><Z_67><Z_45><Z_85><Z_22><Z_31><Z_21><Z_7><Z_46><Z_62><Z_65><ANSWER>

Question: What is the sum of all of the solutions of the equation $\frac{6x}{30}=\frac{8}{x}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train which is 300 m long is running at 80 kmph. It crosses a person moving at a certain speed in the same direction in 15 seconds. What is the speed of the person?<|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 train which is 300 m long is running at 80 kmph. It crosses a person moving at a certain speed in the same direction in 15 seconds. What is the speed of the person?<|im_end|>
<|im_start|>assistant
<Z_94><Z_13><Z_32><Z_105><Z_50><Z_72><Z_63><Z_124><Z_76><Z_119><Z_125><Z_54><Z_81><Z_41><Z_80><Z_48><Z_90><Z_6><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train which is 300 m long is running at 80 kmph. It crosses a person moving at a certain speed in the same direction in 15 seconds. What is the speed of the person?<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train which is 300 m long is running at 80 kmph. It crosses a person moving at a certain speed in the same direction in 15 seconds. What is the speed of the person?<|im_end|>
<|im_start|>assistant
<Z_91><Z_104><Z_104><Z_68><Z_63><Z_39><Z_107><Z_66><Z_69><Z_49><Z_44><Z_76><Z_38><Z_47><Z_38><Z_74><Z_45><Z_33><ANSWER>

Question: A train which is 300 m long is running at 80 kmph. It crosses a person moving at a certain speed in the same direction in 15 seconds. What is the speed of the person?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can five people line up in a straight line if the youngest person cannot be first or last in line?<|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
In how many ways can five people line up in a straight line if the youngest person cannot be first or last in line?<|im_end|>
<|im_start|>assistant
<Z_104><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can five people line up in a straight line if the youngest person cannot be first or last in line?<|im_end|>
<|im_start|>assistant
<Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can five people line up in a straight line if the youngest person cannot be first or last in line?<|im_end|>
<|im_start|>assistant
<Z_43><Z_69><ANSWER>

Question: In how many ways can five people line up in a straight line if the youngest person cannot be first or last in line?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cubical block of metal weighs 3 pounds and has a density of 'D' and is subject to an external force 'F'. How much will another cube of the same metal weigh if its sides are twice as long, the density of the metal is increased by 25%, and the external force applied on it is doubled?<|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 cubical block of metal weighs 3 pounds and has a density of 'D' and is subject to an external force 'F'. How much will another cube of the same metal weigh if its sides are twice as long, the density of the metal is increased by 25%, and the external force applied on it is doubled?<|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 cubical block of metal weighs 3 pounds and has a density of 'D' and is subject to an external force 'F'. How much will another cube of the same metal weigh if its sides are twice as long, the density of the metal is increased by 25%, and the external force applied on it is doubled?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

Question: A cubical block of metal weighs 3 pounds and has a density of 'D' and is subject to an external force 'F'. How much will another cube of the same metal weigh if its sides are twice as long, the density of the metal is increased by 25%, and the external force applied on it is doubled?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the first 1500 terms of a geometric sequence is 300. The sum of the first 3000 terms is 570. Find the sum of the first 4500 terms.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the first 1500 terms of a geometric sequence is 300. The sum of the first 3000 terms is 570. Find the sum of the first 4500 terms.<|im_end|>
<|im_start|>assistant
<Z_106><Z_36><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the first 1500 terms of a geometric sequence is 300. The sum of the first 3000 terms is 570. Find the sum of the first 4500 terms.<|im_end|>
<|im_start|>assistant
<Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the first 1500 terms of a geometric sequence is 300. The sum of the first 3000 terms is 570. Find the sum of the first 4500 terms.<|im_end|>
<|im_start|>assistant
<Z_22><Z_113><Z_97><ANSWER>

Question: The sum of the first 1500 terms of a geometric sequence is 300. The sum of the first 3000 terms is 570. Find the sum of the first 4500 terms.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom bought 14 boxes of chocolate candy, 10 boxes of fruit candy, and 8 boxes of caramel candy. He gave 8 chocolate boxes and 5 fruit boxes to his little brother. If each chocolate box has 3 pieces inside, each fruit box has 4 pieces, and each caramel box has 5 pieces, how many pieces of candy does Tom still 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
Tom bought 14 boxes of chocolate candy, 10 boxes of fruit candy, and 8 boxes of caramel candy. He gave 8 chocolate boxes and 5 fruit boxes to his little brother. If each chocolate box has 3 pieces inside, each fruit box has 4 pieces, and each caramel box has 5 pieces, how many pieces of candy does Tom still have?<|im_end|>
<|im_start|>assistant
<Z_104><Z_33><Z_36><Z_66><Z_56><Z_65><Z_118><Z_60><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom bought 14 boxes of chocolate candy, 10 boxes of fruit candy, and 8 boxes of caramel candy. He gave 8 chocolate boxes and 5 fruit boxes to his little brother. If each chocolate box has 3 pieces inside, each fruit box has 4 pieces, and each caramel box has 5 pieces, how many pieces of candy does Tom still have?<|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
Tom bought 14 boxes of chocolate candy, 10 boxes of fruit candy, and 8 boxes of caramel candy. He gave 8 chocolate boxes and 5 fruit boxes to his little brother. If each chocolate box has 3 pieces inside, each fruit box has 4 pieces, and each caramel box has 5 pieces, how many pieces of candy does Tom still have?<|im_end|>
<|im_start|>assistant
<Z_55><Z_74><Z_105><Z_85><Z_122><Z_7><Z_84><Z_90><Z_23><ANSWER>

Question: Tom bought 14 boxes of chocolate candy, 10 boxes of fruit candy, and 8 boxes of caramel candy. He gave 8 chocolate boxes and 5 fruit boxes to his little brother. If each chocolate box has 3 pieces inside, each fruit box has 4 pieces, and each caramel box has 5 pieces, how many pieces of candy does Tom still have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.<|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 $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.<|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
Given that $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.<|im_end|>
<|im_start|>assistant
<Z_108><ANSWER>

Question: Given that $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.