<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_104><Z_82><Z_50><Z_100><Z_59><Z_126><Z_38><Z_59><Z_87><Z_70><Z_38><Z_121><Z_37><Z_12><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_125><Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_3><Z_97><Z_125><Z_118><Z_93><Z_17><Z_104><Z_69><Z_45><Z_112><Z_54><Z_43><Z_96><Z_124><Z_122><ANSWER>

Question: The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_104><Z_79><Z_62><Z_93><Z_83><Z_95><Z_65><Z_34><Z_81><Z_22><Z_66><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|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
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_26><Z_117><Z_78><Z_105><Z_74><Z_53><Z_87><Z_66><Z_108><Z_81><Z_89><Z_126><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|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
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_113><Z_105><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|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
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_78><Z_107><Z_5><ANSWER>

Question: Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|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 average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_29><Z_78><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|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
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_108><Z_73><Z_76><ANSWER>

Question: The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_94><Z_52><Z_108><Z_37><Z_66><Z_119><Z_99><Z_33><Z_22><Z_118><Z_96><Z_93><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_44><Z_83><Z_124><Z_126><Z_35><Z_5><Z_28><Z_34><Z_106><Z_117><Z_108><Z_5><Z_114><ANSWER>

Question:
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|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 $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_94><Z_50><Z_62><Z_43><Z_96><Z_71><Z_72><Z_91><Z_54><Z_87><Z_39><Z_34><Z_101><Z_88><Z_87><Z_63><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|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
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_102><Z_33><Z_93><Z_15><Z_84><Z_105><Z_19><Z_92><Z_25><Z_123><Z_25><Z_24><Z_47><Z_46><Z_27><Z_125><Z_101><ANSWER>

Question:
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara 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
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_94><Z_36><Z_80><Z_87><Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_125><Z_81><Z_95><Z_8><Z_105><ANSWER>

Question: Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|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 Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_57><Z_51><Z_73><Z_82><Z_34><Z_95><Z_28><Z_115><Z_92><Z_70><Z_83><Z_119><Z_115><Z_98><Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_9><Z_93><Z_99><Z_112><Z_75><Z_108><Z_27><Z_26><Z_3><Z_78><Z_85><Z_102><Z_20><Z_30><Z_39><ANSWER>

Question: On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|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 rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_113><Z_120><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|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
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_24><Z_54><Z_94><ANSWER>

Question: Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_104><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_26><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_37><Z_100><ANSWER>

Question: In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|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 average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_104><Z_33><Z_114><Z_114><Z_119><Z_32><Z_126><Z_59><Z_38><Z_9><Z_22><Z_118><Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_10><Z_87><Z_96><Z_1><Z_93><Z_99><Z_105><Z_119><Z_80><Z_87><Z_74><Z_45><Z_50><ANSWER>

Question: The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_86><Z_70><Z_49><Z_28><Z_28><Z_114><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|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
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_114><Z_8><Z_83><Z_72><Z_57><Z_4><Z_15><Z_16><ANSWER>

Question: Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|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 $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|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
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_45><Z_34><ANSWER>

Question: If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_106><Z_40><Z_66><Z_92><Z_73><Z_120><Z_66><Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_111><Z_16><Z_127><Z_67><Z_38><Z_27><Z_47><Z_3><Z_108><ANSWER>

Question: Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|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
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_113><Z_4><Z_36><Z_81><Z_119><Z_126><Z_124><Z_103><Z_123><Z_92><Z_16><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|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
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_117><Z_42><Z_64><Z_91><Z_14><Z_36><Z_18><Z_103><Z_109><Z_86><Z_38><Z_110><ANSWER>

Question: Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of a triangle whose vertices are at $(3, 2)$, $(3, -4)$, and $(12, 2)$?<|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
What is the area, in square units, of a triangle whose vertices are at $(3, 2)$, $(3, -4)$, and $(12, 2)$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_70><Z_91><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of a triangle whose vertices are at $(3, 2)$, $(3, -4)$, and $(12, 2)$?<|im_end|>
<|im_start|>assistant
<Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of a triangle whose vertices are at $(3, 2)$, $(3, -4)$, and $(12, 2)$?<|im_end|>
<|im_start|>assistant
<Z_53><Z_73><Z_77><Z_44><ANSWER>

Question: What is the area, in square units, of a triangle whose vertices are at $(3, 2)$, $(3, -4)$, and $(12, 2)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The first term of a geometric sequence is 512, and the 6th term is 125. What is the positive, real value for the 4th term?<|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 first term of a geometric sequence is 512, and the 6th term is 125. What is the positive, real value for the 4th term?<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_73><Z_34><Z_73><Z_10><Z_98><Z_91><Z_39><Z_59><Z_96><Z_45><Z_53><Z_16><Z_37><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The first term of a geometric sequence is 512, and the 6th term is 125. What is the positive, real value for the 4th term?<|im_end|>
<|im_start|>assistant
<Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The first term of a geometric sequence is 512, and the 6th term is 125. What is the positive, real value for the 4th term?<|im_end|>
<|im_start|>assistant
<Z_29><Z_21><Z_10><Z_45><Z_53><Z_91><Z_58><Z_12><Z_49><Z_23><Z_16><Z_25><Z_72><Z_50><Z_92><Z_24><ANSWER>

Question: The first term of a geometric sequence is 512, and the 6th term is 125. What is the positive, real value for the 4th term?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man is 20 years older than his son, and he is also 15 years older than his daughter. In two years, his age will be twice the age of his son and three times the age of his daughter. What are the present ages of the son, daughter, and the man?<|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 man is 20 years older than his son, and he is also 15 years older than his daughter. In two years, his age will be twice the age of his son and three times the age of his daughter. What are the present ages of the son, daughter, and the man?<|im_end|>
<|im_start|>assistant
<Z_57><Z_29><Z_106><Z_107><Z_81><Z_50><Z_100><Z_98><Z_98><Z_82><Z_98><Z_118><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man is 20 years older than his son, and he is also 15 years older than his daughter. In two years, his age will be twice the age of his son and three times the age of his daughter. What are the present ages of the son, daughter, and the man?<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man is 20 years older than his son, and he is also 15 years older than his daughter. In two years, his age will be twice the age of his son and three times the age of his daughter. What are the present ages of the son, daughter, and the man?<|im_end|>
<|im_start|>assistant
<Z_76><Z_119><Z_87><Z_99><Z_26><Z_36><Z_63><Z_69><Z_51><Z_126><Z_26><Z_102><Z_51><ANSWER>

Question: A man is 20 years older than his son, and he is also 15 years older than his daughter. In two years, his age will be twice the age of his son and three times the age of his daughter. What are the present ages of the son, daughter, and the man?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A petri dish originally contained 600 bacteria . A scientist let the bacteria grow and now there are 8917 of them . How many more bacteria are there now ? <|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 petri dish originally contained 600 bacteria . A scientist let the bacteria grow and now there are 8917 of them . How many more bacteria are there now ? <|im_end|>
<|im_start|>assistant
<Z_29><Z_34><Z_99><Z_37><Z_53><Z_88><Z_28><Z_49><Z_125><Z_78><Z_58><Z_87><Z_71><Z_120><Z_61><Z_63><Z_117><Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A petri dish originally contained 600 bacteria . A scientist let the bacteria grow and now there are 8917 of them . How many more bacteria are there now ? <|im_end|>
<|im_start|>assistant
<Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A petri dish originally contained 600 bacteria . A scientist let the bacteria grow and now there are 8917 of them . How many more bacteria are there now ? <|im_end|>
<|im_start|>assistant
<Z_120><Z_119><Z_97><Z_79><Z_21><Z_87><Z_115><Z_0><Z_43><Z_53><Z_101><Z_43><Z_52><Z_48><Z_62><Z_82><Z_18><Z_80><ANSWER>

