instruction_seed stringclasses 3
values | source stringclasses 2
values | to_be_used bool 1
class | classifier_reasoning stringclasses 3
values | __original_row_idx int64 0 2 |
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To be eligible for an algebra class a student must have an average of at least $83\%$ over all four quarters in his or her pre-algebra class. If Fisher had an $82\%$, $77\%$, and $80\%$ in the first three quarters, what is the minimum score he must earn in the 4th quarter to move on to algebra? | tiger_math | true | The question requires a calculation to determine the minimum score needed in the fourth quarter to achieve an average of at least 83% across four quarters. This involves reasoning and mathematical computation, similar to the positive examples that ask for a specific solution based on given conditions. | 0 |
Evaluate the limit:
\[
\lim_{x \to \infty} \frac{3x^4 - 2x + 5}{7x^4 + 8x^3 - 4}
\]
What is the simplified value of this limit? | automath | true | The provided question asks for the evaluation of a mathematical limit, specifically expressing a rational function as x approaches infinity. This aligns with the positive examples, which involve mathematical problems requiring solutions or calculations, such as finding points of intersection, expectation values, or pro... | 1 |
In a block cipher using S-boxes, consider an 8x8 S-box that is a bijective function mapping $\{0,1\}^8$ to $\{0,1\}^8$. If there are $256!$ possible 8x8 S-boxes, what is the approximate logarithmic scale of the number of distinct S-boxes, expressed in base 2? | automath | true | The question involves a computation related to cryptography, specifically analyzing properties of S-boxes used in block ciphers. It requires an understanding of mathematical functions and combinatorial principles, much like the positive examples provided. The positive examples involve complex mathematical reasoning, pr... | 2 |
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