<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?<|im_end|>
<|im_start|>assistant
<Z_369><Z_173><Z_205><Z_463><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?<|im_end|>
<|im_start|>assistant
<Z_177><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?<|im_end|>
<|im_start|>assistant
<Z_359><Z_123><Z_309><Z_449><Z_27><ANSWER>

Question: There are 3 garages at Liam's house. In the first garage, there are 5 bicycles, 6 tricycles, 9 unicycles, and 3 quadracycles, but 2 of the bicycles are missing a wheel. Each bicycle typically has 2 wheels, each tricycle has 3 wheels, each unicycle has 1 wheel, and each quadracycle has 4 wheels. In the second garage, there are 2 bicycles, 1 tricycle, 3 unicycles, 4 quadracycles, and 2 pentacycles, with 1 of the pentacycles missing 2 wheels. Each pentacycle typically has 5 wheels. In the third garage, there are 3 bicycles, 4 tricycles, 2 unicycles, 2 quadracycles, 1 pentacycle, and a hexacycle with a sidecar, but 1 of the unicycles is missing a wheel, and the hexacycle with a sidecar is missing 1 wheel. Each hexacycle typically has 6 wheels, and a sidecar adds 1 extra wheel. How many wheels are there in total across all three garages?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the lengths of the medians of a triangle whose side lengths are $13, 13,$ and $10$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the lengths of the medians of a triangle whose side lengths are $13, 13,$ and $10$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_310><Z_372><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the lengths of the medians of a triangle whose side lengths are $13, 13,$ and $10$?<|im_end|>
<|im_start|>assistant
<Z_493><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the lengths of the medians of a triangle whose side lengths are $13, 13,$ and $10$?<|im_end|>
<|im_start|>assistant
<Z_198><Z_105><Z_185><ANSWER>

Question: What is the sum of the squares of the lengths of the medians of a triangle whose side lengths are $13, 13,$ and $10$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $\bold{u} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\bold{z} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{u}$, $\bold{z}$, and $\bold{u} + \bold{z}$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $\bold{u} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\bold{z} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{u}$, $\bold{z}$, and $\bold{u} + \bold{z}$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_219><Z_295><Z_236><Z_306><Z_320><Z_432><Z_134><Z_173><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $\bold{u} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\bold{z} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{u}$, $\bold{z}$, and $\bold{u} + \bold{z}$.<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $\bold{u} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\bold{z} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{u}$, $\bold{z}$, and $\bold{u} + \bold{z}$.<|im_end|>
<|im_start|>assistant
<Z_406><Z_117><Z_392><Z_256><Z_389><Z_263><Z_465><Z_131><Z_233><ANSWER>

Question: Let $\bold{u} = \begin{pmatrix} 4 \\ 7 \end{pmatrix}$ and $\bold{z} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{u}$, $\bold{z}$, and $\bold{u} + \bold{z}$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 There are 40 boys and some girls on the playground. There are 117 children altogether. How many girls are on the playground?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 There are 40 boys and some girls on the playground. There are 117 children altogether. How many girls are on the playground?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 There are 40 boys and some girls on the playground. There are 117 children altogether. How many girls are on the playground?<|im_end|>
<|im_start|>assistant
<Z_219><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
 There are 40 boys and some girls on the playground. There are 117 children altogether. How many girls are on the playground?<|im_end|>
<|im_start|>assistant
<Z_368><ANSWER>

Question: There are 40 boys and some girls on the playground. There are 117 children altogether. How many girls are on the playground?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The center of the circle inscribed in a trapezoid is at distances of 5 and 12 from the ends of one of the non-parallel sides. Find the length of this side.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The center of the circle inscribed in a trapezoid is at distances of 5 and 12 from the ends of one of the non-parallel sides. Find the length of this side.<|im_end|>
<|im_start|>assistant
<Z_397><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The center of the circle inscribed in a trapezoid is at distances of 5 and 12 from the ends of one of the non-parallel sides. Find the length of this side.<|im_end|>
<|im_start|>assistant
<Z_51><ANSWER>

Question: The center of the circle inscribed in a trapezoid is at distances of 5 and 12 from the ends of one of the non-parallel sides. Find the length of this side.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit integer each of whose digits is equal to $c$. What is the smallest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - A_n = B_n^2$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit integer each of whose digits is equal to $c$. What is the smallest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - A_n = B_n^2$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_87><Z_280><Z_343><Z_349><Z_165><Z_230><Z_313><Z_386><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit integer each of whose digits is equal to $c$. What is the smallest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - A_n = B_n^2$?<|im_end|>
<|im_start|>assistant
<Z_357><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit integer each of whose digits is equal to $c$. What is the smallest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - A_n = B_n^2$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_372><Z_211><Z_67><Z_32><Z_363><Z_42><Z_45><Z_318><ANSWER>

Question: For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit integer each of whose digits is equal to $c$. What is the smallest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - A_n = B_n^2$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul was collecting cans for recycling. On Saturday he filled 6 bags up, and on Sunday he filled 3 more bags. If each bag had 8 cans in it, how many cans did he pick up in total?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul was collecting cans for recycling. On Saturday he filled 6 bags up, and on Sunday he filled 3 more bags. If each bag had 8 cans in it, how many cans did he pick up in total?<|im_end|>
<|im_start|>assistant
<Z_369><Z_256><Z_321><Z_123><Z_456><Z_298><Z_130><Z_485><Z_378><Z_253><Z_178><Z_194><Z_440><Z_443><Z_73><Z_141><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul was collecting cans for recycling. On Saturday he filled 6 bags up, and on Sunday he filled 3 more bags. If each bag had 8 cans in it, how many cans did he pick up in total?<|im_end|>
<|im_start|>assistant
<Z_406><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul was collecting cans for recycling. On Saturday he filled 6 bags up, and on Sunday he filled 3 more bags. If each bag had 8 cans in it, how many cans did he pick up in total?<|im_end|>
<|im_start|>assistant
<Z_243><Z_510><Z_157><Z_373><Z_315><Z_214><Z_330><Z_429><Z_295><Z_404><Z_237><Z_19><Z_155><Z_76><Z_188><Z_130><ANSWER>

