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Irina18 [472]
2 years ago
15

A circle with area 100π has a sector with a central angle of 2/5π radians.

Mathematics
1 answer:
Snowcat [4.5K]2 years ago
3 0

Answer:

  20π square units

Step-by-step explanation:

The sector area is found using the proportion ...

  sector area / circle area = sector angle / whole circle angle

Multiplying by "circle area", we get ...

  sector area = (circle area)( sector angle / whole circle angle)

  = (100π)(2/5π)/(2π)

  = (100π)(1/5)

  sector area = 20π

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f(x)=x^2+6x+3

Complete the square:

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And we have:

f(x)=x^2+6x+3\\\\f(x)=x^2+6x+3^2-3^2+3\\\\f(x)=(x+3)^2-9+3\\\\\boxed{f(x)=(x+3)^2-6}

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g A researcher wants to construct a 95% confidence interval for the proportion of children aged 8-10 living in Atlanta who own a
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Answer:

The sample size needed is 2401.

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.

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In which

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The margin of error of the interval is:

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So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Estimate the sample size needed if no estimate of p is available so that the confidence interval will have a margin of error of 0.02.

We have to find n, for which M = 0.02.

There is no estimate of p available, so we use \pi = 0.5

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0.02\sqrt{n} = 1.96*0.5

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(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}

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