<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( R \) be a semicircle with diameter \( XY \). A trapezoid \( ABCD \) in which \( AB \) is parallel to \( CD \) is circumscribed about \( R \) such that \( AB \) contains \( XY \). If \( AD = 4 \), \( CD = 5 \), and \( BC = 6 \), determine \( AB \).<|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 \( R \) be a semicircle with diameter \( XY \). A trapezoid \( ABCD \) in which \( AB \) is parallel to \( CD \) is circumscribed about \( R \) such that \( AB \) contains \( XY \). If \( AD = 4 \), \( CD = 5 \), and \( BC = 6 \), determine \( AB \).<|im_end|>
<|im_start|>assistant
<Z_113><Z_89><Z_29><Z_89><Z_70><Z_125><Z_76><Z_70><Z_19><Z_75><Z_38><Z_39><Z_124><Z_59><Z_73><Z_103><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( R \) be a semicircle with diameter \( XY \). A trapezoid \( ABCD \) in which \( AB \) is parallel to \( CD \) is circumscribed about \( R \) such that \( AB \) contains \( XY \). If \( AD = 4 \), \( CD = 5 \), and \( BC = 6 \), determine \( AB \).<|im_end|>
<|im_start|>assistant
<Z_19><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( R \) be a semicircle with diameter \( XY \). A trapezoid \( ABCD \) in which \( AB \) is parallel to \( CD \) is circumscribed about \( R \) such that \( AB \) contains \( XY \). If \( AD = 4 \), \( CD = 5 \), and \( BC = 6 \), determine \( AB \).<|im_end|>
<|im_start|>assistant
<Z_39><Z_55><Z_82><Z_70><Z_2><Z_6><Z_63><Z_80><Z_15><Z_102><Z_66><Z_96><Z_32><Z_61><Z_80><Z_9><Z_5><ANSWER>

Question: Let \( R \) be a semicircle with diameter \( XY \). A trapezoid \( ABCD \) in which \( AB \) is parallel to \( CD \) is circumscribed about \( R \) such that \( AB \) contains \( XY \). If \( AD = 4 \), \( CD = 5 \), and \( BC = 6 \), determine \( AB \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Express $343_{8} - 265_{7}$ as a base 10 integer.<|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
Express $343_{8} - 265_{7}$ as a base 10 integer.<|im_end|>
<|im_start|>assistant
<Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Express $343_{8} - 265_{7}$ as a base 10 integer.<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

Question: Express $343_{8} - 265_{7}$ as a base 10 integer.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P \) be a polynomial with integer coefficients such that \( P(0)+P(90)=2018 \). Find the least possible value for \( |P(20)+P(70)| \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P \) be a polynomial with integer coefficients such that \( P(0)+P(90)=2018 \). Find the least possible value for \( |P(20)+P(70)| \).<|im_end|>
<|im_start|>assistant
<Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( P \) be a polynomial with integer coefficients such that \( P(0)+P(90)=2018 \). Find the least possible value for \( |P(20)+P(70)| \).<|im_end|>
<|im_start|>assistant
<Z_67><ANSWER>

Question: Let \( P \) be a polynomial with integer coefficients such that \( P(0)+P(90)=2018 \). Find the least possible value for \( |P(20)+P(70)| \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer 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
if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><Z_81><Z_107><Z_89><Z_100><Z_37><Z_30><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is<|im_end|>
<|im_start|>assistant
<Z_21><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is<|im_end|>
<|im_start|>assistant
<Z_31><Z_72><Z_87><Z_39><Z_9><Z_25><Z_68><Z_10><Z_3><ANSWER>

Question: if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a car has two front tires with a diameter of 10 inches, and two rear tires with a diameter of 12 inches, what is the least common multiple of the total number of revolutions made by each set of tires when the car travels 1/2 mile?<|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 a car has two front tires with a diameter of 10 inches, and two rear tires with a diameter of 12 inches, what is the least common multiple of the total number of revolutions made by each set of tires when the car travels 1/2 mile?<|im_end|>
<|im_start|>assistant
<Z_113><Z_62><Z_43><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a car has two front tires with a diameter of 10 inches, and two rear tires with a diameter of 12 inches, what is the least common multiple of the total number of revolutions made by each set of tires when the car travels 1/2 mile?<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a car has two front tires with a diameter of 10 inches, and two rear tires with a diameter of 12 inches, what is the least common multiple of the total number of revolutions made by each set of tires when the car travels 1/2 mile?<|im_end|>
<|im_start|>assistant
<Z_22><Z_84><Z_31><Z_123><ANSWER>

Question: If a car has two front tires with a diameter of 10 inches, and two rear tires with a diameter of 12 inches, what is the least common multiple of the total number of revolutions made by each set of tires when the car travels 1/2 mile?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Linda is building a new hotel with two wings. The first wing has 9 floors and each floor has 6 halls each with 32 rooms. The second wing has 7 floors each with some halls with 40 rooms each. The hotel has a total of 4248 rooms. How many halls are on each floor of the second wing?<|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
Linda is building a new hotel with two wings. The first wing has 9 floors and each floor has 6 halls each with 32 rooms. The second wing has 7 floors each with some halls with 40 rooms each. The hotel has a total of 4248 rooms. How many halls are on each floor of the second wing?<|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
Linda is building a new hotel with two wings. The first wing has 9 floors and each floor has 6 halls each with 32 rooms. The second wing has 7 floors each with some halls with 40 rooms each. The hotel has a total of 4248 rooms. How many halls are on each floor of the second wing?<|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
Linda is building a new hotel with two wings. The first wing has 9 floors and each floor has 6 halls each with 32 rooms. The second wing has 7 floors each with some halls with 40 rooms each. The hotel has a total of 4248 rooms. How many halls are on each floor of the second wing?<|im_end|>
<|im_start|>assistant
<Z_90><ANSWER>

Question: Linda is building a new hotel with two wings. The first wing has 9 floors and each floor has 6 halls each with 32 rooms. The second wing has 7 floors each with some halls with 40 rooms each. The hotel has a total of 4248 rooms. How many halls are on each floor of the second wing?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the arithmetic sequence $21, x, y, z, 53$, what is the value of $y$?<|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 the arithmetic sequence $21, x, y, z, 53$, what is the value of $y$?<|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 $21, x, y, z, 53$, what is the value of $y$?<|im_end|>
<|im_start|>assistant
<Z_80><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 $21, x, y, z, 53$, what is the value of $y$?<|im_end|>
<|im_start|>assistant
<Z_115><ANSWER>

Question: In the arithmetic sequence $21, x, y, z, 53$, what is the value of $y$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.<|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 student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.<|im_end|>
<|im_start|>assistant
<Z_113><Z_81><Z_81><Z_120><Z_100><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.<|im_end|>
<|im_start|>assistant
<Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.<|im_end|>
<|im_start|>assistant
<Z_13><Z_78><Z_75><Z_2><Z_60><Z_6><ANSWER>

Question: A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The weights of 10 students are 41, 48, 50, 53, 49, 50, 53, 53, 51, 67 (in kg). The range of this set of data is ____ kg.<|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 weights of 10 students are 41, 48, 50, 53, 49, 50, 53, 53, 51, 67 (in kg). The range of this set of data is ____ kg.<|im_end|>
<|im_start|>assistant
<Z_57><Z_108><Z_119><Z_68><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The weights of 10 students are 41, 48, 50, 53, 49, 50, 53, 53, 51, 67 (in kg). The range of this set of data is ____ kg.<|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
The weights of 10 students are 41, 48, 50, 53, 49, 50, 53, 53, 51, 67 (in kg). The range of this set of data is ____ kg.<|im_end|>
<|im_start|>assistant
<Z_56><Z_10><Z_87><Z_77><Z_3><ANSWER>

Question: The weights of 10 students are 41, 48, 50, 53, 49, 50, 53, 53, 51, 67 (in kg). The range of this set of data is ____ kg.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The polynomial
$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The polynomial
$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_86><Z_65><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The polynomial
$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The polynomial
$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.<|im_end|>
<|im_start|>assistant
<Z_54><Z_38><Z_67><Z_72><ANSWER>

Question:
The polynomial
$$g(x) = x^3 - x^2 - (m^2 + m) x + 2m^2 + 4m + 2$$is divisible by $x-4$ and all of its zeroes are integers. Find all possible values of $m$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There were 17 fewer children than adults on the train at the first station. At the next station, 57 adults and 18 children got on and 44 got off. If there are 502 people on the train right now, how many adults got on the train at the first station?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There were 17 fewer children than adults on the train at the first station. At the next station, 57 adults and 18 children got on and 44 got off. If there are 502 people on the train right now, how many adults got on the train at the first station?<|im_end|>
<|im_start|>assistant
<Z_57><Z_30><Z_1><Z_41><Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There were 17 fewer children than adults on the train at the first station. At the next station, 57 adults and 18 children got on and 44 got off. If there are 502 people on the train right now, how many adults got on the train at the first station?<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There were 17 fewer children than adults on the train at the first station. At the next station, 57 adults and 18 children got on and 44 got off. If there are 502 people on the train right now, how many adults got on the train at the first station?<|im_end|>
<|im_start|>assistant
<Z_72><Z_34><Z_123><Z_96><Z_60><ANSWER>

Question: There were 17 fewer children than adults on the train at the first station. At the next station, 57 adults and 18 children got on and 44 got off. If there are 502 people on the train right now, how many adults got on the train at the first station?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum and product of the distinct prime factors of 420?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum and product of the distinct prime factors of 420?<|im_end|>
<|im_start|>assistant
<Z_57><Z_62><Z_41><Z_107><Z_80><Z_114><Z_59><Z_95><Z_126><Z_92><Z_53><Z_56><Z_65><Z_103><Z_80><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 and product of the distinct prime factors of 420?<|im_end|>
<|im_start|>assistant
<Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum and product of the distinct prime factors of 420?<|im_end|>
<|im_start|>assistant
<Z_17><Z_22><Z_8><Z_72><Z_121><Z_19><Z_104><Z_15><Z_51><Z_57><Z_122><Z_97><Z_52><Z_43><Z_27><ANSWER>

Question: What is the sum and product of the distinct prime factors of 420?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can the digits of 1225 be arranged to get a four-digit multiple of 5?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can the digits of 1225 be arranged to get a four-digit multiple of 5?<|im_end|>
<|im_start|>assistant
<Z_106><Z_105><Z_82><Z_107><Z_47><Z_78><Z_37><Z_41><Z_49><Z_124><Z_114><Z_41><Z_93><Z_41><Z_115><Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can the digits of 1225 be arranged to get a four-digit multiple of 5?<|im_end|>
<|im_start|>assistant
<Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can the digits of 1225 be arranged to get a four-digit multiple of 5?<|im_end|>
<|im_start|>assistant
<Z_52><Z_108><Z_21><Z_50><Z_51><Z_56><Z_9><Z_112><Z_122><Z_4><Z_117><Z_12><Z_118><Z_9><Z_21><Z_92><ANSWER>

Question: In how many ways can the digits of 1225 be arranged to get a four-digit multiple of 5?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute: $\boxed{0.027\;^{- \frac {1}{3}}-(- \frac {1}{7})^{-2}+256\;^{ \frac {3}{4}}-3^{-1}+( \sqrt {2}-1)^{0}} \_\_\_\_\_\_ \;\;.$<|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
Compute: $\boxed{0.027\;^{- \frac {1}{3}}-(- \frac {1}{7})^{-2}+256\;^{ \frac {3}{4}}-3^{-1}+( \sqrt {2}-1)^{0}} \_\_\_\_\_\_ \;\;.$<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

Question: Compute: $\boxed{0.027\;^{- \frac {1}{3}}-(- \frac {1}{7})^{-2}+256\;^{ \frac {3}{4}}-3^{-1}+( \sqrt {2}-1)^{0}} \_\_\_\_\_\_ \;\;.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the longest possible sequence of distinct positive integers with the first member 1 and the last member 31 such that each member is divisible by its predecessor? How many such sequences have this length?<|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 longest possible sequence of distinct positive integers with the first member 1 and the last member 31 such that each member is divisible by its predecessor? How many such sequences have this length?<|im_end|>
<|im_start|>assistant
<Z_57><Z_106><Z_91><Z_119><Z_30><Z_92><Z_36><Z_80><Z_101><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the longest possible sequence of distinct positive integers with the first member 1 and the last member 31 such that each member is divisible by its predecessor? How many such sequences have this length?<|im_end|>
<|im_start|>assistant
<Z_26><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the longest possible sequence of distinct positive integers with the first member 1 and the last member 31 such that each member is divisible by its predecessor? How many such sequences have this length?<|im_end|>
<|im_start|>assistant
<Z_91><Z_116><Z_127><Z_105><Z_111><Z_3><Z_118><Z_127><Z_33><Z_43><ANSWER>

Question: What is the longest possible sequence of distinct positive integers with the first member 1 and the last member 31 such that each member is divisible by its predecessor? How many such sequences have this length?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mia is at a picnic with six other friends. They decide to play a team game and need to form teams of four. However, only four people can be on a team. How many different teams of four can the seven of them form?<|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
Mia is at a picnic with six other friends. They decide to play a team game and need to form teams of four. However, only four people can be on a team. How many different teams of four can the seven of them form?<|im_end|>
<|im_start|>assistant
<Z_94><Z_62><Z_34><Z_114><Z_31><Z_87><Z_117><Z_96><Z_70><Z_22><Z_39><Z_79><Z_33><Z_59><Z_10><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mia is at a picnic with six other friends. They decide to play a team game and need to form teams of four. However, only four people can be on a team. How many different teams of four can the seven of them form?<|im_end|>
<|im_start|>assistant
<Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mia is at a picnic with six other friends. They decide to play a team game and need to form teams of four. However, only four people can be on a team. How many different teams of four can the seven of them form?<|im_end|>
<|im_start|>assistant
<Z_88><Z_110><Z_100><Z_22><Z_110><Z_105><Z_68><Z_72><Z_115><Z_40><Z_102><Z_99><Z_50><Z_32><Z_72><Z_87><ANSWER>

Question: Mia is at a picnic with six other friends. They decide to play a team game and need to form teams of four. However, only four people can be on a team. How many different teams of four can the seven of them form?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If x > 0, x / some number + x / 25 is 6% of x. What is the number?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If x > 0, x / some number + x / 25 is 6% of x. What is the number?<|im_end|>
<|im_start|>assistant
<Z_104><Z_100><Z_51><Z_68><Z_124><Z_65><Z_45><Z_16><Z_48><Z_45><Z_24><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If x > 0, x / some number + x / 25 is 6% of x. What is the number?<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If x > 0, x / some number + x / 25 is 6% of x. What is the number?<|im_end|>
<|im_start|>assistant
<Z_65><Z_40><Z_15><Z_82><Z_83><Z_35><Z_63><Z_0><Z_117><Z_108><Z_81><Z_71><ANSWER>

Question: If x > 0, x / some number + x / 25 is 6% of x. What is the number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?<|im_end|>
<|im_start|>assistant
<Z_94><Z_125><Z_68><Z_126><Z_22><Z_58><Z_66><Z_99><Z_53><Z_114><Z_37><Z_60><Z_65><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?<|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
For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?<|im_end|>
<|im_start|>assistant
<Z_90><Z_83><Z_106><Z_18><Z_75><Z_10><Z_102><Z_66><Z_106><Z_127><Z_124><Z_15><Z_2><Z_59><ANSWER>

Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jorge bought some tickets for $7 each. For purchasing so many, he is given a discount of 50%. He spent $84 on tickets. How many tickets did he buy?<|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
Jorge bought some tickets for $7 each. For purchasing so many, he is given a discount of 50%. He spent $84 on tickets. How many tickets did he buy?<|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
Jorge bought some tickets for $7 each. For purchasing so many, he is given a discount of 50%. He spent $84 on tickets. How many tickets did he buy?<|im_end|>
<|im_start|>assistant
<Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jorge bought some tickets for $7 each. For purchasing so many, he is given a discount of 50%. He spent $84 on tickets. How many tickets did he buy?<|im_end|>
<|im_start|>assistant
<Z_63><ANSWER>

Question: Jorge bought some tickets for $7 each. For purchasing so many, he is given a discount of 50%. He spent $84 on tickets. How many tickets did he buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(5, 20)$ and $(11, -8)$ are the coordinates of two opposite vertices of a rectangle, find the sum of the $y$-coordinates of the other two vertices after the rectangle is rotated 90 degrees around its center.<|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 $(5, 20)$ and $(11, -8)$ are the coordinates of two opposite vertices of a rectangle, find the sum of the $y$-coordinates of the other two vertices after the rectangle is rotated 90 degrees around its center.<|im_end|>
<|im_start|>assistant
<Z_104><Z_30><Z_32><Z_64><Z_12><Z_9><Z_99><Z_79><Z_37><Z_60><Z_34><Z_41><Z_20><Z_107><Z_10><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(5, 20)$ and $(11, -8)$ are the coordinates of two opposite vertices of a rectangle, find the sum of the $y$-coordinates of the other two vertices after the rectangle is rotated 90 degrees around its center.<|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
If $(5, 20)$ and $(11, -8)$ are the coordinates of two opposite vertices of a rectangle, find the sum of the $y$-coordinates of the other two vertices after the rectangle is rotated 90 degrees around its center.<|im_end|>
<|im_start|>assistant
<Z_34><Z_2><Z_33><Z_12><Z_63><Z_121><Z_38><Z_58><Z_56><Z_108><Z_7><Z_126><Z_84><Z_57><Z_94><Z_127><ANSWER>

