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nlexa [21]
3 years ago
5

Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL

CREDIT!

Mathematics
1 answer:
kobusy [5.1K]3 years ago
4 0
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.

The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
   h = √((15 in)² - (10 in)²) = √115 in

The volume of the conical part of the figure is then
   V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³


The volume of the hemispherical part of the figure is given by
   V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³

Then the total volume of the figure is
   V = (volume of conical part) + (volume of hemispherical part)
   V = (100π√115)/3 in³ + 2000π/3 in³
   V = (100π/3)(20 + √115) in³
   V ≈ 3217.39 in³
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Answer:

Step-by-step explanation:

The expected value is the probability of an event multiplied by the number of times the event happens. And if there is more than 1 event, the expected value is the sum of those.

There are 52 cards in a deck.

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There are 4 ace in a deck. (gain 20)

Any other card is 36 of them. (lose 5)

The probability of face card is 12/52

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The probability of any other card is 36/52

Thus the expected values is:

(12/52)(10) + (4/52)(20) + (36/52)(-5) = $0.38

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19 * 42 + 19 * 58 =
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The moon has a radius of
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Answer:

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Heeeeeelp! I’m literally so behind
olchik [2.2K]

Answer:

That would be 9 my good sir ( or ma'am )

Step-by-step explanation:

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Have a nice day

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A forester studying diameter growth of red pine believes that the mean diameter growth will be different from the known mean gro
-Dominant- [34]

Answer:

t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07  

The degrees of freedom are given by:

df =n-1= 32-1=31

Since is a two-sided test the p value would be:  

p_v =2*P(t_{31}>3.07)=0.0044  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example (\alpha=0.01,0.05, 0.1, 0.15).

Step-by-step explanation:

Data given and notation  

\bar X=1.6 represent the sample mean

s=0.46 represent the sample deviation

n=32 sample size  

\mu_o =1.35 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 1.35 in/year, the system of hypothesis would be:  

Null hypothesis:\mu =1.35  

Alternative hypothesis:\mu \neq 1.35  

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07  

P-value  

The degrees of freedom are given by:

df =n-1= 32-1=31

Since is a two-sided test the p value would be:  

p_v =2*P(t_{31}>3.07)=0.0044  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example (\alpha=0.01,0.05, 0.1, 0.15).

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