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Law Incorporation [45]
2 years ago
12

A toy rocket is a composite of a cylindrical body with a cone for a nose. The base of the cylinder and cone are the same size. C

alculate the entire volume of the rocket if the radius of the base is 2 inches, the height of the cone tip is 4 inches, and the height of the entire rocket is 12 inches.
Mathematics
1 answer:
inysia [295]2 years ago
6 0

The volume of the entire rocket given the volumes of the cylindrical body and the cone nose is 117.23 in³.

<h3>What is the volume of the entire rocket?</h3>

The volume of the entire rocket is the sum of the volume of the cylinder and the volume of the cone.

Volume of the cylinder = πr²h

Where:

  • π = 3.14
  • r = radius 2
  • h= height = 12 - 4 = 8 inches

3.14 x 2² x 8 = 100.48 in³

Volume of the cone = 1/3 πr²h

1/3 x 2² x 3.14 x 4 = 16.75 in³

Volume of the rocket = 100.48 + 16.75 = 117.23 in³

To learn more about the volume of a cone, please check: brainly.com/question/13705125

#SPJ1

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Answer : 52 girls

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Your ratio of boys to girls is 3:4

Set up a fractional proportion and cross multiply

3/4 = 39/x

cross multiply

3x = 4(39)

3x = 156

x = 156/3

x = 52 girls

Hope this was helpful!❤

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According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 20
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Testing the hypothesis, it is found that since the p-value of the test is of 0.3015, which is greater than the significance level of 0.05, the data does not provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%.

At the null hypothesis, we <u>test if the proportion is of 23%</u>, that is:

H_0: p = 0.23

At the alternative hypothesis, we <u>test if this proportion is lower than 23%</u>, that is:

H_1: p < 0.23

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

  • \overline{p} is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

In this problem, the parameters are: p = 0.23, n = 1432, \overline{p} = \frac{321}{1432} = 0.2242

Then, the value of the <u>test statistic</u> is:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

z = \frac{0.2242 - 0.23}{\sqrt{\frac{0.23(0.77)}{1432}}}

z = -0.52

The p-value of the test is the probability of finding a sample proportion of 0.2242 or below, which is the <u>p-value of z = -0.52</u>.

  • Looking at the z-table, z = -0.52 has a p-value of 0.3015.

Since the p-value of the test is of 0.3015, which is greater than the significance level of 0.05, the data does not provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%.

A similar problem is given at brainly.com/question/14639462

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