Question: Paul was collecting cans for recycling. On Saturday he filled 6 bags up, and on Sunday he filled 3 more bags. If each bag had 8 cans in it, how many cans did he pick up in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At Sunshine Orchard, there are 12 more than three times the number of pumpkins at another orchard. If Sunshine Orchard has 54 pumpkins, how many pumpkins are there at the other orchard?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At Sunshine Orchard, there are 12 more than three times the number of pumpkins at another orchard. If Sunshine Orchard has 54 pumpkins, how many pumpkins are there at the other orchard?<|im_end|>
<|im_start|>assistant
<Z_477><Z_227><Z_159><Z_425><Z_335><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At Sunshine Orchard, there are 12 more than three times the number of pumpkins at another orchard. If Sunshine Orchard has 54 pumpkins, how many pumpkins are there at the other orchard?<|im_end|>
<|im_start|>assistant
<Z_169><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At Sunshine Orchard, there are 12 more than three times the number of pumpkins at another orchard. If Sunshine Orchard has 54 pumpkins, how many pumpkins are there at the other orchard?<|im_end|>
<|im_start|>assistant
<Z_446><Z_223><Z_3><Z_258><Z_43><ANSWER>

Question: At Sunshine Orchard, there are 12 more than three times the number of pumpkins at another orchard. If Sunshine Orchard has 54 pumpkins, how many pumpkins are there at the other orchard?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a convex pentagon \(ABCDE\), the diagonals \(BE\) and \(CE\) are the angle bisectors at vertices \(B\) and \(C\) respectively, \(\angle A = 35^{\circ}\), \(\angle D = 145^{\circ}\), and the area of triangle \(BCE\) is 11. Find the area of the pentagon \(ABCDE\).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a convex pentagon \(ABCDE\), the diagonals \(BE\) and \(CE\) are the angle bisectors at vertices \(B\) and \(C\) respectively, \(\angle A = 35^{\circ}\), \(\angle D = 145^{\circ}\), and the area of triangle \(BCE\) is 11. Find the area of the pentagon \(ABCDE\).<|im_end|>
<|im_start|>assistant
<Z_24><Z_204><Z_197><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a convex pentagon \(ABCDE\), the diagonals \(BE\) and \(CE\) are the angle bisectors at vertices \(B\) and \(C\) respectively, \(\angle A = 35^{\circ}\), \(\angle D = 145^{\circ}\), and the area of triangle \(BCE\) is 11. Find the area of the pentagon \(ABCDE\).<|im_end|>
<|im_start|>assistant
<Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a convex pentagon \(ABCDE\), the diagonals \(BE\) and \(CE\) are the angle bisectors at vertices \(B\) and \(C\) respectively, \(\angle A = 35^{\circ}\), \(\angle D = 145^{\circ}\), and the area of triangle \(BCE\) is 11. Find the area of the pentagon \(ABCDE\).<|im_end|>
<|im_start|>assistant
<Z_463><Z_317><Z_400><ANSWER>

Question: In a convex pentagon \(ABCDE\), the diagonals \(BE\) and \(CE\) are the angle bisectors at vertices \(B\) and \(C\) respectively, \(\angle A = 35^{\circ}\), \(\angle D = 145^{\circ}\), and the area of triangle \(BCE\) is 11. Find the area of the pentagon \(ABCDE\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_374><Z_294><Z_386><Z_193><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?<|im_end|>
<|im_start|>assistant
<Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?<|im_end|>
<|im_start|>assistant
<Z_41><Z_310><Z_309><Z_418><Z_348><ANSWER>

Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two lines $l_{1}$: $ax+y+1=0$ and $l_{2}$: $x-2y+1=0$, if $l_{1}\perp l_{2}$, then the real number $a=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two lines $l_{1}$: $ax+y+1=0$ and $l_{2}$: $x-2y+1=0$, if $l_{1}\perp l_{2}$, then the real number $a=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_420><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two lines $l_{1}$: $ax+y+1=0$ and $l_{2}$: $x-2y+1=0$, if $l_{1}\perp l_{2}$, then the real number $a=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_156><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given two lines $l_{1}$: $ax+y+1=0$ and $l_{2}$: $x-2y+1=0$, if $l_{1}\perp l_{2}$, then the real number $a=\_\_\_\_\_\_$.<|im_end|>
<|im_start|>assistant
<Z_150><Z_125><ANSWER>

Question: Given two lines $l_{1}$: $ax+y+1=0$ and $l_{2}$: $x-2y+1=0$, if $l_{1}\perp l_{2}$, then the real number $a=\_\_\_\_\_\_$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?<|im_end|>
<|im_start|>assistant
<Z_24><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?<|im_end|>
<|im_start|>assistant
<Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?<|im_end|>
<|im_start|>assistant
<Z_502><Z_32><ANSWER>

Question: we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two numbers are in ratio 4 : 5 and their LCM is a certain value. The smaller number is 36. What is the LCM of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two numbers are in ratio 4 : 5 and their LCM is a certain value. The smaller number is 36. What is the LCM of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_369><Z_307><Z_104><Z_418><Z_158><Z_53><Z_214><Z_255><Z_129><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two numbers are in ratio 4 : 5 and their LCM is a certain value. The smaller number is 36. What is the LCM of the two numbers?<|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
Two numbers are in ratio 4 : 5 and their LCM is a certain value. The smaller number is 36. What is the LCM of the two numbers?<|im_end|>
<|im_start|>assistant
<Z_45><Z_120><Z_376><Z_435><Z_247><Z_223><Z_96><Z_212><Z_482><ANSWER>

Question: Two numbers are in ratio 4 : 5 and their LCM is a certain value. The smaller number is 36. What is the LCM of the two numbers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of two numbers is 40. Their difference is 12. Find the numbers.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of two numbers is 40. Their difference is 12. Find the numbers.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of two numbers is 40. Their difference is 12. Find the numbers.<|im_end|>
<|im_start|>assistant
<Z_490><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of two numbers is 40. Their difference is 12. Find the numbers.<|im_end|>
<|im_start|>assistant
<Z_389><ANSWER>

Question: The sum of two numbers is 40. Their difference is 12. Find the numbers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?<|im_end|>
<|im_start|>assistant
<Z_54><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?<|im_end|>
<|im_start|>assistant
<Z_248><ANSWER>

Question: a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of ordered pairs $(x, y)$ of real numbers such that
\[9^{x^2 + y} + 9^{x + y^2} = \sqrt{2}.\]<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of ordered pairs $(x, y)$ of real numbers such that
\[9^{x^2 + y} + 9^{x + y^2} = \sqrt{2}.\]<|im_end|>
<|im_start|>assistant
<Z_477><Z_201><Z_305><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 ordered pairs $(x, y)$ of real numbers such that
\[9^{x^2 + y} + 9^{x + y^2} = \sqrt{2}.\]<|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 number of ordered pairs $(x, y)$ of real numbers such that
\[9^{x^2 + y} + 9^{x + y^2} = \sqrt{2}.\]<|im_end|>
<|im_start|>assistant
<Z_59><Z_374><Z_486><ANSWER>

Question:
Find the number of ordered pairs $(x, y)$ of real numbers such that
\[9^{x^2 + y} + 9^{x + y^2} = \sqrt{2}.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain table tennis singles tournament, each pair of players was originally scheduled to play one match against each other. However, after three players each played two matches and then withdrew, a total of only 50 matches were conducted. How many matches were played among the aforementioned three players?
A. 0
B. 1
C. 2
D. 3<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain table tennis singles tournament, each pair of players was originally scheduled to play one match against each other. However, after three players each played two matches and then withdrew, a total of only 50 matches were conducted. How many matches were played among the aforementioned three players?
A. 0
B. 1
C. 2
D. 3<|im_end|>
<|im_start|>assistant
<Z_24><Z_426><Z_461><Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain table tennis singles tournament, each pair of players was originally scheduled to play one match against each other. However, after three players each played two matches and then withdrew, a total of only 50 matches were conducted. How many matches were played among the aforementioned three players?
A. 0
B. 1
C. 2
D. 3<|im_end|>
<|im_start|>assistant
<Z_357><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain table tennis singles tournament, each pair of players was originally scheduled to play one match against each other. However, after three players each played two matches and then withdrew, a total of only 50 matches were conducted. How many matches were played among the aforementioned three players?
A. 0
B. 1
C. 2
D. 3<|im_end|>
<|im_start|>assistant
<Z_406><Z_5><Z_392><Z_500><ANSWER>

Question:
In a certain table tennis singles tournament, each pair of players was originally scheduled to play one match against each other. However, after three players each played two matches and then withdrew, a total of only 50 matches were conducted. How many matches were played among the aforementioned three players?
A. 0
B. 1
C. 2
D. 3


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by some inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the height of the carton?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by some inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the height of the carton?<|im_end|>
<|im_start|>assistant
<Z_477><Z_197><Z_210><Z_214><Z_250><Z_406><Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by some inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the height of the carton?<|im_end|>
<|im_start|>assistant
<Z_184><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by some inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the height of the carton?<|im_end|>
<|im_start|>assistant
<Z_116><Z_424><Z_349><Z_42><Z_463><Z_375><Z_130><ANSWER>

Question: Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by some inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, and the maximum number of cake boxes that can be placed in each carton is 210, what is the height of the carton?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a programming bootcamp, there are 50 members with an average age of 20 years. The group is made up of 25 girls, 20 boys, and 5 adults. If the average age of the girls is 18 and the average age of the boys is 22, what is the average age of the adults?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a programming bootcamp, there are 50 members with an average age of 20 years. The group is made up of 25 girls, 20 boys, and 5 adults. If the average age of the girls is 18 and the average age of the boys is 22, what is the average age of the adults?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a programming bootcamp, there are 50 members with an average age of 20 years. The group is made up of 25 girls, 20 boys, and 5 adults. If the average age of the girls is 18 and the average age of the boys is 22, what is the average age of the adults?<|im_end|>
<|im_start|>assistant
<Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a programming bootcamp, there are 50 members with an average age of 20 years. The group is made up of 25 girls, 20 boys, and 5 adults. If the average age of the girls is 18 and the average age of the boys is 22, what is the average age of the adults?<|im_end|>
<|im_start|>assistant
<Z_284><ANSWER>

Question: In a programming bootcamp, there are 50 members with an average age of 20 years. The group is made up of 25 girls, 20 boys, and 5 adults. If the average age of the girls is 18 and the average age of the boys is 22, what is the average age of the adults?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The distance between cities A and B is an integer number of kilometers. Along the road between the cities, there are markers every kilometer: on one side, the distance to city A is written, and on the other side, the distance to city B is written. Slava was walking from city A to city B. During his journey, Slava calculated the GCD (Greatest Common Divisor) for the numbers written on each marker. It turned out that only the numbers 1, 3, and 13 appeared as GCDs. What is the distance between the cities?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The distance between cities A and B is an integer number of kilometers. Along the road between the cities, there are markers every kilometer: on one side, the distance to city A is written, and on the other side, the distance to city B is written. Slava was walking from city A to city B. During his journey, Slava calculated the GCD (Greatest Common Divisor) for the numbers written on each marker. It turned out that only the numbers 1, 3, and 13 appeared as GCDs. What is the distance between the cities?<|im_end|>
<|im_start|>assistant
<Z_477><Z_267><Z_367><Z_245><Z_376><Z_502><Z_425><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The distance between cities A and B is an integer number of kilometers. Along the road between the cities, there are markers every kilometer: on one side, the distance to city A is written, and on the other side, the distance to city B is written. Slava was walking from city A to city B. During his journey, Slava calculated the GCD (Greatest Common Divisor) for the numbers written on each marker. It turned out that only the numbers 1, 3, and 13 appeared as GCDs. What is the distance between the cities?<|im_end|>
<|im_start|>assistant
<Z_46><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The distance between cities A and B is an integer number of kilometers. Along the road between the cities, there are markers every kilometer: on one side, the distance to city A is written, and on the other side, the distance to city B is written. Slava was walking from city A to city B. During his journey, Slava calculated the GCD (Greatest Common Divisor) for the numbers written on each marker. It turned out that only the numbers 1, 3, and 13 appeared as GCDs. What is the distance between the cities?<|im_end|>
<|im_start|>assistant
<Z_504><Z_60><Z_389><Z_47><Z_390><Z_85><Z_463><ANSWER>

Question: The distance between cities A and B is an integer number of kilometers. Along the road between the cities, there are markers every kilometer: on one side, the distance to city A is written, and on the other side, the distance to city B is written. Slava was walking from city A to city B. During his journey, Slava calculated the GCD (Greatest Common Divisor) for the numbers written on each marker. It turned out that only the numbers 1, 3, and 13 appeared as GCDs. What is the distance between the cities?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?<|im_end|>
<|im_start|>assistant
<Z_477><Z_326><Z_114><Z_381><Z_434><Z_240><Z_185><Z_422><Z_299><Z_276><Z_194><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?<|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
The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?<|im_end|>
<|im_start|>assistant
<Z_240><Z_476><Z_476><Z_495><Z_86><Z_259><Z_224><Z_436><Z_419><Z_8><Z_394><ANSWER>

