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Andrew [12]
3 years ago
6

A can holds 4 golf balls. The diameter of each golf ball is 5 cm. What is the volume of the empty space inside the can?

Mathematics
1 answer:
forsale [732]3 years ago
7 0

Answer:

Volume of the empty space in the can  is 327.05  cm^3

Step-by-step explanation:

Given:

Number of golf ball the can holds = 4

Diameter of the golf ball = 5 cm

To Find:

Volume of the empty space in the can = ?

Solution:

Step 1:  Finding the volume of one golf ball

Ball is shape of the sphere

So lets use the volume of the sphere formula

Volume of the  golf ball = \frac{4}{3}\pi r^3

Radius =\frac{5}{2} = 2.5 cm

Substituting the values

Volume of the  golf ball  

=\frac{4}{3} \pi \times(2.5)^3

=\frac{4}{3} \pi \times (15.625)

= \frac{4}{3} \times 49.06

= \frac{196.24}{3}

= 65.41

Step 2:  Finding the volume of empty space of the can

volume of empty space of the can =  volume of 5 golf ball

= 5 X 65.41

= 327.05

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Answer:

a) \mu_{\bar X} =13.35

e.none of the above

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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".  

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Solution to the problem

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

X \sim N(13.35,0.12)  

Where \mu=13.35 and \sigma=0.12

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

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

Part a

\mu_{\bar X} =13.35

Part b

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Part c

We want this probability:

P(\bar X< 13.32)

For this case we can use the z score formula given by:

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

And using this formula we got:

z = \frac{13.32-13.35}{\frac{0.12}{\sqrt{36}}}= -1.5

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We want this probability:

P(13.30

For this case we can use the z score formula given by:

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

And using this formula we got:

z = \frac{13.30-13.35}{\frac{0.12}{\sqrt{36}}}= -2.5

z = \frac{13.36-13.35}{\frac{0.12}{\sqrt{36}}}= 0.5

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