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neonofarm [45]
3 years ago
6

Let f(x) = 7x - 13. Find f-1(x).

Mathematics
1 answer:
nika2105 [10]3 years ago
4 0
f(x)=7x-13 \\ \\ y=7x-13 \ \ \ |+13 \\
y+13=7x \ \ \ |\div 7 \\
x=\frac{1}{7}y+\frac{13}{7} \\ \\
\boxed{f^{-1}(x)=\frac{1}{7}x+\frac{13}{7}}
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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.755.75 millimeters and a standard de
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Convert <em>D</em> to a random variable <em>Z</em> following the standard normal distribution using

<em>Z</em> = (<em>D</em> - <em>µ</em>) / <em>σ</em>

Then

P(<em>D</em> < <em>d</em>₂) = P((<em>D</em> - 5.75) / 0.07 < (<em>d</em>₂ - 5.75) / 0.07)

0.94 = P(<em>Z</em> < (<em>d</em>₂ - 5.75) / 0.07)

→   (<em>d</em>₂ - 5.75) / 0.07 ≈ 1.55477

→   <em>d</em>₂ ≈ 5.86

P(<em>D</em> < <em>d</em>₁) = P((<em>D</em> - 5.75) / 0.07 < (<em>d</em>₁ - 5.75) / 0.07)

0.06 = P(<em>Z</em> < (<em>d</em>₁ - 5.75) / 0.07)

→   (<em>d</em>₁ - 5.75) / 0.07 ≈ -1.55477

→   <em>d</em>₁ ≈ 5.64

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3 years ago
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