<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|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 natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_57><Z_33><Z_48><Z_126><Z_91><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_2><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?<|im_end|>
<|im_start|>assistant
<Z_19><Z_53><Z_120><Z_124><Z_27><Z_16><ANSWER>

Question:
A natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_104><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 numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_104><Z_73><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_95><Z_45><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)<|im_end|>
<|im_start|>assistant
<Z_116><Z_86><Z_20><ANSWER>

Question:
The numbers from 1 to 9 are arranged in the cells of a $3 \times 3$ table such that the sum of the numbers on one diagonal is 7, and on the other diagonal, it is 21. What is the sum of the numbers in the five shaded cells?

![Table with shaded cells](https://cdn.mathpix.com/cropped/2024_05_06_ff369b3e8ca7495bdf12g-28.jpg?height=416&width=428&top_left_y=105&top_left_x=513)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make 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
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|im_end|>
<|im_start|>assistant
<Z_106><Z_52><Z_83><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?<|im_end|>
<|im_start|>assistant
<Z_62><Z_112><Z_98><Z_90><ANSWER>

Question: Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make a certain amount of feed worth 0.36 dollars per pound by mixing one kind worth 0.18 dollars per pound with another worth 0.53 dollars per pound. They used 17 pounds of the cheaper kind in the mix. How many pounds of feed did they make in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_104><Z_27><Z_81><Z_51><Z_68><Z_92><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].<|im_end|>
<|im_start|>assistant
<Z_62><Z_79><Z_5><Z_127><Z_20><Z_107><Z_81><ANSWER>

Question:
Given that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|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
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_38><Z_97><Z_78><Z_11><Z_43><Z_50><Z_103><Z_22><Z_66><Z_39><Z_121><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|im_end|>
<|im_start|>assistant
<Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.<|im_end|>
<|im_start|>assistant
<Z_15><Z_48><Z_114><Z_86><Z_110><Z_37><Z_38><Z_62><Z_104><Z_36><Z_14><Z_108><Z_95><ANSWER>

Question:
Calculate:
$(1)-9+5\times \left(-6\right)-18\div \left(-3\right)$;
$(2)(-\frac{3}{4}-\frac{5}{8}+\frac{9}{12})\times \left(-24\right)+\left(-8\right)\div \frac{2}{3}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|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 $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_57><Z_1><Z_50><Z_103><Z_100><Z_95><Z_88><Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.<|im_end|>
<|im_start|>assistant
<Z_93><Z_102><Z_75><Z_25><Z_110><Z_13><Z_12><Z_86><ANSWER>

Question: Evaluate $\lceil e \rceil$, where $e$ is the base of natural logarithms.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|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
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_57><Z_119><Z_91><Z_99><Z_80><Z_63><Z_114><Z_119><Z_33><Z_71><Z_33><Z_90><Z_72><Z_78><Z_96><Z_76><Z_123><Z_5><Z_107><Z_87><Z_83><Z_95><Z_124><Z_124><Z_34><Z_59><Z_52><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.<|im_end|>
<|im_start|>assistant
<Z_90><Z_43><Z_99><Z_34><Z_53><Z_99><Z_101><Z_37><Z_56><Z_96><Z_5><Z_49><Z_107><Z_85><Z_58><Z_4><Z_39><Z_41><Z_84><Z_103><Z_69><Z_1><Z_125><Z_103><Z_77><Z_89><Z_66><Z_17><ANSWER>

Question: Kara mixes cups of sugar and water in the ratio of 3:5 to make 50 liters of lemonade. Calculate the total volume of sugar used in liters if she used 1200 cups to make lemonade.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|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 certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|im_end|>
<|im_start|>assistant
<Z_105><Z_70><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|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
A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?<|im_end|>
<|im_start|>assistant
<Z_14><Z_82><Z_19><ANSWER>

Question: A certain school's physical education final assessment includes "sit-ups" and "800 meters", with a ratio of $4:6$ to calculate the final score. It is known that Xiaolin scored $80$ points and $90$ points in these two items respectively. What is Xiaolin's final score in physical education?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|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 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|im_end|>
<|im_start|>assistant
<Z_104><Z_30><Z_37><Z_44><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|im_end|>
<|im_start|>assistant
<Z_20><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?<|im_end|>
<|im_start|>assistant
<Z_87><Z_48><Z_21><Z_109><ANSWER>

Question: In 1990, the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|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 metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_57><Z_49><Z_50><Z_78><Z_40><Z_63><Z_49><Z_20><Z_53><Z_31><Z_93><Z_48><Z_66><Z_48><Z_98><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_105><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?<|im_end|>
<|im_start|>assistant
<Z_2><Z_61><Z_98><Z_107><Z_1><Z_18><Z_88><Z_67><Z_9><Z_55><Z_29><Z_46><Z_74><Z_69><Z_79><Z_10><ANSWER>

Question: A metal company's old machine makes bolts at a certain rate. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, it takes the two machines 96 minutes to make a total of 400 bolts. What is the rate at which the old machine makes bolts?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|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 box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_113><Z_50><Z_81><Z_59><Z_78><Z_72><Z_87><Z_124><Z_12><Z_19><Z_101><Z_119><Z_48><Z_121><Z_70><Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?<|im_end|>
<|im_start|>assistant
<Z_9><Z_101><Z_86><Z_42><Z_85><Z_72><Z_73><Z_112><Z_54><Z_91><Z_90><Z_2><Z_2><Z_23><Z_80><Z_9><ANSWER>

Question: A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|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
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_104><Z_78><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?<|im_end|>
<|im_start|>assistant
<Z_120><Z_66><Z_98><ANSWER>

Question: Jack and Sam have a combined weight of 96 pounds. Jack is 8 pounds heavier than Sam. How much does Jack weigh?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?<|im_end|>
<|im_start|>assistant
<Z_88><ANSWER>

