Answer:
The number of parents who volunteered to bring refreshments is 16.
Step-by-step explanation:
The information provided is:
N = 84
n (S) = 35
n (S ∩ R) = 11
n (R) = 1.5 × n (S' ∪ R')
Compute the value of n (S ∪ R) as follows:
![n(S\cup R)=n(S)+n(R)-n (S\cap R)\\\\n(S\cup R)=n(S)+[1.5(N-n(S\cup R)]-n (S\cap R)\\\\n(S\cup R)=n(S)+1.5N-1.5n(S\cup R)-n (S\cap R)\\\\2.5n(S\cup R)=n(S)+1.5N-n (S\cap R)\\\\2.5n(S\cup R)=35+(1.5\times84)-11\\\\2.5n(S\cup R)=150\\\\n(S\cup R)=\frac{150}{2.5}\\\\n(S\cup R)=60](https://tex.z-dn.net/?f=n%28S%5Ccup%20R%29%3Dn%28S%29%2Bn%28R%29-n%20%28S%5Ccap%20R%29%5C%5C%5C%5Cn%28S%5Ccup%20R%29%3Dn%28S%29%2B%5B1.5%28N-n%28S%5Ccup%20R%29%5D-n%20%28S%5Ccap%20R%29%5C%5C%5C%5Cn%28S%5Ccup%20R%29%3Dn%28S%29%2B1.5N-1.5n%28S%5Ccup%20R%29-n%20%28S%5Ccap%20R%29%5C%5C%5C%5C2.5n%28S%5Ccup%20R%29%3Dn%28S%29%2B1.5N-n%20%28S%5Ccap%20R%29%5C%5C%5C%5C2.5n%28S%5Ccup%20R%29%3D35%2B%281.5%5Ctimes84%29-11%5C%5C%5C%5C2.5n%28S%5Ccup%20R%29%3D150%5C%5C%5C%5Cn%28S%5Ccup%20R%29%3D%5Cfrac%7B150%7D%7B2.5%7D%5C%5C%5C%5Cn%28S%5Ccup%20R%29%3D60)
Now compute the value of n (R) as follows:
![n (R) = 1.5 \times n (S' \cup R') \\\\n (R) = 1.5 \times [N-n (S \cup R)]\\\\n (R) = 1.5 \times [84-60]\\\\n(R)=16](https://tex.z-dn.net/?f=n%20%28R%29%20%3D%201.5%20%5Ctimes%20%20n%20%28S%27%20%5Ccup%20R%27%29%20%5C%5C%5C%5Cn%20%28R%29%20%3D%201.5%20%5Ctimes%20%20%5BN-n%20%28S%20%5Ccup%20R%29%5D%5C%5C%5C%5Cn%20%28R%29%20%3D%201.5%20%5Ctimes%20%20%5B84-60%5D%5C%5C%5C%5Cn%28R%29%3D16)
Thus, the number of parents who volunteered to bring refreshments is 16.
7.) the equation of the circle is
(x - 3)^2 + (y - 4)^2 = 25
If you substitute the point in you get
(6-3)^2 + (8-4)^2 = 25
3^2 + 4^2 = 25
9 + 16 = 25
25 = 25
Both sides of the equation are the same so it proves it lies on the circle
8.) you add the x coordinates together and divide by 2
7 + 4 = 11
11/2 = 5.5
You use +7 because you need to find the midpoint.
You then add 5.5 to - 7 or - 5.5 from 4
-7 + 5.5 = - 1.5
You do the same for y coordinates
6+5 = 11
11/2 = 5.5
6-5.5 = 0.5
So the coordinates of Rachel's house are
(-1.5, 0.5)
X=-2 and y=3.
The first step we take is to substitute the value for y from the second equation into the first equation:
4x+5(3x+9)=7
This is justified by substitution. The next step is:
4x+5*3x+5*9=7
4x+15x+45=7
This is justified by the distributive property. The next step is:
19x+45=7
This is justified by addition of like terms. The next step is:
19x+45-45=7-45
19x=-38
This is justified by the subtraction property of equality. The next step is:
19x/19 = -38/19
x=-2
This is justified by the division property of equality. The next step is:
y=3(-2)+9
y=-6+9
y=3
This is justified by substitution, multiplication and addition, in that order.
