Astudent earned a grade of 60% on a math test that had 30 problems. how many problems on this test did the student answer correctly

The student answered 18 problem correctly.

Step-by-step explanation:

We can find the number of problems answered correctly out of a test that had 30 problems by setting up equivalent fractions, or a proportion:

'x' is equal to the number of problems answered correctly.  Since 60% is the number answered correctly and 100% is the total amount, we can compare 60% to 'x' and 100% to 30.  In order to solve for 'x', we can cross-multiply and divide:  

100x = (60)(3) or 100x = 180

Divide both sides by 100:  

x = 18

Check the explanation

Step-by-step explanation:

The given problem can be modeled into a geometric distribution as follows.

Suppose, X be the number of at-bats required to get a home run. As each at-bat is independent.

A.

Required probability is given by

P(X=5)=(1-0.16)^{5-1}0.16=0.07965942

B.

We have to calculate E(X).

Subtracting later from earlier we get,

So, expected number of at-bats until home run = 1/0.16 = 6.25