Question: In the number \(2016 * * * * 02 * *\), each of the 6 asterisks needs to be replaced with any of the digits \(0, 2, 4, 5, 7, 9\) (digits can repeat) so that the resulting 12-digit number is divisible by 15. How many ways can this be done?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|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
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|im_end|>
<|im_start|>assistant
<Z_106><Z_38><Z_36><Z_64><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|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
To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?<|im_end|>
<|im_start|>assistant
<Z_5><Z_113><Z_44><Z_72><Z_79><ANSWER>

Question: To be considered for "movie of the year," a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy's 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for "movie of the year"?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|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
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|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
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|im_end|>
<|im_start|>assistant
<Z_3><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

Question: Sidney does 20 jumping jacks on Monday, some on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney and did 438 jumping jacks. How many jumping jacks did Sidney do on Tuesday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|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
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_104><Z_100><Z_97><Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.<|im_end|>
<|im_start|>assistant
<Z_7><Z_17><Z_84><Z_92><ANSWER>

Question:
The integers $P$ and $Q$ are such that
\[\frac{P}{x+7}+\frac{Q}{x^2-6x}=\frac{x^2-6x+14}{x^3+x^2-30x}\] for all real values of $x$ except $-7$, $0$, and $5$. Find $Q/P$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|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 certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_104><Z_81><Z_107><Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?<|im_end|>
<|im_start|>assistant
<Z_119><Z_101><Z_91><Z_94><ANSWER>

Question: A certain number of paving stones are required to pave a rectangular courtyard 30 m long and 16 m wide. If each paving stone measures a certain length and 1 m wide, and 240 paving stones are needed in total, what is the length of each paving stone?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|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 bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_63><Z_12><Z_83><Z_41><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?<|im_end|>
<|im_start|>assistant
<Z_64><Z_78><Z_69><Z_19><Z_93><Z_51><Z_41><ANSWER>

Question: A bike is moving at a constant speed and covers a distance of 5400 meters in 9 minutes. What is the speed of the bike in meters per second?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|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 Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_104><Z_64><Z_78><Z_120><Z_50><Z_65><Z_38><Z_103><Z_65><Z_82><Z_121><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_46><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?<|im_end|>
<|im_start|>assistant
<Z_58><Z_69><Z_21><Z_65><Z_75><Z_76><Z_90><Z_23><Z_11><Z_79><Z_30><Z_118><ANSWER>

Question: In Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs.  How many chairs are left in Rodrigo's classroom?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle  $\vartriangle A_0A_1A_2$  in the plane has sidelengths  $A_0A_1 = 7$ , $A_1A_2 = 8$ , $A_2A_0 = 9$ . For  $i \ge 0$ , given  $\vartriangle A_iA_{i+1}A_{i+2}$ , let  $A_{i+3}$  be the midpoint of  $A_iA_{i+1}$  and let Gi be the centroid of  $\vartriangle A_iA_{i+1}A_{i+2}$ . Let point  $G$  be the limit of the sequence of points  $\{G_i\}^{\infty}_{i=0}$ . If the distance between  $G$  and  $G_0$  can be written as  $\frac{a\sqrt{b}}{c}$  , where  $a, b, c$  are positive integers such that  $a$  and  $c$  are relatively prime and  $b$  is not divisible by the square of any prime, find  $a^2 + b^2 + c^2$ .<|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
A triangle  $\vartriangle A_0A_1A_2$  in the plane has sidelengths  $A_0A_1 = 7$ , $A_1A_2 = 8$ , $A_2A_0 = 9$ . For  $i \ge 0$ , given  $\vartriangle A_iA_{i+1}A_{i+2}$ , let  $A_{i+3}$  be the midpoint of  $A_iA_{i+1}$  and let Gi be the centroid of  $\vartriangle A_iA_{i+1}A_{i+2}$ . Let point  $G$  be the limit of the sequence of points  $\{G_i\}^{\infty}_{i=0}$ . If the distance between  $G$  and  $G_0$  can be written as  $\frac{a\sqrt{b}}{c}$  , where  $a, b, c$  are positive integers such that  $a$  and  $c$  are relatively prime and  $b$  is not divisible by the square of any prime, find  $a^2 + b^2 + c^2$ .<|im_end|>
<|im_start|>assistant
<Z_113><Z_34><Z_12><Z_115><Z_125><Z_125><Z_98><Z_83><Z_115><Z_59><Z_90><Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle  $\vartriangle A_0A_1A_2$  in the plane has sidelengths  $A_0A_1 = 7$ , $A_1A_2 = 8$ , $A_2A_0 = 9$ . For  $i \ge 0$ , given  $\vartriangle A_iA_{i+1}A_{i+2}$ , let  $A_{i+3}$  be the midpoint of  $A_iA_{i+1}$  and let Gi be the centroid of  $\vartriangle A_iA_{i+1}A_{i+2}$ . Let point  $G$  be the limit of the sequence of points  $\{G_i\}^{\infty}_{i=0}$ . If the distance between  $G$  and  $G_0$  can be written as  $\frac{a\sqrt{b}}{c}$  , where  $a, b, c$  are positive integers such that  $a$  and  $c$  are relatively prime and  $b$  is not divisible by the square of any prime, find  $a^2 + b^2 + c^2$ .<|im_end|>
<|im_start|>assistant
<Z_44><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle  $\vartriangle A_0A_1A_2$  in the plane has sidelengths  $A_0A_1 = 7$ , $A_1A_2 = 8$ , $A_2A_0 = 9$ . For  $i \ge 0$ , given  $\vartriangle A_iA_{i+1}A_{i+2}$ , let  $A_{i+3}$  be the midpoint of  $A_iA_{i+1}$  and let Gi be the centroid of  $\vartriangle A_iA_{i+1}A_{i+2}$ . Let point  $G$  be the limit of the sequence of points  $\{G_i\}^{\infty}_{i=0}$ . If the distance between  $G$  and  $G_0$  can be written as  $\frac{a\sqrt{b}}{c}$  , where  $a, b, c$  are positive integers such that  $a$  and  $c$  are relatively prime and  $b$  is not divisible by the square of any prime, find  $a^2 + b^2 + c^2$ .<|im_end|>
<|im_start|>assistant
<Z_57><Z_62><Z_72><Z_26><Z_101><Z_97><Z_57><Z_16><Z_92><Z_67><Z_77><Z_36><ANSWER>

Question: A triangle  $\vartriangle A_0A_1A_2$  in the plane has sidelengths  $A_0A_1 = 7$ , $A_1A_2 = 8$ , $A_2A_0 = 9$ . For  $i \ge 0$ , given  $\vartriangle A_iA_{i+1}A_{i+2}$ , let  $A_{i+3}$  be the midpoint of  $A_iA_{i+1}$  and let Gi be the centroid of  $\vartriangle A_iA_{i+1}A_{i+2}$ . Let point  $G$  be the limit of the sequence of points  $\{G_i\}^{\infty}_{i=0}$ . If the distance between  $G$  and  $G_0$  can be written as  $\frac{a\sqrt{b}}{c}$  , where  $a, b, c$  are positive integers such that  $a$  and  $c$  are relatively prime and  $b$  is not divisible by the square of any prime, find  $a^2 + b^2 + c^2$ .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The perimeter of a smaller square is 8 cm, and the area of a larger square is 64 cm². The squares are arranged such that the top side of the smaller square is collinear with the bottom side of the larger square. What is the distance from point A at the top left corner of the larger square to point B at the bottom right corner of the smaller square?<|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 perimeter of a smaller square is 8 cm, and the area of a larger square is 64 cm². The squares are arranged such that the top side of the smaller square is collinear with the bottom side of the larger square. What is the distance from point A at the top left corner of the larger square to point B at the bottom right corner of the smaller square?<|im_end|>
<|im_start|>assistant
<Z_94><Z_30><Z_64><Z_51><Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The perimeter of a smaller square is 8 cm, and the area of a larger square is 64 cm². The squares are arranged such that the top side of the smaller square is collinear with the bottom side of the larger square. What is the distance from point A at the top left corner of the larger square to point B at the bottom right corner of the smaller square?<|im_end|>
<|im_start|>assistant
<Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The perimeter of a smaller square is 8 cm, and the area of a larger square is 64 cm². The squares are arranged such that the top side of the smaller square is collinear with the bottom side of the larger square. What is the distance from point A at the top left corner of the larger square to point B at the bottom right corner of the smaller square?<|im_end|>
<|im_start|>assistant
<Z_18><Z_101><Z_51><Z_119><Z_15><ANSWER>

Question: The perimeter of a smaller square is 8 cm, and the area of a larger square is 64 cm². The squares are arranged such that the top side of the smaller square is collinear with the bottom side of the larger square. What is the distance from point A at the top left corner of the larger square to point B at the bottom right corner of the smaller square?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?<|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
3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?<|im_end|>
<|im_start|>assistant
<Z_57><Z_87><Z_108><Z_43><Z_68><Z_125><Z_45><Z_49><Z_19><Z_96><Z_117><Z_66><Z_33><Z_24><Z_22><Z_114><Z_96><Z_117><Z_83><Z_91><Z_67><Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?<|im_end|>
<|im_start|>assistant
<Z_105><Z_21><Z_119><Z_36><Z_64><Z_102><Z_55><Z_67><Z_88><Z_59><Z_110><Z_114><Z_56><Z_119><Z_10><Z_124><Z_59><Z_100><Z_124><Z_114><Z_84><Z_68><ANSWER>

Question: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits?<|im_end|>
<|im_start|>assistant
<Z_113><Z_49><Z_107><Z_30><Z_47><Z_124><Z_78><Z_73><Z_10><Z_90><Z_34><Z_36><Z_119><Z_66><Z_119><Z_114><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits?<|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
What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits?<|im_end|>
<|im_start|>assistant
<Z_59><Z_28><Z_26><Z_118><Z_15><Z_87><Z_101><Z_2><Z_53><Z_116><Z_42><Z_49><Z_105><Z_72><Z_44><Z_95><Z_93><ANSWER>

Question: What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dr. Harry wants to examine Susan's candy consumption in a week, considering she has a daily limit of candies she can consume and the daily prices of the candies are variable. On Tuesday, she buys 3 candies for a total of $2. On Wednesday, she doesn't buy any candies. On Thursday, she buys 5 candies, but the price per candy has increased to $1. On Friday, she purchases 2 candies for a total cost of $1 while the price per candy has decreased. At the end of the week (Sunday night), she sees she has only 4 candies left and her total spending over the week was $9. Considering she doesn't exceed eating more than 3 candies a day, how many candies did she eat during the week?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dr. Harry wants to examine Susan's candy consumption in a week, considering she has a daily limit of candies she can consume and the daily prices of the candies are variable. On Tuesday, she buys 3 candies for a total of $2. On Wednesday, she doesn't buy any candies. On Thursday, she buys 5 candies, but the price per candy has increased to $1. On Friday, she purchases 2 candies for a total cost of $1 while the price per candy has decreased. At the end of the week (Sunday night), she sees she has only 4 candies left and her total spending over the week was $9. Considering she doesn't exceed eating more than 3 candies a day, how many candies did she eat during the week?<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><Z_78><Z_73><Z_22><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dr. Harry wants to examine Susan's candy consumption in a week, considering she has a daily limit of candies she can consume and the daily prices of the candies are variable. On Tuesday, she buys 3 candies for a total of $2. On Wednesday, she doesn't buy any candies. On Thursday, she buys 5 candies, but the price per candy has increased to $1. On Friday, she purchases 2 candies for a total cost of $1 while the price per candy has decreased. At the end of the week (Sunday night), she sees she has only 4 candies left and her total spending over the week was $9. Considering she doesn't exceed eating more than 3 candies a day, how many candies did she eat during the week?<|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
Dr. Harry wants to examine Susan's candy consumption in a week, considering she has a daily limit of candies she can consume and the daily prices of the candies are variable. On Tuesday, she buys 3 candies for a total of $2. On Wednesday, she doesn't buy any candies. On Thursday, she buys 5 candies, but the price per candy has increased to $1. On Friday, she purchases 2 candies for a total cost of $1 while the price per candy has decreased. At the end of the week (Sunday night), she sees she has only 4 candies left and her total spending over the week was $9. Considering she doesn't exceed eating more than 3 candies a day, how many candies did she eat during the week?<|im_end|>
<|im_start|>assistant
<Z_55><Z_119><Z_53><Z_60><Z_35><Z_43><ANSWER>

