Answer:
When increasing the radius 3 times the volume increases 9 times and when it is reduced to a third the volume decreases 9 times
Step-by-step explanation:
We have that the formula for the volume of a cone is:
Vc = pi * (r ^ 2) * h
We first calculate the original volume, where the radius is 2 and the height is 9, replacing:
Vc = 3.14 * (2 ^ 2) * 9
Vc = 113.04
Now if the radius is tripled it would be: 2 * 3 = 6, the radius would be 6, replacing:
Vc = 3.14 * (6 ^ 2) * 9
Vc = 1017.36
If we compare:
1017.36 / 113.04 = 9
This means that when the radius is tripled, the volume increases 9 times.
When if re reduces to a third the radius would be: 2/3, replacing:
Vc = 3.14 * ((2/3) ^ 2) * 9
Vc = 12.56
113.04 / 12.56 = 9
Which means that by reducing it to a third the volume becomes 9 times smaller.
Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
In which:
is the sample proportion.
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of 
, so the critical value is z = 1.645.
The sample size and the estimate are given by:
Hence, the bounds of the interval are given by:
The 90% confidence interval is given by: (0.6350, 0.6984).
More can be learned about the z-distribution at brainly.com/question/25890103
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To work out the distance of the path, you need to find out the circumference.
Formula for circumference = pi multiplied by the diameter
So you simply do:
pi multiplied by 1.4 miles
And you should get:
4.39822971503... miles
Simply round the result to an appropriate value (e.g. 3 decimal places).
Answer: 4.398 miles (to 3dp)
Hope the answer helps :)
