Arectangle with the length of 75 miles and width of 25 miles can be used to model building usage at one of florida's universities. only 70% of the buildings at this university are used for instruction. if 32,125 students are enrolled at this university, what is the average student population density per square mile of building space used for instruction, rounded to the nearest student?

24 students per mile

Step-by-step explanation:

Given in the question,

Length of rectangle for building university = 75 miles

Width of rectangle for building university = 25 miles

Total area:

Length x Width

= 75 x 25

= 1875 miles²

Only 70% of the buildings at this university are used for instruction

70% of 1875 miles²

70/100 x 1875

= 1312.5 miles²

32,125 students are enrolled at this university

So,

1312.5 miles² = 32,125 students

1 mile =  32,125/1312.5

          = 24 students per mile

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