<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the complex conjugate $\bar{z}$ of a complex number $z$ satisfies $(1+i) \cdot \bar{z} = 3 + i$, the point corresponding to the complex number $z$ in the complex plane lies in the \_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the complex conjugate $\bar{z}$ of a complex number $z$ satisfies $(1+i) \cdot \bar{z} = 3 + i$, the point corresponding to the complex number $z$ in the complex plane lies in the \_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_176><Z_409><Z_270><Z_155><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the complex conjugate $\bar{z}$ of a complex number $z$ satisfies $(1+i) \cdot \bar{z} = 3 + i$, the point corresponding to the complex number $z$ in the complex plane lies in the \_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_162><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the complex conjugate $\bar{z}$ of a complex number $z$ satisfies $(1+i) \cdot \bar{z} = 3 + i$, the point corresponding to the complex number $z$ in the complex plane lies in the \_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_290><Z_77><Z_295><Z_371><ANSWER>

Question: Given that the complex conjugate $\bar{z}$ of a complex number $z$ satisfies $(1+i) \cdot \bar{z} = 3 + i$, the point corresponding to the complex number $z$ in the complex plane lies in the \_\_ quadrant.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The natural number \( n \) greater than 0 is a multiple of 3, and \( 3n \) is a multiple of 5. What is the smallest value of \( n \)?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The natural number \( n \) greater than 0 is a multiple of 3, and \( 3n \) is a multiple of 5. What is the smallest value of \( n \)?<|im_end|>
<|im_start|>assistant
<Z_5><Z_340><Z_117><Z_310><Z_458><Z_85><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The natural number \( n \) greater than 0 is a multiple of 3, and \( 3n \) is a multiple of 5. What is the smallest value of \( n \)?<|im_end|>
<|im_start|>assistant
<Z_252><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The natural number \( n \) greater than 0 is a multiple of 3, and \( 3n \) is a multiple of 5. What is the smallest value of \( n \)?<|im_end|>
<|im_start|>assistant
<Z_244><Z_482><Z_321><Z_170><Z_287><Z_174><ANSWER>

Question: The natural number \( n \) greater than 0 is a multiple of 3, and \( 3n \) is a multiple of 5. What is the smallest value of \( n \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?<|im_end|>
<|im_start|>assistant
<Z_358><Z_314><Z_173><Z_273><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?<|im_end|>
<|im_start|>assistant
<Z_10><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?<|im_end|>
<|im_start|>assistant
<Z_300><Z_89><Z_383><Z_365><ANSWER>

Question:
We say an integer  $n$  is naoish if  $n \geq 90$  and the second-to-last digit of  $n$  (in decimal notation) is equal to  $9$ . For example,  $10798$ ,  $1999$  and  $90$  are naoish, whereas  $9900$ ,  $2009$  and  $9$  are not. Nino expresses 2020 as a sum:
    \[
    2020=n_{1}+n_{2}+\ldots+n_{k}
    \]
    where each of the  $n_{j}$  is naoish.

    What is the smallest positive number  $k$  for which Nino can do this?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?<|im_end|>
<|im_start|>assistant
<Z_35><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?<|im_end|>
<|im_start|>assistant
<Z_162><ANSWER>

Question: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An aquarium holds an equal number of clownfish and blowfish. 26 of the blowfish stay in their own tank, and the remaining blowfish swim into a display tank. An equal number of clownfish join the blowfish in the display tank, but then a third of these clownfish swim back into their own tank. The aquarium holds a combined total of some number of fish, and there are now 16 clownfish in the display tank. How many fish are there in total in the aquarium?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An aquarium holds an equal number of clownfish and blowfish. 26 of the blowfish stay in their own tank, and the remaining blowfish swim into a display tank. An equal number of clownfish join the blowfish in the display tank, but then a third of these clownfish swim back into their own tank. The aquarium holds a combined total of some number of fish, and there are now 16 clownfish in the display tank. How many fish are there in total in the aquarium?<|im_end|>
<|im_start|>assistant
<Z_358><Z_228><Z_69><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An aquarium holds an equal number of clownfish and blowfish. 26 of the blowfish stay in their own tank, and the remaining blowfish swim into a display tank. An equal number of clownfish join the blowfish in the display tank, but then a third of these clownfish swim back into their own tank. The aquarium holds a combined total of some number of fish, and there are now 16 clownfish in the display tank. How many fish are there in total in the aquarium?<|im_end|>
<|im_start|>assistant
<Z_361><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An aquarium holds an equal number of clownfish and blowfish. 26 of the blowfish stay in their own tank, and the remaining blowfish swim into a display tank. An equal number of clownfish join the blowfish in the display tank, but then a third of these clownfish swim back into their own tank. The aquarium holds a combined total of some number of fish, and there are now 16 clownfish in the display tank. How many fish are there in total in the aquarium?<|im_end|>
<|im_start|>assistant
<Z_17><Z_254><Z_198><ANSWER>

Question: An aquarium holds an equal number of clownfish and blowfish. 26 of the blowfish stay in their own tank, and the remaining blowfish swim into a display tank. An equal number of clownfish join the blowfish in the display tank, but then a third of these clownfish swim back into their own tank. The aquarium holds a combined total of some number of fish, and there are now 16 clownfish in the display tank. How many fish are there in total in the aquarium?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a $4$-digit number arithmetic if it has $4$ distinct digits which, when read from left to right, form an arithmetic sequence. Find the difference between the largest and smallest arithmetic numbers.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a $4$-digit number arithmetic if it has $4$ distinct digits which, when read from left to right, form an arithmetic sequence. Find the difference between the largest and smallest arithmetic numbers.<|im_end|>
<|im_start|>assistant
<Z_66><Z_316><Z_348><Z_112><Z_418><Z_69><Z_203><Z_461><Z_318><Z_273><Z_260><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a $4$-digit number arithmetic if it has $4$ distinct digits which, when read from left to right, form an arithmetic sequence. Find the difference between the largest and smallest arithmetic numbers.<|im_end|>
<|im_start|>assistant
<Z_143><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a $4$-digit number arithmetic if it has $4$ distinct digits which, when read from left to right, form an arithmetic sequence. Find the difference between the largest and smallest arithmetic numbers.<|im_end|>
<|im_start|>assistant
<Z_139><Z_499><Z_77><Z_180><Z_398><Z_242><Z_478><Z_285><Z_76><Z_19><Z_221><ANSWER>

Question: Call a $4$-digit number arithmetic if it has $4$ distinct digits which, when read from left to right, form an arithmetic sequence. Find the difference between the largest and smallest arithmetic numbers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the coefficient of the $x^{3}$ term in the expansion of $((ax^{2}+bx^{-1})^{6})$ is $20$, find the minimum value of $a^{2}+b^{2}$.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the coefficient of the $x^{3}$ term in the expansion of $((ax^{2}+bx^{-1})^{6})$ is $20$, find the minimum value of $a^{2}+b^{2}$.<|im_end|>
<|im_start|>assistant
<Z_5><Z_175><Z_203><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the coefficient of the $x^{3}$ term in the expansion of $((ax^{2}+bx^{-1})^{6})$ is $20$, find the minimum value of $a^{2}+b^{2}$.<|im_end|>
<|im_start|>assistant
<Z_247><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the coefficient of the $x^{3}$ term in the expansion of $((ax^{2}+bx^{-1})^{6})$ is $20$, find the minimum value of $a^{2}+b^{2}$.<|im_end|>
<|im_start|>assistant
<Z_184><Z_263><Z_63><ANSWER>

