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Given that the variance of 𝑋 equals 28, find the variance of four 𝑋 plus nine.
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We need to remember that this kind of variance has certain properties.
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One of those properties looks like this.
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The variance of 𝐴𝑋 plus 𝐵 is equal to 𝐴 squared times the variance of 𝑋.
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We can plug in 28 for the variance of 𝑋.
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And we can substitute the variance of four 𝑋 plus nine in place of 𝐴𝑋 plus 𝐵.
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When we do this, we see that the 𝐴 value is equal to four.
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So we plug in four for the 𝐴 value.
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Four squared times 28 equals 16 times 28, which equals 448.
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The variance of four 𝑋 plus nine is equal to 448.
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We know this is true based on the properties of variances.