Question: Dr. Harry wants to examine Susan's candy consumption in a week, considering she has a daily limit of candies she can consume and the daily prices of the candies are variable. On Tuesday, she buys 3 candies for a total of $2. On Wednesday, she doesn't buy any candies. On Thursday, she buys 5 candies, but the price per candy has increased to $1. On Friday, she purchases 2 candies for a total cost of $1 while the price per candy has decreased. At the end of the week (Sunday night), she sees she has only 4 candies left and her total spending over the week was $9. Considering she doesn't exceed eating more than 3 candies a day, how many candies did she eat during the week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dima, an amateur, and Fedya, a professional, broke some firewood and boasted to each other about their achievements. Dima exaggerated his work results by 2 times, and Fedya by 7 times. In total, their boasted amount was three times more than the actual amount of firewood broken. Who broke more firewood and by how much?<|im_end|>
<|im_start|>assistant
<Z_104><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dima, an amateur, and Fedya, a professional, broke some firewood and boasted to each other about their achievements. Dima exaggerated his work results by 2 times, and Fedya by 7 times. In total, their boasted amount was three times more than the actual amount of firewood broken. Who broke more firewood and by how much?<|im_end|>
<|im_start|>assistant
<Z_57><Z_93><Z_40><Z_64><Z_65><Z_49><Z_119><Z_53><Z_16><Z_115><Z_38><Z_34><Z_72><Z_20><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dima, an amateur, and Fedya, a professional, broke some firewood and boasted to each other about their achievements. Dima exaggerated his work results by 2 times, and Fedya by 7 times. In total, their boasted amount was three times more than the actual amount of firewood broken. Who broke more firewood and by how much?<|im_end|>
<|im_start|>assistant
<Z_5><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dima, an amateur, and Fedya, a professional, broke some firewood and boasted to each other about their achievements. Dima exaggerated his work results by 2 times, and Fedya by 7 times. In total, their boasted amount was three times more than the actual amount of firewood broken. Who broke more firewood and by how much?<|im_end|>
<|im_start|>assistant
<Z_66><Z_100><Z_32><Z_84><Z_91><Z_61><Z_31><Z_65><Z_81><Z_73><Z_110><Z_66><Z_127><Z_63><Z_79><ANSWER>

Question: Dima, an amateur, and Fedya, a professional, broke some firewood and boasted to each other about their achievements. Dima exaggerated his work results by 2 times, and Fedya by 7 times. In total, their boasted amount was three times more than the actual amount of firewood broken. Who broke more firewood and by how much?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Optimus Prime departs in robot form from point $A$ to point $B$ and arrives at $B$ on time. If he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, allowing him to arrive at $B$ 1 hour earlier. If he travels 150 km in robot form first, then transforms into a car, and his speed increases by $\frac{1}{5}$, he can arrive 40 minutes earlier. How far apart are points $A$ and $B$ in kilometers?<|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
Optimus Prime departs in robot form from point $A$ to point $B$ and arrives at $B$ on time. If he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, allowing him to arrive at $B$ 1 hour earlier. If he travels 150 km in robot form first, then transforms into a car, and his speed increases by $\frac{1}{5}$, he can arrive 40 minutes earlier. How far apart are points $A$ and $B$ in kilometers?<|im_end|>
<|im_start|>assistant
<Z_94><Z_110><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Optimus Prime departs in robot form from point $A$ to point $B$ and arrives at $B$ on time. If he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, allowing him to arrive at $B$ 1 hour earlier. If he travels 150 km in robot form first, then transforms into a car, and his speed increases by $\frac{1}{5}$, he can arrive 40 minutes earlier. How far apart are points $A$ and $B$ in kilometers?<|im_end|>
<|im_start|>assistant
<Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Optimus Prime departs in robot form from point $A$ to point $B$ and arrives at $B$ on time. If he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, allowing him to arrive at $B$ 1 hour earlier. If he travels 150 km in robot form first, then transforms into a car, and his speed increases by $\frac{1}{5}$, he can arrive 40 minutes earlier. How far apart are points $A$ and $B$ in kilometers?<|im_end|>
<|im_start|>assistant
<Z_94><Z_39><Z_99><ANSWER>

Question: Optimus Prime departs in robot form from point $A$ to point $B$ and arrives at $B$ on time. If he transforms into a car from the beginning, his speed increases by $\frac{1}{4}$, allowing him to arrive at $B$ 1 hour earlier. If he travels 150 km in robot form first, then transforms into a car, and his speed increases by $\frac{1}{5}$, he can arrive 40 minutes earlier. How far apart are points $A$ and $B$ in kilometers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jacqueline had some plums, 18 guavas, and 21 apples. She gave 40 fruits to Jane and had 15 fruits left. How many plums did Jacqueline 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
Jacqueline had some plums, 18 guavas, and 21 apples. She gave 40 fruits to Jane and had 15 fruits left. How many plums did Jacqueline have initially?<|im_end|>
<|im_start|>assistant
<Z_113><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jacqueline had some plums, 18 guavas, and 21 apples. She gave 40 fruits to Jane and had 15 fruits left. How many plums did Jacqueline have initially?<|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
Jacqueline had some plums, 18 guavas, and 21 apples. She gave 40 fruits to Jane and had 15 fruits left. How many plums did Jacqueline have initially?<|im_end|>
<|im_start|>assistant
<Z_125><Z_47><ANSWER>

Question: Jacqueline had some plums, 18 guavas, and 21 apples. She gave 40 fruits to Jane and had 15 fruits left. How many plums did Jacqueline have initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $9\times 1$ board is completely covered by tiles without overlap; each tile may be $1\times 1$, $2\times 1$, or $3\times 1$ in size and lies completely on the board. Each tile is either red, blue, or green. Calculate the number of ways to tile the $9\times 1$ board such that all three colors are used at least once. Let $N$ denote this number, and give the remainder when $N$ is divided by $1000$.<|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 $9\times 1$ board is completely covered by tiles without overlap; each tile may be $1\times 1$, $2\times 1$, or $3\times 1$ in size and lies completely on the board. Each tile is either red, blue, or green. Calculate the number of ways to tile the $9\times 1$ board such that all three colors are used at least once. Let $N$ denote this number, and give the remainder when $N$ is divided by $1000$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_29><Z_87><Z_78><Z_88><Z_73><Z_73><Z_34><Z_47><Z_65><Z_78><Z_95><Z_117><Z_61><Z_39><Z_114><Z_124><Z_34><Z_26><Z_26><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $9\times 1$ board is completely covered by tiles without overlap; each tile may be $1\times 1$, $2\times 1$, or $3\times 1$ in size and lies completely on the board. Each tile is either red, blue, or green. Calculate the number of ways to tile the $9\times 1$ board such that all three colors are used at least once. Let $N$ denote this number, and give the remainder when $N$ is divided by $1000$.<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $9\times 1$ board is completely covered by tiles without overlap; each tile may be $1\times 1$, $2\times 1$, or $3\times 1$ in size and lies completely on the board. Each tile is either red, blue, or green. Calculate the number of ways to tile the $9\times 1$ board such that all three colors are used at least once. Let $N$ denote this number, and give the remainder when $N$ is divided by $1000$.<|im_end|>
<|im_start|>assistant
<Z_118><Z_111><Z_116><Z_63><Z_59><Z_35><Z_91><Z_64><Z_110><Z_52><Z_27><Z_20><Z_50><Z_71><Z_69><Z_89><Z_106><Z_65><Z_10><Z_118><ANSWER>

Question: A $9\times 1$ board is completely covered by tiles without overlap; each tile may be $1\times 1$, $2\times 1$, or $3\times 1$ in size and lies completely on the board. Each tile is either red, blue, or green. Calculate the number of ways to tile the $9\times 1$ board such that all three colors are used at least once. Let $N$ denote this number, and give the remainder when $N$ is divided by $1000$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a positive integer \( n \) such that \( n \leq 2016 \) and \(\left\{\frac{n}{2}\right\}+\left\{\frac{n}{4}\right\}+\left\{\frac{n}{6}\right\}+\left\{\frac{n}{12}\right\}=3\), where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \), find the number of such integers \( n \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a positive integer \( n \) such that \( n \leq 2016 \) and \(\left\{\frac{n}{2}\right\}+\left\{\frac{n}{4}\right\}+\left\{\frac{n}{6}\right\}+\left\{\frac{n}{12}\right\}=3\), where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \), find the number of such integers \( n \).<|im_end|>
<|im_start|>assistant
<Z_57><Z_37><Z_36><Z_107><Z_83><Z_90><Z_52><Z_120><Z_117><Z_58><Z_95><Z_119><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a positive integer \( n \) such that \( n \leq 2016 \) and \(\left\{\frac{n}{2}\right\}+\left\{\frac{n}{4}\right\}+\left\{\frac{n}{6}\right\}+\left\{\frac{n}{12}\right\}=3\), where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \), find the number of such integers \( n \).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a positive integer \( n \) such that \( n \leq 2016 \) and \(\left\{\frac{n}{2}\right\}+\left\{\frac{n}{4}\right\}+\left\{\frac{n}{6}\right\}+\left\{\frac{n}{12}\right\}=3\), where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \), find the number of such integers \( n \).<|im_end|>
<|im_start|>assistant
<Z_123><Z_84><Z_27><Z_91><Z_115><Z_93><Z_18><Z_54><Z_81><Z_65><Z_65><Z_52><Z_53><ANSWER>

Question: Given a positive integer \( n \) such that \( n \leq 2016 \) and \(\left\{\frac{n}{2}\right\}+\left\{\frac{n}{4}\right\}+\left\{\frac{n}{6}\right\}+\left\{\frac{n}{12}\right\}=3\), where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \), find the number of such integers \( n \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer?<|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 integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer?<|im_end|>
<|im_start|>assistant
<Z_113><Z_13><Z_89><Z_97><Z_98><Z_126><Z_90><Z_103><Z_41><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer?<|im_end|>
<|im_start|>assistant
<Z_92><Z_1><Z_3><Z_101><Z_65><Z_94><Z_121><Z_48><Z_52><Z_123><ANSWER>

Question: Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train covers a distance in 276 min, if it runs at a certain speed on an average. To reduce the time of journey to 69 min, the train must run at a speed of 16 kmph. What is the average speed of the train when it takes 276 min to cover the distance?<|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 train covers a distance in 276 min, if it runs at a certain speed on an average. To reduce the time of journey to 69 min, the train must run at a speed of 16 kmph. What is the average speed of the train when it takes 276 min to cover the distance?<|im_end|>
<|im_start|>assistant
<Z_57><Z_4><Z_50><Z_98><Z_114><Z_119><Z_58><Z_119><Z_10><Z_34><Z_39><Z_22><Z_70><Z_37><Z_121><Z_95><Z_88><Z_125><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train covers a distance in 276 min, if it runs at a certain speed on an average. To reduce the time of journey to 69 min, the train must run at a speed of 16 kmph. What is the average speed of the train when it takes 276 min to cover the distance?<|im_end|>
<|im_start|>assistant
<Z_0><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train covers a distance in 276 min, if it runs at a certain speed on an average. To reduce the time of journey to 69 min, the train must run at a speed of 16 kmph. What is the average speed of the train when it takes 276 min to cover the distance?<|im_end|>
<|im_start|>assistant
<Z_61><Z_92><Z_1><Z_91><Z_23><Z_33><Z_52><Z_86><Z_85><Z_5><Z_24><Z_18><Z_107><Z_85><Z_98><Z_122><Z_116><Z_19><Z_27><ANSWER>

Question: A train covers a distance in 276 min, if it runs at a certain speed on an average. To reduce the time of journey to 69 min, the train must run at a speed of 16 kmph. What is the average speed of the train when it takes 276 min to cover the distance?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Seventy percent of a cruise ship's passengers are women, and fifteen percent of those women are in luxury suites. What is the number of women in luxury suites if the cruise ship is carrying 250 passengers?<|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
Seventy percent of a cruise ship's passengers are women, and fifteen percent of those women are in luxury suites. What is the number of women in luxury suites if the cruise ship is carrying 250 passengers?<|im_end|>
<|im_start|>assistant
<Z_113><Z_50><Z_83><Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Seventy percent of a cruise ship's passengers are women, and fifteen percent of those women are in luxury suites. What is the number of women in luxury suites if the cruise ship is carrying 250 passengers?<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Seventy percent of a cruise ship's passengers are women, and fifteen percent of those women are in luxury suites. What is the number of women in luxury suites if the cruise ship is carrying 250 passengers?<|im_end|>
<|im_start|>assistant
<Z_91><Z_63><Z_99><Z_68><ANSWER>

Question: Seventy percent of a cruise ship's passengers are women, and fifteen percent of those women are in luxury suites. What is the number of women in luxury suites if the cruise ship is carrying 250 passengers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 240 third grade students at Heesu's school. If the number of third grade students who were glasses is 3/5 of the number of students who do not were glasses, how may third grade students do not were glasses?<|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
There are 240 third grade students at Heesu's school. If the number of third grade students who were glasses is 3/5 of the number of students who do not were glasses, how may third grade students do not were glasses?<|im_end|>
<|im_start|>assistant
<Z_57><Z_43><Z_43><Z_40><Z_70><Z_114><Z_31><Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 240 third grade students at Heesu's school. If the number of third grade students who were glasses is 3/5 of the number of students who do not were glasses, how may third grade students do not were glasses?<|im_end|>
<|im_start|>assistant
<Z_111><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 240 third grade students at Heesu's school. If the number of third grade students who were glasses is 3/5 of the number of students who do not were glasses, how may third grade students do not were glasses?<|im_end|>
<|im_start|>assistant
<Z_29><Z_58><Z_35><Z_104><Z_16><Z_125><Z_87><Z_21><ANSWER>

Question: There are 240 third grade students at Heesu's school. If the number of third grade students who were glasses is 3/5 of the number of students who do not were glasses, how may third grade students do not were glasses?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three-fifths of the people in a room are seated in four-fifths of the chairs. The rest of the people are standing. If there are 5 empty chairs, how many people are in the room?<|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
Three-fifths of the people in a room are seated in four-fifths of the chairs. The rest of the people are standing. If there are 5 empty chairs, how many people are in the room?<|im_end|>
<|im_start|>assistant
<Z_104><Z_89><Z_82><Z_47><Z_12><Z_41><Z_22><Z_82><Z_91><Z_71><Z_16><Z_87><Z_125><Z_126><Z_76><Z_87><Z_11><Z_26><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three-fifths of the people in a room are seated in four-fifths of the chairs. The rest of the people are standing. If there are 5 empty chairs, how many people are in the room?<|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
Three-fifths of the people in a room are seated in four-fifths of the chairs. The rest of the people are standing. If there are 5 empty chairs, how many people are in the room?<|im_end|>
<|im_start|>assistant
<Z_77><Z_117><Z_77><Z_92><Z_52><Z_106><Z_123><Z_63><Z_105><Z_82><Z_110><Z_16><Z_104><Z_64><Z_32><Z_39><Z_76><Z_50><Z_98><ANSWER>

Question: Three-fifths of the people in a room are seated in four-fifths of the chairs. The rest of the people are standing. If there are 5 empty chairs, how many people are in the room?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve C is $\rho=1$, and the parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {1}{2}t \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter).
(1) Find the Cartesian equations of line $l$ and curve $C$;
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$. Find the maximum value of $$x+2 \sqrt {3}y$$.<|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
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve C is $\rho=1$, and the parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {1}{2}t \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter).
(1) Find the Cartesian equations of line $l$ and curve $C$;
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$. Find the maximum value of $$x+2 \sqrt {3}y$$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_1><Z_125><Z_124><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve C is $\rho=1$, and the parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {1}{2}t \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter).
(1) Find the Cartesian equations of line $l$ and curve $C$;
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$. Find the maximum value of $$x+2 \sqrt {3}y$$.<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve C is $\rho=1$, and the parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {1}{2}t \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter).
(1) Find the Cartesian equations of line $l$ and curve $C$;
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$. Find the maximum value of $$x+2 \sqrt {3}y$$.<|im_end|>
<|im_start|>assistant
<Z_110><Z_54><Z_66><Z_116><Z_115><ANSWER>

Question:
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve C is $\rho=1$, and the parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {1}{2}t \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases}$$ (where $t$ is the parameter).
(1) Find the Cartesian equations of line $l$ and curve $C$;
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$. Find the maximum value of $$x+2 \sqrt {3}y$$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A boy takes 64 seconds to run round a square field of a certain side length, if he runs at the rate of 9 km/hr. What is the side length of the square field?<|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 boy takes 64 seconds to run round a square field of a certain side length, if he runs at the rate of 9 km/hr. What is the side length of the square field?<|im_end|>
<|im_start|>assistant
<Z_113><Z_31><Z_78><Z_52><Z_48><Z_120><Z_96><Z_98><Z_120><Z_124><Z_39><Z_6><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A boy takes 64 seconds to run round a square field of a certain side length, if he runs at the rate of 9 km/hr. What is the side length of the square field?<|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
A boy takes 64 seconds to run round a square field of a certain side length, if he runs at the rate of 9 km/hr. What is the side length of the square field?<|im_end|>
<|im_start|>assistant
<Z_97><Z_103><Z_47><Z_2><Z_78><Z_54><Z_72><Z_114><Z_96><Z_11><Z_88><Z_90><ANSWER>

Question: A boy takes 64 seconds to run round a square field of a certain side length, if he runs at the rate of 9 km/hr. What is the side length of the square field?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A = (0,0)$ and $B = (b,4)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 150^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,4,8,12,16,20\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers, and n is not divisible by the square of any prime. Find $m + n.$<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A = (0,0)$ and $B = (b,4)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 150^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,4,8,12,16,20\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers, and n is not divisible by the square of any prime. Find $m + n.$<|im_end|>
<|im_start|>assistant
<Z_94><Z_115><Z_82><Z_77><Z_92><Z_92><Z_72><Z_58><Z_70><Z_115><Z_11><Z_115><Z_83><Z_126><Z_11><Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A = (0,0)$ and $B = (b,4)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 150^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,4,8,12,16,20\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers, and n is not divisible by the square of any prime. Find $m + n.$<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A = (0,0)$ and $B = (b,4)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 150^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,4,8,12,16,20\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers, and n is not divisible by the square of any prime. Find $m + n.$<|im_end|>
<|im_start|>assistant
<Z_120><Z_37><Z_76><Z_73><Z_7><Z_65><Z_56><Z_38><Z_82><Z_21><Z_62><Z_35><Z_16><Z_16><Z_50><Z_97><ANSWER>

Question: Let $A = (0,0)$ and $B = (b,4)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 150^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,4,8,12,16,20\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers, and n is not divisible by the square of any prime. Find $m + n.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A classroom contains 48 chairs, and they need to be arranged in a rectangular array with at least two chairs in every row and column. How many distinct arrays can be formed?<|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 classroom contains 48 chairs, and they need to be arranged in a rectangular array with at least two chairs in every row and column. How many distinct arrays can be formed?<|im_end|>
<|im_start|>assistant
<Z_94><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A classroom contains 48 chairs, and they need to be arranged in a rectangular array with at least two chairs in every row and column. How many distinct arrays can be formed?<|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 classroom contains 48 chairs, and they need to be arranged in a rectangular array with at least two chairs in every row and column. How many distinct arrays can be formed?<|im_end|>
<|im_start|>assistant
<Z_50><Z_91><ANSWER>

Question: A classroom contains 48 chairs, and they need to be arranged in a rectangular array with at least two chairs in every row and column. How many distinct arrays can be formed?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 660 = 0$ has integral solutions?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 660 = 0$ has integral solutions?<|im_end|>
<|im_start|>assistant
<Z_94><Z_64><Z_99><Z_97><Z_97><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 660 = 0$ has integral solutions?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 660 = 0$ has integral solutions?<|im_end|>
<|im_start|>assistant
<Z_84><Z_9><Z_72><Z_125><Z_70><ANSWER>

Question: What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 660 = 0$ has integral solutions?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stick 6 cm long, a stick 10 cm long, and a third stick $m$ cm long form a triangle. What is the sum of all possible whole number values of $m$?<|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 stick 6 cm long, a stick 10 cm long, and a third stick $m$ cm long form a triangle. What is the sum of all possible whole number values of $m$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_105><Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stick 6 cm long, a stick 10 cm long, and a third stick $m$ cm long form a triangle. What is the sum of all possible whole number values of $m$?<|im_end|>
<|im_start|>assistant
<Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A stick 6 cm long, a stick 10 cm long, and a third stick $m$ cm long form a triangle. What is the sum of all possible whole number values of $m$?<|im_end|>
<|im_start|>assistant
<Z_0><Z_20><Z_63><ANSWER>

Question: A stick 6 cm long, a stick 10 cm long, and a third stick $m$ cm long form a triangle. What is the sum of all possible whole number values of $m$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Blake wants to spend his Friday making milkshakes for his family. He knows that he needs 4 ounces of milk and 12 ounces of ice cream for each milkshake. If he has 72 ounces of milk and 192 ounces of ice cream, how much milk will be left over when he is done?<|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
Blake wants to spend his Friday making milkshakes for his family. He knows that he needs 4 ounces of milk and 12 ounces of ice cream for each milkshake. If he has 72 ounces of milk and 192 ounces of ice cream, how much milk will be left over when he is done?<|im_end|>
<|im_start|>assistant
<Z_113><Z_108><Z_49><Z_110><Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Blake wants to spend his Friday making milkshakes for his family. He knows that he needs 4 ounces of milk and 12 ounces of ice cream for each milkshake. If he has 72 ounces of milk and 192 ounces of ice cream, how much milk will be left over when he is done?<|im_end|>
<|im_start|>assistant
<Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Blake wants to spend his Friday making milkshakes for his family. He knows that he needs 4 ounces of milk and 12 ounces of ice cream for each milkshake. If he has 72 ounces of milk and 192 ounces of ice cream, how much milk will be left over when he is done?<|im_end|>
<|im_start|>assistant
<Z_92><Z_75><Z_54><Z_29><Z_79><ANSWER>

Question: Blake wants to spend his Friday making milkshakes for his family. He knows that he needs 4 ounces of milk and 12 ounces of ice cream for each milkshake. If he has 72 ounces of milk and 192 ounces of ice cream, how much milk will be left over when he is done?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?<|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
United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?<|im_end|>
<|im_start|>assistant
<Z_94><Z_108><Z_87><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?<|im_end|>
<|im_start|>assistant
<Z_80><Z_32><Z_40><Z_117><ANSWER>

Question: United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
$2\lg 2+ \frac {\lg 5}{\lg \sqrt {10}}=$ ______.<|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
$2\lg 2+ \frac {\lg 5}{\lg \sqrt {10}}=$ ______.<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_107><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
$2\lg 2+ \frac {\lg 5}{\lg \sqrt {10}}=$ ______.<|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
$2\lg 2+ \frac {\lg 5}{\lg \sqrt {10}}=$ ______.<|im_end|>
<|im_start|>assistant
<Z_60><Z_80><Z_79><Z_3><ANSWER>

Question: $2\lg 2+ \frac {\lg 5}{\lg \sqrt {10}}=$ ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?<|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
a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><Z_83><Z_47><Z_91><Z_49><Z_90><Z_87><Z_37><Z_90><Z_78><Z_22><Z_58><Z_80><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?<|im_end|>
<|im_start|>assistant
<Z_70><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?<|im_end|>
<|im_start|>assistant
<Z_120><Z_91><Z_64><Z_96><Z_59><Z_50><Z_117><Z_69><Z_113><Z_44><Z_53><Z_52><Z_76><Z_102><Z_11><ANSWER>

Question: a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute: \((15+12)^2-(15-12)^2\).<|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
Compute: \((15+12)^2-(15-12)^2\).<|im_end|>
<|im_start|>assistant
<Z_104><Z_74><Z_37><Z_33><Z_72><Z_119><Z_123><Z_41><Z_91><Z_76><Z_107><Z_32><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute: \((15+12)^2-(15-12)^2\).<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute: \((15+12)^2-(15-12)^2\).<|im_end|>
<|im_start|>assistant
<Z_20><Z_1><Z_85><Z_100><Z_36><Z_94><Z_113><Z_109><Z_90><Z_88><Z_22><Z_126><Z_115><ANSWER>

Question: Compute: \((15+12)^2-(15-12)^2\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a, b, c, d$ be real numbers, each different from $-1$, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1$. If
\[
\frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{4}{\omega^2},
\]
then find
\[
\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}.
\]<|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
Let $a, b, c, d$ be real numbers, each different from $-1$, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1$. If
\[
\frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{4}{\omega^2},
\]
then find
\[
\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}.
\]<|im_end|>
<|im_start|>assistant
<Z_104><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a, b, c, d$ be real numbers, each different from $-1$, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1$. If
\[
\frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{4}{\omega^2},
\]
then find
\[
\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}.
\]<|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
Let $a, b, c, d$ be real numbers, each different from $-1$, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1$. If
\[
\frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{4}{\omega^2},
\]
then find
\[
\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}.
\]<|im_end|>
<|im_start|>assistant
<Z_18><Z_6><ANSWER>

Question:
Let $a, b, c, d$ be real numbers, each different from $-1$, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1$. If
\[
\frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{4}{\omega^2},
\]
then find
\[
\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}.
\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different positive, six-digit integers can be formed using the digits 2, 2, 2, 5, 5, and 9?<|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
How many different positive, six-digit integers can be formed using the digits 2, 2, 2, 5, 5, and 9?<|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
How many different positive, six-digit integers can be formed using the digits 2, 2, 2, 5, 5, and 9?<|im_end|>
<|im_start|>assistant
<Z_78><ANSWER>

Question: How many different positive, six-digit integers can be formed using the digits 2, 2, 2, 5, 5, and 9?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many six-digit numbers with the penultimate digit being 1 are divisible by 4?<|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 six-digit numbers with the penultimate digit being 1 are divisible by 4?<|im_end|>
<|im_start|>assistant
<Z_113><Z_115><Z_64><Z_66><Z_53><Z_123><Z_103><Z_124><Z_121><Z_125><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many six-digit numbers with the penultimate digit being 1 are divisible by 4?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many six-digit numbers with the penultimate digit being 1 are divisible by 4?<|im_end|>
<|im_start|>assistant
<Z_0><Z_3><Z_32><Z_74><Z_98><Z_81><Z_72><Z_108><Z_59><Z_83><Z_109><ANSWER>

Question: How many six-digit numbers with the penultimate digit being 1 are divisible by 4?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Apples are sold at the farmer’s market at a rate of $\$3$ per 3 pounds, and bananas are sold at a rate of $\$2$ per 2 pounds. How much does it cost to buy 9 pounds of apples and 6 pounds of bananas?<|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
Apples are sold at the farmer’s market at a rate of $\$3$ per 3 pounds, and bananas are sold at a rate of $\$2$ per 2 pounds. How much does it cost to buy 9 pounds of apples and 6 pounds of bananas?<|im_end|>
<|im_start|>assistant
<Z_94><Z_119><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Apples are sold at the farmer’s market at a rate of $\$3$ per 3 pounds, and bananas are sold at a rate of $\$2$ per 2 pounds. How much does it cost to buy 9 pounds of apples and 6 pounds of bananas?<|im_end|>
<|im_start|>assistant
<Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Apples are sold at the farmer’s market at a rate of $\$3$ per 3 pounds, and bananas are sold at a rate of $\$2$ per 2 pounds. How much does it cost to buy 9 pounds of apples and 6 pounds of bananas?<|im_end|>
<|im_start|>assistant
<Z_12><Z_76><Z_45><ANSWER>

Question: Apples are sold at the farmer’s market at a rate of $\$3$ per 3 pounds, and bananas are sold at a rate of $\$2$ per 2 pounds. How much does it cost to buy 9 pounds of apples and 6 pounds of bananas?