Answer:
Step-by-step explanation:
Part A.
Coordinates of A and B are,
A(-2, 2) and B(3, 2)
Rule for dilation of a point (x, y) by a scale factor k about the origin,
(x, y) → (kx, ky)
If the points A and B are dilated by a scale factor 3, image points will be,
A(-2, 2) → A'(-6, 6)
B(3, 2) → B'(9, 6)
Part B.
Following the same rule of dilation about the origin by a scale factor of 
about the origin,
A(-2, 2) → D(-1, 1)
B(3, 2) → 
Quotient of a number and 7 = 7N
Reciprocal = 1/7N
(6)(1/7N) = 6/7N
All you need to do is to subtract the x-coord. of G from the x-coord of H:
-2 - 3 = -5. Distance is not a signed quantity, so we'll give the final distance between points G and H as 5.
The expected value is just the weighted average of how much one ticket wins. To calculate it, we need to find the probabilities of winning each dollar amount, multiply each probability with it's respective dollar amount, then find the sum.
Let's call the winnings from one ticket X:
P(X=30) = 4000/2000000 = 0.002
P(X=800) = 500/2000000 = 0.00025
P(X=1200000) = 1/2000000 = 0.0000005
E(X) = 30*P(X=30) + 800*P(X=800) + 1200000*P(X=1200000) = 0.06 + 0.2 + 0.6 = 0.86
The answer is $0.86