Question: The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Amy was playing a video game where she scores 4 points for each treasure she finds. She found 6 treasures on the first level and 2 on the second level. What was her total score?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Amy was playing a video game where she scores 4 points for each treasure she finds. She found 6 treasures on the first level and 2 on the second level. What was her total score?<|im_end|>
<|im_start|>assistant
<Z_477><Z_453><Z_102><Z_508><Z_246><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Amy was playing a video game where she scores 4 points for each treasure she finds. She found 6 treasures on the first level and 2 on the second level. What was her total score?<|im_end|>
<|im_start|>assistant
<Z_392><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Amy was playing a video game where she scores 4 points for each treasure she finds. She found 6 treasures on the first level and 2 on the second level. What was her total score?<|im_end|>
<|im_start|>assistant
<Z_89><Z_162><Z_4><Z_373><Z_220><ANSWER>

Question: Amy was playing a video game where she scores 4 points for each treasure she finds. She found 6 treasures on the first level and 2 on the second level. What was her total score?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.<|im_end|>
<|im_start|>assistant
<Z_24><Z_276><Z_344><Z_194><Z_335><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.<|im_end|>
<|im_start|>assistant
<Z_238><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.<|im_end|>
<|im_start|>assistant
<Z_444><Z_301><Z_3><Z_192><Z_106><ANSWER>

Question:
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation \[\frac{x+6}{x-3}=4\] for \(x\).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation \[\frac{x+6}{x-3}=4\] for \(x\).<|im_end|>
<|im_start|>assistant
<Z_24><Z_162><Z_414><Z_240><Z_475><Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation \[\frac{x+6}{x-3}=4\] for \(x\).<|im_end|>
<|im_start|>assistant
<Z_282><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation \[\frac{x+6}{x-3}=4\] for \(x\).<|im_end|>
<|im_start|>assistant
<Z_221><Z_482><Z_256><Z_269><Z_418><Z_493><ANSWER>

Question: Solve the equation \[\frac{x+6}{x-3}=4\] for \(x\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\dfrac{1}{3}$, its foci are respectively $A$, $B$, and $C$ is any point on the ellipse other than the endpoints of the major axis. Then, in $\triangle ABC$, the value of $\dfrac{\sin A + \sin B}{\sin C}$ equals \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\dfrac{1}{3}$, its foci are respectively $A$, $B$, and $C$ is any point on the ellipse other than the endpoints of the major axis. Then, in $\triangle ABC$, the value of $\dfrac{\sin A + \sin B}{\sin C}$ equals \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_24><Z_358><Z_295><Z_425><Z_470><Z_232><Z_456><Z_386><Z_460><Z_433><Z_272><Z_260><Z_246><Z_185><Z_420><Z_98><Z_353><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\dfrac{1}{3}$, its foci are respectively $A$, $B$, and $C$ is any point on the ellipse other than the endpoints of the major axis. Then, in $\triangle ABC$, the value of $\dfrac{\sin A + \sin B}{\sin C}$ equals \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_276><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\dfrac{1}{3}$, its foci are respectively $A$, $B$, and $C$ is any point on the ellipse other than the endpoints of the major axis. Then, in $\triangle ABC$, the value of $\dfrac{\sin A + \sin B}{\sin C}$ equals \_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_368><Z_211><Z_42><Z_444><Z_71><Z_199><Z_255><Z_105><Z_325><Z_448><Z_63><Z_486><Z_336><Z_73><Z_138><Z_398><Z_64><ANSWER>

Question: Given an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\dfrac{1}{3}$, its foci are respectively $A$, $B$, and $C$ is any point on the ellipse other than the endpoints of the major axis. Then, in $\triangle ABC$, the value of $\dfrac{\sin A + \sin B}{\sin C}$ equals \_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive perfect squares less than $10^8$ are multiples of 36?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive perfect squares less than $10^8$ are multiples of 36?<|im_end|>
<|im_start|>assistant
<Z_477><Z_484><Z_458><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive perfect squares less than $10^8$ are multiples of 36?<|im_end|>
<|im_start|>assistant
<Z_392><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive perfect squares less than $10^8$ are multiples of 36?<|im_end|>
<|im_start|>assistant
<Z_11><Z_298><Z_34><ANSWER>

Question: How many positive perfect squares less than $10^8$ are multiples of 36?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What number results when 80 is increased by $150\%$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What number results when 80 is increased by $150\%$?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What number results when 80 is increased by $150\%$?<|im_end|>
<|im_start|>assistant
<Z_199><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What number results when 80 is increased by $150\%$?<|im_end|>
<|im_start|>assistant
<Z_190><ANSWER>

Question: What number results when 80 is increased by $150\%$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many perfect squares are between 50 and 1000?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many perfect squares are between 50 and 1000?<|im_end|>
<|im_start|>assistant
<Z_477><Z_229><Z_321><Z_274><Z_151><Z_366><Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many perfect squares are between 50 and 1000?<|im_end|>
<|im_start|>assistant
<Z_498><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many perfect squares are between 50 and 1000?<|im_end|>
<|im_start|>assistant
<Z_144><Z_27><Z_307><Z_207><Z_441><Z_260><Z_126><ANSWER>

Question: How many perfect squares are between 50 and 1000?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . The points ( m , n ) and ( m + p , n + some value ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ). The value of p is 3. What is the increase in the y-coordinate from the first point to the second point?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . The points ( m , n ) and ( m + p , n + some value ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ). The value of p is 3. What is the increase in the y-coordinate from the first point to the second point?<|im_end|>
<|im_start|>assistant
<Z_477><Z_50><Z_255><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . The points ( m , n ) and ( m + p , n + some value ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ). The value of p is 3. What is the increase in the y-coordinate from the first point to the second point?<|im_end|>
<|im_start|>assistant
<Z_492><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . The points ( m , n ) and ( m + p , n + some value ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ). The value of p is 3. What is the increase in the y-coordinate from the first point to the second point?<|im_end|>
<|im_start|>assistant
<Z_110><Z_473><Z_283><ANSWER>

Question: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . The points ( m , n ) and ( m + p , n + some value ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ). The value of p is 3. What is the increase in the y-coordinate from the first point to the second point?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive three-digit integers have an odd number of positive factors?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive three-digit integers have an odd number of positive factors?<|im_end|>
<|im_start|>assistant
<Z_369><Z_245><Z_321><Z_161><Z_506><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive three-digit integers have an odd number of positive factors?<|im_end|>
<|im_start|>assistant
<Z_189><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many positive three-digit integers have an odd number of positive factors?<|im_end|>
<|im_start|>assistant
<Z_464><Z_350><Z_73><Z_81><Z_438><ANSWER>

