The Solomon, Smith, and Samson law firm produces many legal documents that must be word processed for clients and the firm. Requests average of eight pages of documents per hour, and they arrive according to a Poisson distribution. The secretary can word process 10 pages per hour on average according to an exponential distribution.(a) The average utilization rate of the secretary is ___%. (Enter your response as a percentage rounded to the nearest whole number.)(b) The probability that more than four pages are waiting or being word processed is . (Enter your response rounded to three decimal places.)(c) The average number of pages waiting to be word processed is pages. (Enter your response rounded to two decimal places.)

4

step-by-step explanation:

5

step-by-step explanation:

thus, the first answer choice, y = sec x, is the correct one

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.