Three musicians pick seven pieces of music out of 22 pieces independently of each other. they play one piece of music together only if the piece is chosen by all three of them. let x be the random variable which denote the number of pieces of music played. determine the expected value and the variance of x and compute p{x\geqslant1}. hint: to do this let xi to be 1 if the three musicians picks the ith music piece and 0 otherwise. express x in terms of xi. are the xi's independent?

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

a 90 degree rotation across the the origin followed by a reflection across the x-axis.

step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal