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Furkat [3]
3 years ago
13

How to find the standard deviation and variance of 93,73,76,86,98?

Mathematics
1 answer:
liq [111]3 years ago
3 0
Mean = (93 + 73 + 76 + 86 + 98) / 5 = 426/5 = 85.2

Variance = ((93 - 85.2)^2 + (73 - 85.2)^2 + (76 - 85.2)^2 + (86 - 85.2)^2 + (98 - 85.2)^2) / 5 = (60.84 + 148.84 + 84.64 + 0.64 + 163.84) / 5 = 458.8 / 5 = 91.76

standard deviation = sqrt(91.76) = 9.58
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Convert the following sum into a product. cosx + cos3x + cos5x + cos7x
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Answer:

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Step-by-step explanation:

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To convert: the given sum into product

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Use formula: \cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )

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cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)

4 0
3 years ago
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