Question: How many positive three-digit integers have an odd number of positive factors?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A regular 15-gon is inscribed in a circle of radius 10. The sum of the lengths of all sides and diagonals of this 15-gon can be written in the form
\[a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5},\] where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find \(a+b+c+d\).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A regular 15-gon is inscribed in a circle of radius 10. The sum of the lengths of all sides and diagonals of this 15-gon can be written in the form
\[a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5},\] where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find \(a+b+c+d\).<|im_end|>
<|im_start|>assistant
<Z_369><Z_158><Z_316><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A regular 15-gon is inscribed in a circle of radius 10. The sum of the lengths of all sides and diagonals of this 15-gon can be written in the form
\[a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5},\] where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find \(a+b+c+d\).<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A regular 15-gon is inscribed in a circle of radius 10. The sum of the lengths of all sides and diagonals of this 15-gon can be written in the form
\[a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5},\] where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find \(a+b+c+d\).<|im_end|>
<|im_start|>assistant
<Z_404><Z_225><Z_417><Z_415><ANSWER>

Question:
A regular 15-gon is inscribed in a circle of radius 10. The sum of the lengths of all sides and diagonals of this 15-gon can be written in the form
\[a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5},\] where \(a\), \(b\), \(c\), and \(d\) are positive integers. Find \(a+b+c+d\).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \(3^x + 3^x + 3^x + 3^x = 243\), what is the value of \( (x+2)(x-2) \)?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that \(3^x + 3^x + 3^x + 3^x = 243\), what is the value of \( (x+2)(x-2) \)?<|im_end|>
<|im_start|>assistant
<Z_307><ANSWER>

Question: Given that \(3^x + 3^x + 3^x + 3^x = 243\), what is the value of \( (x+2)(x-2) \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dave had 15 apps on his phone. He added 71 new apps. After deleting some, he had a certain number of apps left and had deleted 1 more app than he added. How many apps did Dave have left on his phone?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dave had 15 apps on his phone. He added 71 new apps. After deleting some, he had a certain number of apps left and had deleted 1 more app than he added. How many apps did Dave have left on his phone?<|im_end|>
<|im_start|>assistant
<Z_369><Z_254><Z_68><Z_69><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dave had 15 apps on his phone. He added 71 new apps. After deleting some, he had a certain number of apps left and had deleted 1 more app than he added. How many apps did Dave have left on his phone?<|im_end|>
<|im_start|>assistant
<Z_453><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dave had 15 apps on his phone. He added 71 new apps. After deleting some, he had a certain number of apps left and had deleted 1 more app than he added. How many apps did Dave have left on his phone?<|im_end|>
<|im_start|>assistant
<Z_359><Z_435><Z_288><Z_59><ANSWER>

Question: Dave had 15 apps on his phone. He added 71 new apps. After deleting some, he had a certain number of apps left and had deleted 1 more app than he added. How many apps did Dave have left on his phone?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the integers from $-50$ to $80$, inclusive?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the integers from $-50$ to $80$, inclusive?<|im_end|>
<|im_start|>assistant
<Z_369><Z_373><Z_37><Z_460><Z_253><Z_493><Z_261><Z_217><Z_465><Z_330><Z_430><Z_86><Z_413><Z_348><Z_194><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the integers from $-50$ to $80$, inclusive?<|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
What is the sum of the integers from $-50$ to $80$, inclusive?<|im_end|>
<|im_start|>assistant
<Z_467><Z_216><Z_349><Z_314><Z_110><Z_256><Z_457><Z_108><Z_398><Z_476><Z_441><Z_134><Z_64><Z_120><Z_364><ANSWER>

Question: What is the sum of the integers from $-50$ to $80$, inclusive?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers 45, 336, and 339 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 600 modulo 3599. (Express your answer as an integer \( n \) with \(0 \leq n < 3599\)).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers 45, 336, and 339 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 600 modulo 3599. (Express your answer as an integer \( n \) with \(0 \leq n < 3599\)).<|im_end|>
<|im_start|>assistant
<Z_477><Z_377><Z_479><Z_378><Z_434><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers 45, 336, and 339 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 600 modulo 3599. (Express your answer as an integer \( n \) with \(0 \leq n < 3599\)).<|im_end|>
<|im_start|>assistant
<Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The numbers 45, 336, and 339 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 600 modulo 3599. (Express your answer as an integer \( n \) with \(0 \leq n < 3599\)).<|im_end|>
<|im_start|>assistant
<Z_277><Z_346><Z_417><Z_168><Z_317><ANSWER>

Question: The numbers 45, 336, and 339 are the legs and hypotenuse of a right triangle. Find the multiplicative inverse to 600 modulo 3599. (Express your answer as an integer \( n \) with \(0 \leq n < 3599\)).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that:
\[f(x^2 + 2f(y)) = xf(x) + yf(z)\]
for all real numbers $x,$ $y,$ and $z.$

Find the number $n$ of possible functions $f$, and determine the sum $s$ of $f(3)$ among all possible functions. Calculate $n \times s.$<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that:
\[f(x^2 + 2f(y)) = xf(x) + yf(z)\]
for all real numbers $x,$ $y,$ and $z.$

Find the number $n$ of possible functions $f$, and determine the sum $s$ of $f(3)$ among all possible functions. Calculate $n \times s.$<|im_end|>
<|im_start|>assistant
<Z_477><Z_483><Z_188><Z_287><Z_286><Z_101><Z_54><Z_287><Z_378><Z_185><Z_174><Z_237><Z_255><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that:
\[f(x^2 + 2f(y)) = xf(x) + yf(z)\]
for all real numbers $x,$ $y,$ and $z.$

Find the number $n$ of possible functions $f$, and determine the sum $s$ of $f(3)$ among all possible functions. Calculate $n \times s.$<|im_end|>
<|im_start|>assistant
<Z_3><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that:
\[f(x^2 + 2f(y)) = xf(x) + yf(z)\]
for all real numbers $x,$ $y,$ and $z.$

Find the number $n$ of possible functions $f$, and determine the sum $s$ of $f(3)$ among all possible functions. Calculate $n \times s.$<|im_end|>
<|im_start|>assistant
<Z_206><Z_183><Z_159><Z_362><Z_511><Z_411><Z_494><Z_22><Z_13><Z_170><Z_268><Z_30><Z_424><ANSWER>

