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Gennadij [26K]
2 years ago
14

Calculate the area of the shaded sector in the circle​

Mathematics
1 answer:
scZoUnD [109]2 years ago
5 0

Answer:

area ≈ 6.3 units²

Step-by-step explanation:

Calculate the area (A ) of the sector as

A = area of circle × fraction of circle

   = πr² × \frac{45}{360}

   = π × 4² × \frac{1}{8}

    = 16π × \frac{1}{8} ← cancel 8 and 16 by 8, leaving

A = 2π ≈ 6.3 units² ( to 1 dec. place )

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Answer:

A sample of 1077 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

42% of freshmen do not visit their counselors regularly.

This means that \pi = 0.42

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.

How large of a sample size is required?

A sample size of n is required, and n is found when M = 0.035. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.035 = 2.327\sqrt{\frac{0.42*0.58}{n}}

0.035\sqrt{n} = 2.327\sqrt{0.42*0.58}

\sqrt{n} = \frac{2.327\sqrt{0.42*0.58}}{0.035}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.42*0.58}}{0.035})^2

n = 1076.8

Rounding up:

A sample of 1077 is required.

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Step-by-step explanation:

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