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2 years ago

What is the EXACT volume of this composite figure?

Mathematics

1 answer:

mariarad [96]2 years ago

5 0

Answer:

324π in.³

Step-by-step explanation:

The figure is a cone and a half sphere.

V = (1/3)πr²h + [(4/3)πr³]/2

V = (1/3)π(36 in.²)(15 in.) + (2/3)π(216 in.³)

V = [180π + 144π] in.³

V = 324π in.³

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A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

Ivanshal [37]

Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

c) $z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

d) $z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

8 0

3 years ago

P(A) = ? <br> Explain how you got the answer as well.

Leto [7]

Answer:

0.5

Step-by-step explanation:

we see that A is 1 of 2 choices, so theoretically, P(A) = 1/2 = 0.5

5 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Readme [11.4K]

Answer:

3/11

Step-by-step explanation:

Divide both the numerator and denominator by 2.

$\dfrac{6}{22}=\dfrac{2*3}{2*11}=\dfrac{3}{11}$

8 0

2 years ago

Coordinate pairs for 12x-3y<12

timurjin [86]

Answer:

y>4x-4

Step-by-step explanation:

7 0

2 years ago

Given that X ~ N(120, 35). We survey samples of 25 and are interested in the distribution of X-bar. Find the z-score associated

lubasha [3.4K]

Answer:

Option c -2.8571

Step-by-step explanation:

z-score are calculated as

$z=\frac{xbar-mean}{\frac{S.D}{\sqrt{n} } }$ .

We are given that mean=120 and standard deviation=S.D=35 as X~N(120,35).

Sample size=n=25.

We have to find z-score for x-bar=100. So,

z-score=[100-120]/[35/√25]

z-score=[-20]/[35/5]

z-score=-20/7

z-score=-2.8571.

Thus, the z-score associated with x-bar = 100 is -2.8571.

8 0

3 years ago