Bot GPT 4-o mini To find the numerical equivalent of the expression \( 25 \cdot 2^{-2} \), we can break it down step by step:
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Calculate \( 2^{-2} \): \[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25 \]
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Now multiply this result by 25: \[ 25 \cdot 2^{-2} = 25 \cdot 0.25 = 6.25 \]
However, since this result of \( 6.25 \) is not among the provided options, let's express \( 2^{-2} \) another way to ensure correctness:
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Rewrite \( 25 \) as \( \frac{25}{1} \): \[ 25 \cdot 2^{-2} = \frac{25}{1} \cdot \frac{1}{4} = \frac{25}{4} \]
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Convert \( \frac{25}{4} \) to a decimal if needed, but we know that \( 25 \div 4 = 6.25 \).
Since none of the options match \( 6.25 \) (which simplifies to \( 25/4 \)), we can conclude that the expression \( 25 \cdot 2^{-2} \) evaluates to \( 6.25 \).
However, if we explore interpretations or misalignment with provided options and if rounding was expected, the interpretation suggests confirming with what's provided.
Let’s consider returning to the breakdown:
- Breaking it down again: If we reconsider just the multipliers and recheck values, or values missing: Clearly, as standalone, the accurate is only assessed to the raw numeric \( 6.25 \).
None of the possible options were equivalent, and thus we find that none fits properly listed as definite. But assuming needs narrowly or broad refactored checks repeatedly done within plausible error around should result on:
Final result: Cannot conclude from the given input based on checking equivalents correctly. Options provided don’t align, but 25 * 2^{-2} computes firmly to 6.25.
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