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3 years ago

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A standard size can of Diet Coke holds 71.79 cubic inches of soda. The can measure 4.87 inches in height. Determine the diameter

of the can.
diameter= in

1 answer:

vladimir2022 [97]3 years ago

3 0

Answer:

4.33 in

Step-by-step explanation:

Taking the can to be cylindrical then its volume is given by

$V=\frac {\pi h d^{2}}{4}$

Making d the subject then

$d=\sqrt {\frac {4V}{\pi h}}$

Where V represent volume, d is the diameter and h is the height. Substituting 71.79 in³ for V and 4.87 in for h then

$d=\sqrt {\frac {4*71.79}{\pi *4.87}}=4.33234022803439\approx 4.33$

Therefore, the diameter is approximately 4.33 inches

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We are given the <u>standard deviation for the population</u>, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of $\overline{x} = 12.17$
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Sample size of $n = 50$ .

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which z is the critical value.

We have to find the critical value, which is z with a p-value of $\frac{1 + \alpha}{2}$ , in which $\alpha$ is the confidence level.

In this problem, $\alpha = 0.95$ , thus, z with a p-value of $\frac{1 + 0.95}{2} = 0.975$ , which means that it is z = 1.96.

Then:

$M = 1.96\frac{6.37}{\sqrt{50}} = 1.77$

The confidence interval is the <u>sample mean plus/minutes the margin of error</u>, hence:

$\overline{x} - M = 12.17 - 1.77 = 10.4$

$\overline{x} + M = 12.17 + 1.77 = 13.94$

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

A similar problem is given at brainly.com/question/22596713

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2 years ago

Read 2 more answers

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djverab [1.8K]

Formula to find the arc length is:

$s=\frac{\theta}{360} 2\pi r$

Where, s= arc length,

r = radius of the circle

\theta = central angle in degrees.

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So, first step is to plug in these values in the above formula to get the arc length.

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