Your neighbor has an alarm system that has three alarms (main, backup, and second backup) with reliability of 80%, 70%, and 60%. Compute the probability of a system failure by creating a tree diagram.

Because the probabilities of success of the three alarms are 80%, 70%, and 60%, the probabilities of failure are 20%, 30%, and 40%, respectively. Multiply the three probabilities to find the probability of a system failure: 0.2 × 0.3 × 0.4 = 0.024. The probability of a system failure in this example is 2.4%.

Step-by-step explanation:

(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