Question: If the coefficient of the $x^{3}$ term in the expansion of $((ax^{2}+bx^{-1})^{6})$ is $20$, find the minimum value of $a^{2}+b^{2}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 60 kinds of school supplies, such as pencils, notebooks, erasers, and ballpoint pens. If there are 5 pencils, 10 notebooks, and 32 erasers, how many ballpoint pens are there?<|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
There are 60 kinds of school supplies, such as pencils, notebooks, erasers, and ballpoint pens. If there are 5 pencils, 10 notebooks, and 32 erasers, how many ballpoint pens are there?<|im_end|>
<|im_start|>assistant
<Z_195><Z_461><Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 60 kinds of school supplies, such as pencils, notebooks, erasers, and ballpoint pens. If there are 5 pencils, 10 notebooks, and 32 erasers, how many ballpoint pens are there?<|im_end|>
<|im_start|>assistant
<Z_386><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 60 kinds of school supplies, such as pencils, notebooks, erasers, and ballpoint pens. If there are 5 pencils, 10 notebooks, and 32 erasers, how many ballpoint pens are there?<|im_end|>
<|im_start|>assistant
<Z_244><Z_300><Z_400><ANSWER>

Question: There are 60 kinds of school supplies, such as pencils, notebooks, erasers, and ballpoint pens. If there are 5 pencils, 10 notebooks, and 32 erasers, how many ballpoint pens are there?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the diagram, point \( C \) is on \( BD \), \(\triangle ABC\) is right-angled at \( B \), \(\triangle ACE\) is right-angled at \( C \), and \(\triangle CDE\) is right-angled at \( D \). Also, \( AB = 2t \), \( BD = DE = 9t \), and \( BC : CD = 2 : 1 \). If the area of \(\triangle ACE\) is \( k \), what is the value of \(\frac{1}{36} k \)?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the diagram, point \( C \) is on \( BD \), \(\triangle ABC\) is right-angled at \( B \), \(\triangle ACE\) is right-angled at \( C \), and \(\triangle CDE\) is right-angled at \( D \). Also, \( AB = 2t \), \( BD = DE = 9t \), and \( BC : CD = 2 : 1 \). If the area of \(\triangle ACE\) is \( k \), what is the value of \(\frac{1}{36} k \)?<|im_end|>
<|im_start|>assistant
<Z_5><Z_382><Z_173><Z_483><Z_168><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the diagram, point \( C \) is on \( BD \), \(\triangle ABC\) is right-angled at \( B \), \(\triangle ACE\) is right-angled at \( C \), and \(\triangle CDE\) is right-angled at \( D \). Also, \( AB = 2t \), \( BD = DE = 9t \), and \( BC : CD = 2 : 1 \). If the area of \(\triangle ACE\) is \( k \), what is the value of \(\frac{1}{36} k \)?<|im_end|>
<|im_start|>assistant
<Z_418><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the diagram, point \( C \) is on \( BD \), \(\triangle ABC\) is right-angled at \( B \), \(\triangle ACE\) is right-angled at \( C \), and \(\triangle CDE\) is right-angled at \( D \). Also, \( AB = 2t \), \( BD = DE = 9t \), and \( BC : CD = 2 : 1 \). If the area of \(\triangle ACE\) is \( k \), what is the value of \(\frac{1}{36} k \)?<|im_end|>
<|im_start|>assistant
<Z_43><Z_280><Z_377><Z_179><Z_278><ANSWER>

Question: In the diagram, point \( C \) is on \( BD \), \(\triangle ABC\) is right-angled at \( B \), \(\triangle ACE\) is right-angled at \( C \), and \(\triangle CDE\) is right-angled at \( D \). Also, \( AB = 2t \), \( BD = DE = 9t \), and \( BC : CD = 2 : 1 \). If the area of \(\triangle ACE\) is \( k \), what is the value of \(\frac{1}{36} k \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^3 - 3x - 1$, if for any $x_1$, $x_2$ in the interval $[-3,2]$, it holds that $|f(x_1) - f(x_2)| \leq t$, then the minimum value of the real number $t$ is ______.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^3 - 3x - 1$, if for any $x_1$, $x_2$ in the interval $[-3,2]$, it holds that $|f(x_1) - f(x_2)| \leq t$, then the minimum value of the real number $t$ is ______.<|im_end|>
<|im_start|>assistant
<Z_66><Z_351><Z_392><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^3 - 3x - 1$, if for any $x_1$, $x_2$ in the interval $[-3,2]$, it holds that $|f(x_1) - f(x_2)| \leq t$, then the minimum value of the real number $t$ is ______.<|im_end|>
<|im_start|>assistant
<Z_214><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x^3 - 3x - 1$, if for any $x_1$, $x_2$ in the interval $[-3,2]$, it holds that $|f(x_1) - f(x_2)| \leq t$, then the minimum value of the real number $t$ is ______.<|im_end|>
<|im_start|>assistant
<Z_30><Z_496><Z_146><ANSWER>

Question: Given the function $f(x) = x^3 - 3x - 1$, if for any $x_1$, $x_2$ in the interval $[-3,2]$, it holds that $|f(x_1) - f(x_2)| \leq t$, then the minimum value of the real number $t$ is ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of ( 7 x + 2 y ) / ( x - some number y ) when x / 2 y = 3 / 2 and the result is 23. What is that number?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of ( 7 x + 2 y ) / ( x - some number y ) when x / 2 y = 3 / 2 and the result is 23. What is that number?<|im_end|>
<|im_start|>assistant
<Z_195><Z_395><Z_138><Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of ( 7 x + 2 y ) / ( x - some number y ) when x / 2 y = 3 / 2 and the result is 23. What is that number?<|im_end|>
<|im_start|>assistant
<Z_423><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the value of ( 7 x + 2 y ) / ( x - some number y ) when x / 2 y = 3 / 2 and the result is 23. What is that number?<|im_end|>
<|im_start|>assistant
<Z_45><Z_235><Z_425><Z_507><ANSWER>

Question: Find the value of ( 7 x + 2 y ) / ( x - some number y ) when x / 2 y = 3 / 2 and the result is 23. What is that number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the nearest integer to $(3+\sqrt2)^4$?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the nearest integer to $(3+\sqrt2)^4$?<|im_end|>
<|im_start|>assistant
<Z_66><Z_485><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the nearest integer to $(3+\sqrt2)^4$?<|im_end|>
<|im_start|>assistant
<Z_307><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the nearest integer to $(3+\sqrt2)^4$?<|im_end|>
<|im_start|>assistant
<Z_451><Z_130><ANSWER>

Question: What is the nearest integer to $(3+\sqrt2)^4$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ has the property that $f(4x-1) = x^2 + 2x + 2$ for all real numbers $x$. What is $f(7)$?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ has the property that $f(4x-1) = x^2 + 2x + 2$ for all real numbers $x$. What is $f(7)$?<|im_end|>
<|im_start|>assistant
<Z_195><Z_110><Z_239><Z_73><Z_373><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ has the property that $f(4x-1) = x^2 + 2x + 2$ for all real numbers $x$. What is $f(7)$?<|im_end|>
<|im_start|>assistant
<Z_328><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ has the property that $f(4x-1) = x^2 + 2x + 2$ for all real numbers $x$. What is $f(7)$?<|im_end|>
<|im_start|>assistant
<Z_259><Z_78><Z_254><Z_203><Z_96><ANSWER>

Question: A function $f$ has the property that $f(4x-1) = x^2 + 2x + 2$ for all real numbers $x$. What is $f(7)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the coefficient of the $x^2$ term in the expansion of $\left(1-\frac{1}{x}\right)(1+x)^4$.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the coefficient of the $x^2$ term in the expansion of $\left(1-\frac{1}{x}\right)(1+x)^4$.<|im_end|>
<|im_start|>assistant
<Z_358><Z_370><Z_476><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the coefficient of the $x^2$ term in the expansion of $\left(1-\frac{1}{x}\right)(1+x)^4$.<|im_end|>
<|im_start|>assistant
<Z_187><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the coefficient of the $x^2$ term in the expansion of $\left(1-\frac{1}{x}\right)(1+x)^4$.<|im_end|>
<|im_start|>assistant
<Z_454><Z_423><Z_196><ANSWER>

