The associative property allows you to change the <em>grouping</em> of addends or factors without changing the value of the expression.
Ask your self what is -2*?=23.
Then times that answer by 2.
Answer:
Volume: ![\frac{2}{3}\pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Ratio: ![\frac{2}{9}r](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B9%7Dr)
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
![V=\frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
![V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3](https://tex.z-dn.net/?f=V%27%3D%5Cfrac%7BV%7D%7B2%7D%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
![A=4 \pi r^2](https://tex.z-dn.net/?f=A%3D4%20%5Cpi%20r%5E2)
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so
. Moreover, we have to add the surface of the base, which is
. So the total surface area of the hemispherical tank is
![A'=2\pi r^2 + \pi r^2 = 3 \pi r^2](https://tex.z-dn.net/?f=A%27%3D2%5Cpi%20r%5E2%20%2B%20%5Cpi%20r%5E2%20%3D%203%20%5Cpi%20r%5E2)
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
![\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r](https://tex.z-dn.net/?f=%5Cfrac%7BV%27%7D%7BA%27%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3%7D%7B3%5Cpi%20r%5E2%7D%3D%5Cfrac%7B2%7D%7B9%7Dr)
If c = the cost of one table, the cost of all 25 tables before sales tax is 25·c
Since the sales tax is 5%, or 0.05, the sales tax for 25 tables is 25·c·0.05
Adding the sales tax to the original cost of the 25 tables can give you:
25·c + 25·c·0.05 = 1706.25
1.05·25·c = 1706.25
26.25·c = 1706.25
c =
![\frac{1706.25}{26.25}](https://tex.z-dn.net/?f=%5Cfrac%7B1706.25%7D%7B26.25%7D%20)
= 65
so the refund for 5 tables would be 5*65 = $325
Answer:
m' (-2, 4)
n' (-2, 1)
o' (3, 1)
p' (3, 4)
Step-by-step explanation: