A college has 500 students. A survey has determined that:72 read French 40 read German 39 read Spanish 18 read French and German 18 read French and Spanish 9 read German and Spanish 6 read all three languages. Put this information into a venn diagram and use it to answer the following questions. Give your answers correct to 3 decimal places. What is the probability a randomly selected student reads exactly 2 of these 3 languages?

The probability that a student reads exactly 2 of these 3 languages is 0.054.

Step-by-step explanation:

Denote the languages as follows:

F = French, G = German and S = Spanish.

The information provided is:

Compute the number of students who study only French and German as follows:

Compute the number of students who study only French and Spanish as follows:

Compute the number of students who study only German and Spanish as follows:

Compute the number of students who reads exactly 2 of these 3 languages as follows:

Thus, there are 27 students who reads exactly 2 of these 3 languages.

Compute the probability that a student reads exactly 2 of these 3 languages as follows:

Thus, the probability that a student reads exactly 2 of these 3 languages is 0.054.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

c > -10.55

step-by-step explanation: