Which relation describes a function?
{(0,0), (0, 2), (2.0), (2, 2)}
{(-2, -3), (-3, -2), (2,3), (3, 2)}
{(2,-1), (2, 1), (3,-1), (3, 1)}
{(2, 2), (2, 3), (3, 2), (3, 3)}

{(-2, -3), (-3, -2), (2,3), (3, 2)}

Step-by-step explanation:

A function is a set of ordered pairs in which no two pairs have the same first number.

In other words, an x cannot be paired with two y's.

A function takes an x and pairs it with one and only one y.

{(0,0), (0, 2), (2.0), (2, 2)} is not a function because it pairs 0 with both 0 and 2.

{(2,-1), (2, 1), (3,-1), (3, 1)} is not a function because it pairs 2 with both -1 and 1.

{(2, 2), (2, 3), (3, 2), (3, 3)} is not a function because it pairs 2 with both 2 and 3.

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