Answer:

Step-by-step explanation:
we know that
To find the the rate per studen, we need to divide the total amout spent by the number of students
so

Answer:
50 I think. let me know if I'm wrong.
Answer: 150
Step-by-step explanation:
To solve arithmetic progression, the nth term is calculated using the formula = a + (n - 1)d
From the question,
First term = a = 4
12th term = 31.5
We need to get the common difference which will be:
Since 12th term = 31.5
a + (n - 1)d = 31.5
a + (12 - 1)d = 31.5
a + 11d = 31.5
Recall that a = 4
4 + 11d = 31.5.
11d = 31.5 - 4
11d = 27.5
d = 27.5 / 11
d = 2.5
Since last term is 376.5, the number of terms in it will be calculated as:
a + (n - 1)d = 376.5
4 + (n - 1)2.5 = 376.5
4 + 2.5n - 2.5 = 376.5
2.5n = 376.5 - 4 + 2.5
2.5n = 375
n = 375 / 2.5
n = 150
The number of terms in the series is 150.
Answer:
![A = [\frac{32}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B32%7D%7B3%7D%5D)
Step-by-step explanation:
Given


Required
Determine the area bounded by the curves
First, we need to determine their points of intersection

Subtract 2x from both sides

Multiply through by -1

Take square root of both sides
or 
This Area is then calculated as thus
![A = \int\limits^a_b {[y_1 - y_2]} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5Ea_b%20%7B%5By_1%20-%20y_2%5D%7D%20%5C%2C%20dx)
<em>Where a = 2 and b = -2</em>
Substitute values for
and 

Open Brackets

Collect Like Terms


Integrate
](https://tex.z-dn.net/?f=A%20%3D%20%5B-%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%20%2B4x%5D%282%2C-2%29)
![A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)]](https://tex.z-dn.net/?f=A%20%3D%20%5B-%5Cfrac%7B2%5E%7B3%7D%7D%7B3%7D%20%2B4%282%29%5D%20-%20%5B-%5Cfrac%7B-2%5E%7B3%7D%7D%7B3%7D%20%2B4%28-2%29%5D)
![A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8]](https://tex.z-dn.net/?f=A%20%3D%20%5B-%5Cfrac%7B8%7D%7B3%7D%20%2B8%5D%20-%20%5B-%5Cfrac%7B-8%7D%7B3%7D%20-8%5D)
![A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B-8%2B%2024%7D%7B3%7D%5D%20-%20%5B%5Cfrac%7B8%7D%7B3%7D%20-8%5D)
![A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B-8%2B%2024%7D%7B3%7D%5D%20-%20%5B%5Cfrac%7B8-24%7D%7B3%7D%5D)
![A = [\frac{16}{3}] - [\frac{-16}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B16%7D%7B3%7D%5D%20-%20%5B%5Cfrac%7B-16%7D%7B3%7D%5D)
![A = [\frac{16}{3}] + [\frac{16}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B16%7D%7B3%7D%5D%20%2B%20%5B%5Cfrac%7B16%7D%7B3%7D%5D)
![A = [\frac{16 + 16}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B16%20%2B%2016%7D%7B3%7D%5D)
![A = [\frac{32}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B32%7D%7B3%7D%5D)
Hence, the Area is:
![A = [\frac{32}{3}]](https://tex.z-dn.net/?f=A%20%3D%20%5B%5Cfrac%7B32%7D%7B3%7D%5D)
Answer:
Teachers are tough
Step-by-step explanation:
your welcome i hope you do good in ur test! :)