Question: A petri dish originally contained 600 bacteria . A scientist let the bacteria grow and now there are 8917 of them . How many more bacteria are there now ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three different numbers are chosen at random from the list \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\). The probability that one of them is the mean of the other two is \(p\). What is the value of \(\frac{120}{p}\) ?<|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
Three different numbers are chosen at random from the list \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\). The probability that one of them is the mean of the other two is \(p\). What is the value of \(\frac{120}{p}\) ?<|im_end|>
<|im_start|>assistant
<Z_104><Z_62><Z_50><Z_99><Z_87><Z_20><Z_61><Z_96><Z_47><Z_61><Z_41><Z_10><Z_48><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three different numbers are chosen at random from the list \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\). The probability that one of them is the mean of the other two is \(p\). What is the value of \(\frac{120}{p}\) ?<|im_end|>
<|im_start|>assistant
<Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three different numbers are chosen at random from the list \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\). The probability that one of them is the mean of the other two is \(p\). What is the value of \(\frac{120}{p}\) ?<|im_end|>
<|im_start|>assistant
<Z_5><Z_68><Z_114><Z_97><Z_86><Z_80><Z_52><Z_47><Z_23><Z_81><Z_31><Z_96><Z_69><Z_6><ANSWER>

Question: Three different numbers are chosen at random from the list \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\). The probability that one of them is the mean of the other two is \(p\). What is the value of \(\frac{120}{p}\) ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A checker can move in one direction along a strip divided into cells, shifting either to an adjacent cell or jumping over one cell in a single move. In how many ways can it move 10 cells?<|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 checker can move in one direction along a strip divided into cells, shifting either to an adjacent cell or jumping over one cell in a single move. In how many ways can it move 10 cells?<|im_end|>
<|im_start|>assistant
<Z_113><Z_91><Z_125><Z_43><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A checker can move in one direction along a strip divided into cells, shifting either to an adjacent cell or jumping over one cell in a single move. In how many ways can it move 10 cells?<|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
A checker can move in one direction along a strip divided into cells, shifting either to an adjacent cell or jumping over one cell in a single move. In how many ways can it move 10 cells?<|im_end|>
<|im_start|>assistant
<Z_46><Z_64><Z_3><Z_20><Z_96><ANSWER>

Question: A checker can move in one direction along a strip divided into cells, shifting either to an adjacent cell or jumping over one cell in a single move. In how many ways can it move 10 cells?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For what value of \( c \) will the circle with equation \( x^2 + 8x + y^2 - 6y + c = 0 \) have a radius of length 5?<|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 what value of \( c \) will the circle with equation \( x^2 + 8x + y^2 - 6y + c = 0 \) have a radius of length 5?<|im_end|>
<|im_start|>assistant
<Z_57><Z_119><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For what value of \( c \) will the circle with equation \( x^2 + 8x + y^2 - 6y + c = 0 \) have a radius of length 5?<|im_end|>
<|im_start|>assistant
<Z_8><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For what value of \( c \) will the circle with equation \( x^2 + 8x + y^2 - 6y + c = 0 \) have a radius of length 5?<|im_end|>
<|im_start|>assistant
<Z_49><Z_102><Z_54><ANSWER>

Question: For what value of \( c \) will the circle with equation \( x^2 + 8x + y^2 - 6y + c = 0 \) have a radius of length 5?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a square playground and a rectangular basketball court. The perimeter of the playground is 36 meters (m), and the perimeter of the basketball court is 38 meters (m). If the width of the basketball court is 15 meters (m), find the difference between the area of the playground and that of the basketball court.<|im_end|>
<|im_start|>assistant
<Z_95><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_106><Z_119><Z_51><Z_96><Z_98><Z_98><Z_126><Z_48><Z_38><Z_96><Z_56><Z_80><Z_53><Z_90><Z_83><Z_5><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_15><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many distinct right triangles exist with one leg equal to \( \sqrt{2016} \), and the other leg and hypotenuse expressed as natural numbers?<|im_end|>
<|im_start|>assistant
<Z_96><Z_95><Z_7><Z_101><Z_26><Z_11><Z_21><Z_56><Z_84><Z_65><Z_49><Z_17><Z_3><Z_42><Z_103><Z_52><Z_52><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_104><Z_86><Z_65><Z_65><Z_79><Z_80><Z_45><Z_47><Z_39><Z_91><Z_63><Z_52><Z_76><Z_20><Z_28><Z_32><Z_123><Z_125><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When a piece of paper with digits is turned upside down, the digits $0, 1, 8$ remain unchanged, the digits $6$ and $9$ become each other, and the other digits have no meaning when viewed upside down. Find the number of nine-digit numbers that remain unchanged when the paper is turned upside down.<|im_end|>
<|im_start|>assistant
<Z_35><Z_123><Z_60><Z_82><Z_87><Z_59><Z_41><Z_19><Z_23><Z_78><Z_92><Z_12><Z_109><Z_32><Z_99><Z_82><Z_68><Z_71><Z_94><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_94><Z_108><Z_73><Z_93><Z_125><Z_126><Z_76><Z_63><Z_37><Z_65><Z_72><Z_88><Z_96><Z_9><Z_55><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jiawei is drawing triangles using three of the points in the given grid as vertices. If the first two examples provided are considered to be different, how many triangles of positive area can Jiawei draw in this way?<|im_end|>
<|im_start|>assistant
<Z_118><Z_35><Z_114><Z_54><Z_39><Z_16><Z_33><Z_51><Z_101><Z_2><Z_67><Z_51><Z_99><Z_108><Z_72><Z_46><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_27><Z_27><Z_43><Z_99><Z_62><Z_91><Z_98><Z_39><Z_70><Z_61><Z_91><Z_80><Z_121><Z_119><Z_34><Z_3><Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
sides of a rectangular park are in the ratio 3 : 2 and its area is 4704 sq m , the cost of fencing it at 50 ps per meter is ?<|im_end|>
<|im_start|>assistant
<Z_80><Z_39><Z_54><Z_79><Z_48><Z_30><Z_11><Z_40><Z_3><Z_44><Z_103><Z_126><Z_104><Z_125><Z_113><Z_59><Z_6><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_113><Z_1><Z_13><Z_93><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has some stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. Hilary has to shuck 237,600 kernels of corn. How many stalks does she have growing?<|im_end|>
<|im_start|>assistant
<Z_63><Z_57><Z_105><Z_113><Z_75><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_37><Z_73><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_86><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $3x^{y+1} + 4y^{x+1}$ when $x=3$ and $y=2$.<|im_end|>
<|im_start|>assistant
<Z_127><Z_49><Z_94><Z_1><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_57><Z_64><Z_87><Z_107><Z_92><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_19><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stack of logs has 15 logs on the bottom row, and one less in each successive row, ending with five logs at the top. How many logs are in the stack?<|im_end|>
<|im_start|>assistant
<Z_47><Z_40><Z_125><Z_95><Z_66><Z_45><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_94><Z_74><Z_65><Z_103><Z_89><Z_115><Z_32><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )<|im_end|>
<|im_start|>assistant
<Z_104><Z_52><Z_30><Z_48><Z_14><Z_73><Z_43><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_104><Z_50><Z_4><Z_99><Z_4><Z_62><Z_66><Z_72><Z_52><Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24 / 96 = 1 / 4. The positive integer y is less than some number and the connection between y and 6 is equal to 1 / 1. There are 7 possible values of y. What is that number?<|im_end|>
<|im_start|>assistant
<Z_91><Z_112><Z_44><Z_76><Z_110><Z_96><Z_29><Z_124><Z_13><Z_52><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_104><Z_58><Z_83><Z_65><Z_55><Z_117><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Each circle in an arrangement of four circles, which perfectly fit into a square, has a radius of 8 inches. Calculate the area, in square inches, of the square.<|im_end|>
<|im_start|>assistant
<Z_40><Z_84><Z_112><Z_105><Z_121><Z_64><Z_17><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_104><Z_72><Z_49><Z_34><Z_93><Z_99><Z_56><Z_114><Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie has 8 pairs of shoes. Riley has 3 fewer pairs of shoes than Ellie, and Jordan has 1.5 times the combined total of Ellie and Riley's pairs. How many pairs of shoes do they have in total?<|im_end|>
<|im_start|>assistant
<Z_52><Z_14><Z_83><Z_52><Z_120><Z_108><Z_80><Z_103><Z_1><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?<|im_end|>
<|im_start|>assistant
<Z_63><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of $x^2$ when $3(x - 2x^3) - 5(2x^2 - x^3 + 3x^4) + 4(3x^2 - 2x^8)$ is simplified.<|im_end|>
<|im_start|>assistant
<Z_16><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_113><Z_89><Z_50><Z_52><Z_41><Z_107><Z_33><Z_38><Z_72><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $PQR$ has a perimeter of 2023 units. The sides have lengths that are all integer values with $PQ \leq QR < PR$. What is the smallest possible value of $PR - QR$?<|im_end|>
<|im_start|>assistant
<Z_102><Z_24><Z_105><Z_56><Z_116><Z_61><Z_55><Z_0><Z_108><Z_86><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_37><Z_36><Z_124><Z_115><Z_34><Z_115><Z_120><Z_93><Z_12><Z_103><Z_123><Z_58><Z_126><Z_125><Z_52><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_21><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $B$ lies on line segment $\overline{AC}$ with $AB=16$ and $BC=4$. Points $D$ and $E$ lie on the same side of line $AC$ forming equilateral triangles $\triangle ABD$ and $\triangle BCE$. Let $M$ be the midpoint of $\overline{AE}$, and $N$ be the midpoint of $\overline{CD}$. The area of $\triangle BMN$ is $x$. Find $x^2$.<|im_end|>
<|im_start|>assistant
<Z_17><Z_120><Z_21><Z_41><Z_102><Z_101><Z_83><Z_122><Z_25><Z_86><Z_122><Z_49><Z_98><Z_121><Z_55><Z_70><Z_72><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_113><Z_103><Z_31><Z_78><Z_72><Z_78><Z_28><Z_90><Z_41><Z_95><Z_124><Z_41><Z_80><Z_95><Z_31><Z_83><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an extended hexagonal lattice, each point is still one unit from its nearest neighbor. The lattice is now composed of two concentric hexagons where the outer hexagon has sides twice the length of the inner hexagon. All vertices are connected to their nearest neighbors. How many equilateral triangles have all three vertices in this extended lattice?<|im_end|>
<|im_start|>assistant
<Z_3><Z_65><Z_98><Z_56><Z_74><Z_109><Z_77><Z_35><Z_98><Z_107><Z_24><Z_5><Z_113><Z_43><Z_80><Z_40><Z_5><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many zeros are in the expansion of $999,\!999,\!999,\!999,\!995^2$?<|im_end|>
<|im_start|>assistant
<Z_47><Z_17><Z_13><Z_59><Z_123><Z_110><Z_60><Z_101><Z_99><Z_79><Z_61><Z_87><Z_65><Z_9><Z_52><Z_121><Z_63><Z_80><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_113><Z_125><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A compound has some Aluminium and 3 Sulphur atoms. The molecular weight of the compound is 150. How many Aluminium atoms are in the compound?<|im_end|>
<|im_start|>assistant
<Z_45><Z_41><Z_118><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_113><Z_52><Z_1><Z_120><Z_115><Z_52><Z_90><Z_99><Z_61><Z_80><Z_61><Z_75><Z_121><Z_126><Z_10><Z_60><Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker made 19 cakes and 131 pastries. He sold 70 cakes and a certain number of pastries. Baker made 112 more pastries than cakes. How many pastries did he sell?<|im_end|>
<|im_start|>assistant
<Z_71><Z_0><Z_103><Z_9><Z_55><Z_122><Z_22><Z_118><Z_81><Z_90><Z_118><Z_92><Z_44><Z_42><Z_19><Z_27><Z_20><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_113><Z_87><Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_109><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P M O \) be a triangle with \( P M = 2 \) and \( \angle P M O = 120^\circ \). Let \( B \) be a point on \( P O \) such that \( P M \) is perpendicular to \( M B \), and suppose that \( P M = B O \). The product of the lengths of the sides of the triangle can be expressed in the form \( a + b \sqrt[3]{c} \), where \( a, b, c \) are positive integers, and \( c \) is minimized. Find \( a + b + c \).<|im_end|>
<|im_start|>assistant
