42 brotha you gotta cut down the data set until you reach the median
Answer:
A)3.375
Step-by-step explanation:
0.75 * 4.5 = 3.375
If r(x) is an inverse of s(x), then we know that r(s(x)) = x and s(r(x)) = x.
Let's think about what inverses are in order to help us understand.
We know that a function, in order to be an inverse of another, has to be reflected about the y = x line.
So, if a function is reflected about the y = x line, then if we have a composite function, they will always result in the same input (ie x)
Answer:
The volume of the toy is ![V=5.23\ ft^3](https://tex.z-dn.net/?f=V%3D5.23%5C%20ft%5E3)
Step-by-step explanation:
step 1
Find the volume of the hemisphere
The volume of the hemisphere is given by the formula
![V=\frac{2}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
In this problem, the wide of the toy is equal to the diameter of the hemisphere
so
![D=2\ ft](https://tex.z-dn.net/?f=D%3D2%5C%20ft)
----> the radius is half the diameter
substitute
![V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20%281%29%5E%7B3%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%5C%20ft%5E3)
step 2
Find the volume of the cone
The volume of the cone is given by
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
we know that
The radius of the cone is the same that the radius of the hemisphere
so
![r=1\ ft](https://tex.z-dn.net/?f=r%3D1%5C%20ft)
The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy
![h=4-1=3\ ft](https://tex.z-dn.net/?f=h%3D4-1%3D3%5C%20ft)
substitute the given values
![V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%281%29%5E%7B2%7D%283%29%3D%5Cpi%5C%20ft%5E3)
step 3
Find the volume of the toy
we know that
The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.
so
![V=(\frac{2}{3} \pi+\pi)\ ft^3](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%2B%5Cpi%29%5C%20ft%5E3)
![V=(\frac{5}{3}\pi)\ ft^3](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7B5%7D%7B3%7D%5Cpi%29%5C%20ft%5E3)
assume
![\pi=3.14](https://tex.z-dn.net/?f=%5Cpi%3D3.14)
![V=\frac{5}{3}(3.14)=5.23\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B5%7D%7B3%7D%283.14%29%3D5.23%5C%20ft%5E3)