For this case we have the following table:
X F(x)
-1 -11
0 -1
1 9
From here, we look for the function f (x).
We then have that as the equation is linear:

Where,

We choose an ordered pair:

Substituting values:

Rewriting:

Thus, the function f (x) is:

On the other hand, the function g (x) is:
Answer:
The slope of f (x) is greater than the slope of g (x) (10> 5)
The intersection with the y axis of g (x) is greater than the intersection with the y axis of f (x) (1> -1)
Answer: First option 13
Solution
If ABCD is a rhombus, the diagonals must be perpendicular, then the angle (5x+25)° must be a right angle (90°):
(5x+25)°=90°
5x+25=90
Solving for x: Subtracting 25 both sides of the equation:
5x+25-25=90-25
Subtracting:
5x=65
Dividing both sides of the equation by 5:
5x/5=65/5
Dividing:
x=13
Answer: The value of x must be 13
Answer:

so at the long run we can conclude that the best option is :
A) win 0.20 cents per play
Step-by-step explanation:
Previous concepts
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
Solution to the problem
Let X the random variable who represent the ampunt of money win/loss at the game defined.
The probability of loss $3.00 for this game is 0.2 and the probability of win is 1-0.2=0.8 and you will recieve $1.00 if you win. The expected value is given by:

And for this case if we replace we got:

so at the long run we can conclude that the best option is :
A) win 0.20 cents per play
It is neither. Distributive is like 20x9 20x5 then add those products. Associative is like (20x9) x5. You can however use both for this equation