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54 lines
2.7 KiB
Python
54 lines
2.7 KiB
Python
from opencompass.openicl.icl_prompt_template import PromptTemplate
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from opencompass.openicl.icl_retriever import ZeroRetriever
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from opencompass.openicl.icl_inferencer import GenInferencer
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from opencompass.datasets import MATHDataset, MATHEvaluator, math_postprocess
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math_reader_cfg = dict(input_columns=['problem'], output_column='solution')
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math_infer_cfg = dict(
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prompt_template=dict(
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type=PromptTemplate,
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template='''Problem:
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Find the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}
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Solution:
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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 $\\boxed{{[2,5)}}$.
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Final Answer: The final answer is $[2,5)$. I hope it is correct.
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Problem:
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If $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$
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Solution:
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We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$
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Final Answer: The final answer is $24$. I hope it is correct.
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Problem:
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Terrell 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?
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Solution:
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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*}}
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Final Answer: The final answer is $16$. I hope it is correct.
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Problem:
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If 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.
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Solution:
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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 $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$
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Final Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.
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Problem:
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{problem}
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Solution:
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{solution}'''),
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retriever=dict(type=ZeroRetriever),
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inferencer=dict(type=GenInferencer, max_out_len=512))
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math_eval_cfg = dict(
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evaluator=dict(type=MATHEvaluator), pred_postprocessor=dict(type=math_postprocess))
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math_datasets = [
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dict(
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type=MATHDataset,
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abbr='math',
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path='./data/math/math.json',
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reader_cfg=math_reader_cfg,
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infer_cfg=math_infer_cfg,
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eval_cfg=math_eval_cfg)
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]
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