Possible grades for a class are a, b, c, d, and f. (no +/− 's.)
(a) how many ways are there to assign grades to a class of eight students?
(b) how many ways are there to assign grades to a class of seven students if nobody receives an f and exactly one person receives an a?

a) 390,625, b) 2916.

Step-by-step explanation:

Since we have given that

Number of possible grades = 5

a) Number of students = 8

Using the "Fundamental theorem of counting", we get that

b) Number of students = 7

Number of students receive F = 0

Number of students receive A = 1

Number of remaining grades = 4

So, Using fundamental theorem of counting , we get that

Hence, a) 390,625, b) 2916.

Distance traveled in 6 revolution = 56.52 ft

Step-by-step explanation:

Formula:

Circumference  of circle = 2πr

r - Radius of circle

It is given that,

A hula hoop has a three foot diameter.

Diameter = 3 ft

Therefore the radius r = diameter/2 = 3/2 = 1.5 ft

To find the circumference of loop

r = 1.5 ft

Circumference = 2πr = 2 * 3.14 * 1.5 = 9.42 ft

To find the distance traveled in 6 revolution

Distance traveled in one revolution =  9.42 ft

Distance traveled in 6 revolution = 6 * 9.42 = 56.52 ft