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1f \(x \propto \frac{1}{n}\) and \(n = 8\), find x when n = 20.


Question

1f \(x \propto \frac{1}{n}\) and \(n = 8\), find x when n = 20.

Options

A) 29

B) 26.9

C) 27.8

D) 28.6

The correct answer is A.

Explanation:

If \(x \propto \cfrac{1}{n}\), then \(x = \cfrac{k}{n}\) at x = 72 and n = 8,
\(72 = \cfrac{k}{8}\) therefore \(k = 72 \times 8 = 576\)
\(x = \cfrac{576}{n}\)
at x = 20
\(x = \cfrac{576}{20} = 28.8 \approx 29\)

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Dicussion (1)

  • If \(x \propto \cfrac{1}{n}\), then \(x = \cfrac{k}{n}\) at x = 72 and n = 8,
    \(72 = \cfrac{k}{8}\) therefore \(k = 72 \times 8 = 576\)
    \(x = \cfrac{576}{n}\)
    at x = 20
    \(x = \cfrac{576}{20} = 28.8 \approx 29\)