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My name is Ann [436]
3 years ago
10

2. Find the volume of the cylinder pictured below. Use 3.14 for pi. Give your answer to the nearest tenth. Show your work to rec

eive full credit
Volume =


3.Find the volume of the sphere pictured below. The sphere has a radius of 20 cm. Use 3.14 for pi. Give your answer to the nearest tenth. Show your work to receive full credit.
Volume=

Mathematics
1 answer:
Blababa [14]3 years ago
7 0
Question 2

------------------------------------------------------------------------------------------
Formula
------------------------------------------------------------------------------------------
Volume of the cylinder = πr²h

------------------------------------------------------------------------------------------
Find Radius
------------------------------------------------------------------------------------------
Radius = Diameter ÷ 2
Radius = 10 ÷ 2
Radius = 5 ft

------------------------------------------------------------------------------------------
Find Volume
------------------------------------------------------------------------------------------
Volume = πr²h
Volume = 3.14 x 5² x 21
Volume = 1648.5 ft³

------------------------------------------------------------------------------------------
Answer: Volume = 1648.5 ft³
------------------------------------------------------------------------------------------

Question 3

------------------------------------------------------------------------------------------
Formula
-----------------------------------------------------------------------------------------
Volume of a sphere = 4/3πr³

------------------------------------------------------------------------------------------
Find Volume
------------------------------------------------------------------------------------------
Volume = 4/3 x 3.14 x 20³
Volume = 33493.3 ft³ (nearest tenth)

------------------------------------------------------------------------------------------
Answer: Volume = 33493.3 ft³ 
------------------------------------------------------------------------------------------
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Answer:

a=49.5 -1.28*15=30.3

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(49.5,15)  

Where \mu=49.5 and \sigma=15

We are interested in the bottom 10% of the data.

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.9   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.28

And if we solve for a we got

a=49.5 -1.28*15=30.3

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

If the score is lower than 30.3 we consider this score as risk averse

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