An english instructor asserted that students' test grades are directly proportional to the amount of time spent studying. lisa studies 9 hr for a particular test and gets a score of 72. at this rate, how many hours would she have had to study to get a score of 96?

12 hours.

Step-by-step explanation:

1. The direct proportion has the following form:

Where k is the constant of proportionality.

2. Let's call the student's test grade and  the amount of time spent studying , then if Lisa studies 9 hr for a particular test and gets a score of 72, you can find k:

3. Then, the amount of time she have had to study to get a score of 96 is:

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.