64 point question

√(5-2x) - √(2-x) = 1

x = 2 and x = -2

Step-by-step explanation:

The easiest way is to guess. We know that you can't have a square root of a negative number. This constrains x between negative infinity to 2. Testing 2 and -2, we see that it satisfy the equation.

The more systematic approach is shown below

x= -2, 2

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