Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. there are 15 questions on the test and the students have been given 55 minutes to complete it. a table titled test time, showing number of questions, time per item in minutes, and total time in minutes. the first row shows multiple choice, with m, 3, and 3 m. the second row shows free response, with 15 minus m, 8, and x. the third row shows total, with 15, blank, and 55. which value could replace x in the table? 7 – m 23 – m 8(15 – m) 8(15) – m

Step-by-step explanation:

In the table, x represents the total time students take to respond free-response question. So, the replacement of the variable must be the product between the number of free-response questions and the time per questions students take.

Number of free-response questions: 15-m

Time per Item (minutes): 8

Therefore the product would be: 8(15-m), which is the expression that must replace x.

(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

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %