Step-by-step explanation:
Slope = y2-y1 / X2-x1
= 8-4/2-(-3)
=4/5
Answer: 
This is the same as writing y < (-1/2)x+3
==============================================================
Explanation:
The dashed boundary line goes through (0,3) and (4,1)
Apply the slope formula for those two points
m = (y2-y1)/(x2-x1)
m = (1-3)/(4-0)
m = -2/4
m = -1/2
The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing 
We shade below the dashed line to represent the inequality
. Points in the shaded region are solutions to the inequality. One example point is (0,0).
Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.
Answer:
tan D =
or 0.545
tan F =
or 1.833
Step-by-step explanation:
To find tangent is always 
so the opposite of angle D is line EF which is 4.8 and the adjacent side is line ED which is 8.8 so
which is
or 0.545
The opposite of angle f is line ED which is 8.8 and the adjacent is line EF which is 4.8 so
is
or 1.833
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