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1 March, 02:29

1. The mean of the data set{9,5, y, 2, x} is twice the data set {8, x, 4,1,3}. What is (y-x) squared.

2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?

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  1. 1 March, 02:56
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    1. (y - x) ² = 256

    2. 128g needed to be added

    Step-by-step explanation:

    1.

    9 + 5 + 2 + y + x = 2 (8 + 4 + 1 + 3 + x)

    16 + y + x = 32 + 2x

    y - x = 16

    ∴ (y - x) ² = 256

    2.

    x = mass of alcohol to add

    480 * 0.24 = 115.2 ← current mass of alcohol

    0.4 (480 + x) = 115.2 + x (*5)

    2 (480 + x) = 576 + 5x

    960 + 2x = 576 + 5x

    3x = 384

    x = 128g
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