Question:
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that:
\[f(x^2 + 2f(y)) = xf(x) + yf(z)\]
for all real numbers $x,$ $y,$ and $z.$

Find the number $n$ of possible functions $f$, and determine the sum $s$ of $f(3)$ among all possible functions. Calculate $n \times s.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Linda's bag has 2 dimes, some quarters, and 5 nickels. Her mother gives her 2 more dimes, 10 quarters, and twice as many nickels as she has. Linda has 35 coins altogether. How many quarters does Linda have initially?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Linda's bag has 2 dimes, some quarters, and 5 nickels. Her mother gives her 2 more dimes, 10 quarters, and twice as many nickels as she has. Linda has 35 coins altogether. How many quarters does Linda have initially?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Linda's bag has 2 dimes, some quarters, and 5 nickels. Her mother gives her 2 more dimes, 10 quarters, and twice as many nickels as she has. Linda has 35 coins altogether. How many quarters does Linda have initially?<|im_end|>
<|im_start|>assistant
<Z_471><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Linda's bag has 2 dimes, some quarters, and 5 nickels. Her mother gives her 2 more dimes, 10 quarters, and twice as many nickels as she has. Linda has 35 coins altogether. How many quarters does Linda have initially?<|im_end|>
<|im_start|>assistant
<Z_361><ANSWER>

Question: Linda's bag has 2 dimes, some quarters, and 5 nickels. Her mother gives her 2 more dimes, 10 quarters, and twice as many nickels as she has. Linda has 35 coins altogether. How many quarters does Linda have initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
All people named Barry are nice, while only half of the people named Kevin are nice.  Three-fourths of people named Julie are nice, while 10% of people named Joe are nice.  If a crowd contains 24 people named Barry, 20 people named Kevin, 80 people named Julie, and 50 people named Joe, how many nice people are in the crowd?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
All people named Barry are nice, while only half of the people named Kevin are nice.  Three-fourths of people named Julie are nice, while 10% of people named Joe are nice.  If a crowd contains 24 people named Barry, 20 people named Kevin, 80 people named Julie, and 50 people named Joe, how many nice people are in the crowd?<|im_end|>
<|im_start|>assistant
<Z_24><Z_117><Z_129><Z_464><Z_118><Z_39><Z_181><Z_52><Z_464><Z_98><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
All people named Barry are nice, while only half of the people named Kevin are nice.  Three-fourths of people named Julie are nice, while 10% of people named Joe are nice.  If a crowd contains 24 people named Barry, 20 people named Kevin, 80 people named Julie, and 50 people named Joe, how many nice people are in the crowd?<|im_end|>
<|im_start|>assistant
<Z_465><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
All people named Barry are nice, while only half of the people named Kevin are nice.  Three-fourths of people named Julie are nice, while 10% of people named Joe are nice.  If a crowd contains 24 people named Barry, 20 people named Kevin, 80 people named Julie, and 50 people named Joe, how many nice people are in the crowd?<|im_end|>
<|im_start|>assistant
<Z_16><Z_79><Z_322><Z_427><Z_32><Z_483><Z_28><Z_158><Z_266><Z_73><Z_347><ANSWER>

Question: All people named Barry are nice, while only half of the people named Kevin are nice.  Three-fourths of people named Julie are nice, while 10% of people named Joe are nice.  If a crowd contains 24 people named Barry, 20 people named Kevin, 80 people named Julie, and 50 people named Joe, how many nice people are in the crowd?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(p\), \(q\), \(r\), \(s\), and \(t\) be positive integers such that \(p+q+r+s+t=3015\) and let \(N\) be the largest of the sums \(p+q\), \(q+r\), \(r+s\), and \(s+t\). What is the smallest possible value of \(N\)?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(p\), \(q\), \(r\), \(s\), and \(t\) be positive integers such that \(p+q+r+s+t=3015\) and let \(N\) be the largest of the sums \(p+q\), \(q+r\), \(r+s\), and \(s+t\). What is the smallest possible value of \(N\)?<|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
Let \(p\), \(q\), \(r\), \(s\), and \(t\) be positive integers such that \(p+q+r+s+t=3015\) and let \(N\) be the largest of the sums \(p+q\), \(q+r\), \(r+s\), and \(s+t\). What is the smallest possible value of \(N\)?<|im_end|>
<|im_start|>assistant
<Z_478><ANSWER>

Question: Let \(p\), \(q\), \(r\), \(s\), and \(t\) be positive integers such that \(p+q+r+s+t=3015\) and let \(N\) be the largest of the sums \(p+q\), \(q+r\), \(r+s\), and \(s+t\). What is the smallest possible value of \(N\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a random variable $\xi \sim B(n, p)$, and $E\xi=6$, $D\xi=3$, then $n=$ \_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a random variable $\xi \sim B(n, p)$, and $E\xi=6$, $D\xi=3$, then $n=$ \_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_369><Z_231><Z_118><Z_79><Z_213><Z_178><Z_487><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a random variable $\xi \sim B(n, p)$, and $E\xi=6$, $D\xi=3$, then $n=$ \_\_\_\_\_\_\_\_\_.<|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
Given a random variable $\xi \sim B(n, p)$, and $E\xi=6$, $D\xi=3$, then $n=$ \_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_29><Z_429><Z_501><Z_293><Z_486><Z_341><Z_476><ANSWER>

Question: Given a random variable $\xi \sim B(n, p)$, and $E\xi=6$, $D\xi=3$, then $n=$ \_\_\_\_\_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two trains of different lengths run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is 11.879049676025918 seconds. If the length of the second train is 160 m, what is the length of the first train?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two trains of different lengths run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is 11.879049676025918 seconds. If the length of the second train is 160 m, what is the length of the first train?<|im_end|>
<|im_start|>assistant
<Z_477><Z_341><Z_260><Z_273><Z_102><Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two trains of different lengths run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is 11.879049676025918 seconds. If the length of the second train is 160 m, what is the length of the first train?<|im_end|>
<|im_start|>assistant
<Z_258><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two trains of different lengths run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is 11.879049676025918 seconds. If the length of the second train is 160 m, what is the length of the first train?<|im_end|>
<|im_start|>assistant
<Z_112><Z_322><Z_221><Z_305><Z_187><Z_127><ANSWER>

Question: Two trains of different lengths run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is 11.879049676025918 seconds. If the length of the second train is 160 m, what is the length of the first train?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).<|im_end|>
<|im_start|>assistant
<Z_369><Z_246><Z_494><Z_52><Z_335><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).<|im_end|>
<|im_start|>assistant
<Z_109><Z_194><Z_424><Z_113><Z_293><ANSWER>

Question: A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A three-digit number is divided by a two-digit number, resulting in a quotient which is the sum of the digits of the divisor. The remainder is a number formed by reversing the digits of the divisor. If the remainder is multiplied by the quotient and the divisor is added, the resulting number consists of the digits of the dividend but in reverse order. What are the dividend and the divisor?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A three-digit number is divided by a two-digit number, resulting in a quotient which is the sum of the digits of the divisor. The remainder is a number formed by reversing the digits of the divisor. If the remainder is multiplied by the quotient and the divisor is added, the resulting number consists of the digits of the dividend but in reverse order. What are the dividend and the divisor?<|im_end|>
<|im_start|>assistant
<Z_24><Z_498><Z_490><Z_470><Z_264><Z_490><Z_109><Z_87><Z_97><Z_238><Z_279><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A three-digit number is divided by a two-digit number, resulting in a quotient which is the sum of the digits of the divisor. The remainder is a number formed by reversing the digits of the divisor. If the remainder is multiplied by the quotient and the divisor is added, the resulting number consists of the digits of the dividend but in reverse order. What are the dividend and the divisor?<|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
A three-digit number is divided by a two-digit number, resulting in a quotient which is the sum of the digits of the divisor. The remainder is a number formed by reversing the digits of the divisor. If the remainder is multiplied by the quotient and the divisor is added, the resulting number consists of the digits of the dividend but in reverse order. What are the dividend and the divisor?<|im_end|>
<|im_start|>assistant
<Z_510><Z_441><Z_300><Z_49><Z_302><Z_400><Z_35><Z_116><Z_369><Z_375><Z_348><Z_330><ANSWER>

Question: A three-digit number is divided by a two-digit number, resulting in a quotient which is the sum of the digits of the divisor. The remainder is a number formed by reversing the digits of the divisor. If the remainder is multiplied by the quotient and the divisor is added, the resulting number consists of the digits of the dividend but in reverse order. What are the dividend and the divisor?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the expansion of $(1+2x)^{10}$, the coefficient of the $x^{2}$ term is $\boxed{\text{answer}}$. (Express the answer in numerical value.)<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the expansion of $(1+2x)^{10}$, the coefficient of the $x^{2}$ term is $\boxed{\text{answer}}$. (Express the answer in numerical value.)<|im_end|>
<|im_start|>assistant
<Z_24><Z_360><Z_162><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the expansion of $(1+2x)^{10}$, the coefficient of the $x^{2}$ term is $\boxed{\text{answer}}$. (Express the answer in numerical value.)<|im_end|>
<|im_start|>assistant
<Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the expansion of $(1+2x)^{10}$, the coefficient of the $x^{2}$ term is $\boxed{\text{answer}}$. (Express the answer in numerical value.)<|im_end|>
<|im_start|>assistant
<Z_426><Z_429><Z_224><Z_445><ANSWER>

Question: In the expansion of $(1+2x)^{10}$, the coefficient of the $x^{2}$ term is $\boxed{\text{answer}}$. (Express the answer in numerical value.)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A number is divided by 6 and then divided by 4, resulting in 370.8333333333333. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A number is divided by 6 and then divided by 4, resulting in 370.8333333333333. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_369><Z_350><Z_102><Z_276><Z_391><Z_509><Z_451><Z_214><Z_371><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A number is divided by 6 and then divided by 4, resulting in 370.8333333333333. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_199><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A number is divided by 6 and then divided by 4, resulting in 370.8333333333333. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_1><Z_443><Z_24><Z_428><Z_388><Z_104><Z_339><Z_478><Z_126><ANSWER>

Question: A number is divided by 6 and then divided by 4, resulting in 370.8333333333333. What is the original number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group?  Note that identically sized groups are indistinguishable.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group?  Note that identically sized groups are indistinguishable.<|im_end|>
<|im_start|>assistant
<Z_369><Z_501><Z_406><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group?  Note that identically sized groups are indistinguishable.<|im_end|>
<|im_start|>assistant
<Z_139><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group?  Note that identically sized groups are indistinguishable.<|im_end|>
<|im_start|>assistant
<Z_239><Z_338><Z_340><ANSWER>

Question: In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group?  Note that identically sized groups are indistinguishable.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( A B C D E F \) be a convex equilateral hexagon such that lines \( B C \), \( A D \), and \( E F \) are parallel. Let \( H \) be the orthocenter of triangle \( A B D \). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \( H A D \) in degrees.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( A B C D E F \) be a convex equilateral hexagon such that lines \( B C \), \( A D \), and \( E F \) are parallel. Let \( H \) be the orthocenter of triangle \( A B D \). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \( H A D \) in degrees.<|im_end|>
<|im_start|>assistant
<Z_369><Z_72><Z_217><Z_423><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( A B C D E F \) be a convex equilateral hexagon such that lines \( B C \), \( A D \), and \( E F \) are parallel. Let \( H \) be the orthocenter of triangle \( A B D \). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \( H A D \) in degrees.<|im_end|>
<|im_start|>assistant
<Z_363><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( A B C D E F \) be a convex equilateral hexagon such that lines \( B C \), \( A D \), and \( E F \) are parallel. Let \( H \) be the orthocenter of triangle \( A B D \). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \( H A D \) in degrees.<|im_end|>
<|im_start|>assistant
<Z_261><Z_5><Z_208><Z_156><ANSWER>

Question: Let \( A B C D E F \) be a convex equilateral hexagon such that lines \( B C \), \( A D \), and \( E F \) are parallel. Let \( H \) be the orthocenter of triangle \( A B D \). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \( H A D \) in degrees.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $3\times 4$ rectangle and a $4\times 5$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the rectangles. What is the smallest possible area of the square?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $3\times 4$ rectangle and a $4\times 5$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the rectangles. What is the smallest possible area of the square?<|im_end|>
<|im_start|>assistant
<Z_477><Z_43><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $3\times 4$ rectangle and a $4\times 5$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the rectangles. What is the smallest possible area of the square?<|im_end|>
<|im_start|>assistant
<Z_497><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $3\times 4$ rectangle and a $4\times 5$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the rectangles. What is the smallest possible area of the square?<|im_end|>
<|im_start|>assistant
<Z_108><Z_499><Z_164><ANSWER>

Question: A $3\times 4$ rectangle and a $4\times 5$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the rectangles. What is the smallest possible area of the square?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The graph of the linear function $y=-2x+1$ definitely does not pass through the \_\_\_\_\_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The graph of the linear function $y=-2x+1$ definitely does not pass through the \_\_\_\_\_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_369><Z_278><Z_349><Z_499><Z_117><Z_313><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The graph of the linear function $y=-2x+1$ definitely does not pass through the \_\_\_\_\_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The graph of the linear function $y=-2x+1$ definitely does not pass through the \_\_\_\_\_\_ quadrant.<|im_end|>
<|im_start|>assistant
<Z_484><Z_255><Z_135><Z_422><Z_316><Z_151><ANSWER>

Question: The graph of the linear function $y=-2x+1$ definitely does not pass through the \_\_\_\_\_\_ quadrant.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. By the end of the year, Julie's savings from these monthly savings were some multiple of the amount she spent per month. The fraction of her salary that she spent each month is 0.75. What is the multiple of the amount she saved to the amount she spent per month?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. By the end of the year, Julie's savings from these monthly savings were some multiple of the amount she spent per month. The fraction of her salary that she spent each month is 0.75. What is the multiple of the amount she saved to the amount she spent per month?<|im_end|>
<|im_start|>assistant
<Z_24><Z_286><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. By the end of the year, Julie's savings from these monthly savings were some multiple of the amount she spent per month. The fraction of her salary that she spent each month is 0.75. What is the multiple of the amount she saved to the amount she spent per month?<|im_end|>
<|im_start|>assistant
<Z_215><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. By the end of the year, Julie's savings from these monthly savings were some multiple of the amount she spent per month. The fraction of her salary that she spent each month is 0.75. What is the multiple of the amount she saved to the amount she spent per month?<|im_end|>
<|im_start|>assistant
<Z_263><Z_462><ANSWER>

Question: Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. By the end of the year, Julie's savings from these monthly savings were some multiple of the amount she spent per month. The fraction of her salary that she spent each month is 0.75. What is the multiple of the amount she saved to the amount she spent per month?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A marble is placed on each  $33$  unit square of a  $10*10$  chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?

<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A marble is placed on each  $33$  unit square of a  $10*10$  chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?

<|im_end|>
<|im_start|>assistant
<Z_24><Z_111><Z_497><Z_155><Z_173><Z_497><Z_173><Z_227><Z_453><Z_460><Z_74><Z_341><Z_202><Z_361><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A marble is placed on each  $33$  unit square of a  $10*10$  chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?

<|im_end|>
<|im_start|>assistant
<Z_455><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A marble is placed on each  $33$  unit square of a  $10*10$  chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?

<|im_end|>
<|im_start|>assistant
<Z_230><Z_284><Z_95><Z_242><Z_371><Z_104><Z_300><Z_420><Z_12><Z_116><Z_505><Z_1><Z_162><Z_213><ANSWER>

Question: A marble is placed on each  $33$  unit square of a  $10*10$  chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equations:
$(1)2y^{2}+3y-1=0$;
$(2)x\left(x-4\right)=-4$.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equations:
$(1)2y^{2}+3y-1=0$;
$(2)x\left(x-4\right)=-4$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_374><Z_42><Z_197><Z_381><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equations:
$(1)2y^{2}+3y-1=0$;
$(2)x\left(x-4\right)=-4$.<|im_end|>
<|im_start|>assistant
<Z_385><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equations:
$(1)2y^{2}+3y-1=0$;
$(2)x\left(x-4\right)=-4$.<|im_end|>
<|im_start|>assistant
<Z_232><Z_125><Z_99><Z_54><Z_443><ANSWER>

Question:
Solve the equations:
$(1)2y^{2}+3y-1=0$;
$(2)x\left(x-4\right)=-4$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division, the dividend is 760, the divisor is 36 and the quotient is 21. What is the remainder?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division, the dividend is 760, the divisor is 36 and the quotient is 21. What is the remainder?<|im_end|>
<|im_start|>assistant
<Z_477><Z_439><Z_273><Z_201><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division, the dividend is 760, the divisor is 36 and the quotient is 21. What is the remainder?<|im_end|>
<|im_start|>assistant
<Z_159><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division, the dividend is 760, the divisor is 36 and the quotient is 21. What is the remainder?<|im_end|>
<|im_start|>assistant
<Z_335><Z_431><Z_36><Z_341><ANSWER>

Question: In a division, the dividend is 760, the divisor is 36 and the quotient is 21. What is the remainder?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are five beaches in the area: Malibu beach, Santa Monica beach, Venice beach, Huntington beach, and Newport beach. The ratio of the number of surfers on these beaches is 7:4.5:3.5:2:1.5, respectively. If there are 36 surfers on Santa Monica beach (which is the second beach in the ratio), calculate the total number of surfers on all five beaches.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are five beaches in the area: Malibu beach, Santa Monica beach, Venice beach, Huntington beach, and Newport beach. The ratio of the number of surfers on these beaches is 7:4.5:3.5:2:1.5, respectively. If there are 36 surfers on Santa Monica beach (which is the second beach in the ratio), calculate the total number of surfers on all five beaches.<|im_end|>
<|im_start|>assistant
<Z_24><Z_407><Z_64><Z_219><Z_220><Z_30><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are five beaches in the area: Malibu beach, Santa Monica beach, Venice beach, Huntington beach, and Newport beach. The ratio of the number of surfers on these beaches is 7:4.5:3.5:2:1.5, respectively. If there are 36 surfers on Santa Monica beach (which is the second beach in the ratio), calculate the total number of surfers on all five beaches.<|im_end|>
<|im_start|>assistant
<Z_192><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are five beaches in the area: Malibu beach, Santa Monica beach, Venice beach, Huntington beach, and Newport beach. The ratio of the number of surfers on these beaches is 7:4.5:3.5:2:1.5, respectively. If there are 36 surfers on Santa Monica beach (which is the second beach in the ratio), calculate the total number of surfers on all five beaches.<|im_end|>
<|im_start|>assistant
<Z_477><Z_483><Z_432><Z_273><Z_213><Z_210><ANSWER>

Question: There are five beaches in the area: Malibu beach, Santa Monica beach, Venice beach, Huntington beach, and Newport beach. The ratio of the number of surfers on these beaches is 7:4.5:3.5:2:1.5, respectively. If there are 36 surfers on Santa Monica beach (which is the second beach in the ratio), calculate the total number of surfers on all five beaches.