olymmath

HMMT November 2023 U10

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A real number xx is chosen uniformly at random from the interval (0,10)(0,10). Compute the probability that x,x+7\sqrt{x}, \sqrt{x+7}, and 10−x\sqrt{10-x} are the side lengths of a non-degenerate triangle.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{22}{25}

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