<Z_82><Z_101><Z_35><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_104><Z_36><Z_41><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_21><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The variables $x$ and $y$ are inversely proportional. When the sum of $x$ and $y$ is 36 and their difference is 12, find the value of $y$ when $x$ is 8.<|im_end|>
<|im_start|>assistant
<Z_99><Z_83><Z_0><Z_75><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_13><Z_13><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_87><Z_106><Z_52><Z_125><Z_31><Z_98><Z_52><Z_126><Z_98><Z_61><Z_120><Z_37><Z_59><Z_53><Z_101><Z_66><Z_33><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_69><Z_86><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of the areas of two squares is $\frac{27}{50}$. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?<|im_end|>
<|im_start|>assistant
<Z_54><Z_109><Z_84><Z_46><Z_112><Z_51><Z_40><Z_24><Z_117><Z_91><Z_109><Z_38><Z_111><Z_72><Z_83><Z_97><Z_75><Z_89><Z_48><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_57><Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_19><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rachel bought seven new chairs and three new tables for her house. If she spent four minutes on each piece furniture putting it together, how many minutes did it take her to finish?<|im_end|>
<|im_start|>assistant
<Z_93><Z_80><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_40><Z_120><Z_4><Z_52><Z_82><Z_99><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. When they came on Sunday, they were able to complete 15 rounds. Calculate the total time, in minutes, the Polar Bears spent circling the island over that weekend.<|im_end|>
<|im_start|>assistant
<Z_28><Z_91><Z_38><Z_84><Z_97><Z_27><Z_45><Z_126><Z_87><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_93><Z_98><Z_70><Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The volume of a rectangular prism is 360 cubic units where $a, b,$ and $c$ are integers with $1 < c < b < a$. What is the largest possible value of $b$?<|im_end|>
<|im_start|>assistant
<Z_125><Z_100><Z_14><Z_54><Z_95><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_104><Z_36><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nancy obtained 66 marks in American Literature, some marks in History, 52 in Home Economics, 68 in Physical Education, and 89 in Art. Her average marks are 70. How many marks did she obtain in History?<|im_end|>
<|im_start|>assistant
<Z_83><Z_25><Z_0><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_94><Z_93><Z_40><Z_88><Z_78><Z_11><Z_83><Z_32><Z_117><Z_65><Z_83><Z_72><Z_80><Z_114><Z_88><Z_92><Z_91><Z_72><Z_92><Z_47><Z_59><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bathing suit manufacturer has a supply of 14797 bathing suits for men . In addition , it has 4969 bathing suits for women . How many bathing suits are available overall ? <|im_end|>
<|im_start|>assistant
<Z_103><Z_62><Z_45><Z_57><Z_3><Z_16><Z_117><Z_38><Z_99><Z_115><Z_9><Z_43><Z_79><Z_8><Z_34><Z_27><Z_52><Z_60><Z_57><Z_119><Z_115><Z_111><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the polynomial $x^3+x^{10}=a_0+a_1(x+1)+\ldots+a_9(x+1)^9+a_{10}(x+1)^{10}$, then $a_2=$ ______.<|im_end|>
<|im_start|>assistant
<Z_19><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_106><Z_4><Z_47><Z_50><Z_98><Z_82><Z_126><Z_79><Z_56><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?<|im_end|>
<|im_start|>assistant
<Z_70><Z_99><Z_124><Z_62><Z_6><Z_64><Z_67><Z_83><Z_41><Z_86><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_57><Z_49><Z_63><Z_64><Z_52><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_97><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?<|im_end|>
<|im_start|>assistant
<Z_104><Z_115><Z_93><Z_7><Z_49><Z_61><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest common factor (GCF) of $7!$ and $8!$.<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

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


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_57><Z_12><Z_86><Z_124><Z_70><Z_82><Z_12><Z_125><Z_126><Z_22><Z_45><Z_52><Z_124><Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mr. Fat takes 15 minutes to eat a pound of cereal, while Mr. Thin needs 45 minutes. How long will it take them to finish 4 pounds of cereal together?<|im_end|>
<|im_start|>assistant
<Z_96><Z_51><Z_115><Z_27><Z_80><Z_92><Z_10><Z_25><Z_105><Z_32><Z_70><Z_69><Z_107><Z_21><ANSWER>

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