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Paul [167]
3 years ago
8

What is the radius of a circle with an area of 64 square feet

Mathematics
1 answer:
butalik [34]3 years ago
6 0

Answer:

r = +(8 ft) / (√π)

Step-by-step explanation:

Formula for the area of a circle:  A = πr²

Here,                                     64 ft^2 = πr²

Solving for r², we get

        64 ft^2

r² = ---------------

              π

so that r is the positive square root of this expression:

                64 ft^2  

r = +sqrt ( -------------- )

                     π

 = +(8 ft) / (√π)

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3 years ago
The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30
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Answer:

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Step-by-step explanation:

Previous concepts and notation

The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".

\bar X represent the sample mean

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s= 0.2 represent the sample deviation

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t represent the statistic

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State the null and alternative hypothesis

On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:

H0: \sigma \leq 0.027

H1: \sigma >0.027

In order to check the hypothesis we need to calculate the statistic given by the following formula:

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This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

t=(30-1) [\frac{0.2}{0.164}]^2 =42.963

What is the approximate p-value of the test?

The degrees of freedom are given by:

df=n-1= 30-1=29

For this case since we have a right tailed test the p value is given by:

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And the best option would be:

b. between .025 and .05

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