<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|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 salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

Question: The salary of A is Rs. 10000 per month, while B, C, D, and E have different salaries. The average salary of A, B, C, D, and E per month is Rs. 8400. What are the combined salaries of B, C, D, and E per month?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|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
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_57><Z_99><Z_63><Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|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
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?<|im_end|>
<|im_start|>assistant
<Z_123><Z_41><Z_22><Z_94><ANSWER>

Question:
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.

When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but he received 50 candies. How many dollars did Buratino spend for such a "gift"?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|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
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_94><Z_105><Z_65><Z_47><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_32><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?<|im_end|>
<|im_start|>assistant
<Z_120><Z_127><Z_24><Z_18><Z_76><ANSWER>

Question: Twelve jellies, each 18 centimeters (cm) long, were overlapped the same amount to form a round ring. If its circumference is 210 centimeters (cm), how many millimeters (mm) is the overlapping portion of jelly?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|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
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_29><Z_74><Z_50><Z_4><Z_119><Z_126><Z_32><Z_103><Z_45><Z_95><Z_63><Z_61><Z_125><Z_93><Z_52><Z_123><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|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
Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?<|im_end|>
<|im_start|>assistant
<Z_39><Z_81><Z_104><Z_52><Z_7><Z_93><Z_38><Z_54><Z_23><Z_124><Z_69><Z_89><Z_98><Z_77><Z_47><Z_61><Z_92><ANSWER>

Question: Huasheng Education held a math competition with a total of 12 questions. For each correct answer, 10 points are awarded, and for each wrong or unanswered question, 5 points are deducted. Xiao Hong scored 75 points in the end. How many questions did Xiao Hong answer correctly?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_106><Z_97><Z_93><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_9><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?<|im_end|>
<|im_start|>assistant
<Z_32><Z_58><Z_104><Z_8><ANSWER>

Question: Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the monomials $3x^{m}y$ and $-x^{3}y^{n}$ are like terms, then $m-n=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the monomials $3x^{m}y$ and $-x^{3}y^{n}$ are like terms, then $m-n=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_47><Z_100><Z_32><Z_91><Z_22><Z_117><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the monomials $3x^{m}y$ and $-x^{3}y^{n}$ are like terms, then $m-n=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the monomials $3x^{m}y$ and $-x^{3}y^{n}$ are like terms, then $m-n=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_101><Z_57><Z_31><Z_80><Z_11><Z_121><Z_45><Z_45><ANSWER>

Question: If the monomials $3x^{m}y$ and $-x^{3}y^{n}$ are like terms, then $m-n=\_\_\_\_\_\_$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define a mountain number as a non-palindromic 4-digit number where the second-largest digit is larger than that of other digits. For example, 3927 and 7431 are mountain numbers. How many 4-digit mountain numbers are there?<|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
Define a mountain number as a non-palindromic 4-digit number where the second-largest digit is larger than that of other digits. For example, 3927 and 7431 are mountain numbers. How many 4-digit mountain numbers are there?<|im_end|>
<|im_start|>assistant
<Z_106><Z_68><Z_125><Z_103><Z_52><Z_96><Z_82><Z_70><Z_26><Z_16><Z_96><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define a mountain number as a non-palindromic 4-digit number where the second-largest digit is larger than that of other digits. For example, 3927 and 7431 are mountain numbers. How many 4-digit mountain numbers are there?<|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
Define a mountain number as a non-palindromic 4-digit number where the second-largest digit is larger than that of other digits. For example, 3927 and 7431 are mountain numbers. How many 4-digit mountain numbers are there?<|im_end|>
<|im_start|>assistant
<Z_108><Z_95><Z_48><Z_109><Z_27><Z_12><Z_74><Z_110><Z_19><Z_118><Z_15><Z_7><ANSWER>

Question: Define a mountain number as a non-palindromic 4-digit number where the second-largest digit is larger than that of other digits. For example, 3927 and 7431 are mountain numbers. How many 4-digit mountain numbers are there?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh went to the shopping center. He bought 9 films and some books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. Josh spent $79 in all. How many books did he buy?<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh went to the shopping center. He bought 9 films and some books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. Josh spent $79 in all. How many books did he buy?<|im_end|>
<|im_start|>assistant
<Z_113><Z_97><Z_89><Z_125><Z_68><Z_81><Z_41><Z_99><Z_98><Z_81><Z_126><Z_82><Z_64><Z_59><Z_114><Z_79><Z_95><Z_124><Z_95><Z_123><Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh went to the shopping center. He bought 9 films and some books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. Josh spent $79 in all. How many books did he buy?<|im_end|>
<|im_start|>assistant
<Z_39><Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Josh went to the shopping center. He bought 9 films and some books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. Josh spent $79 in all. How many books did he buy?<|im_end|>
<|im_start|>assistant
<Z_61><Z_3><Z_65><Z_106><Z_104><Z_41><Z_62><Z_17><Z_80><Z_126><Z_84><Z_104><Z_35><Z_100><Z_107><Z_33><Z_113><Z_78><Z_120><Z_103><Z_15><ANSWER>

Question: Josh went to the shopping center. He bought 9 films and some books. He also bought 6 CDs. Each film cost $5, each book cost $4 and each CD cost $3. Josh spent $79 in all. How many books did he buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
which number can we add to 425897 to get a number exactly divisible by 456 ?<|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
which number can we add to 425897 to get a number exactly divisible by 456 ?<|im_end|>
<|im_start|>assistant
<Z_106><Z_51><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
which number can we add to 425897 to get a number exactly divisible by 456 ?<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
which number can we add to 425897 to get a number exactly divisible by 456 ?<|im_end|>
<|im_start|>assistant
<Z_14><Z_40><Z_50><ANSWER>

Question: which number can we add to 425897 to get a number exactly divisible by 456 ?


<|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 exist such that the sum of their digits is 51?<|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 six-digit numbers exist such that the sum of their digits is 51?<|im_end|>
<|im_start|>assistant
<Z_113><Z_81><Z_91><Z_75><Z_82><Z_92><Z_41><Z_12><Z_26><Z_55><Z_61><Z_99><Z_75><Z_76><Z_124><Z_12><Z_11><Z_92><Z_76><Z_12><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 exist such that the sum of their digits is 51?<|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
How many six-digit numbers exist such that the sum of their digits is 51?<|im_end|>
<|im_start|>assistant
<Z_1><Z_60><Z_63><Z_1><Z_122><Z_41><Z_28><Z_70><Z_34><Z_127><Z_37><Z_25><Z_82><Z_25><Z_103><Z_38><Z_19><Z_29><Z_118><Z_93><ANSWER>

Question: How many six-digit numbers exist such that the sum of their digits is 51?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \( O \) is the center of the circle. What is the value of angle \( x \) in degrees?

![Circle with angle \( x \)](https://cdn.mathpix.com/cropped/2024_05_06_d9f67fd4a24dc8d44db8g-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)<|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
Point \( O \) is the center of the circle. What is the value of angle \( x \) in degrees?

![Circle with angle \( x \)](https://cdn.mathpix.com/cropped/2024_05_06_d9f67fd4a24dc8d44db8g-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)<|im_end|>
<|im_start|>assistant
<Z_94><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \( O \) is the center of the circle. What is the value of angle \( x \) in degrees?