Question: Determine the coefficient of the $x^2$ term in the expansion of $\left(1-\frac{1}{x}\right)(1+x)^4$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive prime number that divides \(n^2 + 5n + 23\) for some integer \(n\).<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive prime number that divides \(n^2 + 5n + 23\) for some integer \(n\).<|im_end|>
<|im_start|>assistant
<Z_358><Z_484><Z_307><Z_187><Z_180><Z_449><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive prime number that divides \(n^2 + 5n + 23\) for some integer \(n\).<|im_end|>
<|im_start|>assistant
<Z_152><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the smallest positive prime number that divides \(n^2 + 5n + 23\) for some integer \(n\).<|im_end|>
<|im_start|>assistant
<Z_457><Z_409><Z_226><Z_257><Z_364><Z_365><ANSWER>

Question: Find the smallest positive prime number that divides \(n^2 + 5n + 23\) for some integer \(n\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\log_{10} 50 + \log_{10} 20$.<|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
Calculate $\log_{10} 50 + \log_{10} 20$.<|im_end|>
<|im_start|>assistant
<Z_176><Z_472><Z_141><Z_53><Z_441><Z_333><Z_133><Z_341><Z_295><Z_364><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\log_{10} 50 + \log_{10} 20$.<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate $\log_{10} 50 + \log_{10} 20$.<|im_end|>
<|im_start|>assistant
<Z_128><Z_358><Z_449><Z_213><Z_293><Z_362><Z_25><Z_94><Z_380><Z_191><ANSWER>

Question: Calculate $\log_{10} 50 + \log_{10} 20$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\sqrt{3a+1}$ is the simplest quadratic root, and $a$ is an integer, then the minimum value of $a$ is ______.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\sqrt{3a+1}$ is the simplest quadratic root, and $a$ is an integer, then the minimum value of $a$ is ______.<|im_end|>
<|im_start|>assistant
<Z_195><Z_447><Z_478><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\sqrt{3a+1}$ is the simplest quadratic root, and $a$ is an integer, then the minimum value of $a$ is ______.<|im_end|>
<|im_start|>assistant
<Z_266><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\sqrt{3a+1}$ is the simplest quadratic root, and $a$ is an integer, then the minimum value of $a$ is ______.<|im_end|>
<|im_start|>assistant
<Z_489><Z_483><Z_97><ANSWER>

Question: If $\sqrt{3a+1}$ is the simplest quadratic root, and $a$ is an integer, then the minimum value of $a$ is ______.


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

The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

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

The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.<|im_end|>
<|im_start|>assistant
<Z_5><Z_486><ANSWER>

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

The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.<|im_end|>
<|im_start|>assistant
<Z_423><ANSWER>

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

The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.<|im_end|>
<|im_start|>assistant
<Z_432><Z_183><ANSWER>

Question:
The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 28 and 28.2.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 28 and 28.2.<|im_end|>
<|im_start|>assistant
<Z_509><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a positive integer that is divisible by 18 and has a square root between 28 and 28.2.<|im_end|>
<|im_start|>assistant
<Z_391><ANSWER>

Question: Find a positive integer that is divisible by 18 and has a square root between 28 and 28.2.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For each permutation $a_1,a_2,a_3,\cdots,a_{12}$ of the integers $1,2,3,\cdots,12$, compute the sum
\[|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|+|a_{11}-a_{12}|.\]
Calculate the average value of all such sums. The average value can be expressed as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For each permutation $a_1,a_2,a_3,\cdots,a_{12}$ of the integers $1,2,3,\cdots,12$, compute the sum
\[|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|+|a_{11}-a_{12}|.\]
Calculate the average value of all such sums. The average value can be expressed as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.<|im_end|>
<|im_start|>assistant
<Z_176><Z_503><Z_223><Z_246><Z_510><Z_110><Z_149><Z_399><Z_259><Z_485><Z_334><Z_394><Z_187><Z_48><Z_234><Z_416><Z_110><Z_324><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For each permutation $a_1,a_2,a_3,\cdots,a_{12}$ of the integers $1,2,3,\cdots,12$, compute the sum
\[|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|+|a_{11}-a_{12}|.\]
Calculate the average value of all such sums. The average value can be expressed as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.<|im_end|>
<|im_start|>assistant
<Z_433><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For each permutation $a_1,a_2,a_3,\cdots,a_{12}$ of the integers $1,2,3,\cdots,12$, compute the sum
\[|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|+|a_{11}-a_{12}|.\]
Calculate the average value of all such sums. The average value can be expressed as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.<|im_end|>
<|im_start|>assistant
<Z_491><Z_218><Z_54><Z_195><Z_55><Z_218><Z_470><Z_396><Z_309><Z_390><Z_243><Z_441><Z_204><Z_202><Z_7><Z_390><Z_447><Z_399><ANSWER>

Question:
For each permutation $a_1,a_2,a_3,\cdots,a_{12}$ of the integers $1,2,3,\cdots,12$, compute the sum
\[|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|+|a_{11}-a_{12}|.\]
Calculate the average value of all such sums. The average value can be expressed as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest number which leaves the same remainder when it divides 20, 40, and 90. What is the greatest number?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest number which leaves the same remainder when it divides 20, 40, and 90. What is the greatest number?<|im_end|>
<|im_start|>assistant
<Z_176><Z_446><Z_43><Z_372><Z_383><Z_158><Z_84><Z_462><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest number which leaves the same remainder when it divides 20, 40, and 90. What is the greatest number?<|im_end|>
<|im_start|>assistant
<Z_372><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the greatest number which leaves the same remainder when it divides 20, 40, and 90. What is the greatest number?<|im_end|>
<|im_start|>assistant
<Z_199><Z_332><Z_509><Z_336><Z_173><Z_249><Z_179><Z_85><ANSWER>

Question: Find the greatest number which leaves the same remainder when it divides 20, 40, and 90. What is the greatest number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What integer $n$ satisfies $0\le n<23$ and $$39548\equiv n\pmod{23}~?$$<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What integer $n$ satisfies $0\le n<23$ and $$39548\equiv n\pmod{23}~?$$<|im_end|>
<|im_start|>assistant
<Z_5><Z_363><Z_369><Z_394><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What integer $n$ satisfies $0\le n<23$ and $$39548\equiv n\pmod{23}~?$$<|im_end|>
<|im_start|>assistant
<Z_434><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What integer $n$ satisfies $0\le n<23$ and $$39548\equiv n\pmod{23}~?$$<|im_end|>
<|im_start|>assistant
<Z_5><Z_268><Z_207><Z_359><Z_313><ANSWER>

Question: What integer $n$ satisfies $0\le n<23$ and $$39548\equiv n\pmod{23}~?$$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[3]{8}|=4$?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[3]{8}|=4$?<|im_end|>
<|im_start|>assistant
<Z_66><Z_469><Z_445><Z_499><Z_203><Z_463><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[3]{8}|=4$?<|im_end|>
<|im_start|>assistant
<Z_188><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[3]{8}|=4$?<|im_end|>
<|im_start|>assistant
<Z_253><Z_226><Z_41><Z_124><Z_161><Z_193><ANSWER>

Question: What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[3]{8}|=4$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
find the lowest common multiple of 24 , 36 and 42 .<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
find the lowest common multiple of 24 , 36 and 42 .<|im_end|>
<|im_start|>assistant
<Z_5><Z_366><Z_382><Z_333><Z_63><Z_475><Z_239><Z_442><Z_489><Z_388><Z_337><Z_503><Z_244><Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
find the lowest common multiple of 24 , 36 and 42 .<|im_end|>
<|im_start|>assistant
<Z_446><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
find the lowest common multiple of 24 , 36 and 42 .<|im_end|>
<|im_start|>assistant
<Z_225><Z_223><Z_471><Z_69><Z_4><Z_127><Z_115><Z_30><Z_498><Z_104><Z_0><Z_468><Z_377><Z_92><ANSWER>

Question: find the lowest common multiple of 24 , 36 and 42 .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the average speed of a bus is 60 km/hr, and including stoppages, the average speed of the bus is some km/hr. The bus stops for 15 minutes per hour. What is the average speed of the bus including stoppages?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the average speed of a bus is 60 km/hr, and including stoppages, the average speed of the bus is some km/hr. The bus stops for 15 minutes per hour. What is the average speed of the bus including stoppages?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Excluding stoppages, the average speed of a bus is 60 km/hr, and including stoppages, the average speed of the bus is some km/hr. The bus stops for 15 minutes per hour. What is the average speed of the bus including stoppages?<|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
Excluding stoppages, the average speed of a bus is 60 km/hr, and including stoppages, the average speed of the bus is some km/hr. The bus stops for 15 minutes per hour. What is the average speed of the bus including stoppages?<|im_end|>
<|im_start|>assistant
<Z_58><ANSWER>

Question: Excluding stoppages, the average speed of a bus is 60 km/hr, and including stoppages, the average speed of the bus is some km/hr. The bus stops for 15 minutes per hour. What is the average speed of the bus including stoppages?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pad of paper comes with some sheets. Evelyn uses a pad of paper writing notes at work every week. She takes Monday and Friday off from work. She uses 12 sheets of paper per day at work. How many sheets does a pad of paper come with?<|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
A pad of paper comes with some sheets. Evelyn uses a pad of paper writing notes at work every week. She takes Monday and Friday off from work. She uses 12 sheets of paper per day at work. How many sheets does a pad of paper come with?<|im_end|>
<|im_start|>assistant
<Z_195><Z_492><Z_307><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pad of paper comes with some sheets. Evelyn uses a pad of paper writing notes at work every week. She takes Monday and Friday off from work. She uses 12 sheets of paper per day at work. How many sheets does a pad of paper come with?<|im_end|>
<|im_start|>assistant
<Z_325><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pad of paper comes with some sheets. Evelyn uses a pad of paper writing notes at work every week. She takes Monday and Friday off from work. She uses 12 sheets of paper per day at work. How many sheets does a pad of paper come with?<|im_end|>
<|im_start|>assistant
<Z_8><Z_128><Z_464><ANSWER>

Question: A pad of paper comes with some sheets. Evelyn uses a pad of paper writing notes at work every week. She takes Monday and Friday off from work. She uses 12 sheets of paper per day at work. How many sheets does a pad of paper come with?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $5^{3y} = 125$, what is the value of $5^{3y-2}$?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $5^{3y} = 125$, what is the value of $5^{3y-2}$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_485><Z_263><Z_233><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $5^{3y} = 125$, what is the value of $5^{3y-2}$?<|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
If $5^{3y} = 125$, what is the value of $5^{3y-2}$?<|im_end|>
<|im_start|>assistant
<Z_475><Z_425><Z_341><Z_107><ANSWER>

Question: If $5^{3y} = 125$, what is the value of $5^{3y-2}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider the sequence of numbers defined recursively by $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider the sequence of numbers defined recursively by $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.<|im_end|>
<|im_start|>assistant
<Z_176><Z_260><Z_500><Z_91><Z_233><Z_234><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider the sequence of numbers defined recursively by $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.<|im_end|>
<|im_start|>assistant
<Z_466><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider the sequence of numbers defined recursively by $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.<|im_end|>
<|im_start|>assistant
<Z_251><Z_97><Z_39><Z_190><Z_156><Z_222><ANSWER>

Question: Consider the sequence of numbers defined recursively by $u_1 = 2$ and for $m > 1$ by $u_m = 2 + u_{m/3}$ when $m$ is divisible by 3 and by $u_m = \frac{1}{u_{m-1}}$ when $m$ is not divisible by 3. Given that $u_m = \frac{7}{24}$, find $m$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer with exactly $12$ positive factors?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer with exactly $12$ positive factors?<|im_end|>
<|im_start|>assistant
<Z_195><Z_119><Z_149><Z_387><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer with exactly $12$ positive factors?<|im_end|>
<|im_start|>assistant
<Z_295><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer with exactly $12$ positive factors?<|im_end|>
<|im_start|>assistant
<Z_337><Z_318><Z_344><Z_116><ANSWER>

Question: What is the least positive integer with exactly $12$ positive factors?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pet store had 15 siamese cats and 49 house cats. During a sale, they sold 19 cats. How many cats do they have left?<|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
A pet store had 15 siamese cats and 49 house cats. During a sale, they sold 19 cats. How many cats do they have left?<|im_end|>
<|im_start|>assistant
<Z_195><Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pet store had 15 siamese cats and 49 house cats. During a sale, they sold 19 cats. How many cats do they have left?<|im_end|>
<|im_start|>assistant
<Z_355><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pet store had 15 siamese cats and 49 house cats. During a sale, they sold 19 cats. How many cats do they have left?<|im_end|>
<|im_start|>assistant
<Z_222><Z_152><ANSWER>

Question: A pet store had 15 siamese cats and 49 house cats. During a sale, they sold 19 cats. How many cats do they have left?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ on the complex plane are the vertices of a right triangle. Find the square of the length of the hypotenuse, $h^2$, given that the triangle's centroid is at the origin.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ on the complex plane are the vertices of a right triangle. Find the square of the length of the hypotenuse, $h^2$, given that the triangle's centroid is at the origin.<|im_end|>
<|im_start|>assistant
<Z_66><Z_473><Z_67><Z_56><Z_268><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ on the complex plane are the vertices of a right triangle. Find the square of the length of the hypotenuse, $h^2$, given that the triangle's centroid is at the origin.<|im_end|>
<|im_start|>assistant
<Z_302><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ on the complex plane are the vertices of a right triangle. Find the square of the length of the hypotenuse, $h^2$, given that the triangle's centroid is at the origin.<|im_end|>
<|im_start|>assistant
<Z_211><Z_97><Z_179><Z_62><Z_409><ANSWER>

Question: Given that complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ on the complex plane are the vertices of a right triangle. Find the square of the length of the hypotenuse, $h^2$, given that the triangle's centroid is at the origin.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the product of the digits in the base 8 representation of $6543_{10}$?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the product of the digits in the base 8 representation of $6543_{10}$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_265><Z_335><Z_294><Z_407><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the product of the digits in the base 8 representation of $6543_{10}$?<|im_end|>
<|im_start|>assistant
<Z_367><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the product of the digits in the base 8 representation of $6543_{10}$?<|im_end|>
<|im_start|>assistant
<Z_312><Z_31><Z_238><Z_38><Z_421><ANSWER>

Question: What is the product of the digits in the base 8 representation of $6543_{10}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car salesman sold some cars on Monday, 3 on Tuesday, 10 on Wednesday, 4 on Thursday, 4 on Friday and 4 on Saturday. The mean of the number of cars he sold is 5.5. How many cars did he sell on Monday?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car salesman sold some cars on Monday, 3 on Tuesday, 10 on Wednesday, 4 on Thursday, 4 on Friday and 4 on Saturday. The mean of the number of cars he sold is 5.5. How many cars did he sell on Monday?<|im_end|>
<|im_start|>assistant
<Z_66><Z_161><Z_358><Z_483><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car salesman sold some cars on Monday, 3 on Tuesday, 10 on Wednesday, 4 on Thursday, 4 on Friday and 4 on Saturday. The mean of the number of cars he sold is 5.5. How many cars did he sell on Monday?<|im_end|>
<|im_start|>assistant
<Z_394><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car salesman sold some cars on Monday, 3 on Tuesday, 10 on Wednesday, 4 on Thursday, 4 on Friday and 4 on Saturday. The mean of the number of cars he sold is 5.5. How many cars did he sell on Monday?<|im_end|>
<|im_start|>assistant
<Z_46><Z_60><Z_223><Z_236><ANSWER>

Question: A car salesman sold some cars on Monday, 3 on Tuesday, 10 on Wednesday, 4 on Thursday, 4 on Friday and 4 on Saturday. The mean of the number of cars he sold is 5.5. How many cars did he sell on Monday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twice $a$ plus 2 equals $b$; twice $b$ plus 2 equals $c$; twice $c$ plus 2 equals $d$; twice $d$ plus 2 equals 62. What is the value of $a$?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twice $a$ plus 2 equals $b$; twice $b$ plus 2 equals $c$; twice $c$ plus 2 equals $d$; twice $d$ plus 2 equals 62. What is the value of $a$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_340><Z_241><Z_159><Z_163><Z_51><Z_435><Z_278><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twice $a$ plus 2 equals $b$; twice $b$ plus 2 equals $c$; twice $c$ plus 2 equals $d$; twice $d$ plus 2 equals 62. What is the value of $a$?<|im_end|>
<|im_start|>assistant
<Z_476><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Twice $a$ plus 2 equals $b$; twice $b$ plus 2 equals $c$; twice $c$ plus 2 equals $d$; twice $d$ plus 2 equals 62. What is the value of $a$?<|im_end|>
<|im_start|>assistant
<Z_273><Z_273><Z_170><Z_345><Z_429><Z_458><Z_33><Z_195><ANSWER>

Question: Twice $a$ plus 2 equals $b$; twice $b$ plus 2 equals $c$; twice $c$ plus 2 equals $d$; twice $d$ plus 2 equals 62. What is the value of $a$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A?<|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
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A?<|im_end|>
<|im_start|>assistant
<Z_66><Z_483><Z_126><Z_351><Z_254><Z_457><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A?<|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
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A?<|im_end|>
<|im_start|>assistant
<Z_376><Z_21><Z_125><Z_205><Z_443><Z_349><ANSWER>

Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are solutions to the equation $$(x-3)^{(30-x^2)}=1$$ such that $x+2 > 0$?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are solutions to the equation $$(x-3)^{(30-x^2)}=1$$ such that $x+2 > 0$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_463><Z_184><Z_341><Z_251><Z_256><Z_36><Z_241><Z_275><Z_429><Z_410><Z_303><Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are solutions to the equation $$(x-3)^{(30-x^2)}=1$$ such that $x+2 > 0$?<|im_end|>
<|im_start|>assistant
<Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many integers are solutions to the equation $$(x-3)^{(30-x^2)}=1$$ such that $x+2 > 0$?<|im_end|>
<|im_start|>assistant
<Z_487><Z_67><Z_275><Z_56><Z_433><Z_449><Z_215><Z_108><Z_396><Z_376><Z_48><Z_75><Z_510><ANSWER>

Question: How many integers are solutions to the equation $$(x-3)^{(30-x^2)}=1$$ such that $x+2 > 0$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two players take turns naming prime numbers not exceeding 100, such that the last digit of a number named by one player matches the first digit of the number named by the other player in the next turn (except for the very first prime number named in the game). Repeating previously named numbers is not allowed. The player who cannot name a prime number according to these rules loses. Prove that one of the players can guarantee a win, and find the minimum possible number of prime numbers that will be used by both players in such a game.<|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
Two players take turns naming prime numbers not exceeding 100, such that the last digit of a number named by one player matches the first digit of the number named by the other player in the next turn (except for the very first prime number named in the game). Repeating previously named numbers is not allowed. The player who cannot name a prime number according to these rules loses. Prove that one of the players can guarantee a win, and find the minimum possible number of prime numbers that will be used by both players in such a game.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two players take turns naming prime numbers not exceeding 100, such that the last digit of a number named by one player matches the first digit of the number named by the other player in the next turn (except for the very first prime number named in the game). Repeating previously named numbers is not allowed. The player who cannot name a prime number according to these rules loses. Prove that one of the players can guarantee a win, and find the minimum possible number of prime numbers that will be used by both players in such a game.<|im_end|>
<|im_start|>assistant
<Z_447><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two players take turns naming prime numbers not exceeding 100, such that the last digit of a number named by one player matches the first digit of the number named by the other player in the next turn (except for the very first prime number named in the game). Repeating previously named numbers is not allowed. The player who cannot name a prime number according to these rules loses. Prove that one of the players can guarantee a win, and find the minimum possible number of prime numbers that will be used by both players in such a game.<|im_end|>
<|im_start|>assistant
<Z_210><ANSWER>

Question: Two players take turns naming prime numbers not exceeding 100, such that the last digit of a number named by one player matches the first digit of the number named by the other player in the next turn (except for the very first prime number named in the game). Repeating previously named numbers is not allowed. The player who cannot name a prime number according to these rules loses. Prove that one of the players can guarantee a win, and find the minimum possible number of prime numbers that will be used by both players in such a game.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what least number should be added to 1019 , so that the sum is completely divisible by 25 ?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what least number should be added to 1019 , so that the sum is completely divisible by 25 ?<|im_end|>
<|im_start|>assistant
<Z_5><Z_488><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what least number should be added to 1019 , so that the sum is completely divisible by 25 ?<|im_end|>
<|im_start|>assistant
<Z_466><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what least number should be added to 1019 , so that the sum is completely divisible by 25 ?<|im_end|>
<|im_start|>assistant
<Z_247><Z_367><ANSWER>

Question: what least number should be added to 1019 , so that the sum is completely divisible by 25 ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?<|im_end|>
<|im_start|>assistant
<Z_66><Z_258><Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?<|im_end|>
<|im_start|>assistant
<Z_346><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?<|im_end|>
<|im_start|>assistant
<Z_353><Z_0><Z_464><ANSWER>

Question: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
I have 15 books, of which I want to bring three to read on vacation. How many different groups of three can I choose?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
I have 15 books, of which I want to bring three to read on vacation. How many different groups of three can I choose?<|im_end|>
<|im_start|>assistant
<Z_358><Z_372><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
I have 15 books, of which I want to bring three to read on vacation. How many different groups of three can I choose?<|im_end|>
<|im_start|>assistant
<Z_411><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
I have 15 books, of which I want to bring three to read on vacation. How many different groups of three can I choose?<|im_end|>
<|im_start|>assistant
<Z_198><Z_210><ANSWER>

