HELP ASAP TAKING A TEST I DONT KNOW HOW TO DO THESE I HAVE 1 HOUR PLEASE!

diagonal is 11.14 cm

Step-by-step explanation:

We start by writing the equation for the width (w) in terms of the length (L):

w = 2 L - 8

from the area = w * L = 62

we replace w in it:    w * L = (2 L -8) * L = 62

2 L^2 - 8 L = 62

2 L^2 - 8 L - 62 = 0

extract 2 common factor:

2 (L^2 - 4 L - 31) = 0

Using quadratic formula we get:

So, we pick the positive answer L = 7.916 cm

Then we now know the with of the rectangle as well:

w = 2 * L - 8 = 2 * 7.916 - 8 = 7.832  cm

Now we estimate the diagonal of the rectangle using the Pythagorean theorem:

which rounded to two decimal places is 11.14 cm

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