Question: If $(5, 20)$ and $(11, -8)$ are the coordinates of two opposite vertices of a rectangle, find the sum of the $y$-coordinates of the other two vertices after the rectangle is rotated 90 degrees around its center.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_78><Z_43><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|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
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_43><Z_97><Z_62><Z_54><Z_39><ANSWER>

Question: For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|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
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_104><Z_37><Z_123><Z_11><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_98><Z_36><Z_61><Z_68><ANSWER>

Question: Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy 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
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_104><Z_13><Z_70><Z_71><Z_89><Z_47><Z_54><Z_39><Z_124><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_64><Z_40><Z_98><Z_4><Z_98><Z_80><Z_9><Z_20><Z_31><Z_79><ANSWER>

Question: Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|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
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_113><Z_121><Z_105><Z_47><Z_9><Z_70><Z_56><Z_93><Z_83><Z_55><Z_96><Z_61><Z_62><Z_121><Z_38><Z_114><Z_52><Z_41><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_94><Z_9><Z_18><Z_79><Z_30><Z_80><Z_97><Z_73><Z_77><Z_38><Z_54><Z_125><Z_67><Z_74><Z_53><Z_86><Z_115><Z_85><Z_38><ANSWER>

Question: Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_40><Z_121><Z_99><Z_66><Z_65><Z_12><Z_76><Z_41><Z_41><Z_24><Z_53><Z_90><Z_61><Z_16><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_92><Z_90><Z_73><Z_29><Z_46><Z_49><Z_4><Z_60><Z_127><Z_8><Z_115><Z_41><Z_10><Z_15><Z_79><Z_121><Z_92><ANSWER>

Question: Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_57><Z_36><Z_86><Z_33><Z_80><Z_47><Z_76><Z_55><Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_124><Z_99><Z_89><Z_96><Z_22><Z_66><Z_37><Z_20><Z_33><ANSWER>

Question: It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_57><Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><Z_72><Z_33><Z_12><Z_107><Z_38><Z_125><Z_28><Z_58><Z_60><Z_53><Z_72><Z_61><Z_98><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_93><Z_9><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_83><Z_60><Z_16><Z_124><Z_12><Z_98><Z_71><Z_56><Z_108><Z_110><Z_90><Z_89><Z_67><Z_94><Z_85><Z_102><ANSWER>

Question: Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_113><Z_125><Z_27><Z_64><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|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
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_25><Z_65><Z_107><Z_13><Z_125><ANSWER>

Question: Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|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
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_113><Z_120><Z_32><Z_115><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_42><Z_40><Z_34><Z_48><Z_76><ANSWER>

Question:
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_100><Z_74><Z_120><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_32><Z_122><Z_45><Z_51><Z_35><ANSWER>

Question:
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_104><Z_125><Z_82><Z_103><Z_22><Z_67><Z_121><Z_124><Z_32><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_9><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_82><Z_93><Z_97><Z_78><Z_109><Z_83><Z_37><Z_5><Z_85><Z_34><ANSWER>

Question: On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|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
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_57><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|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
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_85><Z_67><ANSWER>

Question: Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|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
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_94><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_109><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_77><Z_21><ANSWER>

Question: Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|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
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

Question: John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_97><Z_93><Z_72><Z_23><Z_19><Z_38><Z_15><Z_79><Z_74><Z_98><Z_16><Z_49><Z_102><Z_0><Z_2><Z_86><Z_120><Z_120><Z_66><ANSWER>

Question: Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|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 organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_94><Z_89><Z_59><Z_58><Z_99><Z_49><Z_93><Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|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
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_22><Z_11><Z_119><Z_43><Z_47><Z_102><Z_65><Z_8><ANSWER>

Question: The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|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
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_104><Z_30><Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|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
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_71><Z_55><Z_107><ANSWER>

Question: Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_94><Z_108><Z_34><Z_93><Z_12><Z_33><Z_37><Z_88><Z_82><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_30><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_121><Z_59><Z_67><Z_30><Z_94><Z_108><Z_85><Z_91><Z_63><Z_14><ANSWER>

Question: Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|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
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_104><Z_33><Z_126><Z_58><Z_119><Z_125><Z_119><Z_78><Z_93><Z_24><Z_126><Z_76><Z_10><Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_125><Z_0><Z_72><Z_27><Z_95><Z_12><Z_86><Z_99><Z_110><Z_79><Z_16><Z_73><Z_46><Z_39><ANSWER>

