after studying the clues, sherlock holmes _____________ that the butler had committed the murder.

reconciled
endeavored
extrapolated
aquiesced
infused

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extrapolated

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After studying the clues, Sherlock Holmes *extrapolated* that the butler had committed the murder.

To arrive at this conclusion, Sherlock Holmes would have closely examined all the evidence and analyzed the available information. Extrapolation refers to making an educated guess or inference based on the evidence or clues at hand. In this case, Holmes would have carefully examined the facts and deduced that the butler was the most likely culprit based on the evidence he found.