![Circle with angle \( x \)](https://cdn.mathpix.com/cropped/2024_05_06_d9f67fd4a24dc8d44db8g-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)<|im_end|>
<|im_start|>assistant
<Z_8><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \( O \) is the center of the circle. What is the value of angle \( x \) in degrees?

![Circle with angle \( x \)](https://cdn.mathpix.com/cropped/2024_05_06_d9f67fd4a24dc8d44db8g-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)<|im_end|>
<|im_start|>assistant
<Z_113><Z_100><ANSWER>

Question:
Point \( O \) is the center of the circle. What is the value of angle \( x \) in degrees?

![Circle with angle \( x \)](https://cdn.mathpix.com/cropped/2024_05_06_d9f67fd4a24dc8d44db8g-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is 5.2 km. What is the speed of the boat in still water?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is 5.2 km. What is the speed of the boat in still water?<|im_end|>
<|im_start|>assistant
<Z_94><Z_124><Z_37><Z_28><Z_36><Z_8><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is 5.2 km. What is the speed of the boat in still water?<|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
The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is 5.2 km. What is the speed of the boat in still water?<|im_end|>
<|im_start|>assistant
<Z_57><Z_124><Z_50><Z_109><Z_45><Z_22><Z_9><ANSWER>

Question: The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is 5.2 km. What is the speed of the boat in still water?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of $x$-intercepts on the graph of $y = \sin \frac{2}{x}$ (evaluated in terms of radians) in the interval $(0.0002, 0.002).$<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of $x$-intercepts on the graph of $y = \sin \frac{2}{x}$ (evaluated in terms of radians) in the interval $(0.0002, 0.002).$<|im_end|>
<|im_start|>assistant
<Z_113><Z_105><Z_68><Z_38><Z_58><Z_12><Z_28><Z_34><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of $x$-intercepts on the graph of $y = \sin \frac{2}{x}$ (evaluated in terms of radians) in the interval $(0.0002, 0.002).$<|im_end|>
<|im_start|>assistant
<Z_120><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of $x$-intercepts on the graph of $y = \sin \frac{2}{x}$ (evaluated in terms of radians) in the interval $(0.0002, 0.002).$<|im_end|>
<|im_start|>assistant
<Z_31><Z_108><Z_47><Z_77><Z_2><Z_10><Z_104><Z_48><Z_77><ANSWER>

Question: Find the number of $x$-intercepts on the graph of $y = \sin \frac{2}{x}$ (evaluated in terms of radians) in the interval $(0.0002, 0.002).$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are enough provisions in a castle to feed 300 people for a certain number of days. After 30 days, 100 people leave the castle. There are 90 more days left until all the food runs out. How many days were the provisions initially meant to last?<|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 enough provisions in a castle to feed 300 people for a certain number of days. After 30 days, 100 people leave the castle. There are 90 more days left until all the food runs out. How many days were the provisions initially meant to last?<|im_end|>
<|im_start|>assistant
<Z_94><Z_97><Z_51><Z_100><Z_47><Z_107><Z_54><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are enough provisions in a castle to feed 300 people for a certain number of days. After 30 days, 100 people leave the castle. There are 90 more days left until all the food runs out. How many days were the provisions initially meant to last?<|im_end|>
<|im_start|>assistant
<Z_85><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are enough provisions in a castle to feed 300 people for a certain number of days. After 30 days, 100 people leave the castle. There are 90 more days left until all the food runs out. How many days were the provisions initially meant to last?<|im_end|>
<|im_start|>assistant
<Z_96><Z_72><Z_44><Z_73><Z_89><Z_112><Z_95><ANSWER>

Question: There are enough provisions in a castle to feed 300 people for a certain number of days. After 30 days, 100 people leave the castle. There are 90 more days left until all the food runs out. How many days were the provisions initially meant to last?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The value of "a" varies in inverse proportion as the square of "b". If the value of "a" is equal to 40 when "b" is equal to 12, what would be the value of "b" when "a" is equal to 10?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The value of "a" varies in inverse proportion as the square of "b". If the value of "a" is equal to 40 when "b" is equal to 12, what would be the value of "b" when "a" is equal to 10?<|im_end|>
<|im_start|>assistant
<Z_104><Z_37><Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The value of "a" varies in inverse proportion as the square of "b". If the value of "a" is equal to 40 when "b" is equal to 12, what would be the value of "b" when "a" is equal to 10?<|im_end|>
<|im_start|>assistant
<Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The value of "a" varies in inverse proportion as the square of "b". If the value of "a" is equal to 40 when "b" is equal to 12, what would be the value of "b" when "a" is equal to 10?<|im_end|>
<|im_start|>assistant
<Z_3><Z_39><Z_13><ANSWER>

Question: The value of "a" varies in inverse proportion as the square of "b". If the value of "a" is equal to 40 when "b" is equal to 12, what would be the value of "b" when "a" is equal to 10?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A fly moves from the origin only to the right or upwards along the lines of an integer grid (monotonic movement). At each grid node, the fly randomly chooses the direction of further movement: upwards or to the right.

a) Prove that, sooner or later, the fly will reach the point with the x-coordinate 2011.

b) Find the expected value of the fly's y-coordinate at the moment when the fly reaches the x-coordinate 2011.<|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 fly moves from the origin only to the right or upwards along the lines of an integer grid (monotonic movement). At each grid node, the fly randomly chooses the direction of further movement: upwards or to the right.

a) Prove that, sooner or later, the fly will reach the point with the x-coordinate 2011.

b) Find the expected value of the fly's y-coordinate at the moment when the fly reaches the x-coordinate 2011.<|im_end|>
<|im_start|>assistant
<Z_57><Z_78><Z_82><Z_65><Z_22><Z_20><Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A fly moves from the origin only to the right or upwards along the lines of an integer grid (monotonic movement). At each grid node, the fly randomly chooses the direction of further movement: upwards or to the right.

a) Prove that, sooner or later, the fly will reach the point with the x-coordinate 2011.

b) Find the expected value of the fly's y-coordinate at the moment when the fly reaches the x-coordinate 2011.<|im_end|>
<|im_start|>assistant
<Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A fly moves from the origin only to the right or upwards along the lines of an integer grid (monotonic movement). At each grid node, the fly randomly chooses the direction of further movement: upwards or to the right.

a) Prove that, sooner or later, the fly will reach the point with the x-coordinate 2011.

b) Find the expected value of the fly's y-coordinate at the moment when the fly reaches the x-coordinate 2011.<|im_end|>
<|im_start|>assistant
<Z_68><Z_79><Z_26><Z_11><Z_66><Z_91><Z_29><ANSWER>

Question:
A fly moves from the origin only to the right or upwards along the lines of an integer grid (monotonic movement). At each grid node, the fly randomly chooses the direction of further movement: upwards or to the right.

a) Prove that, sooner or later, the fly will reach the point with the x-coordinate 2011.

