Problems 31-33 are very complicated

31.

The top row is the x value, the bottom row are the Y values.

The first point (0,)) would remain the same.

The second point (0,-4) , the -4 moves the the x location and the sign reverses and the X value becomes the y value, so would become (4,0)

The third point the x value becomes the Y value and the Y value becomes the X value, so becomes (0,5)

To get 0,4,0 on the top and 0,0,5 on the bottom.

The answer is B.

32.

Reflecting on the Y, the X values change sign, the Y values stay the same.

First point (-2,0) becomes 2,0

2nd point -5,3 becomes 5,3

3rd point (0,5) becomes 0,5 ( it stays the same since Y = 0)

The answer is D.

33.

Subtract 2 from the X values and subtract 1 from the y values.

5,7 becomes 3,6

3,1 becomes 1,0

2,3 becomes 0,2

The answer is A.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

srry ask agian

step-by-step explanation: