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Fiesta28 [93]
3 years ago
14

A club has 800 members. 100 of the members were randomly picked and were asked if the dues should be raised. 6 of the members sa

id that dues should be raised. Based on these results, about how many members in the club would be expected to say that dues should be raised?
Mathematics
1 answer:
frez [133]3 years ago
5 0

Answer:

About 48 members would be expected to say that dues be raised

Step-by-step explanation:

Here, we shall be using a case of a representative sampling to determine the actual.

Out of the 100 selected members, 6 said the dues should be raised;

This represents a percentage of 6/100 = 6%

So out of the 800, the expected number of members that would ask for a dues raising will be;

6/100 * 800 = 48

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ddd [48]

Check where the first-order partial derivatives vanish to find any critical points within the given region:

f(x,y)=2x^3+y^4\implies\begin{cases}f_x=6x^2=0\\f_y=4y^3=0\end{cases}\implies(x,y)=(0,0)

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Now check for points along the boundary. We can parameterize the boundary by

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F'(t)=0\implies\begin{matrix}\sin t=0\implies t=0,\,t=\pi\\\\\cos t=0\implies t=\dfrac\pi2,\,t=\dfrac{3\pi}2\\\\16\sin^2t-3\cos t=0\implies t=2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3},\,t=2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\end{matrix}

At these critical points, we get

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F\left(2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\right)\approx893

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t=\dfrac\pi2\implies(x,y)=(0,8)

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t=\dfrac{3\pi}2\implies(x,y)=(0,-8)

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