Answer: There are 1,816,214,400 ways for arrangements.
Step-by-step explanation:
Since we have given that
"REPRESENTATION"
Here, number of letters = 14
There are 2 R's, 3 E's, 2 T's, 2 N's
So, number of permutations would be

Hence, there are 1,816,214,400 ways for arrangements.
Answer:
-1 or 4
Step-by-step explanation:
f(x) = g(x)
-x^2 + 4x + 12=x + 8
-x^2+3x+4=0
(x+1)(x-4)=0
x=-1,x=4
Well first do 20 children minus 8 girls to find how many boys there are:
20-8=16
So there are 16 boys. Therefore we can write the ratio of girls to boys as:
8/16
Then we can simplify this ratio by dividing it by 8 to get:
1/2
So the answer is the ratio of girls to boys in the group in simplest form is 1/2.
Answer:
C. y +3 = x +3
Step-by-step explanation:
We need to find in below option x has direct variation with y.
We solve for each;
A. 
From above equation we can state that 2 times y is equal to 7 less than 3 times of x.
Hence it doesn't represent direct variation.
B. 
Solving above expression we get;

From above equation we can state that y is equal to 10 more than x.
Hence it doesn't represent direct variation.
C. 
Solving above expression we get;

From above equation we can state that y is equal to x.
Hence it represent direct variation.
D. 
Solving above expression we get;

From above equation we can state that 4 times y is equal to 2 less than 4 times of x.
Hence it doesn't represent direct variation.
Hence the Answer which represent direct variation of x and y is,
C. 