prompt="Please answer the following questions based on the given article.\n\nArticle: {context}\n\nPlease answer the following questions based on the above article.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Please answer the following questions based on the given article.\n\nArticle: {context}\n\nPlease answer the following questions based on the above article.\n\nQuestion: {input}\nAnswer:',
prompt="Answer the question based on the given passages. Questions and answers are only relevant to some passages. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to some passages. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Answer the question based on the given passages. Questions and answers are only relevant to some passages. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to some passages. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:',
prompt="Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:',
prompt="Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:',
prompt="Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:',
prompt="Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:",
role='HUMAN',
prompt='Please answer the following question based on the given passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nArticle: {context}\n\nPlease answer the following question based on the above passages. Questions and answers are only relevant to one passage. Only give me the answer and do not output any other explanation and evidence.\n\nQuestion: {input}\nAnswer:',
dict(role="HUMAN",prompt="Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:"),
dict(role="BOT",prompt="The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:"),
dict(role="BOT",prompt="We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:"),
dict(role="BOT",prompt="If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:"),
dict(role="BOT",prompt="If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n"),
dict(role='HUMAN',prompt='Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:'),
dict(role='BOT',prompt='The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:'),
dict(role='BOT',prompt='We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:'),
dict(role='BOT',prompt='If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:'),
dict(role='BOT',prompt='If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n'),
dict(role="HUMAN",prompt="Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:"),
dict(role="BOT",prompt="The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:"),
dict(role="BOT",prompt="We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:"),
dict(role="BOT",prompt="If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:"),
dict(role="BOT",prompt="If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n"),
dict(role='HUMAN',prompt='Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:'),
dict(role='BOT',prompt='The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:'),
dict(role='BOT',prompt='We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:'),
dict(role='BOT',prompt='If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:'),
dict(role='BOT',prompt='If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n'),
dict(role="HUMAN",prompt="Problem:\nFind the domain of the expression $\\frac{\sqrt{x-2}}{\sqrt{5-x}}$.}\nSolution:"),
dict(role="BOT",prompt="The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{[2,5)}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf $\det \mathbf{A} = 2$ and $\det \mathbf{B} = 12,$ then find $\det (\mathbf{A} \mathbf{B}).$\nSolution:"),
dict(role="BOT",prompt="We have that $\det (\mathbf{A} \mathbf{B}) = (\det \mathbf{A})(\det \mathbf{B}) = (2)(12) = \\boxed{24}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:"),
dict(role="BOT",prompt="If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{align*} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{16} \end{align*}\nFinal Answer: The final answer is $16$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf the system of equations: \\begin{align*} 6x-4y&=a,\\\\ 6y-9x &=b. \end{align*}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{a}{b},$ assuming $b$ is nonzero.\nSolution:"),
dict(role="BOT",prompt="If we multiply the first equation by $-\\frac{3}{2}$, we obtain $$6y-9x=-\\frac{3}{2}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{3}{2}a=b\Rightarrow\\frac{a}{b}=\\boxed{-\\frac{2}{3}}.$$\nFinal Answer: The final answer is $-\\frac{2}{3}$. I hope it is correct.\n"),
dict(role='HUMAN',prompt='Problem:\nFind the domain of the expression $\\frac{\sqrt{x-2}}{\sqrt{5-x}}$.}\nSolution:'),
dict(role='BOT',prompt='The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{[2,5)}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf $\det \mathbf{A} = 2$ and $\det \mathbf{B} = 12,$ then find $\det (\mathbf{A} \mathbf{B}).$\nSolution:'),
dict(role='BOT',prompt='We have that $\det (\mathbf{A} \mathbf{B}) = (\det \mathbf{A})(\det \mathbf{B}) = (2)(12) = \\boxed{24}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:'),
dict(role='BOT',prompt='If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{align*} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{16} \end{align*}\nFinal Answer: The final answer is $16$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf the system of equations: \\begin{align*} 6x-4y&=a,\\\\ 6y-9x &=b. \end{align*}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{a}{b},$ assuming $b$ is nonzero.\nSolution:'),
dict(role='BOT',prompt='If we multiply the first equation by $-\\frac{3}{2}$, we obtain $$6y-9x=-\\frac{3}{2}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{3}{2}a=b\Rightarrow\\frac{a}{b}=\\boxed{-\\frac{2}{3}}.$$\nFinal Answer: The final answer is $-\\frac{2}{3}$. I hope it is correct.\n'),
dict(role="HUMAN",prompt="Problem:\nFind the coefficient of $x^3$ when $3(x^2 - x^3+x) +3(x +2x^3- 3x^2 + 3x^5+x^3) -5(1+x-4x^3 - x^2)$ is simplified.\nSolution:"),
dict(role="BOT",prompt="Combine like terms to simplify the expression. The coefficient of $x^3$ is calculated as $$(-3+2\cdot(2+1))+(-5)\cdot(-4))$ = 26$. Thus, the coefficient of $x^3$ is $\\boxed{26}$.\nFinal Answer: The final answer is $26$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nThe surface area of a sphere with radius $r$ is $4\pi r^2$. Including the area of its circular base, what is the total surface area of a hemisphere with radius 6 cm? Express your answer in terms of $\pi$.\nSolution:"),
dict(role="BOT",prompt="The surface area of a hemisphere (not including the base) is half that of a sphere, so it is $2\pi r^2$. The area of the base is $\pi r^2$. Therefore, for a hemisphere with radius 6 cm, the total surface area is $2\pi (6)^2 + \pi (6)^2 = 108\pi$ square cm.\nFinal Answer: The final answer is $108\pi$ square cm. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nMonica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.\nSolution:"),
dict(role="BOT",prompt="The prime numbers rolled could be 2, 3, or 5, and each has a 1/6 chance of being rolled. The composite number 4 or 6 has a 2/6 chance of being rolled, but it results in $0 win. The remaining non-prime and non-composite number is 1 , and it results in a loss of $3, with a 1/6 chance. So, the expected winnings are $(2+3+5)(1/6)+0(2/6)+(-3)(1/6) = \$1.17$.\nFinal Answer: The final answer is $\$1.17$. I hope it is correct.\n"),
dict(role="BOT",prompt="We find $3 \mathbf{b}$ first, which is $\\begin{pmatrix} 12 \\ 6 \\ -3 \end{pmatrix}$. Then we subtract this vector from $\mathbf{a}$. So, $\mathbf{a} - 3 \mathbf{b} = \\begin{pmatrix} -7 - 12 \\ 0 - 6 \\ 1 - (-3) \end{pmatrix} = \\begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}.$\nFinal Answer: The final answer is $\\begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}$. I hope it is correct.\n"),
dict(role='HUMAN',prompt='Problem:\nFind the coefficient of $x^3$ when $3(x^2 - x^3+x) +3(x +2x^3- 3x^2 + 3x^5+x^3) -5(1+x-4x^3 - x^2)$ is simplified.\nSolution:'),
dict(role='BOT',prompt='Combine like terms to simplify the expression. The coefficient of $x^3$ is calculated as $$(-3+2\cdot(2+1))+(-5)\cdot(-4))$ = 26$. Thus, the coefficient of $x^3$ is $\\boxed{26}$.\nFinal Answer: The final answer is $26$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nThe surface area of a sphere with radius $r$ is $4\pi r^2$. Including the area of its circular base, what is the total surface area of a hemisphere with radius 6 cm? Express your answer in terms of $\pi$.\nSolution:'),
dict(role='BOT',prompt='The surface area of a hemisphere (not including the base) is half that of a sphere, so it is $2\pi r^2$. The area of the base is $\pi r^2$. Therefore, for a hemisphere with radius 6 cm, the total surface area is $2\pi (6)^2 + \pi (6)^2 = 108\pi$ square cm.\nFinal Answer: The final answer is $108\pi$ square cm. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nMonica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.\nSolution:'),
dict(role='BOT',prompt='The prime numbers rolled could be 2, 3, or 5, and each has a 1/6 chance of being rolled. The composite number 4 or 6 has a 2/6 chance of being rolled, but it results in $0 win. The remaining non-prime and non-composite number is 1 , and it results in a loss of $3, with a 1/6 chance. So, the expected winnings are $(2+3+5)(1/6)+0(2/6)+(-3)(1/6) = \$1.17$.\nFinal Answer: The final answer is $\$1.17$. I hope it is correct.\n'),
dict(role='BOT',prompt='We find $3 \mathbf{b}$ first, which is $\\begin{pmatrix} 12 \\ 6 \\ -3 \end{pmatrix}$. Then we subtract this vector from $\mathbf{a}$. So, $\mathbf{a} - 3 \mathbf{b} = \\begin{pmatrix} -7 - 12 \\ 0 - 6 \\ 1 - (-3) \end{pmatrix} = \\begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}.$\nFinal Answer: The final answer is $\\begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}$. I hope it is correct.\n'),
dict(role="HUMAN",prompt="Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:"),
dict(role="BOT",prompt="The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:"),
dict(role="BOT",prompt="We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:"),
dict(role="BOT",prompt="If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n"),
dict(role="HUMAN",prompt="Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:"),
dict(role="BOT",prompt="If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n"),
dict(role='HUMAN',prompt='Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:'),
dict(role='BOT',prompt='The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:'),
dict(role='BOT',prompt='We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:'),
dict(role='BOT',prompt='If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n'),
dict(role='HUMAN',prompt='Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:'),
dict(role='BOT',prompt='If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n'),