b) Find the expected value of the fly's y-coordinate at the moment when the fly reaches the x-coordinate 2011.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From unit cubes, a large parallelepiped with side lengths greater than 3 was assembled. Two cubes are called neighboring if they share a face. Therefore, one cube can have up to 6 neighbors. It is known that the number of cubes with exactly 6 neighbors is 429. Find the number of cubes that have exactly 4 neighbors.<|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
From unit cubes, a large parallelepiped with side lengths greater than 3 was assembled. Two cubes are called neighboring if they share a face. Therefore, one cube can have up to 6 neighbors. It is known that the number of cubes with exactly 6 neighbors is 429. Find the number of cubes that have exactly 4 neighbors.<|im_end|>
<|im_start|>assistant
<Z_57><Z_66><Z_91><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From unit cubes, a large parallelepiped with side lengths greater than 3 was assembled. Two cubes are called neighboring if they share a face. Therefore, one cube can have up to 6 neighbors. It is known that the number of cubes with exactly 6 neighbors is 429. Find the number of cubes that have exactly 4 neighbors.<|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
From unit cubes, a large parallelepiped with side lengths greater than 3 was assembled. Two cubes are called neighboring if they share a face. Therefore, one cube can have up to 6 neighbors. It is known that the number of cubes with exactly 6 neighbors is 429. Find the number of cubes that have exactly 4 neighbors.<|im_end|>
<|im_start|>assistant
<Z_87><Z_127><Z_94><Z_41><ANSWER>

Question: From unit cubes, a large parallelepiped with side lengths greater than 3 was assembled. Two cubes are called neighboring if they share a face. Therefore, one cube can have up to 6 neighbors. It is known that the number of cubes with exactly 6 neighbors is 429. Find the number of cubes that have exactly 4 neighbors.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 2014 is $2 \times 19 \times 53$. How many ordered pairs of positive integers $(x, y)$ satisfy the equation $xy = 2014$?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 2014 is $2 \times 19 \times 53$. How many ordered pairs of positive integers $(x, y)$ satisfy the equation $xy = 2014$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_97><Z_77><Z_91><Z_12><Z_32><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 2014 is $2 \times 19 \times 53$. How many ordered pairs of positive integers $(x, y)$ satisfy the equation $xy = 2014$?<|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
The prime factorization of 2014 is $2 \times 19 \times 53$. How many ordered pairs of positive integers $(x, y)$ satisfy the equation $xy = 2014$?<|im_end|>
<|im_start|>assistant
<Z_67><Z_97><Z_47><Z_86><Z_115><Z_30><ANSWER>

Question: The prime factorization of 2014 is $2 \times 19 \times 53$. How many ordered pairs of positive integers $(x, y)$ satisfy the equation $xy = 2014$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train running at a certain speed crosses a pole in 15 seconds. The length of the train is 375 meters. What is the speed of the train in km/hr?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train running at a certain speed crosses a pole in 15 seconds. The length of the train is 375 meters. What is the speed of the train in km/hr?<|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 train running at a certain speed crosses a pole in 15 seconds. The length of the train is 375 meters. What is the speed of the train in km/hr?<|im_end|>
<|im_start|>assistant
<Z_112><ANSWER>

Question: A train running at a certain speed crosses a pole in 15 seconds. The length of the train is 375 meters. What is the speed of the train in km/hr?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

The volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.<|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 volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.<|im_end|>
<|im_start|>assistant
<Z_104><Z_73><Z_44><Z_99><Z_40><Z_124><Z_91><Z_88><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

The volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.<|im_end|>
<|im_start|>assistant
<Z_97><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

The volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.<|im_end|>
<|im_start|>assistant
<Z_65><Z_92><Z_42><Z_78><Z_97><Z_23><Z_13><Z_68><Z_112><ANSWER>

Question:
The volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The grasshopper, the frog, the mouse, and the squirrel had a jumping contest with obstacles. The grasshopper jumped 19 inches, but it encountered an obstacle which reduced its jump distance by 3 inches. The frog jumped 10 inches farther than the grasshopper without encountering any obstacles. The mouse jumped 20 inches farther than the frog, but encountered an obstacle that reduced its jump distance by 5 inches. The squirrel jumped 7 inches less than the mouse, and it faced a 2-inch obstacle. How much farther did the mouse jump than the grasshopper, considering the obstacles they encountered?<|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 grasshopper, the frog, the mouse, and the squirrel had a jumping contest with obstacles. The grasshopper jumped 19 inches, but it encountered an obstacle which reduced its jump distance by 3 inches. The frog jumped 10 inches farther than the grasshopper without encountering any obstacles. The mouse jumped 20 inches farther than the frog, but encountered an obstacle that reduced its jump distance by 5 inches. The squirrel jumped 7 inches less than the mouse, and it faced a 2-inch obstacle. How much farther did the mouse jump than the grasshopper, considering the obstacles they encountered?<|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
The grasshopper, the frog, the mouse, and the squirrel had a jumping contest with obstacles. The grasshopper jumped 19 inches, but it encountered an obstacle which reduced its jump distance by 3 inches. The frog jumped 10 inches farther than the grasshopper without encountering any obstacles. The mouse jumped 20 inches farther than the frog, but encountered an obstacle that reduced its jump distance by 5 inches. The squirrel jumped 7 inches less than the mouse, and it faced a 2-inch obstacle. How much farther did the mouse jump than the grasshopper, considering the obstacles they encountered?<|im_end|>
<|im_start|>assistant
<Z_11><ANSWER>

Question: The grasshopper, the frog, the mouse, and the squirrel had a jumping contest with obstacles. The grasshopper jumped 19 inches, but it encountered an obstacle which reduced its jump distance by 3 inches. The frog jumped 10 inches farther than the grasshopper without encountering any obstacles. The mouse jumped 20 inches farther than the frog, but encountered an obstacle that reduced its jump distance by 5 inches. The squirrel jumped 7 inches less than the mouse, and it faced a 2-inch obstacle. How much farther did the mouse jump than the grasshopper, considering the obstacles they encountered?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rhombus whose two diagonals are 14 centimeters (cm) and 24 centimeters (cm).<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rhombus whose two diagonals are 14 centimeters (cm) and 24 centimeters (cm).<|im_end|>
<|im_start|>assistant
<Z_94><Z_97><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rhombus whose two diagonals are 14 centimeters (cm) and 24 centimeters (cm).<|im_end|>
<|im_start|>assistant
<Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rhombus whose two diagonals are 14 centimeters (cm) and 24 centimeters (cm).<|im_end|>
<|im_start|>assistant
<Z_42><Z_62><ANSWER>

Question: Find the area of a rhombus whose two diagonals are 14 centimeters (cm) and 24 centimeters (cm).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the remainder when $4 \times 14 \times 24 \times 34 \times \ldots \times 184 \times 194$ is divided by $5$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the remainder when $4 \times 14 \times 24 \times 34 \times \ldots \times 184 \times 194$ is divided by $5$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_51><Z_83><Z_107><Z_62><Z_93><Z_79><Z_32><Z_55><Z_90><Z_91><Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the remainder when $4 \times 14 \times 24 \times 34 \times \ldots \times 184 \times 194$ is divided by $5$.<|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
Find the remainder when $4 \times 14 \times 24 \times 34 \times \ldots \times 184 \times 194$ is divided by $5$.<|im_end|>
<|im_start|>assistant
<Z_36><Z_18><Z_65><Z_25><Z_83><Z_95><Z_75><Z_16><Z_66><Z_46><Z_81><Z_22><ANSWER>

