Answer:
Step-by-step explanation:
a) r = 10/2 = 5 feet
Area of floor =πr² =3.14*5*5 = 78.5 feet²
B) h = 3 foot
Volume of cylinder = πr²h = 3.14*5*5*3 = 235.5 cubic feet
Volume of hemisphere =2/3πr³= 2*3.14*5*5*5/3=261.67 cubic feet
Volume of space inside the observatory = 497.17 cubic feet
Let h = height of the box,
x = side length of the base.
Volume of the box is

.
So

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is


The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then

So the box is 4.86 in. wide and 4.87 in. high.
Given:
p = 7.6% = 0.076, the percentage of people who stay overnight at the hospital.
E = 1.5% = 0.015, margin of error
95% confidence interval.
The standard error is
Es =

where
n = the sample size.
The margin of error is

where
z* = 1.96 at the 95% confidence level.
Because the margin of error is given, there is no need to calculate it.
The 95% confidence interval is
p +/- E = 0.076 +/- 0.015 = (0.061, 0.091) = (6.1%, 9.1%)
Answer:
The 95% confidence interval is between 6.1% and 9.1%.
12 is divisible by 1,2,3,4,6,12 and 27 is by 1,3,9,27 so the GCF is 3
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