Answer:
19.2
Step-by-step explanation:
You get the mean of a set of numbers by adding them and dividing the sum by how many numbers there are. In this case, you don't know what the individual 8 numbers are, but you can find out what they add up to.
Mean = (sum) / 8
17 = (sum) / 8
17 x 8 = sum
136 = sum
Now take out the numbers 9, 11, 20, which reduces the sum by 40. There are 5 numbers left and they add up to 136 - 40 = 96.
The new mean is 96 / 5 = 19.2
Answer:
1.) 8 = 8
2.) -12 = -12
3.) -3y² = -3y²
4.) 6x² + 36x = 6x(x + 6)
5.) 7x - 14x² = 7x(1 - 2x)
~
Step-by-step explanation:
![9 {( - \frac{8}{3}) }^{} {}^{2} + 48( - \frac{8}{3} ) + 64 \\ \\ 9( - \frac{64}{9} ) - \frac{48}{3} + 64 \\ \\ - 64 - 16 + 64 = - 16](https://tex.z-dn.net/?f=9%20%7B%28%20-%20%20%5Cfrac%7B8%7D%7B3%7D%29%20%7D%5E%7B%7D%20%20%7B%7D%5E%7B2%7D%20%20%2B%2048%28%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20%29%20%2B%2064%20%20%5C%5C%20%20%5C%5C%209%28%20-%20%20%5Cfrac%7B64%7D%7B9%7D%20%29%20-%20%20%5Cfrac%7B48%7D%7B3%7D%20%20%2B%2064%20%20%5C%5C%20%20%5C%5C%20%20-%2064%20-%2016%20%2B%2064%20%3D%20%20-%2016)
<u>Given</u>:
The sides of the base of the triangle are 8, 15 and 17.
The height of the prism is 15 units.
We need to determine the volume of the right triangular prism.
<u>Area of the base of the triangle:</u>
The area of the base of the triangle can be determined using the Heron's formula.
![S=\frac{a+b+c}{2}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
Substituting a = 8, b = 15 and c = 17. Thus, we have;
![S=\frac{8+15+17}{2}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B8%2B15%2B17%7D%7B2%7D)
![S=\frac{40}{2}=20](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B40%7D%7B2%7D%3D20)
Using Heron's formula, we have;
![Area = \sqrt{S(S-a)(S-b)(S-c)}](https://tex.z-dn.net/?f=Area%20%3D%20%5Csqrt%7BS%28S-a%29%28S-b%29%28S-c%29%7D)
![Area = \sqrt{20(20-8)(20-15)(20-17)}](https://tex.z-dn.net/?f=Area%20%3D%20%5Csqrt%7B20%2820-8%29%2820-15%29%2820-17%29%7D)
![Area = \sqrt{20(12)(5)(3)}](https://tex.z-dn.net/?f=Area%20%3D%20%5Csqrt%7B20%2812%29%285%29%283%29%7D)
![Area = \sqrt{3600}](https://tex.z-dn.net/?f=Area%20%3D%20%5Csqrt%7B3600%7D)
![Area = 36](https://tex.z-dn.net/?f=Area%20%3D%2036)
Thus, the area of the base of the right triangular prism is 36 square units.
<u>Volume of the right triangular prism:</u>
The volume of the right triangular prism can be determined using the formula,
![V=\frac{1}{2}A_b h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B2%7DA_b%20h)
where
is the area of the base of the prism and h is the height of the prism.
Substituting the values, we have;
![V=\frac{1}{2}(60\times 15)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B2%7D%2860%5Ctimes%2015%29)
![V=450](https://tex.z-dn.net/?f=V%3D450)
Thus, the volume of the right triangular prism is 450 cubic units.
26 27 28 29 30 so 25 24 23 22 21---so 30 is the awnser