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o-na [289]
2 years ago
14

What is the volume of a sphere with a radius of 21 units?

Mathematics
2 answers:
Inessa [10]2 years ago
4 0

Answer: B: 12,348π units³ which is 38,772.72 units³

Step-by-step explanation:

The formula of the volume of a sphere is V = \frac{4}{3}πr³

Since we know that the radius is 21, we can fill in the given numbers:

V =  \frac{4}{3}π(21)³

Now, the new formula is V =  \frac{4}{3}π(9,261) = 38,772.72

Crank2 years ago
3 0

Answer:

B

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = \frac{4}{3}πr³ ( r is the radius ), thus

V = \frac{4}{3}π × 21³

   = \frac{4}{3}π ×9261 = \frac{4(9261)}{3}π = 12348π units³ → B

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Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if there is no difference, that is:

H_0: \mu_A - \mu_B = 0

At the alternative hypothesis, it is tested if there is difference, that is:

H_1: \mu_A - \mu_B = 0

<h3>What are the mean and the standard error of the distribution of differences?</h3>

For each sample, we have that:

\mu_A = 73, s_A = \frac{2}{\sqrt{100}} = 0.2

\mu_B = 74, s_B = \frac{4}{\sqrt{100}} = 0.4

For the distribution of differences, we have that:

\overline{x} = \mu_A - \mu_B = 73 - 74 = -1

s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.2^2 + 0.4^2} = 0.447

<h3>What is the test statistic?</h3>

It is given by:

t = \frac{\overline{x} - \mu}{s}

In which \mu = 0 is the value tested at the null hypothesis.

Hence:

t = \frac{\overline{x} - \mu}{s}

t = \frac{-1 - 0}{0.447}

t = -2.24

<h3>What is the p-value and the decision?</h3>

Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.

Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.

More can be learned about the t-distribution at brainly.com/question/16313918

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