A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If 10% of the students have never taken a statistics class, 35% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that at least one of the first two groupmates you meet has studied more than one semester of statistics?

The probability that at least one of the first two groupmates you meet has studied more than one semester of statistics = 0.55 (1 - 0.45).

Step-by-step explanation:

Probability of those who have never taken a statistics class = 0.1 (10%)

Probability of those who have taken only one semester of a statistics class = 0.35 (35%)

Therefore, the probability of those who have taken two or more semesters of statistics = 0.55 or 55% (1 - 0.35 - 0.1).

(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