Question: Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_94><Z_81><Z_78><Z_115><Z_87><Z_71><Z_58><Z_72><Z_54><Z_60><Z_126><Z_70><Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_97><Z_117><Z_27><Z_44><Z_121><Z_40><Z_112><Z_104><Z_46><Z_75><Z_111><Z_125><Z_29><ANSWER>

Question:
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_113><Z_100><Z_87><Z_37><Z_49><Z_90><Z_119><Z_76><Z_39><Z_117><Z_76><Z_26><Z_125><Z_70><Z_83><Z_83><Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_70><Z_75><Z_61><Z_63><Z_95><Z_107><Z_85><Z_65><Z_12><Z_100><Z_108><Z_92><Z_59><Z_85><Z_72><Z_84><Z_29><ANSWER>

Question: There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_104><Z_103><Z_47><Z_54><Z_55><Z_90><Z_76><Z_83><Z_61><Z_61><Z_83><Z_76><Z_41><Z_66><Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|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
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_52><Z_15><Z_69><Z_9><Z_2><Z_58><Z_41><Z_10><Z_33><Z_25><Z_44><Z_56><Z_35><Z_16><Z_27><ANSWER>

Question: Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_113><Z_77><Z_44><Z_89><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_119><Z_11><Z_105><Z_41><Z_111><ANSWER>

Question: The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|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 rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_104><Z_97><Z_110><Z_98><Z_33><Z_92><Z_120><Z_45><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|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
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_107><Z_126><Z_119><Z_14><Z_14><Z_79><Z_30><Z_15><Z_55><ANSWER>

Question: A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_94><Z_115><Z_107><Z_32><Z_119><Z_72><Z_125><Z_48><Z_26><Z_81><Z_11><Z_79><Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_92><Z_54><Z_122><Z_49><Z_11><Z_13><Z_97><Z_28><Z_81><Z_10><Z_47><Z_98><Z_45><ANSWER>

Question: A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><Z_120><Z_110><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_82><Z_45><Z_122><Z_118><Z_5><ANSWER>

Question: Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|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
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_104><Z_52><Z_121><Z_88><Z_98><Z_34><Z_87><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_7><Z_15><Z_111><Z_5><Z_33><Z_47><Z_117><Z_3><ANSWER>

Question: Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_27><Z_103><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_77><Z_86><Z_40><ANSWER>

Question: A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|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 four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_114><Z_87><Z_110><Z_40><Z_53><Z_72><Z_31><Z_82><Z_41><Z_59><Z_55><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 four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_14><Z_63><Z_87><Z_127><Z_112><Z_119><Z_84><Z_99><Z_127><Z_108><Z_118><Z_72><ANSWER>

Question: What is the smallest four-digit number that is divisible by $25$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|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 $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><Z_51><Z_119><Z_66><Z_40><Z_58><Z_125><Z_54><Z_96><Z_63><Z_70><Z_26><Z_38><Z_41><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_45><Z_121><Z_121><Z_47><Z_64><Z_86><Z_120><Z_83><Z_6><Z_28><Z_18><Z_75><Z_37><Z_118><Z_101><Z_46><ANSWER>

Question: A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|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 store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|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
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_84><ANSWER>

Question: In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|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 sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_104><Z_38><Z_62><Z_40><Z_87><Z_28><Z_28><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|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 sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_89><Z_61><Z_122><Z_7><Z_12><Z_45><Z_78><Z_11><ANSWER>

Question: The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_57><Z_93><Z_99><Z_115><Z_82><Z_98><Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_99><Z_11><Z_86><Z_126><Z_67><Z_120><Z_46><ANSWER>

Question: A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ 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 $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_94><Z_77><Z_36><Z_79><Z_38><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_123><Z_69><Z_112><Z_20><Z_58><Z_8><ANSWER>

Question: Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.


<|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 $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|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 value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_63><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 $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_11><Z_43><ANSWER>

Question: What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_113><Z_43><Z_98><Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_103><Z_100><Z_88><Z_127><ANSWER>

Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|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
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_57><Z_99><Z_82><Z_33><Z_90><Z_91><Z_48><Z_117><Z_96><Z_63><Z_16><Z_55><Z_31><Z_82><Z_41><Z_90><Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|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
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_70><Z_20><Z_126><Z_120><Z_26><Z_105><Z_92><Z_7><Z_102><Z_72><Z_58><Z_43><Z_50><Z_74><Z_42><Z_54><Z_105><ANSWER>

Question: Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.