Question: I have 15 books, of which I want to bring three to read on vacation. How many different groups of three can I choose?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Melody needs to read 60 pages for her English class, 35.5 pages for her Math class, 48 pages for her History class, 25 chapters for her Chinese class, 22 illustrations for her Art class, and 150 minutes for her Audio book class. She plans to read 1/3 of the English book, 46.5% of the Math book, 3/8 of the History book, 40% of the Chinese chapters, 27.3% of the illustrations, and 75% of the Audio book tomorrow. How many pages, chapters, illustrations, and minutes will she read tomorrow?<|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
Melody needs to read 60 pages for her English class, 35.5 pages for her Math class, 48 pages for her History class, 25 chapters for her Chinese class, 22 illustrations for her Art class, and 150 minutes for her Audio book class. She plans to read 1/3 of the English book, 46.5% of the Math book, 3/8 of the History book, 40% of the Chinese chapters, 27.3% of the illustrations, and 75% of the Audio book tomorrow. How many pages, chapters, illustrations, and minutes will she read tomorrow?<|im_end|>
<|im_start|>assistant
<Z_176><Z_434><Z_388><Z_169><Z_294><Z_52><Z_368><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Melody needs to read 60 pages for her English class, 35.5 pages for her Math class, 48 pages for her History class, 25 chapters for her Chinese class, 22 illustrations for her Art class, and 150 minutes for her Audio book class. She plans to read 1/3 of the English book, 46.5% of the Math book, 3/8 of the History book, 40% of the Chinese chapters, 27.3% of the illustrations, and 75% of the Audio book tomorrow. How many pages, chapters, illustrations, and minutes will she read tomorrow?<|im_end|>
<|im_start|>assistant
<Z_235><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Melody needs to read 60 pages for her English class, 35.5 pages for her Math class, 48 pages for her History class, 25 chapters for her Chinese class, 22 illustrations for her Art class, and 150 minutes for her Audio book class. She plans to read 1/3 of the English book, 46.5% of the Math book, 3/8 of the History book, 40% of the Chinese chapters, 27.3% of the illustrations, and 75% of the Audio book tomorrow. How many pages, chapters, illustrations, and minutes will she read tomorrow?<|im_end|>
<|im_start|>assistant
<Z_204><Z_260><Z_186><Z_345><Z_485><Z_240><Z_389><ANSWER>

Question: Melody needs to read 60 pages for her English class, 35.5 pages for her Math class, 48 pages for her History class, 25 chapters for her Chinese class, 22 illustrations for her Art class, and 150 minutes for her Audio book class. She plans to read 1/3 of the English book, 46.5% of the Math book, 3/8 of the History book, 40% of the Chinese chapters, 27.3% of the illustrations, and 75% of the Audio book tomorrow. How many pages, chapters, illustrations, and minutes will she read tomorrow?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the expression \[(3^{1006} + 7^{1007})^2 - (3^{1006} - 7^{1007})^2\] and express it as \(k \cdot 10^{1007}\) for some positive integer \(k\).<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the expression \[(3^{1006} + 7^{1007})^2 - (3^{1006} - 7^{1007})^2\] and express it as \(k \cdot 10^{1007}\) for some positive integer \(k\).<|im_end|>
<|im_start|>assistant
<Z_176><Z_183><Z_354><Z_182><Z_469><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the expression \[(3^{1006} + 7^{1007})^2 - (3^{1006} - 7^{1007})^2\] and express it as \(k \cdot 10^{1007}\) for some positive integer \(k\).<|im_end|>
<|im_start|>assistant
<Z_165><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the expression \[(3^{1006} + 7^{1007})^2 - (3^{1006} - 7^{1007})^2\] and express it as \(k \cdot 10^{1007}\) for some positive integer \(k\).<|im_end|>
<|im_start|>assistant
<Z_0><Z_286><Z_63><Z_341><Z_384><ANSWER>

Question: Calculate the value of the expression \[(3^{1006} + 7^{1007})^2 - (3^{1006} - 7^{1007})^2\] and express it as \(k \cdot 10^{1007}\) for some positive integer \(k\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An ellipse is tangent to both the $x$-axis and the $y$-axis, with its foci located at $(1 + \sqrt{3}, 2)$ and $(1 - \sqrt{3}, 2)$. Find the length of the major axis.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An ellipse is tangent to both the $x$-axis and the $y$-axis, with its foci located at $(1 + \sqrt{3}, 2)$ and $(1 - \sqrt{3}, 2)$. Find the length of the major axis.<|im_end|>
<|im_start|>assistant
<Z_176><Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An ellipse is tangent to both the $x$-axis and the $y$-axis, with its foci located at $(1 + \sqrt{3}, 2)$ and $(1 - \sqrt{3}, 2)$. Find the length of the major axis.<|im_end|>
<|im_start|>assistant
<Z_500><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An ellipse is tangent to both the $x$-axis and the $y$-axis, with its foci located at $(1 + \sqrt{3}, 2)$ and $(1 - \sqrt{3}, 2)$. Find the length of the major axis.<|im_end|>
<|im_start|>assistant
<Z_158><Z_260><ANSWER>

Question: An ellipse is tangent to both the $x$-axis and the $y$-axis, with its foci located at $(1 + \sqrt{3}, 2)$ and $(1 - \sqrt{3}, 2)$. Find the length of the major axis.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car manufacturing company that produces 100 cars per month wants to increase its production to reach a certain number of cars per year. The company should add 50 cars to the monthly production rate to reach that target. What is the company's yearly production target?<|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
A car manufacturing company that produces 100 cars per month wants to increase its production to reach a certain number of cars per year. The company should add 50 cars to the monthly production rate to reach that target. What is the company's yearly production target?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car manufacturing company that produces 100 cars per month wants to increase its production to reach a certain number of cars per year. The company should add 50 cars to the monthly production rate to reach that target. What is the company's yearly production target?<|im_end|>
<|im_start|>assistant
<Z_295><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A car manufacturing company that produces 100 cars per month wants to increase its production to reach a certain number of cars per year. The company should add 50 cars to the monthly production rate to reach that target. What is the company's yearly production target?<|im_end|>
<|im_start|>assistant
<Z_323><ANSWER>

Question: A car manufacturing company that produces 100 cars per month wants to increase its production to reach a certain number of cars per year. The company should add 50 cars to the monthly production rate to reach that target. What is the company's yearly production target?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $I$ and side $DC$ at $J$. If $IJ = 40$ and $JH = 30$, then find the length of $BI$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $I$ and side $DC$ at $J$. If $IJ = 40$ and $JH = 30$, then find the length of $BI$.<|im_end|>
<|im_start|>assistant
<Z_195><Z_345><Z_55><Z_473><Z_456><Z_492><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $I$ and side $DC$ at $J$. If $IJ = 40$ and $JH = 30$, then find the length of $BI$.<|im_end|>
<|im_start|>assistant
<Z_415><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $I$ and side $DC$ at $J$. If $IJ = 40$ and $JH = 30$, then find the length of $BI$.<|im_end|>
<|im_start|>assistant
<Z_191><Z_96><Z_421><Z_483><Z_434><Z_78><ANSWER>

Question: Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $I$ and side $DC$ at $J$. If $IJ = 40$ and $JH = 30$, then find the length of $BI$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the following expression:

\[
\frac{\left(5 \frac{4}{45}-4 \frac{1}{6}\right): 5 \frac{8}{15}}{\left(4 \frac{2}{3}+0.75\right) \cdot 3 \frac{9}{13}} \cdot 34 \frac{2}{7}+\frac{0.3: 0.01}{70}+\frac{2}{7}.
\]<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the following expression:

\[
\frac{\left(5 \frac{4}{45}-4 \frac{1}{6}\right): 5 \frac{8}{15}}{\left(4 \frac{2}{3}+0.75\right) \cdot 3 \frac{9}{13}} \cdot 34 \frac{2}{7}+\frac{0.3: 0.01}{70}+\frac{2}{7}.
\]<|im_end|>
<|im_start|>assistant
<Z_358><Z_267><Z_319><Z_325><Z_101><Z_380><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the following expression:

\[
\frac{\left(5 \frac{4}{45}-4 \frac{1}{6}\right): 5 \frac{8}{15}}{\left(4 \frac{2}{3}+0.75\right) \cdot 3 \frac{9}{13}} \cdot 34 \frac{2}{7}+\frac{0.3: 0.01}{70}+\frac{2}{7}.
\]<|im_end|>
<|im_start|>assistant
<Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the value of the following expression:

\[
\frac{\left(5 \frac{4}{45}-4 \frac{1}{6}\right): 5 \frac{8}{15}}{\left(4 \frac{2}{3}+0.75\right) \cdot 3 \frac{9}{13}} \cdot 34 \frac{2}{7}+\frac{0.3: 0.01}{70}+\frac{2}{7}.
\]<|im_end|>
<|im_start|>assistant
<Z_474><Z_232><Z_227><Z_362><Z_299><Z_507><ANSWER>

Question:
Calculate the value of the following expression:

\[
\frac{\left(5 \frac{4}{45}-4 \frac{1}{6}\right): 5 \frac{8}{15}}{\left(4 \frac{2}{3}+0.75\right) \cdot 3 \frac{9}{13}} \cdot 34 \frac{2}{7}+\frac{0.3: 0.01}{70}+\frac{2}{7}.
\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John?<|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
John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John?<|im_end|>
<|im_start|>assistant
<Z_195><Z_267><Z_256><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John?<|im_end|>
<|im_start|>assistant
<Z_495><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John?<|im_end|>
<|im_start|>assistant
<Z_501><Z_242><Z_498><ANSWER>

Question: John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The coefficient of $x^{3}$ in the expansion of $(2x-3)^{5}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The coefficient of $x^{3}$ in the expansion of $(2x-3)^{5}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The coefficient of $x^{3}$ in the expansion of $(2x-3)^{5}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_150><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The coefficient of $x^{3}$ in the expansion of $(2x-3)^{5}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_21><ANSWER>

Question: The coefficient of $x^{3}$ in the expansion of $(2x-3)^{5}$ is ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jason has 44 blue marbles, 16 red marbles, and 8 green marbles. Tom has 24 blue marbles, 10 yellow marbles, and 7 green marbles. Find the difference between the number of blue marbles Jason and Tom have.<|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
Jason has 44 blue marbles, 16 red marbles, and 8 green marbles. Tom has 24 blue marbles, 10 yellow marbles, and 7 green marbles. Find the difference between the number of blue marbles Jason and Tom have.<|im_end|>
<|im_start|>assistant
<Z_72><Z_474><Z_338><Z_71><Z_227><Z_500><Z_93><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jason has 44 blue marbles, 16 red marbles, and 8 green marbles. Tom has 24 blue marbles, 10 yellow marbles, and 7 green marbles. Find the difference between the number of blue marbles Jason and Tom have.<|im_end|>
<|im_start|>assistant
<Z_481><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jason has 44 blue marbles, 16 red marbles, and 8 green marbles. Tom has 24 blue marbles, 10 yellow marbles, and 7 green marbles. Find the difference between the number of blue marbles Jason and Tom have.<|im_end|>
<|im_start|>assistant
<Z_385><Z_324><Z_347><Z_114><Z_10><Z_96><Z_43><Z_382><ANSWER>

Question: Jason has 44 blue marbles, 16 red marbles, and 8 green marbles. Tom has 24 blue marbles, 10 yellow marbles, and 7 green marbles. Find the difference between the number of blue marbles Jason and Tom have.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of integers $n$ that satisfy
\[50 < n^2 < 200.\]<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of integers $n$ that satisfy
\[50 < n^2 < 200.\]<|im_end|>
<|im_start|>assistant
<Z_5><Z_293><Z_158><Z_497><Z_408><Z_318><Z_318><Z_388><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of integers $n$ that satisfy
\[50 < n^2 < 200.\]<|im_end|>
<|im_start|>assistant
<Z_475><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of integers $n$ that satisfy
\[50 < n^2 < 200.\]<|im_end|>
<|im_start|>assistant
<Z_84><Z_175><Z_346><Z_341><Z_339><Z_3><Z_468><Z_464><ANSWER>

Question:
Find the number of integers $n$ that satisfy
\[50 < n^2 < 200.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of the first 95 odd positive integers.<|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
Calculate the sum of the first 95 odd positive integers.<|im_end|>
<|im_start|>assistant
<Z_195><Z_60><Z_427><Z_320><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of the first 95 odd positive integers.<|im_end|>
<|im_start|>assistant
<Z_158><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum of the first 95 odd positive integers.<|im_end|>
<|im_start|>assistant
<Z_162><Z_343><Z_334><Z_56><ANSWER>

Question: Calculate the sum of the first 95 odd positive integers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Factor the expression
\[\frac{(a^2 - b^2)^4 + (b^2 - c^2)^4 + (c^2 - a^2)^4}{(a - b)^4 + (b - c)^4 + (c - a)^4}.\]<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Factor the expression
\[\frac{(a^2 - b^2)^4 + (b^2 - c^2)^4 + (c^2 - a^2)^4}{(a - b)^4 + (b - c)^4 + (c - a)^4}.\]<|im_end|>
<|im_start|>assistant
<Z_358><Z_44><Z_285><Z_75><Z_342><Z_255><Z_295><Z_221><Z_376><Z_407><Z_424><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Factor the expression
\[\frac{(a^2 - b^2)^4 + (b^2 - c^2)^4 + (c^2 - a^2)^4}{(a - b)^4 + (b - c)^4 + (c - a)^4}.\]<|im_end|>
<|im_start|>assistant
<Z_425><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Factor the expression
\[\frac{(a^2 - b^2)^4 + (b^2 - c^2)^4 + (c^2 - a^2)^4}{(a - b)^4 + (b - c)^4 + (c - a)^4}.\]<|im_end|>
<|im_start|>assistant
<Z_55><Z_37><Z_209><Z_143><Z_127><Z_153><Z_394><Z_493><Z_104><Z_422><Z_156><ANSWER>

Question:
Factor the expression
\[\frac{(a^2 - b^2)^4 + (b^2 - c^2)^4 + (c^2 - a^2)^4}{(a - b)^4 + (b - c)^4 + (c - a)^4}.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the volume of a cube is 1331 cc . find its surface .<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the volume of a cube is 1331 cc . find its surface .<|im_end|>
<|im_start|>assistant
<Z_176><Z_477><Z_502><Z_502><Z_463><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the volume of a cube is 1331 cc . find its surface .<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
the volume of a cube is 1331 cc . find its surface .<|im_end|>
<|im_start|>assistant
<Z_240><Z_353><Z_497><Z_385><Z_148><ANSWER>

Question: the volume of a cube is 1331 cc . find its surface .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=2x^{2}-(a+2)x+a$, where $a\in R$.
$(1)$ When $a=-1$, find the solution to the inequality $y \gt 0$ in terms of $x$.
$(2)$ If the equation $2x^{2}-(a+2)x+a=x+1$ has two positive real roots $x_{1}$ and $x_{2}$, find the minimum value of $\frac{x_{2}}{x_{1}}+\frac{x_{1}}{x_{2}}$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=2x^{2}-(a+2)x+a$, where $a\in R$.
$(1)$ When $a=-1$, find the solution to the inequality $y \gt 0$ in terms of $x$.
$(2)$ If the equation $2x^{2}-(a+2)x+a=x+1$ has two positive real roots $x_{1}$ and $x_{2}$, find the minimum value of $\frac{x_{2}}{x_{1}}+\frac{x_{1}}{x_{2}}$.<|im_end|>
<|im_start|>assistant
<Z_5><Z_437><Z_100><Z_71><Z_303><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=2x^{2}-(a+2)x+a$, where $a\in R$.
$(1)$ When $a=-1$, find the solution to the inequality $y \gt 0$ in terms of $x$.
$(2)$ If the equation $2x^{2}-(a+2)x+a=x+1$ has two positive real roots $x_{1}$ and $x_{2}$, find the minimum value of $\frac{x_{2}}{x_{1}}+\frac{x_{1}}{x_{2}}$.<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $y=2x^{2}-(a+2)x+a$, where $a\in R$.
$(1)$ When $a=-1$, find the solution to the inequality $y \gt 0$ in terms of $x$.
$(2)$ If the equation $2x^{2}-(a+2)x+a=x+1$ has two positive real roots $x_{1}$ and $x_{2}$, find the minimum value of $\frac{x_{2}}{x_{1}}+\frac{x_{1}}{x_{2}}$.<|im_end|>
<|im_start|>assistant
<Z_134><Z_442><Z_159><Z_207><Z_321><ANSWER>

