Your friend invested $500 in his shop to start off, and makes a $20 profit every week afterwards. Find the minimum number of wee
1 answer:
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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.
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.
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%.
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%.