completing the square

Step-by-step explanation:

5x² - 15x - 4 = 0

Add 4 to both sides.

5x² - 15x = 4

The coefficient of 5x² is 5, divide both sides by 5.

x² - 3x = 4/5

The coefficient of -3x is -3. Let b=-3.

Then we need to add (b/2)^2=9/4 to both sides to complete the square.

Add 9/4 to both sides.

x² - 3x + 9/4 = 61/20

Factor left side.

(x-3/2)² = 61/20

Take square root of both sides.

x-3/2 = ± √(61/20)

Add 3/2 to both sides.

x = 3/2 ± √(61/20)

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

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