Question: Find the remainder when $4 \times 14 \times 24 \times 34 \times \ldots \times 184 \times 194$ is divided by $5$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worksheet had some problems on it. A teacher had 16 worksheets to grade and had already graded 8 of them. She has 32 more problems to grade. How many problems are on each worksheet?<|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 worksheet had some problems on it. A teacher had 16 worksheets to grade and had already graded 8 of them. She has 32 more problems to grade. How many problems are on each worksheet?<|im_end|>
<|im_start|>assistant
<Z_104><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worksheet had some problems on it. A teacher had 16 worksheets to grade and had already graded 8 of them. She has 32 more problems to grade. How many problems are on each worksheet?<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worksheet had some problems on it. A teacher had 16 worksheets to grade and had already graded 8 of them. She has 32 more problems to grade. How many problems are on each worksheet?<|im_end|>
<|im_start|>assistant
<Z_100><Z_65><ANSWER>

Question: A worksheet had some problems on it. A teacher had 16 worksheets to grade and had already graded 8 of them. She has 32 more problems to grade. How many problems are on each worksheet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a is two years older than b, who is twice as old as c, and d is three years younger than a. If the total of the ages of a, b, c, and d is 44, then how old is b?<|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 is two years older than b, who is twice as old as c, and d is three years younger than a. If the total of the ages of a, b, c, and d is 44, then how old is b?<|im_end|>
<|im_start|>assistant
<Z_104><Z_81><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a is two years older than b, who is twice as old as c, and d is three years younger than a. If the total of the ages of a, b, c, and d is 44, then how old is b?<|im_end|>
<|im_start|>assistant
<Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a is two years older than b, who is twice as old as c, and d is three years younger than a. If the total of the ages of a, b, c, and d is 44, then how old is b?<|im_end|>
<|im_start|>assistant
<Z_19><Z_104><Z_18><ANSWER>

Question: a is two years older than b, who is twice as old as c, and d is three years younger than a. If the total of the ages of a, b, c, and d is 44, then how old is b?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x)=\frac{ax^2+bx+c}{dx+b}$ with $abcd \neq 0$ and ensuring that no division by zero occurs within its domain, and $f(f(x)) = x$ for all $x$ for which $f$ is defined, what is the expression for $a+d$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x)=\frac{ax^2+bx+c}{dx+b}$ with $abcd \neq 0$ and ensuring that no division by zero occurs within its domain, and $f(f(x)) = x$ for all $x$ for which $f$ is defined, what is the expression for $a+d$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_30><Z_32><Z_108><Z_22><Z_63><Z_8><Z_24><Z_33><Z_114><Z_123><Z_126><Z_107><Z_114><Z_72><Z_88><Z_107><Z_81><Z_59><Z_71><Z_5><Z_48><Z_118><Z_67><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x)=\frac{ax^2+bx+c}{dx+b}$ with $abcd \neq 0$ and ensuring that no division by zero occurs within its domain, and $f(f(x)) = x$ for all $x$ for which $f$ is defined, what is the expression for $a+d$?<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x)=\frac{ax^2+bx+c}{dx+b}$ with $abcd \neq 0$ and ensuring that no division by zero occurs within its domain, and $f(f(x)) = x$ for all $x$ for which $f$ is defined, what is the expression for $a+d$?<|im_end|>
<|im_start|>assistant
<Z_95><Z_19><Z_4><Z_31><Z_96><Z_46><Z_107><Z_126><Z_97><Z_52><Z_8><Z_109><Z_88><Z_99><Z_80><Z_125><Z_96><Z_99><Z_30><Z_39><Z_65><Z_35><Z_0><Z_48><Z_36><ANSWER>

Question: If $f(x)=\frac{ax^2+bx+c}{dx+b}$ with $abcd \neq 0$ and ensuring that no division by zero occurs within its domain, and $f(f(x)) = x$ for all $x$ for which $f$ is defined, what is the expression for $a+d$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let the number of terms in the sequences $\{a_{n}\}$ and $\{b_{n}\}$ be $m$. The distance between the sequences $\{a_{n}\}$ and $\{b_{n}\}$ is defined as $\sum_{i=1}^{m}|a_{i}-b_{i}|$.
$(Ⅰ)$ Find the distance between the sequences $1$, $4$, $6$, $7$ and $3$, $4$, $11$, $8$.
$(Ⅱ)$ Let $A$ be the set of all sequences $\{a_{n}\}$ that satisfy the recursive relation $a_{n+1}=\frac{1+a_{n}}{1-a_{n}}$. Let $\{b_{n}\}$ and $\{c_{n}\}$ be two elements in $A$, both with $m$ terms. If $b_{1}=2$, $c_{1}=3$, and the distance between $\{b_{n}\}$ and $\{c_{n}\}$ is less than $2016$, find the maximum value of $m$.
$(Ⅲ)$ Let $S$ be the set of all $7$-term sequences $\{a_{n}|1\leqslant n\leqslant 7$, $a_{n}=0$ or $1\}$. Let $T\subseteq S$ such that the distance between any two elements in $T$ is greater than or equal to $3$. Prove that the number of elements in $T$ is less than or equal to $16$.<|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
Let the number of terms in the sequences $\{a_{n}\}$ and $\{b_{n}\}$ be $m$. The distance between the sequences $\{a_{n}\}$ and $\{b_{n}\}$ is defined as $\sum_{i=1}^{m}|a_{i}-b_{i}|$.
$(Ⅰ)$ Find the distance between the sequences $1$, $4$, $6$, $7$ and $3$, $4$, $11$, $8$.
$(Ⅱ)$ Let $A$ be the set of all sequences $\{a_{n}\}$ that satisfy the recursive relation $a_{n+1}=\frac{1+a_{n}}{1-a_{n}}$. Let $\{b_{n}\}$ and $\{c_{n}\}$ be two elements in $A$, both with $m$ terms. If $b_{1}=2$, $c_{1}=3$, and the distance between $\{b_{n}\}$ and $\{c_{n}\}$ is less than $2016$, find the maximum value of $m$.
$(Ⅲ)$ Let $S$ be the set of all $7$-term sequences $\{a_{n}|1\leqslant n\leqslant 7$, $a_{n}=0$ or $1\}$. Let $T\subseteq S$ such that the distance between any two elements in $T$ is greater than or equal to $3$. Prove that the number of elements in $T$ is less than or equal to $16$.<|im_end|>
<|im_start|>assistant
<Z_29><Z_4><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let the number of terms in the sequences $\{a_{n}\}$ and $\{b_{n}\}$ be $m$. The distance between the sequences $\{a_{n}\}$ and $\{b_{n}\}$ is defined as $\sum_{i=1}^{m}|a_{i}-b_{i}|$.
$(Ⅰ)$ Find the distance between the sequences $1$, $4$, $6$, $7$ and $3$, $4$, $11$, $8$.
$(Ⅱ)$ Let $A$ be the set of all sequences $\{a_{n}\}$ that satisfy the recursive relation $a_{n+1}=\frac{1+a_{n}}{1-a_{n}}$. Let $\{b_{n}\}$ and $\{c_{n}\}$ be two elements in $A$, both with $m$ terms. If $b_{1}=2$, $c_{1}=3$, and the distance between $\{b_{n}\}$ and $\{c_{n}\}$ is less than $2016$, find the maximum value of $m$.
$(Ⅲ)$ Let $S$ be the set of all $7$-term sequences $\{a_{n}|1\leqslant n\leqslant 7$, $a_{n}=0$ or $1\}$. Let $T\subseteq S$ such that the distance between any two elements in $T$ is greater than or equal to $3$. Prove that the number of elements in $T$ is less than or equal to $16$.<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let the number of terms in the sequences $\{a_{n}\}$ and $\{b_{n}\}$ be $m$. The distance between the sequences $\{a_{n}\}$ and $\{b_{n}\}$ is defined as $\sum_{i=1}^{m}|a_{i}-b_{i}|$.
$(Ⅰ)$ Find the distance between the sequences $1$, $4$, $6$, $7$ and $3$, $4$, $11$, $8$.
$(Ⅱ)$ Let $A$ be the set of all sequences $\{a_{n}\}$ that satisfy the recursive relation $a_{n+1}=\frac{1+a_{n}}{1-a_{n}}$. Let $\{b_{n}\}$ and $\{c_{n}\}$ be two elements in $A$, both with $m$ terms. If $b_{1}=2$, $c_{1}=3$, and the distance between $\{b_{n}\}$ and $\{c_{n}\}$ is less than $2016$, find the maximum value of $m$.
$(Ⅲ)$ Let $S$ be the set of all $7$-term sequences $\{a_{n}|1\leqslant n\leqslant 7$, $a_{n}=0$ or $1\}$. Let $T\subseteq S$ such that the distance between any two elements in $T$ is greater than or equal to $3$. Prove that the number of elements in $T$ is less than or equal to $16$.<|im_end|>
<|im_start|>assistant
<Z_4><Z_44><Z_24><ANSWER>

Question:
Let the number of terms in the sequences $\{a_{n}\}$ and $\{b_{n}\}$ be $m$. The distance between the sequences $\{a_{n}\}$ and $\{b_{n}\}$ is defined as $\sum_{i=1}^{m}|a_{i}-b_{i}|$.
$(Ⅰ)$ Find the distance between the sequences $1$, $4$, $6$, $7$ and $3$, $4$, $11$, $8$.
$(Ⅱ)$ Let $A$ be the set of all sequences $\{a_{n}\}$ that satisfy the recursive relation $a_{n+1}=\frac{1+a_{n}}{1-a_{n}}$. Let $\{b_{n}\}$ and $\{c_{n}\}$ be two elements in $A$, both with $m$ terms. If $b_{1}=2$, $c_{1}=3$, and the distance between $\{b_{n}\}$ and $\{c_{n}\}$ is less than $2016$, find the maximum value of $m$.
$(Ⅲ)$ Let $S$ be the set of all $7$-term sequences $\{a_{n}|1\leqslant n\leqslant 7$, $a_{n}=0$ or $1\}$. Let $T\subseteq S$ such that the distance between any two elements in $T$ is greater than or equal to $3$. Prove that the number of elements in $T$ is less than or equal to $16$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?<|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 minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?<|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 minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?<|im_end|>
<|im_start|>assistant
<Z_7><ANSWER>

Question: what is the minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?<|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
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?<|im_end|>
<|im_start|>assistant
<Z_27><Z_13><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?<|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
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?<|im_end|>
<|im_start|>assistant
<Z_73><Z_125><Z_47><ANSWER>

Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Summer, Jolly, Winter, and Autumn all went to the same middle school. When they finished their education, the degrees they earned were in the ratio of 5:4:6:3. If Summer, who had the highest number of degrees, has a total of 150 degrees, what's the combined number of degrees they all have?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Summer, Jolly, Winter, and Autumn all went to the same middle school. When they finished their education, the degrees they earned were in the ratio of 5:4:6:3. If Summer, who had the highest number of degrees, has a total of 150 degrees, what's the combined number of degrees they all have?<|im_end|>
<|im_start|>assistant
<Z_113><Z_65><Z_40><Z_115><Z_32><Z_82><Z_83><Z_66><Z_95><Z_65><Z_119><Z_66><Z_20><Z_33><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Summer, Jolly, Winter, and Autumn all went to the same middle school. When they finished their education, the degrees they earned were in the ratio of 5:4:6:3. If Summer, who had the highest number of degrees, has a total of 150 degrees, what's the combined number of degrees they all have?<|im_end|>
<|im_start|>assistant
<Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Summer, Jolly, Winter, and Autumn all went to the same middle school. When they finished their education, the degrees they earned were in the ratio of 5:4:6:3. If Summer, who had the highest number of degrees, has a total of 150 degrees, what's the combined number of degrees they all have?<|im_end|>
<|im_start|>assistant
<Z_11><Z_43><Z_44><Z_93><Z_49><Z_95><Z_75><Z_122><Z_98><Z_0><Z_65><Z_68><Z_110><Z_82><Z_15><ANSWER>

Question: Summer, Jolly, Winter, and Autumn all went to the same middle school. When they finished their education, the degrees they earned were in the ratio of 5:4:6:3. If Summer, who had the highest number of degrees, has a total of 150 degrees, what's the combined number of degrees they all have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is some amount. The total number of workers in the workshop is 42. What is the average salary of the rest of the workers?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is some amount. The total number of workers in the workshop is 42. What is the average salary of the rest of the workers?<|im_end|>
<|im_start|>assistant
<Z_94><Z_73><Z_58><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is some amount. The total number of workers in the workshop is 42. What is the average salary of the rest of the workers?<|im_end|>
<|im_start|>assistant
<Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is some amount. The total number of workers in the workshop is 42. What is the average salary of the rest of the workers?<|im_end|>
<|im_start|>assistant
<Z_33><Z_81><Z_114><Z_125><ANSWER>

Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is some amount. The total number of workers in the workshop is 42. What is the average salary of the rest of the workers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From the following infinite list of numbers, how many are integers? $$\sqrt{2401},\sqrt[3]{2401},\sqrt[4]{2401},\sqrt[5]{2401},\sqrt[6]{2401},\ldots$$<|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
From the following infinite list of numbers, how many are integers? $$\sqrt{2401},\sqrt[3]{2401},\sqrt[4]{2401},\sqrt[5]{2401},\sqrt[6]{2401},\ldots$$<|im_end|>
<|im_start|>assistant
<Z_94><Z_64><Z_107><Z_120><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From the following infinite list of numbers, how many are integers? $$\sqrt{2401},\sqrt[3]{2401},\sqrt[4]{2401},\sqrt[5]{2401},\sqrt[6]{2401},\ldots$$<|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
From the following infinite list of numbers, how many are integers? $$\sqrt{2401},\sqrt[3]{2401},\sqrt[4]{2401},\sqrt[5]{2401},\sqrt[6]{2401},\ldots$$<|im_end|>
<|im_start|>assistant
<Z_100><Z_39><Z_115><Z_107><Z_0><ANSWER>

Question: From the following infinite list of numbers, how many are integers? $$\sqrt{2401},\sqrt[3]{2401},\sqrt[4]{2401},\sqrt[5]{2401},\sqrt[6]{2401},\ldots$$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different three-letter sets of initials are possible using the letters A through J, if the letter J cannot be the first initial?<|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 three-letter sets of initials are possible using the letters A through J, if the letter J cannot be the first initial?<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_115><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different three-letter sets of initials are possible using the letters A through J, if the letter J cannot be the first initial?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different three-letter sets of initials are possible using the letters A through J, if the letter J cannot be the first initial?<|im_end|>
<|im_start|>assistant
<Z_56><Z_95><Z_41><Z_48><ANSWER>

Question: How many different three-letter sets of initials are possible using the letters A through J, if the letter J cannot be the first initial?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Use $\left[x\right]$ to represent the largest integer not greater than $x$, for example, $\left[2.4\right]=2$, $\left[-3.1\right]=-4$. Please calculate $[{5.5}]+[{-4\frac{1}{2}}]=$____.<|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
Use $\left[x\right]$ to represent the largest integer not greater than $x$, for example, $\left[2.4\right]=2$, $\left[-3.1\right]=-4$. Please calculate $[{5.5}]+[{-4\frac{1}{2}}]=$____.<|im_end|>
<|im_start|>assistant
<Z_105><Z_74><Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Use $\left[x\right]$ to represent the largest integer not greater than $x$, for example, $\left[2.4\right]=2$, $\left[-3.1\right]=-4$. Please calculate $[{5.5}]+[{-4\frac{1}{2}}]=$____.<|im_end|>
<|im_start|>assistant
<Z_13><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Use $\left[x\right]$ to represent the largest integer not greater than $x$, for example, $\left[2.4\right]=2$, $\left[-3.1\right]=-4$. Please calculate $[{5.5}]+[{-4\frac{1}{2}}]=$____.<|im_end|>
<|im_start|>assistant
<Z_116><Z_97><Z_69><ANSWER>

Question: Use $\left[x\right]$ to represent the largest integer not greater than $x$, for example, $\left[2.4\right]=2$, $\left[-3.1\right]=-4$. Please calculate $[{5.5}]+[{-4\frac{1}{2}}]=$____.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paige's team won their dodgeball game and scored 81 points in total. The team scored through the following methods: hitting opponents with the ball (2 points each), catching opponents' throws (5 points each), and eliminating all players in an opponent's team (10 points). If Paige scored 21 points through a combination of hitting and catching, and her teammate Brian scored 20 points through a combination of catching and eliminating opponents' teams, how many points did each of Karen, Jennifer, and Michael individually score in the game, considering that none of them scored any points by eliminating an opponent's team?<|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
Paige's team won their dodgeball game and scored 81 points in total. The team scored through the following methods: hitting opponents with the ball (2 points each), catching opponents' throws (5 points each), and eliminating all players in an opponent's team (10 points). If Paige scored 21 points through a combination of hitting and catching, and her teammate Brian scored 20 points through a combination of catching and eliminating opponents' teams, how many points did each of Karen, Jennifer, and Michael individually score in the game, considering that none of them scored any points by eliminating an opponent's team?<|im_end|>
<|im_start|>assistant
<Z_104><Z_59><Z_33><Z_120><Z_26><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paige's team won their dodgeball game and scored 81 points in total. The team scored through the following methods: hitting opponents with the ball (2 points each), catching opponents' throws (5 points each), and eliminating all players in an opponent's team (10 points). If Paige scored 21 points through a combination of hitting and catching, and her teammate Brian scored 20 points through a combination of catching and eliminating opponents' teams, how many points did each of Karen, Jennifer, and Michael individually score in the game, considering that none of them scored any points by eliminating an opponent's team?<|im_end|>
<|im_start|>assistant
<Z_42><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paige's team won their dodgeball game and scored 81 points in total. The team scored through the following methods: hitting opponents with the ball (2 points each), catching opponents' throws (5 points each), and eliminating all players in an opponent's team (10 points). If Paige scored 21 points through a combination of hitting and catching, and her teammate Brian scored 20 points through a combination of catching and eliminating opponents' teams, how many points did each of Karen, Jennifer, and Michael individually score in the game, considering that none of them scored any points by eliminating an opponent's team?<|im_end|>
<|im_start|>assistant
<Z_56><Z_94><Z_46><Z_17><Z_6><Z_9><ANSWER>

Question: Paige's team won their dodgeball game and scored 81 points in total. The team scored through the following methods: hitting opponents with the ball (2 points each), catching opponents' throws (5 points each), and eliminating all players in an opponent's team (10 points). If Paige scored 21 points through a combination of hitting and catching, and her teammate Brian scored 20 points through a combination of catching and eliminating opponents' teams, how many points did each of Karen, Jennifer, and Michael individually score in the game, considering that none of them scored any points by eliminating an opponent's team?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive $c$ such that $c$ is a multiple of $6$ and $c$ is a multiple of $15$.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive $c$ such that $c$ is a multiple of $6$ and $c$ is a multiple of $15$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_96><Z_32><Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive $c$ such that $c$ is a multiple of $6$ and $c$ is a multiple of $15$.<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive $c$ such that $c$ is a multiple of $6$ and $c$ is a multiple of $15$.<|im_end|>
<|im_start|>assistant
<Z_9><Z_89><Z_118><Z_9><Z_46><ANSWER>

Question: Find the smallest positive $c$ such that $c$ is a multiple of $6$ and $c$ is a multiple of $15$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a group of 86 students, each student is registered for at least one of 3 classes – history, math and English. Some students are registered for history, 20 - 3 students are registered for math, and forty - 4 students are registered for English. Only 3 students are registered for all 3 classes. There are 3 students registered for exactly two classes. How many students are registered for history?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a group of 86 students, each student is registered for at least one of 3 classes – history, math and English. Some students are registered for history, 20 - 3 students are registered for math, and forty - 4 students are registered for English. Only 3 students are registered for all 3 classes. There are 3 students registered for exactly two classes. How many students are registered for history?<|im_end|>
<|im_start|>assistant
<Z_104><Z_86><Z_124><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a group of 86 students, each student is registered for at least one of 3 classes – history, math and English. Some students are registered for history, 20 - 3 students are registered for math, and forty - 4 students are registered for English. Only 3 students are registered for all 3 classes. There are 3 students registered for exactly two classes. How many students are registered for history?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a group of 86 students, each student is registered for at least one of 3 classes – history, math and English. Some students are registered for history, 20 - 3 students are registered for math, and forty - 4 students are registered for English. Only 3 students are registered for all 3 classes. There are 3 students registered for exactly two classes. How many students are registered for history?<|im_end|>
<|im_start|>assistant
<Z_114><Z_32><Z_99><Z_60><ANSWER>

Question: In a group of 86 students, each student is registered for at least one of 3 classes – history, math and English. Some students are registered for history, 20 - 3 students are registered for math, and forty - 4 students are registered for English. Only 3 students are registered for all 3 classes. There are 3 students registered for exactly two classes. How many students are registered for history?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Brooke has 15 math problems, some social studies problems, and 10 science problems for homework. He can answer each math problem for 2 minutes, each social studies problem for 30 seconds, and each science problem for 1.5 minutes. It takes Brooke 48 minutes to answer all his homework. How many social studies problems does he have?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Brooke has 15 math problems, some social studies problems, and 10 science problems for homework. He can answer each math problem for 2 minutes, each social studies problem for 30 seconds, and each science problem for 1.5 minutes. It takes Brooke 48 minutes to answer all his homework. How many social studies problems does he have?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Brooke has 15 math problems, some social studies problems, and 10 science problems for homework. He can answer each math problem for 2 minutes, each social studies problem for 30 seconds, and each science problem for 1.5 minutes. It takes Brooke 48 minutes to answer all his homework. How many social studies problems does he have?<|im_end|>
<|im_start|>assistant
<Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Brooke has 15 math problems, some social studies problems, and 10 science problems for homework. He can answer each math problem for 2 minutes, each social studies problem for 30 seconds, and each science problem for 1.5 minutes. It takes Brooke 48 minutes to answer all his homework. How many social studies problems does he have?<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

Question: Brooke has 15 math problems, some social studies problems, and 10 science problems for homework. He can answer each math problem for 2 minutes, each social studies problem for 30 seconds, and each science problem for 1.5 minutes. It takes Brooke 48 minutes to answer all his homework. How many social studies problems does he have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $XYZ$ is an isosceles triangle with side lengths of 13, 13, and 24 centimeters. What is the area of triangle $XYZ$, in square centimeters?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $XYZ$ is an isosceles triangle with side lengths of 13, 13, and 24 centimeters. What is the area of triangle $XYZ$, in square centimeters?<|im_end|>
<|im_start|>assistant
<Z_94><Z_114><Z_72><Z_73><Z_36><Z_33><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $XYZ$ is an isosceles triangle with side lengths of 13, 13, and 24 centimeters. What is the area of triangle $XYZ$, in square centimeters?<|im_end|>
<|im_start|>assistant
<Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Triangle $XYZ$ is an isosceles triangle with side lengths of 13, 13, and 24 centimeters. What is the area of triangle $XYZ$, in square centimeters?<|im_end|>
<|im_start|>assistant
<Z_72><Z_70><Z_90><Z_29><Z_107><Z_23><Z_64><ANSWER>

Question: Triangle $XYZ$ is an isosceles triangle with side lengths of 13, 13, and 24 centimeters. What is the area of triangle $XYZ$, in square centimeters?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Garcia family consists of two adults (Mr. and Mrs. Garcia), their two children with the eldest being responsible enough to drive, and their grandmother who does not drive. When driving somewhere together in their car, two people sit in the front including the driver, while the three others sit in the back. The driver must be either Mr. Garcia, Mrs. Garcia, or the eldest child. How many seating arrangements are possible?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Garcia family consists of two adults (Mr. and Mrs. Garcia), their two children with the eldest being responsible enough to drive, and their grandmother who does not drive. When driving somewhere together in their car, two people sit in the front including the driver, while the three others sit in the back. The driver must be either Mr. Garcia, Mrs. Garcia, or the eldest child. How many seating arrangements are possible?<|im_end|>
<|im_start|>assistant
<Z_94><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The Garcia family consists of two adults (Mr. and Mrs. Garcia), their two children with the eldest being responsible enough to drive, and their grandmother who does not drive. When driving somewhere together in their car, two people sit in the front including the driver, while the three others sit in the back. The driver must be either Mr. Garcia, Mrs. Garcia, or the eldest child. How many seating arrangements are possible?<|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
The Garcia family consists of two adults (Mr. and Mrs. Garcia), their two children with the eldest being responsible enough to drive, and their grandmother who does not drive. When driving somewhere together in their car, two people sit in the front including the driver, while the three others sit in the back. The driver must be either Mr. Garcia, Mrs. Garcia, or the eldest child. How many seating arrangements are possible?<|im_end|>
<|im_start|>assistant
<Z_59><Z_90><ANSWER>

Question: The Garcia family consists of two adults (Mr. and Mrs. Garcia), their two children with the eldest being responsible enough to drive, and their grandmother who does not drive. When driving somewhere together in their car, two people sit in the front including the driver, while the three others sit in the back. The driver must be either Mr. Garcia, Mrs. Garcia, or the eldest child. How many seating arrangements are possible?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 8x^3 - 20x^2 + 28x - 30 \) is divided by \( 4x - 8 \)?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 8x^3 - 20x^2 + 28x - 30 \) is divided by \( 4x - 8 \)?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 8x^3 - 20x^2 + 28x - 30 \) is divided by \( 4x - 8 \)?<|im_end|>
<|im_start|>assistant
<Z_14><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 8x^3 - 20x^2 + 28x - 30 \) is divided by \( 4x - 8 \)?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

Question: What is the remainder when \( 8x^3 - 20x^2 + 28x - 30 \) is divided by \( 4x - 8 \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The base $8$ representation of a positive integer is $AB$ and its base $5$ representation is $BA$. What is the integer expressed in base $10$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The base $8$ representation of a positive integer is $AB$ and its base $5$ representation is $BA$. What is the integer expressed in base $10$?<|im_end|>
<|im_start|>assistant
<Z_113><Z_120><Z_47><Z_36><Z_91><Z_99><Z_76><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The base $8$ representation of a positive integer is $AB$ and its base $5$ representation is $BA$. What is the integer expressed in base $10$?<|im_end|>
<|im_start|>assistant
<Z_117><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The base $8$ representation of a positive integer is $AB$ and its base $5$ representation is $BA$. What is the integer expressed in base $10$?<|im_end|>
<|im_start|>assistant
<Z_102><Z_15><Z_34><Z_38><Z_112><Z_114><Z_120><Z_73><ANSWER>

Question: The base $8$ representation of a positive integer is $AB$ and its base $5$ representation is $BA$. What is the integer expressed in base $10$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For what maximum integer \( n \) do two solutions of the equation \( x^3 - (n+9)x^2 + (2n^2 - 3n - 34)x + 2(n-4)(n+3) = 0 \) exceed 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
For what maximum integer \( n \) do two solutions of the equation \( x^3 - (n+9)x^2 + (2n^2 - 3n - 34)x + 2(n-4)(n+3) = 0 \) exceed 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
For what maximum integer \( n \) do two solutions of the equation \( x^3 - (n+9)x^2 + (2n^2 - 3n - 34)x + 2(n-4)(n+3) = 0 \) exceed 2?<|im_end|>
<|im_start|>assistant
<Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For what maximum integer \( n \) do two solutions of the equation \( x^3 - (n+9)x^2 + (2n^2 - 3n - 34)x + 2(n-4)(n+3) = 0 \) exceed 2?<|im_end|>
<|im_start|>assistant
<Z_88><ANSWER>

Question: For what maximum integer \( n \) do two solutions of the equation \( x^3 - (n+9)x^2 + (2n^2 - 3n - 34)x + 2(n-4)(n+3) = 0 \) exceed 2?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \[g(n) =
\begin{cases}
n^2 + 2n - 1 & \text{ if } n < 5,
\\ 2n + 3 & \text{ if } n \geq 5.
\end{cases}
\]Find $g(g(g(3)))$.<|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 \[g(n) =
\begin{cases}
n^2 + 2n - 1 & \text{ if } n < 5,
\\ 2n + 3 & \text{ if } n \geq 5.
\end{cases}
\]Find $g(g(g(3)))$.<|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
Let \[g(n) =
\begin{cases}
n^2 + 2n - 1 & \text{ if } n < 5,
\\ 2n + 3 & \text{ if } n \geq 5.
\end{cases}
\]Find $g(g(g(3)))$.<|im_end|>
<|im_start|>assistant
<Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \[g(n) =
\begin{cases}
n^2 + 2n - 1 & \text{ if } n < 5,
\\ 2n + 3 & \text{ if } n \geq 5.
\end{cases}
\]Find $g(g(g(3)))$.<|im_end|>
<|im_start|>assistant
<Z_79><ANSWER>

Question:
Let \[g(n) =
\begin{cases}
n^2 + 2n - 1 & \text{ if } n < 5,
\\ 2n + 3 & \text{ if } n \geq 5.
\end{cases}
\]Find $g(g(g(3)))$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the remainder if 7 ^ 4 is divided by 100 ?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the remainder if 7 ^ 4 is divided by 100 ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_97><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the remainder if 7 ^ 4 is divided by 100 ?<|im_end|>
<|im_start|>assistant
<Z_9><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the remainder if 7 ^ 4 is divided by 100 ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_8><Z_116><ANSWER>

Question: what is the remainder if 7 ^ 4 is divided by 100 ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five plastic bottles are required to make a new bottle. How many new bottles can eventually be made from 625 plastic bottles, assuming that at least three bottles are needed to start a recycling process? Do not include the original 625 bottles in your count.<|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
Five plastic bottles are required to make a new bottle. How many new bottles can eventually be made from 625 plastic bottles, assuming that at least three bottles are needed to start a recycling process? Do not include the original 625 bottles in your count.<|im_end|>
<|im_start|>assistant
<Z_57><Z_107><Z_86><Z_40><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five plastic bottles are required to make a new bottle. How many new bottles can eventually be made from 625 plastic bottles, assuming that at least three bottles are needed to start a recycling process? Do not include the original 625 bottles in your count.<|im_end|>
<|im_start|>assistant
<Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five plastic bottles are required to make a new bottle. How many new bottles can eventually be made from 625 plastic bottles, assuming that at least three bottles are needed to start a recycling process? Do not include the original 625 bottles in your count.<|im_end|>
<|im_start|>assistant
<Z_101><Z_71><Z_105><Z_54><Z_29><ANSWER>

Question: Five plastic bottles are required to make a new bottle. How many new bottles can eventually be made from 625 plastic bottles, assuming that at least three bottles are needed to start a recycling process? Do not include the original 625 bottles in your count.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train 560 m in length crosses a telegraph post in a certain amount of time. The speed of the train is 126 km/h. How many seconds does it take for the train to cross the telegraph post?<|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 560 m in length crosses a telegraph post in a certain amount of time. The speed of the train is 126 km/h. How many seconds does it take for the train to cross the telegraph post?<|im_end|>
<|im_start|>assistant
<Z_57><Z_73><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 560 m in length crosses a telegraph post in a certain amount of time. The speed of the train is 126 km/h. How many seconds does it take for the train to cross the telegraph post?<|im_end|>
<|im_start|>assistant
<Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train 560 m in length crosses a telegraph post in a certain amount of time. The speed of the train is 126 km/h. How many seconds does it take for the train to cross the telegraph post?<|im_end|>
<|im_start|>assistant
<Z_53><Z_104><Z_36><ANSWER>

Question: A train 560 m in length crosses a telegraph post in a certain amount of time. The speed of the train is 126 km/h. How many seconds does it take for the train to cross the telegraph post?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Acme T-Shirt Company charges a $\$80$ set-up fee plus $\$10$ for each shirt printed. Beta T-shirt Company charges a $\$20$ set up fee, but charges $\$15$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?<|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
Acme T-Shirt Company charges a $\$80$ set-up fee plus $\$10$ for each shirt printed. Beta T-shirt Company charges a $\$20$ set up fee, but charges $\$15$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?<|im_end|>
<|im_start|>assistant
<Z_104><Z_107><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Acme T-Shirt Company charges a $\$80$ set-up fee plus $\$10$ for each shirt printed. Beta T-shirt Company charges a $\$20$ set up fee, but charges $\$15$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?<|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
Acme T-Shirt Company charges a $\$80$ set-up fee plus $\$10$ for each shirt printed. Beta T-shirt Company charges a $\$20$ set up fee, but charges $\$15$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?<|im_end|>
<|im_start|>assistant
<Z_112><Z_60><Z_34><ANSWER>

Question: Acme T-Shirt Company charges a $\$80$ set-up fee plus $\$10$ for each shirt printed. Beta T-shirt Company charges a $\$20$ set up fee, but charges $\$15$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An escalator moves towards the top level at the rate of 15 ft/sec and its length is 180 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the rate at which the person walks on the escalator?<|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
An escalator moves towards the top level at the rate of 15 ft/sec and its length is 180 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the rate at which the person walks on the escalator?<|im_end|>
<|im_start|>assistant
<Z_94><Z_59><Z_93><Z_58><Z_37><Z_114><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An escalator moves towards the top level at the rate of 15 ft/sec and its length is 180 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the rate at which the person walks on the escalator?<|im_end|>
<|im_start|>assistant
<Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An escalator moves towards the top level at the rate of 15 ft/sec and its length is 180 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the rate at which the person walks on the escalator?<|im_end|>
<|im_start|>assistant
<Z_22><Z_100><Z_89><Z_66><Z_76><Z_34><Z_39><ANSWER>

Question: An escalator moves towards the top level at the rate of 15 ft/sec and its length is 180 feet. If a person walks on the moving escalator at a certain rate towards the top level, he takes 10 seconds to cover the entire length. What is the rate at which the person walks on the escalator?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To asphalt a 1 km road, 30 men spent 12 days working 8 hours per day. It takes a certain number of men working 9 hours a day 32 days to asphalt a road of 2 km. How many men are working on the second road?<|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 asphalt a 1 km road, 30 men spent 12 days working 8 hours per day. It takes a certain number of men working 9 hours a day 32 days to asphalt a road of 2 km. How many men are working on the second road?<|im_end|>
<|im_start|>assistant
<Z_104><Z_73><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To asphalt a 1 km road, 30 men spent 12 days working 8 hours per day. It takes a certain number of men working 9 hours a day 32 days to asphalt a road of 2 km. How many men are working on the second road?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To asphalt a 1 km road, 30 men spent 12 days working 8 hours per day. It takes a certain number of men working 9 hours a day 32 days to asphalt a road of 2 km. How many men are working on the second road?<|im_end|>
<|im_start|>assistant
<Z_16><Z_96><Z_20><ANSWER>

Question: To asphalt a 1 km road, 30 men spent 12 days working 8 hours per day. It takes a certain number of men working 9 hours a day 32 days to asphalt a road of 2 km. How many men are working on the second road?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?<|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
arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?<|im_end|>
<|im_start|>assistant
<Z_113><Z_89><Z_91><Z_37><Z_20><Z_12><Z_19><Z_118><Z_9><Z_6><Z_22><Z_103><Z_93><Z_80><Z_56><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?<|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
arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?<|im_end|>
<|im_start|>assistant
<Z_74><Z_39><Z_95><Z_46><Z_95><Z_102><Z_63><Z_61><Z_59><Z_79><Z_56><Z_91><Z_111><Z_114><Z_81><Z_57><ANSWER>

Question: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when 2,345,678,901 is divided by 101?<|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 remainder when 2,345,678,901 is divided by 101?<|im_end|>
<|im_start|>assistant
<Z_113><Z_89><Z_103><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when 2,345,678,901 is divided by 101?<|im_end|>
<|im_start|>assistant
<Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when 2,345,678,901 is divided by 101?<|im_end|>
<|im_start|>assistant
<Z_119><Z_124><Z_34><Z_42><ANSWER>

Question: What is the remainder when 2,345,678,901 is divided by 101?