Which graph represents the piece wise-defined function? y={−x+3   if  x< 12x−4   if  x≥1

For the interval (-∞, 1), put x = 0.5, then y = - 0.5 + 3 = 2.5.

Therefore, (0.5, 2.5) is a point on y = -x + 3.

Put x = - 1, then y = -(-1) + 3 = 1 + 3 = 4.

Therefore, (-1, 4) is another point on y = -x + 3.

Joining (0.5, 2.5) and (-1, 4), we get the graph of the line y = -x + 3.

For the interval [1, ∞), put x = 1, then y = 2(1) - 4 = -2.

Therefore, (1, -2) is a point on y = 2x - 4.

Put x = 2, then y = 2(2) - 4 = 4 - 4 = 0.

Therefore, (2, 0) is another point on y = 2x - 4.

Joining (1, -2) and (2, 0), we get the graph of the line y = 2x - 4.

the solution is 12x-6y

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