<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 7?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 7?<|im_end|>
<|im_start|>assistant
<Z_104><Z_105><Z_80><Z_88><Z_55><Z_54><Z_76><Z_16><Z_126><Z_65><Z_118><Z_26><Z_22><Z_101><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 7?<|im_end|>
<|im_start|>assistant
<Z_105><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 7?<|im_end|>
<|im_start|>assistant
<Z_1><Z_78><Z_42><Z_79><Z_60><Z_96><Z_101><Z_21><Z_18><Z_62><Z_121><Z_74><Z_65><Z_121><Z_73><ANSWER>

Question: What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 7?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of all the integer solutions of the equation $x^4 - 13x^2 + 36 = 0$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of all the integer solutions of the equation $x^4 - 13x^2 + 36 = 0$.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of all the integer solutions of the equation $x^4 - 13x^2 + 36 = 0$.<|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
Find the sum of all the integer solutions of the equation $x^4 - 13x^2 + 36 = 0$.<|im_end|>
<|im_start|>assistant
<Z_110><ANSWER>

Question: Find the sum of all the integer solutions of the equation $x^4 - 13x^2 + 36 = 0$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The school level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The school level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?<|im_end|>
<|im_start|>assistant
<Z_104><Z_41><Z_108><Z_87><Z_12><Z_48><Z_92><Z_41><Z_20><Z_76><Z_17><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The school level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?<|im_end|>
<|im_start|>assistant
<Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The school level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?<|im_end|>
<|im_start|>assistant
<Z_99><Z_30><Z_17><Z_54><Z_54><Z_53><Z_6><Z_58><Z_58><Z_62><Z_120><Z_48><ANSWER>

Question:
The school level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(x\) be a positive real number. Find the minimum value of \(9x^7 + 4x^{-6}.\)<|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 \(x\) be a positive real number. Find the minimum value of \(9x^7 + 4x^{-6}.\)<|im_end|>
<|im_start|>assistant
<Z_94><Z_68><Z_51><Z_47><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(x\) be a positive real number. Find the minimum value of \(9x^7 + 4x^{-6}.\)<|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
Let \(x\) be a positive real number. Find the minimum value of \(9x^7 + 4x^{-6}.\)<|im_end|>
<|im_start|>assistant
<Z_49><Z_39><Z_6><Z_41><Z_3><ANSWER>

Question: Let \(x\) be a positive real number. Find the minimum value of \(9x^7 + 4x^{-6}.\)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. The typical dosage is some cubic centimeters per 15 pounds of body weight. The prescribed dosage was 25% lesser than the typical dosage. What is the typical dosage in cubic centimeters per 15 pounds of body weight?<|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 doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. The typical dosage is some cubic centimeters per 15 pounds of body weight. The prescribed dosage was 25% lesser than the typical dosage. What is the typical dosage in cubic centimeters per 15 pounds of body weight?<|im_end|>
<|im_start|>assistant
<Z_57><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
A doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. The typical dosage is some cubic centimeters per 15 pounds of body weight. The prescribed dosage was 25% lesser than the typical dosage. What is the typical dosage in cubic centimeters per 15 pounds of body weight?<|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 doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. The typical dosage is some cubic centimeters per 15 pounds of body weight. The prescribed dosage was 25% lesser than the typical dosage. What is the typical dosage in cubic centimeters per 15 pounds of body weight?<|im_end|>
<|im_start|>assistant
<Z_122><Z_93><Z_62><ANSWER>

Question: A doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. The typical dosage is some cubic centimeters per 15 pounds of body weight. The prescribed dosage was 25% lesser than the typical dosage. What is the typical dosage in cubic centimeters per 15 pounds of body weight?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If there are four times as many apples as oranges and three times as many bananas as oranges in a certain fruit basket, and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 3/5 of the apples, 2/3 of the oranges, and 4/7 of the bananas present in the basket?<|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 there are four times as many apples as oranges and three times as many bananas as oranges in a certain fruit basket, and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 3/5 of the apples, 2/3 of the oranges, and 4/7 of the bananas present in the basket?<|im_end|>
<|im_start|>assistant
<Z_113><Z_58><Z_64><Z_63><Z_124><Z_66><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If there are four times as many apples as oranges and three times as many bananas as oranges in a certain fruit basket, and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 3/5 of the apples, 2/3 of the oranges, and 4/7 of the bananas present in the basket?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If there are four times as many apples as oranges and three times as many bananas as oranges in a certain fruit basket, and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 3/5 of the apples, 2/3 of the oranges, and 4/7 of the bananas present in the basket?<|im_end|>
<|im_start|>assistant
<Z_101><Z_118><Z_83><Z_88><Z_9><Z_24><Z_16><ANSWER>

Question: If there are four times as many apples as oranges and three times as many bananas as oranges in a certain fruit basket, and the basket has 15 apples, how many fruits would Emiliano have consumed if he eats 3/5 of the apples, 2/3 of the oranges, and 4/7 of the bananas present in the basket?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The cross section of a canal is trapezium in shape. The canal is a certain width at the top and 8 m wide at the bottom. The area of the cross section is 840 sq. m, and the depth of the canal is 84 m. What is the width of the canal at the top?<|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 cross section of a canal is trapezium in shape. The canal is a certain width at the top and 8 m wide at the bottom. The area of the cross section is 840 sq. m, and the depth of the canal is 84 m. What is the width of the canal at the top?<|im_end|>
<|im_start|>assistant
<Z_57><Z_82><Z_100><Z_97><Z_97><Z_98><Z_41><Z_31><Z_93><Z_83><Z_41><Z_83><Z_37><Z_76><Z_59><Z_12><Z_72><Z_117><Z_75><Z_119><Z_114><Z_80><Z_80><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The cross section of a canal is trapezium in shape. The canal is a certain width at the top and 8 m wide at the bottom. The area of the cross section is 840 sq. m, and the depth of the canal is 84 m. What is the width of the canal at the top?<|im_end|>
<|im_start|>assistant
<Z_42><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The cross section of a canal is trapezium in shape. The canal is a certain width at the top and 8 m wide at the bottom. The area of the cross section is 840 sq. m, and the depth of the canal is 84 m. What is the width of the canal at the top?<|im_end|>
<|im_start|>assistant
<Z_44><Z_56><Z_114><Z_38><Z_83><Z_32><Z_21><Z_119><Z_121><Z_20><Z_101><Z_103><Z_51><Z_49><Z_79><Z_101><Z_84><Z_70><Z_77><Z_78><Z_14><Z_116><Z_57><Z_82><ANSWER>

Question: The cross section of a canal is trapezium in shape. The canal is a certain width at the top and 8 m wide at the bottom. The area of the cross section is 840 sq. m, and the depth of the canal is 84 m. What is the width of the canal at the top?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).<|im_end|>
<|im_start|>assistant
<Z_113><Z_47><Z_1><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).<|im_end|>
<|im_start|>assistant
<Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).<|im_end|>
<|im_start|>assistant
<Z_82><Z_25><Z_35><Z_87><ANSWER>

Question: Given an odd function \( f(x) \) defined on \(\mathbf{R}\), which satisfies \( f(x) + f(x+2) = a \) and \( f(1) = 0 \), where \( a \) is a constant, determine the minimum number of roots of the equation \( f(x) = 0 \) within the interval \((-3,7)\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the seven-digit number $854n526$ is divisible by $11$, what is $n$?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the seven-digit number $854n526$ is divisible by $11$, what is $n$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_70><Z_110><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the seven-digit number $854n526$ is divisible by $11$, what is $n$?<|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
If the seven-digit number $854n526$ is divisible by $11$, what is $n$?<|im_end|>
<|im_start|>assistant
<Z_9><Z_88><Z_94><Z_6><ANSWER>

Question: If the seven-digit number $854n526$ is divisible by $11$, what is $n$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*<|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
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*<|im_end|>
<|im_start|>assistant
<Z_113><Z_103><Z_114><Z_54><Z_61><Z_95><Z_82><Z_55><Z_83><Z_58><Z_96><Z_88><Z_33><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*<|im_end|>
<|im_start|>assistant
<Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*<|im_end|>
<|im_start|>assistant
<Z_107><Z_112><Z_2><Z_54><Z_94><Z_80><Z_70><Z_34><Z_2><Z_111><Z_119><Z_92><Z_100><Z_27><ANSWER>

Question:
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?<|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 hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?<|im_end|>
<|im_start|>assistant
<Z_29><Z_38><Z_91><Z_63><Z_12><Z_53><Z_20><Z_72><Z_95><Z_87><Z_11><Z_24><Z_101><Z_95><Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?<|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 hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?<|im_end|>
<|im_start|>assistant
<Z_8><Z_16><Z_111><Z_7><Z_83><Z_0><Z_82><Z_106><Z_122><Z_61><Z_44><Z_23><Z_110><Z_5><Z_2><ANSWER>

Question: the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the least positive base ten number which requires six digits for its binary representation?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the least positive base ten number which requires six digits for its binary representation?<|im_end|>
<|im_start|>assistant
<Z_94><Z_36><Z_72><Z_63><Z_65><Z_48><Z_87><Z_76><Z_66><Z_67><Z_72><Z_119><Z_55><Z_66><Z_22><Z_54><Z_90><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the least positive base ten number which requires six digits for its binary representation?<|im_end|>
<|im_start|>assistant
<Z_75><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the least positive base ten number which requires six digits for its binary representation?<|im_end|>
<|im_start|>assistant
<Z_51><Z_52><Z_101><Z_121><Z_73><Z_27><Z_48><Z_90><Z_45><Z_45><Z_40><Z_61><Z_14><Z_4><Z_21><Z_62><Z_36><Z_52><ANSWER>

Question: What is the value of the least positive base ten number which requires six digits for its binary representation?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given 20 distinct points on a plane, excluding seven points that lie on the same line, no three points are collinear. Find out how many lines can be formed by pairing any two of these 20 points.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given 20 distinct points on a plane, excluding seven points that lie on the same line, no three points are collinear. Find out how many lines can be formed by pairing any two of these 20 points.<|im_end|>
<|im_start|>assistant
<Z_94><Z_110><Z_110><Z_41><Z_75><Z_59><Z_9><Z_33><Z_9><Z_115><Z_37><Z_55><Z_34><Z_31><Z_120><Z_76><Z_55><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given 20 distinct points on a plane, excluding seven points that lie on the same line, no three points are collinear. Find out how many lines can be formed by pairing any two of these 20 points.<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given 20 distinct points on a plane, excluding seven points that lie on the same line, no three points are collinear. Find out how many lines can be formed by pairing any two of these 20 points.<|im_end|>
<|im_start|>assistant
<Z_45><Z_120><Z_36><Z_58><Z_53><Z_49><Z_119><Z_23><Z_31><Z_64><Z_38><Z_47><Z_95><Z_106><Z_25><Z_116><Z_109><Z_72><ANSWER>

Question: Given 20 distinct points on a plane, excluding seven points that lie on the same line, no three points are collinear. Find out how many lines can be formed by pairing any two of these 20 points.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :<|im_end|>
<|im_start|>assistant
<Z_104><Z_114><Z_97><Z_126><Z_98><Z_125><Z_53><Z_34><Z_78><Z_92><Z_33><Z_58><Z_53><Z_95><Z_66><Z_55><Z_115><Z_123><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :<|im_end|>
<|im_start|>assistant
<Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :<|im_end|>
<|im_start|>assistant
<Z_65><Z_27><Z_11><Z_87><Z_73><Z_113><Z_77><Z_37><Z_80><Z_47><Z_84><Z_62><Z_20><Z_106><Z_117><Z_30><Z_13><Z_63><Z_100><ANSWER>

Question: a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It costs 10 cents to copy 5 pages. How many pages can you copy for $10?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It costs 10 cents to copy 5 pages. How many pages can you copy for $10?<|im_end|>
<|im_start|>assistant
<Z_104><Z_47><Z_41><Z_119><Z_19><Z_60><Z_90><Z_54><Z_88><Z_61><Z_70><Z_67><Z_16><Z_76><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It costs 10 cents to copy 5 pages. How many pages can you copy for $10?<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It costs 10 cents to copy 5 pages. How many pages can you copy for $10?<|im_end|>
<|im_start|>assistant
<Z_17><Z_29><Z_100><Z_103><Z_110><Z_87><Z_56><Z_125><Z_114><Z_67><Z_115><Z_110><Z_0><Z_41><Z_59><ANSWER>

Question: It costs 10 cents to copy 5 pages. How many pages can you copy for $10?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A judge oversaw thirty-five court cases. Five were immediately dismissed from court. Of the remaining cases, 3/8 were ruled innocent, 1/4 had rulings delayed until a later date, 3/16 were declared mistrials, and the rest were judged guilty. On how many cases did the judge rule guilty?<|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 judge oversaw thirty-five court cases. Five were immediately dismissed from court. Of the remaining cases, 3/8 were ruled innocent, 1/4 had rulings delayed until a later date, 3/16 were declared mistrials, and the rest were judged guilty. On how many cases did the judge rule guilty?<|im_end|>
<|im_start|>assistant
<Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A judge oversaw thirty-five court cases. Five were immediately dismissed from court. Of the remaining cases, 3/8 were ruled innocent, 1/4 had rulings delayed until a later date, 3/16 were declared mistrials, and the rest were judged guilty. On how many cases did the judge rule guilty?<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

Question: A judge oversaw thirty-five court cases. Five were immediately dismissed from court. Of the remaining cases, 3/8 were ruled innocent, 1/4 had rulings delayed until a later date, 3/16 were declared mistrials, and the rest were judged guilty. On how many cases did the judge rule guilty?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon ABCDE has a vertical line of symmetry through CD. What is the $y$-coordinate of vertex C so that the area of the pentagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,20), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

draw(B--C--D--E);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("E(6,0)",E,SE);
label("D(6,6)",D,NE);
label("C",C,NE);
label("B(0,6)",B,NW);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon ABCDE has a vertical line of symmetry through CD. What is the $y$-coordinate of vertex C so that the area of the pentagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,20), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

draw(B--C--D--E);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("E(6,0)",E,SE);
label("D(6,6)",D,NE);
label("C",C,NE);
label("B(0,6)",B,NW);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_57><Z_119><Z_89><Z_65><Z_78><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon ABCDE has a vertical line of symmetry through CD. What is the $y$-coordinate of vertex C so that the area of the pentagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,20), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

draw(B--C--D--E);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("E(6,0)",E,SE);
label("D(6,6)",D,NE);
label("C",C,NE);
label("B(0,6)",B,NW);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_94><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Pentagon ABCDE has a vertical line of symmetry through CD. What is the $y$-coordinate of vertex C so that the area of the pentagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,20), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

draw(B--C--D--E);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("E(6,0)",E,SE);
label("D(6,6)",D,NE);
label("C",C,NE);
label("B(0,6)",B,NW);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_99><Z_42><Z_66><Z_81><Z_62><Z_49><ANSWER>

Question:
Pentagon ABCDE has a vertical line of symmetry through CD. What is the $y$-coordinate of vertex C so that the area of the pentagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,20), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

draw(B--C--D--E);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("E(6,0)",E,SE);
label("D(6,6)",D,NE);
label("C",C,NE);
label("B(0,6)",B,NW);
[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$? [asy]
pair A, B, C, D;
A=(12,0);
D=(0,0);
C=(0,5);
B=(0,9);
draw(A--B--C--A--D--C);
draw((0,.5)--(.5,.5)--(.5,0));
label("$A$", A, dir(-45));
label("$B$", B, dir(135));
label("$C$", C, dir(180));
label("$D$", D, dir(-135));
[/asy]<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$? [asy]
pair A, B, C, D;
A=(12,0);
D=(0,0);
C=(0,5);
B=(0,9);
draw(A--B--C--A--D--C);
draw((0,.5)--(.5,.5)--(.5,0));
label("$A$", A, dir(-45));
label("$B$", B, dir(135));
label("$C$", C, dir(180));
label("$D$", D, dir(-135));
[/asy]<|im_end|>
<|im_start|>assistant
<Z_57><Z_108><Z_106><Z_82><Z_91><Z_63><Z_117><Z_33><Z_70><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 area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$? [asy]
pair A, B, C, D;
A=(12,0);
D=(0,0);
C=(0,5);
B=(0,9);
draw(A--B--C--A--D--C);
draw((0,.5)--(.5,.5)--(.5,0));
label("$A$", A, dir(-45));
label("$B$", B, dir(135));
label("$C$", C, dir(180));
label("$D$", D, dir(-135));
[/asy]<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$? [asy]
pair A, B, C, D;
A=(12,0);
D=(0,0);
C=(0,5);
B=(0,9);
draw(A--B--C--A--D--C);
draw((0,.5)--(.5,.5)--(.5,0));
label("$A$", A, dir(-45));
label("$B$", B, dir(135));
label("$C$", C, dir(180));
label("$D$", D, dir(-135));
[/asy]<|im_end|>
<|im_start|>assistant
<Z_88><Z_10><Z_41><Z_56><Z_118><Z_125><Z_27><Z_0><Z_117><Z_58><ANSWER>

Question:
What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$? [asy]
pair A, B, C, D;
A=(12,0);
D=(0,0);
C=(0,5);
B=(0,9);
draw(A--B--C--A--D--C);
draw((0,.5)--(.5,.5)--(.5,0));
label("$A$", A, dir(-45));
label("$B$", B, dir(135));
label("$C$", C, dir(180));
label("$D$", D, dir(-135));
[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a basketball game, Tobee scored 4 points. Jay scored 6 more than Tobee and Sean scored 2 less than the points of Tobee and Jay together. If Tobee, Jay, and Sean are on the same team, how many points did they score for their 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
In a basketball game, Tobee scored 4 points. Jay scored 6 more than Tobee and Sean scored 2 less than the points of Tobee and Jay together. If Tobee, Jay, and Sean are on the same team, how many points did they score for their team?<|im_end|>
<|im_start|>assistant
<Z_57><Z_34><Z_47><Z_68><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a basketball game, Tobee scored 4 points. Jay scored 6 more than Tobee and Sean scored 2 less than the points of Tobee and Jay together. If Tobee, Jay, and Sean are on the same team, how many points did they score for their team?<|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
In a basketball game, Tobee scored 4 points. Jay scored 6 more than Tobee and Sean scored 2 less than the points of Tobee and Jay together. If Tobee, Jay, and Sean are on the same team, how many points did they score for their team?<|im_end|>
<|im_start|>assistant
<Z_110><Z_38><Z_15><Z_14><Z_74><ANSWER>

Question: In a basketball game, Tobee scored 4 points. Jay scored 6 more than Tobee and Sean scored 2 less than the points of Tobee and Jay together. If Tobee, Jay, and Sean are on the same team, how many points did they score for their team?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an expanded version of Deal or No Deal, participants choose a box at random from a set of $30$ boxes, each containing different predetermined amounts of money ranging from very low to very high. Suppose the amounts are such that eight of these boxes contain at least $200,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a fifty percent chance of holding a box containing at least $200,000$?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an expanded version of Deal or No Deal, participants choose a box at random from a set of $30$ boxes, each containing different predetermined amounts of money ranging from very low to very high. Suppose the amounts are such that eight of these boxes contain at least $200,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a fifty percent chance of holding a box containing at least $200,000$?<|im_end|>
<|im_start|>assistant
<Z_113><Z_74><Z_62><Z_68><Z_123><Z_115><Z_79><Z_99><Z_24><Z_99><Z_17><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an expanded version of Deal or No Deal, participants choose a box at random from a set of $30$ boxes, each containing different predetermined amounts of money ranging from very low to very high. Suppose the amounts are such that eight of these boxes contain at least $200,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a fifty percent chance of holding a box containing at least $200,000$?<|im_end|>
<|im_start|>assistant
<Z_20><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an expanded version of Deal or No Deal, participants choose a box at random from a set of $30$ boxes, each containing different predetermined amounts of money ranging from very low to very high. Suppose the amounts are such that eight of these boxes contain at least $200,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a fifty percent chance of holding a box containing at least $200,000$?<|im_end|>
<|im_start|>assistant
<Z_78><Z_44><Z_53><Z_115><Z_36><Z_48><Z_58><Z_119><Z_105><Z_58><Z_36><ANSWER>

Question: In an expanded version of Deal or No Deal, participants choose a box at random from a set of $30$ boxes, each containing different predetermined amounts of money ranging from very low to very high. Suppose the amounts are such that eight of these boxes contain at least $200,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a fifty percent chance of holding a box containing at least $200,000$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While taking the SAT, you become distracted by your own answer sheet.  Because you are not bound to the College Board's limiting rules, you realize that there are actually  $32$  ways to mark your answer for each question, because you could fight the system and bubble in multiple letters at once: for example, you could mark  $AB$ , or  $AC$ , or  $ABD$ , or even  $ABCDE$ , or nothing at all!

You begin to wonder how many ways you could mark off the 10 questions you haven't yet answered.  To increase the challenge, you wonder how many ways you could mark off the rest of your answer sheet without ever marking the same letter twice in a row.  (For example, if  $ABD$  is marked for one question,  $AC$  cannot be marked for the next one because  $A$  would be marked twice in a row.)  If the number of ways to do this can be expressed in the form  $2^m p^n$ , where  $m,n > 1$  are integers and  $p$  is a prime, compute  $100m+n+p$ .

*Proposed by Alexander Dai*<|im_end|>
<|im_start|>assistant
<Z_104><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While taking the SAT, you become distracted by your own answer sheet.  Because you are not bound to the College Board's limiting rules, you realize that there are actually  $32$  ways to mark your answer for each question, because you could fight the system and bubble in multiple letters at once: for example, you could mark  $AB$ , or  $AC$ , or  $ABD$ , or even  $ABCDE$ , or nothing at all!

You begin to wonder how many ways you could mark off the 10 questions you haven't yet answered.  To increase the challenge, you wonder how many ways you could mark off the rest of your answer sheet without ever marking the same letter twice in a row.  (For example, if  $ABD$  is marked for one question,  $AC$  cannot be marked for the next one because  $A$  would be marked twice in a row.)  If the number of ways to do this can be expressed in the form  $2^m p^n$ , where  $m,n > 1$  are integers and  $p$  is a prime, compute  $100m+n+p$ .

*Proposed by Alexander Dai*<|im_end|>
<|im_start|>assistant
<Z_104><Z_51><Z_58><Z_50><Z_88><Z_65><Z_91><Z_79><Z_99><Z_115><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While taking the SAT, you become distracted by your own answer sheet.  Because you are not bound to the College Board's limiting rules, you realize that there are actually  $32$  ways to mark your answer for each question, because you could fight the system and bubble in multiple letters at once: for example, you could mark  $AB$ , or  $AC$ , or  $ABD$ , or even  $ABCDE$ , or nothing at all!

You begin to wonder how many ways you could mark off the 10 questions you haven't yet answered.  To increase the challenge, you wonder how many ways you could mark off the rest of your answer sheet without ever marking the same letter twice in a row.  (For example, if  $ABD$  is marked for one question,  $AC$  cannot be marked for the next one because  $A$  would be marked twice in a row.)  If the number of ways to do this can be expressed in the form  $2^m p^n$ , where  $m,n > 1$  are integers and  $p$  is a prime, compute  $100m+n+p$ .

*Proposed by Alexander Dai*<|im_end|>
<|im_start|>assistant
<Z_2><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While taking the SAT, you become distracted by your own answer sheet.  Because you are not bound to the College Board's limiting rules, you realize that there are actually  $32$  ways to mark your answer for each question, because you could fight the system and bubble in multiple letters at once: for example, you could mark  $AB$ , or  $AC$ , or  $ABD$ , or even  $ABCDE$ , or nothing at all!

You begin to wonder how many ways you could mark off the 10 questions you haven't yet answered.  To increase the challenge, you wonder how many ways you could mark off the rest of your answer sheet without ever marking the same letter twice in a row.  (For example, if  $ABD$  is marked for one question,  $AC$  cannot be marked for the next one because  $A$  would be marked twice in a row.)  If the number of ways to do this can be expressed in the form  $2^m p^n$ , where  $m,n > 1$  are integers and  $p$  is a prime, compute  $100m+n+p$ .

*Proposed by Alexander Dai*<|im_end|>
<|im_start|>assistant
<Z_101><Z_83><Z_31><Z_2><Z_44><Z_44><Z_77><Z_13><Z_50><Z_109><Z_16><ANSWER>

Question:
While taking the SAT, you become distracted by your own answer sheet.  Because you are not bound to the College Board's limiting rules, you realize that there are actually  $32$  ways to mark your answer for each question, because you could fight the system and bubble in multiple letters at once: for example, you could mark  $AB$ , or  $AC$ , or  $ABD$ , or even  $ABCDE$ , or nothing at all!

You begin to wonder how many ways you could mark off the 10 questions you haven't yet answered.  To increase the challenge, you wonder how many ways you could mark off the rest of your answer sheet without ever marking the same letter twice in a row.  (For example, if  $ABD$  is marked for one question,  $AC$  cannot be marked for the next one because  $A$  would be marked twice in a row.)  If the number of ways to do this can be expressed in the form  $2^m p^n$ , where  $m,n > 1$  are integers and  $p$  is a prime, compute  $100m+n+p$ .

*Proposed by Alexander Dai*


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hefei Shouchun Middle School and Hefei Binhu Shouchun Middle School are the two core educational institutions under the Hefei Shouchun education brand, and they are recruiting students simultaneously this year. They plan to recruit a total of 45 classes with 1800 students for the first year of junior high. Hefei Shouchun Middle School only recruits small classes, while Hefei Binhu Shouchun Middle School recruits both small and large classes, with the number of small classes being twice that of large classes. Each small class has 36 students, and each large class has between 70 and 75 students. How many classes are each school planning to recruit?<|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
Hefei Shouchun Middle School and Hefei Binhu Shouchun Middle School are the two core educational institutions under the Hefei Shouchun education brand, and they are recruiting students simultaneously this year. They plan to recruit a total of 45 classes with 1800 students for the first year of junior high. Hefei Shouchun Middle School only recruits small classes, while Hefei Binhu Shouchun Middle School recruits both small and large classes, with the number of small classes being twice that of large classes. Each small class has 36 students, and each large class has between 70 and 75 students. How many classes are each school planning to recruit?<|im_end|>
<|im_start|>assistant
<Z_94><Z_37><Z_100><Z_91><Z_73><Z_82><Z_80><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hefei Shouchun Middle School and Hefei Binhu Shouchun Middle School are the two core educational institutions under the Hefei Shouchun education brand, and they are recruiting students simultaneously this year. They plan to recruit a total of 45 classes with 1800 students for the first year of junior high. Hefei Shouchun Middle School only recruits small classes, while Hefei Binhu Shouchun Middle School recruits both small and large classes, with the number of small classes being twice that of large classes. Each small class has 36 students, and each large class has between 70 and 75 students. How many classes are each school planning to recruit?<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hefei Shouchun Middle School and Hefei Binhu Shouchun Middle School are the two core educational institutions under the Hefei Shouchun education brand, and they are recruiting students simultaneously this year. They plan to recruit a total of 45 classes with 1800 students for the first year of junior high. Hefei Shouchun Middle School only recruits small classes, while Hefei Binhu Shouchun Middle School recruits both small and large classes, with the number of small classes being twice that of large classes. Each small class has 36 students, and each large class has between 70 and 75 students. How many classes are each school planning to recruit?<|im_end|>
<|im_start|>assistant
<Z_44><Z_2><Z_54><Z_69><Z_9><Z_107><Z_49><Z_24><ANSWER>

Question: Hefei Shouchun Middle School and Hefei Binhu Shouchun Middle School are the two core educational institutions under the Hefei Shouchun education brand, and they are recruiting students simultaneously this year. They plan to recruit a total of 45 classes with 1800 students for the first year of junior high. Hefei Shouchun Middle School only recruits small classes, while Hefei Binhu Shouchun Middle School recruits both small and large classes, with the number of small classes being twice that of large classes. Each small class has 36 students, and each large class has between 70 and 75 students. How many classes are each school planning to recruit?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The lunchroom is full of students: 40% are girls and the remainder are boys. There are 2 monitors for every 15 students. There are a certain number of monitors. Every boy drinks, on average, 1 carton of milk, and every girl drinks, on average, 2 cartons of milk. The students in the lunchroom consume a total of 168 cartons of milk. How many monitors are there?<|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 lunchroom is full of students: 40% are girls and the remainder are boys. There are 2 monitors for every 15 students. There are a certain number of monitors. Every boy drinks, on average, 1 carton of milk, and every girl drinks, on average, 2 cartons of milk. The students in the lunchroom consume a total of 168 cartons of milk. How many monitors are there?<|im_end|>
<|im_start|>assistant
<Z_94><Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The lunchroom is full of students: 40% are girls and the remainder are boys. There are 2 monitors for every 15 students. There are a certain number of monitors. Every boy drinks, on average, 1 carton of milk, and every girl drinks, on average, 2 cartons of milk. The students in the lunchroom consume a total of 168 cartons of milk. How many monitors are there?<|im_end|>
<|im_start|>assistant
<Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The lunchroom is full of students: 40% are girls and the remainder are boys. There are 2 monitors for every 15 students. There are a certain number of monitors. Every boy drinks, on average, 1 carton of milk, and every girl drinks, on average, 2 cartons of milk. The students in the lunchroom consume a total of 168 cartons of milk. How many monitors are there?<|im_end|>
<|im_start|>assistant
<Z_122><Z_63><ANSWER>

Question: The lunchroom is full of students: 40% are girls and the remainder are boys. There are 2 monitors for every 15 students. There are a certain number of monitors. Every boy drinks, on average, 1 carton of milk, and every girl drinks, on average, 2 cartons of milk. The students in the lunchroom consume a total of 168 cartons of milk. How many monitors are there?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Valentine's Day, each male student gave each female student a valentine. It turned out that the number of valentines was 28 more than the total number of students. How many valentines were given?<|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
On Valentine's Day, each male student gave each female student a valentine. It turned out that the number of valentines was 28 more than the total number of students. How many valentines were given?<|im_end|>
<|im_start|>assistant
<Z_106><Z_87><Z_49><Z_124><Z_88><Z_103><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Valentine's Day, each male student gave each female student a valentine. It turned out that the number of valentines was 28 more than the total number of students. How many valentines were given?<|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
On Valentine's Day, each male student gave each female student a valentine. It turned out that the number of valentines was 28 more than the total number of students. How many valentines were given?<|im_end|>
<|im_start|>assistant
<Z_18><Z_122><Z_12><Z_60><Z_122><Z_64><Z_13><ANSWER>

Question: On Valentine's Day, each male student gave each female student a valentine. It turned out that the number of valentines was 28 more than the total number of students. How many valentines were given?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( a > b > c > d \), and \( \frac{1}{a-b} + \frac{1}{h-c} + \frac{1}{c-d} \geq \frac{n}{a-d} \), then the maximum value of the integer \( n \) is ___<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( a > b > c > d \), and \( \frac{1}{a-b} + \frac{1}{h-c} + \frac{1}{c-d} \geq \frac{n}{a-d} \), then the maximum value of the integer \( n \) is ___<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_58><Z_11><Z_39><Z_34><Z_22><Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( a > b > c > d \), and \( \frac{1}{a-b} + \frac{1}{h-c} + \frac{1}{c-d} \geq \frac{n}{a-d} \), then the maximum value of the integer \( n \) is ___<|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
If \( a > b > c > d \), and \( \frac{1}{a-b} + \frac{1}{h-c} + \frac{1}{c-d} \geq \frac{n}{a-d} \), then the maximum value of the integer \( n \) is ___<|im_end|>
<|im_start|>assistant
<Z_107><Z_80><Z_9><Z_1><Z_25><Z_122><Z_117><Z_31><ANSWER>

Question: If \( a > b > c > d \), and \( \frac{1}{a-b} + \frac{1}{h-c} + \frac{1}{c-d} \geq \frac{n}{a-d} \), then the maximum value of the integer \( n \) is ___


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all positive integers less than 200 that are squares of perfect squares?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all positive integers less than 200 that are squares of perfect squares?<|im_end|>
<|im_start|>assistant
<Z_104><Z_27><Z_77><Z_106><Z_50><Z_58><Z_87><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all positive integers less than 200 that are squares of perfect squares?<|im_end|>
<|im_start|>assistant
<Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of all positive integers less than 200 that are squares of perfect squares?<|im_end|>
<|im_start|>assistant
<Z_32><Z_15><Z_61><Z_82><Z_82><Z_25><Z_89><Z_15><ANSWER>

Question: What is the sum of all positive integers less than 200 that are squares of perfect squares?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let
\[ A = 123456 \]
and
\[ B = 769230 \]
Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let
\[ A = 123456 \]
and
\[ B = 769230 \]
Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.<|im_end|>
<|im_start|>assistant
<Z_113><Z_115><Z_77><Z_40><Z_99><Z_37><Z_53><Z_76><Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let
\[ A = 123456 \]
and
\[ B = 769230 \]
Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.<|im_end|>
<|im_start|>assistant
<Z_35><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let
\[ A = 123456 \]
and
\[ B = 769230 \]
Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.<|im_end|>
<|im_start|>assistant
<Z_100><Z_113><Z_61><Z_61><Z_76><Z_105><Z_43><Z_101><Z_89><ANSWER>

Question:
Let
\[ A = 123456 \]
and
\[ B = 769230 \]
Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><Z_40><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?<|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
in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?<|im_end|>
<|im_start|>assistant
<Z_20><Z_34><Z_86><Z_56><ANSWER>

Question: in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=2^{x}+ \frac {1}{2^{x}-1}$ $(x > 0)$, find the minimum value of $f(x)$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=2^{x}+ \frac {1}{2^{x}-1}$ $(x > 0)$, find the minimum value of $f(x)$.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=2^{x}+ \frac {1}{2^{x}-1}$ $(x > 0)$, find the minimum value of $f(x)$.<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x)=2^{x}+ \frac {1}{2^{x}-1}$ $(x > 0)$, find the minimum value of $f(x)$.<|im_end|>
<|im_start|>assistant
<Z_80><ANSWER>

Question: Given the function $f(x)=2^{x}+ \frac {1}{2^{x}-1}$ $(x > 0)$, find the minimum value of $f(x)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a survey of 35 students taking language courses in English, French, or Spanish, Max and Liz are the only two students enrolled in all three courses. Liz notes that the number of students taking solely English is three times the number of students taking solely French. How many students are taking English but not French or Spanish?<|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 survey of 35 students taking language courses in English, French, or Spanish, Max and Liz are the only two students enrolled in all three courses. Liz notes that the number of students taking solely English is three times the number of students taking solely French. How many students are taking English but not French or Spanish?<|im_end|>
<|im_start|>assistant
<Z_104><Z_86><Z_124><Z_80><Z_39><Z_38><Z_125><Z_98><Z_39><Z_41><Z_101><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a survey of 35 students taking language courses in English, French, or Spanish, Max and Liz are the only two students enrolled in all three courses. Liz notes that the number of students taking solely English is three times the number of students taking solely French. How many students are taking English but not French or Spanish?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a survey of 35 students taking language courses in English, French, or Spanish, Max and Liz are the only two students enrolled in all three courses. Liz notes that the number of students taking solely English is three times the number of students taking solely French. How many students are taking English but not French or Spanish?<|im_end|>
<|im_start|>assistant
<Z_92><Z_19><Z_51><Z_8><Z_30><Z_15><Z_5><Z_21><Z_122><Z_91><Z_22><Z_61><ANSWER>

Question: In a survey of 35 students taking language courses in English, French, or Spanish, Max and Liz are the only two students enrolled in all three courses. Liz notes that the number of students taking solely English is three times the number of students taking solely French. How many students are taking English but not French or Spanish?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\frac{6}{b} < x < \frac{10}{b}$, determine the value of $c = \sqrt{x^{2} - 2x + 1} + \sqrt{x^{2} - 6x + 9}$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\frac{6}{b} < x < \frac{10}{b}$, determine the value of $c = \sqrt{x^{2} - 2x + 1} + \sqrt{x^{2} - 6x + 9}$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_74><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\frac{6}{b} < x < \frac{10}{b}$, determine the value of $c = \sqrt{x^{2} - 2x + 1} + \sqrt{x^{2} - 6x + 9}$.<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\frac{6}{b} < x < \frac{10}{b}$, determine the value of $c = \sqrt{x^{2} - 2x + 1} + \sqrt{x^{2} - 6x + 9}$.<|im_end|>
<|im_start|>assistant
<Z_54><Z_38><Z_35><ANSWER>

Question: If $\frac{6}{b} < x < \frac{10}{b}$, determine the value of $c = \sqrt{x^{2} - 2x + 1} + \sqrt{x^{2} - 6x + 9}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?<|im_end|>
<|im_start|>assistant
<Z_94><Z_47><Z_58><Z_65><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?<|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
If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?<|im_end|>
<|im_start|>assistant
<Z_94><Z_68><Z_115><Z_118><Z_21><ANSWER>

Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olga has three stripes on the side of each of her tennis shoes. Rick has a certain number of stripes per shoe. Hortense has double the number of stripes on her tennis shoes as does Olga. The combined number of stripes on all of their pairs of tennis shoes is 22. What is the difference in the number of stripes on Olga's and Rick's tennis shoes?<|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
Olga has three stripes on the side of each of her tennis shoes. Rick has a certain number of stripes per shoe. Hortense has double the number of stripes on her tennis shoes as does Olga. The combined number of stripes on all of their pairs of tennis shoes is 22. What is the difference in the number of stripes on Olga's and Rick's tennis shoes?<|im_end|>
<|im_start|>assistant
<Z_113><Z_119><Z_59><Z_47><Z_66><Z_101><Z_79><Z_41><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olga has three stripes on the side of each of her tennis shoes. Rick has a certain number of stripes per shoe. Hortense has double the number of stripes on her tennis shoes as does Olga. The combined number of stripes on all of their pairs of tennis shoes is 22. What is the difference in the number of stripes on Olga's and Rick's tennis shoes?<|im_end|>
<|im_start|>assistant
<Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olga has three stripes on the side of each of her tennis shoes. Rick has a certain number of stripes per shoe. Hortense has double the number of stripes on her tennis shoes as does Olga. The combined number of stripes on all of their pairs of tennis shoes is 22. What is the difference in the number of stripes on Olga's and Rick's tennis shoes?<|im_end|>
<|im_start|>assistant
<Z_116><Z_76><Z_119><Z_4><Z_108><Z_6><Z_121><Z_80><Z_66><ANSWER>

Question: Olga has three stripes on the side of each of her tennis shoes. Rick has a certain number of stripes per shoe. Hortense has double the number of stripes on her tennis shoes as does Olga. The combined number of stripes on all of their pairs of tennis shoes is 22. What is the difference in the number of stripes on Olga's and Rick's tennis shoes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nhai employs some men to build a highway of 2 km in 50 days working 8 hours a day. In 25 days, they completed 1/3 part of the work. Nhai needs to hire 60 more employees to finish it in time working 10 hours a day. How many men were initially employed by Nhai?<|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
Nhai employs some men to build a highway of 2 km in 50 days working 8 hours a day. In 25 days, they completed 1/3 part of the work. Nhai needs to hire 60 more employees to finish it in time working 10 hours a day. How many men were initially employed by Nhai?<|im_end|>
<|im_start|>assistant
<Z_57><Z_70><Z_81><Z_121><Z_92><Z_78><Z_24><Z_28><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nhai employs some men to build a highway of 2 km in 50 days working 8 hours a day. In 25 days, they completed 1/3 part of the work. Nhai needs to hire 60 more employees to finish it in time working 10 hours a day. How many men were initially employed by Nhai?<|im_end|>
<|im_start|>assistant
<Z_112><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Nhai employs some men to build a highway of 2 km in 50 days working 8 hours a day. In 25 days, they completed 1/3 part of the work. Nhai needs to hire 60 more employees to finish it in time working 10 hours a day. How many men were initially employed by Nhai?<|im_end|>
<|im_start|>assistant
<Z_53><Z_17><Z_122><Z_48><Z_68><Z_1><Z_73><Z_76><Z_120><ANSWER>

Question: Nhai employs some men to build a highway of 2 km in 50 days working 8 hours a day. In 25 days, they completed 1/3 part of the work. Nhai needs to hire 60 more employees to finish it in time working 10 hours a day. How many men were initially employed by Nhai?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $P(x, y)$ is a moving point on the line $y = x$, and $$m= \sqrt {(x-1)^{2}+(y-2)^{2}}+ \sqrt {(x+2)^{2}+(y-1)^{2}}$$, then the minimum value of $m$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $P(x, y)$ is a moving point on the line $y = x$, and $$m= \sqrt {(x-1)^{2}+(y-2)^{2}}+ \sqrt {(x+2)^{2}+(y-1)^{2}}$$, then the minimum value of $m$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_94><Z_77><Z_49><Z_1><Z_1><Z_83><Z_12><Z_83><Z_49><Z_32><Z_54><Z_88><Z_123><Z_72><Z_12><Z_59><Z_58><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $P(x, y)$ is a moving point on the line $y = x$, and $$m= \sqrt {(x-1)^{2}+(y-2)^{2}}+ \sqrt {(x+2)^{2}+(y-1)^{2}}$$, then the minimum value of $m$ is \_\_\_\_\_\_.<|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
Given that $P(x, y)$ is a moving point on the line $y = x$, and $$m= \sqrt {(x-1)^{2}+(y-2)^{2}}+ \sqrt {(x+2)^{2}+(y-1)^{2}}$$, then the minimum value of $m$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_32><Z_84><Z_94><Z_13><Z_17><Z_121><Z_77><Z_92><Z_65><Z_58><Z_58><Z_119><Z_40><Z_78><Z_69><Z_115><Z_40><Z_54><ANSWER>

Question: Given that $P(x, y)$ is a moving point on the line $y = x$, and $$m= \sqrt {(x-1)^{2}+(y-2)^{2}}+ \sqrt {(x+2)^{2}+(y-1)^{2}}$$, then the minimum value of $m$ is \_\_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is.<|im_end|>
<|im_start|>assistant
<Z_57><Z_108><Z_110><Z_108><Z_64><Z_115><Z_65><Z_49><Z_82><Z_39><Z_70><Z_12><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is.<|im_end|>
<|im_start|>assistant
<Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is.<|im_end|>
<|im_start|>assistant
<Z_91><Z_101><Z_104><Z_41><Z_71><Z_28><Z_53><Z_122><Z_116><Z_64><Z_83><Z_70><Z_92><ANSWER>

Question: Three people are sitting in a row of eight seats. If there must be empty seats on both sides of each person, then the number of different seating arrangements is.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a number that is greater than 50 and less than 70. Also, this number has a remainder of 3 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 2 when divided by 8. What is this number?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a number that is greater than 50 and less than 70. Also, this number has a remainder of 3 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 2 when divided by 8. What is this number?<|im_end|>
<|im_start|>assistant
<Z_104><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a number that is greater than 50 and less than 70. Also, this number has a remainder of 3 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 2 when divided by 8. What is this number?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a number that is greater than 50 and less than 70. Also, this number has a remainder of 3 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 2 when divided by 8. What is this number?<|im_end|>
<|im_start|>assistant
<Z_28><Z_114><ANSWER>

Question: There is a number that is greater than 50 and less than 70. Also, this number has a remainder of 3 when divided by 5, a remainder of 2 when divided by 7, and a remainder of 2 when divided by 8. What is this number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tiffany is looking at a lake full of turtles. The turtles are divided into four categories: common, rare, unique, and legendary. The common turtles make up 50% of the turtle population, rare turtles make up 30%, unique turtles make up 15%, and legendary turtles make up the remaining 5%.

Within each category, the turtles are classified into males and females. The percentage of females among common turtles is 60%, among rare turtles is 55%, among unique turtles is 45%, and among legendary turtles is 40%.

Of the male common turtles, 1 in 4 has stripes, while 2 in 5 rare male turtles have stripes. Among unique male turtles, 1 in 3 has stripes, and half of the legendary male turtles have stripes.

Among the striped male turtles in each category, babies make up the following proportions: 20% in common, 25% in rare, 30% in unique, and 35% in legendary. The remaining percentages reflect the adult striped male turtles in each category.

If Tiffany spots 70 striped male adult common turtles, how many turtles are in the lake?<|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
Tiffany is looking at a lake full of turtles. The turtles are divided into four categories: common, rare, unique, and legendary. The common turtles make up 50% of the turtle population, rare turtles make up 30%, unique turtles make up 15%, and legendary turtles make up the remaining 5%.

Within each category, the turtles are classified into males and females. The percentage of females among common turtles is 60%, among rare turtles is 55%, among unique turtles is 45%, and among legendary turtles is 40%.

Of the male common turtles, 1 in 4 has stripes, while 2 in 5 rare male turtles have stripes. Among unique male turtles, 1 in 3 has stripes, and half of the legendary male turtles have stripes.

Among the striped male turtles in each category, babies make up the following proportions: 20% in common, 25% in rare, 30% in unique, and 35% in legendary. The remaining percentages reflect the adult striped male turtles in each category.

If Tiffany spots 70 striped male adult common turtles, how many turtles are in the lake?<|im_end|>
<|im_start|>assistant
<Z_94><Z_49><Z_65><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tiffany is looking at a lake full of turtles. The turtles are divided into four categories: common, rare, unique, and legendary. The common turtles make up 50% of the turtle population, rare turtles make up 30%, unique turtles make up 15%, and legendary turtles make up the remaining 5%.

Within each category, the turtles are classified into males and females. The percentage of females among common turtles is 60%, among rare turtles is 55%, among unique turtles is 45%, and among legendary turtles is 40%.

Of the male common turtles, 1 in 4 has stripes, while 2 in 5 rare male turtles have stripes. Among unique male turtles, 1 in 3 has stripes, and half of the legendary male turtles have stripes.

Among the striped male turtles in each category, babies make up the following proportions: 20% in common, 25% in rare, 30% in unique, and 35% in legendary. The remaining percentages reflect the adult striped male turtles in each category.

If Tiffany spots 70 striped male adult common turtles, how many turtles are in the lake?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tiffany is looking at a lake full of turtles. The turtles are divided into four categories: common, rare, unique, and legendary. The common turtles make up 50% of the turtle population, rare turtles make up 30%, unique turtles make up 15%, and legendary turtles make up the remaining 5%.

Within each category, the turtles are classified into males and females. The percentage of females among common turtles is 60%, among rare turtles is 55%, among unique turtles is 45%, and among legendary turtles is 40%.

Of the male common turtles, 1 in 4 has stripes, while 2 in 5 rare male turtles have stripes. Among unique male turtles, 1 in 3 has stripes, and half of the legendary male turtles have stripes.

Among the striped male turtles in each category, babies make up the following proportions: 20% in common, 25% in rare, 30% in unique, and 35% in legendary. The remaining percentages reflect the adult striped male turtles in each category.

If Tiffany spots 70 striped male adult common turtles, how many turtles are in the lake?<|im_end|>
<|im_start|>assistant
<Z_1><Z_52><Z_26><Z_19><ANSWER>

Question:
Tiffany is looking at a lake full of turtles. The turtles are divided into four categories: common, rare, unique, and legendary. The common turtles make up 50% of the turtle population, rare turtles make up 30%, unique turtles make up 15%, and legendary turtles make up the remaining 5%.

Within each category, the turtles are classified into males and females. The percentage of females among common turtles is 60%, among rare turtles is 55%, among unique turtles is 45%, and among legendary turtles is 40%.

Of the male common turtles, 1 in 4 has stripes, while 2 in 5 rare male turtles have stripes. Among unique male turtles, 1 in 3 has stripes, and half of the legendary male turtles have stripes.

Among the striped male turtles in each category, babies make up the following proportions: 20% in common, 25% in rare, 30% in unique, and 35% in legendary. The remaining percentages reflect the adult striped male turtles in each category.

If Tiffany spots 70 striped male adult common turtles, how many turtles are in the lake?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence consists of all positive multiples of 3 that contain at least one digit that is a 1 or 2. What is the $50^{\mathrm{th}}$ term of this new sequence?<|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 sequence consists of all positive multiples of 3 that contain at least one digit that is a 1 or 2. What is the $50^{\mathrm{th}}$ term of this new sequence?<|im_end|>
<|im_start|>assistant
<Z_113><Z_58><Z_88><Z_87><Z_49><Z_73><Z_41><Z_22><Z_124><Z_98><Z_124><Z_67><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence consists of all positive multiples of 3 that contain at least one digit that is a 1 or 2. What is the $50^{\mathrm{th}}$ term of this new sequence?<|im_end|>
<|im_start|>assistant
<Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence consists of all positive multiples of 3 that contain at least one digit that is a 1 or 2. What is the $50^{\mathrm{th}}$ term of this new sequence?<|im_end|>
<|im_start|>assistant
<Z_93><Z_12><Z_5><Z_11><Z_81><Z_104><Z_48><Z_53><Z_120><Z_110><Z_48><Z_26><Z_51><ANSWER>

Question: The sequence consists of all positive multiples of 3 that contain at least one digit that is a 1 or 2. What is the $50^{\mathrm{th}}$ term of this new sequence?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Anya washes some hairs down the drain when she washes her hair and brushes out half that amount when she brushes it. Anya has to grow back 49 hairs to always have one more hair than she started with after washing, brushing, and growing it. How many hairs does Anya wash down the drain when she washes her hair?<|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
Anya washes some hairs down the drain when she washes her hair and brushes out half that amount when she brushes it. Anya has to grow back 49 hairs to always have one more hair than she started with after washing, brushing, and growing it. How many hairs does Anya wash down the drain when she washes her hair?<|im_end|>
<|im_start|>assistant
<Z_94><Z_65><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Anya washes some hairs down the drain when she washes her hair and brushes out half that amount when she brushes it. Anya has to grow back 49 hairs to always have one more hair than she started with after washing, brushing, and growing it. How many hairs does Anya wash down the drain when she washes her hair?<|im_end|>
<|im_start|>assistant
<Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Anya washes some hairs down the drain when she washes her hair and brushes out half that amount when she brushes it. Anya has to grow back 49 hairs to always have one more hair than she started with after washing, brushing, and growing it. How many hairs does Anya wash down the drain when she washes her hair?<|im_end|>
<|im_start|>assistant
<Z_99><Z_106><Z_58><ANSWER>

Question: Anya washes some hairs down the drain when she washes her hair and brushes out half that amount when she brushes it. Anya has to grow back 49 hairs to always have one more hair than she started with after washing, brushing, and growing it. How many hairs does Anya wash down the drain when she washes her hair?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A parametric graph is defined by the equations:
\[
x = 2\cos t + t, \\
y = 3\sin t.
\]
Determine the number of times the graph intersects itself for $x$ between $1$ and $100$.<|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 parametric graph is defined by the equations:
\[
x = 2\cos t + t, \\
y = 3\sin t.
\]
Determine the number of times the graph intersects itself for $x$ between $1$ and $100$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_72><Z_31><Z_59><Z_62><Z_70><Z_34><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A parametric graph is defined by the equations:
\[
x = 2\cos t + t, \\
y = 3\sin t.
\]
Determine the number of times the graph intersects itself for $x$ between $1$ and $100$.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A parametric graph is defined by the equations:
\[
x = 2\cos t + t, \\
y = 3\sin t.
\]
Determine the number of times the graph intersects itself for $x$ between $1$ and $100$.<|im_end|>
<|im_start|>assistant
<Z_116><Z_101><Z_4><Z_18><Z_50><Z_101><Z_54><Z_41><ANSWER>

Question:
A parametric graph is defined by the equations:
\[
x = 2\cos t + t, \\
y = 3\sin t.
\]
Determine the number of times the graph intersects itself for $x$ between $1$ and $100$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :<|im_end|>
<|im_start|>assistant
<Z_57><Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :<|im_end|>
<|im_start|>assistant
<Z_41><Z_108><ANSWER>

Question: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.<|im_end|>
<|im_start|>assistant
<Z_94><Z_51><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.<|im_end|>
<|im_start|>assistant
<Z_57><Z_93><Z_66><Z_70><Z_73><Z_78><Z_91><Z_119><Z_114><Z_96><Z_39><Z_76><Z_76><Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.<|im_end|>
<|im_start|>assistant
<Z_113><Z_21><Z_54><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.<|im_end|>
<|im_start|>assistant
<Z_9><Z_90><Z_102><Z_114><Z_6><Z_31><Z_95><Z_121><Z_51><Z_77><Z_119><Z_108><Z_0><Z_103><ANSWER>

Question:
Candidates should choose and solve only one of the three sub-problems below. If more than one is answered, only the first one will be graded.
1. If the solution set of the inequality $|x-1|+|x-m|<2m$ is empty, the range of values for $m$ is ____________.
2. The length of the chord cut by the curve $\begin{cases} x=2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (with $\theta$ as the parameter) from the line $3x-4y-1=0$ is ____________.
3. If the incircle of the right triangle $\triangle ABC$ is tangent to the hypotenuse $AB$ at point $D$, and $AD=1$, $BD=2$, then the area of $\triangle ABC$ is ____________.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake delivers some newspapers a week. Miranda delivers twice as many newspapers a week. Miranda delivers 936 more newspapers than Jake in a month. How many newspapers does Jake deliver in a week?<|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
Jake delivers some newspapers a week. Miranda delivers twice as many newspapers a week. Miranda delivers 936 more newspapers than Jake in a month. How many newspapers does Jake deliver in a week?<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><Z_74><Z_72><Z_81><Z_45><Z_34><Z_93><Z_20><Z_92><Z_70><Z_80><Z_28><Z_61><Z_9><Z_75><Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake delivers some newspapers a week. Miranda delivers twice as many newspapers a week. Miranda delivers 936 more newspapers than Jake in a month. How many newspapers does Jake deliver in a week?<|im_end|>
<|im_start|>assistant
<Z_7><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jake delivers some newspapers a week. Miranda delivers twice as many newspapers a week. Miranda delivers 936 more newspapers than Jake in a month. How many newspapers does Jake deliver in a week?<|im_end|>
<|im_start|>assistant
<Z_90><Z_114><Z_110><Z_74><Z_31><Z_90><Z_2><Z_77><Z_95><Z_123><Z_104><Z_90><Z_4><Z_15><Z_19><Z_86><Z_82><ANSWER>

Question: Jake delivers some newspapers a week. Miranda delivers twice as many newspapers a week. Miranda delivers 936 more newspapers than Jake in a month. How many newspapers does Jake deliver in a week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the arithmetic sequence $\{a_n\}$, it is given that $a_1 + a_2 + a_3 = -24$ and $a_{18} + a_{19} + a_{20} = 78$. Find the sum of the first 20 terms of this sequence.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the arithmetic sequence $\{a_n\}$, it is given that $a_1 + a_2 + a_3 = -24$ and $a_{18} + a_{19} + a_{20} = 78$. Find the sum of the first 20 terms of this sequence.<|im_end|>
<|im_start|>assistant
<Z_113><Z_107><Z_110><Z_41><Z_89><Z_92><Z_70><Z_72><Z_120><Z_38><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the arithmetic sequence $\{a_n\}$, it is given that $a_1 + a_2 + a_3 = -24$ and $a_{18} + a_{19} + a_{20} = 78$. Find the sum of the first 20 terms of this sequence.<|im_end|>
<|im_start|>assistant
<Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the arithmetic sequence $\{a_n\}$, it is given that $a_1 + a_2 + a_3 = -24$ and $a_{18} + a_{19} + a_{20} = 78$. Find the sum of the first 20 terms of this sequence.<|im_end|>
<|im_start|>assistant
<Z_51><Z_32><Z_104><Z_12><Z_87><Z_55><Z_36><Z_26><Z_43><Z_21><Z_84><ANSWER>

Question: In the arithmetic sequence $\{a_n\}$, it is given that $a_1 + a_2 + a_3 = -24$ and $a_{18} + a_{19} + a_{20} = 78$. Find the sum of the first 20 terms of this sequence.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Place five cards numbered 1 through 5 into five boxes labeled 1 through 5, putting exactly one card in each box. How many ways can this be done such that card number 2 is not in box 2 and card number 4 is not in box 4?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Place five cards numbered 1 through 5 into five boxes labeled 1 through 5, putting exactly one card in each box. How many ways can this be done such that card number 2 is not in box 2 and card number 4 is not in box 4?<|im_end|>
<|im_start|>assistant
<Z_57><Z_107><Z_88><Z_89><Z_33><Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Place five cards numbered 1 through 5 into five boxes labeled 1 through 5, putting exactly one card in each box. How many ways can this be done such that card number 2 is not in box 2 and card number 4 is not in box 4?<|im_end|>
<|im_start|>assistant
<Z_6><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Place five cards numbered 1 through 5 into five boxes labeled 1 through 5, putting exactly one card in each box. How many ways can this be done such that card number 2 is not in box 2 and card number 4 is not in box 4?<|im_end|>
<|im_start|>assistant
<Z_102><Z_20><Z_25><Z_94><Z_16><Z_38><ANSWER>

Question: Place five cards numbered 1 through 5 into five boxes labeled 1 through 5, putting exactly one card in each box. How many ways can this be done such that card number 2 is not in box 2 and card number 4 is not in box 4?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the $x^4$ term in the expansion of the binomial $(4x^{2}-2x+1)(2x+1)^{5}$.<|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 coefficient of the $x^4$ term in the expansion of the binomial $(4x^{2}-2x+1)(2x+1)^{5}$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the $x^4$ term in the expansion of the binomial $(4x^{2}-2x+1)(2x+1)^{5}$.<|im_end|>
<|im_start|>assistant
<Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the coefficient of the $x^4$ term in the expansion of the binomial $(4x^{2}-2x+1)(2x+1)^{5}$.<|im_end|>
<|im_start|>assistant
<Z_91><Z_75><ANSWER>

Question: Find the coefficient of the $x^4$ term in the expansion of the binomial $(4x^{2}-2x+1)(2x+1)^{5}$.