Question:
Given the function $y=2x^{2}-(a+2)x+a$, where $a\in R$.
$(1)$ When $a=-1$, find the solution to the inequality $y \gt 0$ in terms of $x$.
$(2)$ If the equation $2x^{2}-(a+2)x+a=x+1$ has two positive real roots $x_{1}$ and $x_{2}$, find the minimum value of $\frac{x_{2}}{x_{1}}+\frac{x_{1}}{x_{2}}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the definite integral $\int\_{0}^{2}{(\sin {\pi x}+x-1)dx}=\_\_\_\_\_\_.\ $<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the definite integral $\int\_{0}^{2}{(\sin {\pi x}+x-1)dx}=\_\_\_\_\_\_.\ $<|im_end|>
<|im_start|>assistant
<Z_72><Z_180><Z_481><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Evaluate the definite integral $\int\_{0}^{2}{(\sin {\pi x}+x-1)dx}=\_\_\_\_\_\_.\ $<|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
Evaluate the definite integral $\int\_{0}^{2}{(\sin {\pi x}+x-1)dx}=\_\_\_\_\_\_.\ $<|im_end|>
<|im_start|>assistant
<Z_83><Z_462><Z_107><ANSWER>

Question: Evaluate the definite integral $\int\_{0}^{2}{(\sin {\pi x}+x-1)dx}=\_\_\_\_\_\_.\ $


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular roof shingle has a trapezoidal cut on one of the shorter sides. The uncut side is 10 inches long and 7 inches wide. The trapezoidal cut has a height of 2 inches and a base of 6 inches. What is the area of the resulting irregular-shaped roof shingle?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular roof shingle has a trapezoidal cut on one of the shorter sides. The uncut side is 10 inches long and 7 inches wide. The trapezoidal cut has a height of 2 inches and a base of 6 inches. What is the area of the resulting irregular-shaped roof shingle?<|im_end|>
<|im_start|>assistant
<Z_66><Z_435><Z_427><Z_394><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular roof shingle has a trapezoidal cut on one of the shorter sides. The uncut side is 10 inches long and 7 inches wide. The trapezoidal cut has a height of 2 inches and a base of 6 inches. What is the area of the resulting irregular-shaped roof shingle?<|im_end|>
<|im_start|>assistant
<Z_194><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular roof shingle has a trapezoidal cut on one of the shorter sides. The uncut side is 10 inches long and 7 inches wide. The trapezoidal cut has a height of 2 inches and a base of 6 inches. What is the area of the resulting irregular-shaped roof shingle?<|im_end|>
<|im_start|>assistant
<Z_468><Z_109><Z_263><Z_239><ANSWER>

Question: A rectangular roof shingle has a trapezoidal cut on one of the shorter sides. The uncut side is 10 inches long and 7 inches wide. The trapezoidal cut has a height of 2 inches and a base of 6 inches. What is the area of the resulting irregular-shaped roof shingle?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
15% of 30% of 50% of a number is a certain value. If the number is 5200, what is the value?<|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
15% of 30% of 50% of a number is a certain value. If the number is 5200, what is the value?<|im_end|>
<|im_start|>assistant
<Z_176><Z_295><Z_267><Z_339><Z_214><Z_215><Z_406><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
15% of 30% of 50% of a number is a certain value. If the number is 5200, what is the value?<|im_end|>
<|im_start|>assistant
<Z_35><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
15% of 30% of 50% of a number is a certain value. If the number is 5200, what is the value?<|im_end|>
<|im_start|>assistant
<Z_23><Z_511><Z_172><Z_220><Z_504><Z_141><Z_310><ANSWER>

Question: 15% of 30% of 50% of a number is a certain value. If the number is 5200, what is the value?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A sample of size $n$ is divided into several groups. It is known that the frequency and the rate of a certain group are 36 and 0.25, respectively. Therefore, $n$ equals to \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A sample of size $n$ is divided into several groups. It is known that the frequency and the rate of a certain group are 36 and 0.25, respectively. Therefore, $n$ equals to \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_195><Z_364><Z_408><Z_509><Z_388><Z_218><Z_454><Z_444><Z_253><Z_252><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A sample of size $n$ is divided into several groups. It is known that the frequency and the rate of a certain group are 36 and 0.25, respectively. Therefore, $n$ equals to \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_368><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A sample of size $n$ is divided into several groups. It is known that the frequency and the rate of a certain group are 36 and 0.25, respectively. Therefore, $n$ equals to \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_41><Z_78><Z_175><Z_75><Z_115><Z_504><Z_191><Z_157><Z_359><Z_98><ANSWER>

Question: A sample of size $n$ is divided into several groups. It is known that the frequency and the rate of a certain group are 36 and 0.25, respectively. Therefore, $n$ equals to \_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The 14th National People's Congress was held in Beijing from March 5th to 13th. The government work report summarized the great achievements of the past five years and outlined a beautiful blueprint for the next five years, inspiring and motivating people. To study and implement the spirit of the meeting, 4 speakers are organized to preach the spirit of the meeting, assigned to 3 communities. Each speaker is assigned to only one community, and each community must have at least 1 speaker. How many different distribution schemes are there in total?

A. 72

B. 12

C. 36

D. 24<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The 14th National People's Congress was held in Beijing from March 5th to 13th. The government work report summarized the great achievements of the past five years and outlined a beautiful blueprint for the next five years, inspiring and motivating people. To study and implement the spirit of the meeting, 4 speakers are organized to preach the spirit of the meeting, assigned to 3 communities. Each speaker is assigned to only one community, and each community must have at least 1 speaker. How many different distribution schemes are there in total?

A. 72

B. 12

C. 36

D. 24<|im_end|>
<|im_start|>assistant
<Z_5><Z_187><Z_318><Z_454><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The 14th National People's Congress was held in Beijing from March 5th to 13th. The government work report summarized the great achievements of the past five years and outlined a beautiful blueprint for the next five years, inspiring and motivating people. To study and implement the spirit of the meeting, 4 speakers are organized to preach the spirit of the meeting, assigned to 3 communities. Each speaker is assigned to only one community, and each community must have at least 1 speaker. How many different distribution schemes are there in total?

A. 72

B. 12

C. 36

D. 24<|im_end|>
<|im_start|>assistant
<Z_398><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The 14th National People's Congress was held in Beijing from March 5th to 13th. The government work report summarized the great achievements of the past five years and outlined a beautiful blueprint for the next five years, inspiring and motivating people. To study and implement the spirit of the meeting, 4 speakers are organized to preach the spirit of the meeting, assigned to 3 communities. Each speaker is assigned to only one community, and each community must have at least 1 speaker. How many different distribution schemes are there in total?

A. 72

B. 12

C. 36

D. 24<|im_end|>
<|im_start|>assistant
<Z_280><Z_255><Z_329><Z_494><ANSWER>

Question:
The 14th National People's Congress was held in Beijing from March 5th to 13th. The government work report summarized the great achievements of the past five years and outlined a beautiful blueprint for the next five years, inspiring and motivating people. To study and implement the spirit of the meeting, 4 speakers are organized to preach the spirit of the meeting, assigned to 3 communities. Each speaker is assigned to only one community, and each community must have at least 1 speaker. How many different distribution schemes are there in total?

A. 72

B. 12

C. 36

D. 24