At the one top pizza shop, mushrooms are the only topping. curiously, a pizza sold before noon has mushrooms with probability p = 1/3 while a pizza sold after noon never has mushrooms. also, a pizza is equally likely to be sold before noon as after noon. on a day in which 100 pizzas are sold. let n equal the number of pizzas sold before noon and let m equal the number of mushroom pizzas sold during the day.

a)what is the conditional pmf of m given n? are m and n independent?

b)what is the joint pmf of m and a/?

Abank has $132,000 in excess reserves and the required reserve ratio is 11 percent. this means the bank could have in checkable deposit liabilities and in (total) reserves.

Find the zeros of the polynomial 5 x square + 12 x + 7 by factorization method and verify the relation between zeros and coefficient of the polynomials

The chromosome manufacturing company produces two products, x and y. the company president, jean mutation, is concerned about the fierce competition in the market for product x. she notes that competitors are selling x for a price well below chromosome's price of $13.50. at the same time, she notes that competitors are pricing product y almost twice as high as chromosome's price of $12.50.ms. mutation has obtained the following data for a recent time period: product x product y number of units 11,000 3,000 direct materials cost per unit $3.23 $3.09 direct labor cost per unit $2.22 $2.10 direct labor hours 10,000 3,500 machine hours 2,100 1,800 inspection hours 80 100 purchase orders 10 30ms. mutation has learned that overhead costs are assigned to products on the basis of direct labor hours. the overhead costs for this time period consisted of the following items: overhead cost item amount inspection costs $16,200 purchasing costs 8,000 machine costs 49,000 total $73,200using direct labor hours to allocate overhead costs determine the gross margin per unit for product x. choose the best answer from the list below.a. $1.93b. $3.12c. $7.38d. $2.43e. $1.73using activity-based costing for overhead allocation, determine the gross margin per unit for product y. choose best answer from list below.a. $10.07b. ($2.27)c. ($5.23)d. ($7.02)e. $7.02