Fifteen people work in an office. 8 are women and 7 are men. The flu virus is coming.

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5.Fifteen people work in an office. 8 are women and 7 are men. The flu virus is coming. 

(a) In how many ways can the flu virus randomly select 7 workers out of the 15 to get sick? Show work. 

(b) In how many ways can the flu choose 7 workers, if 3 must be women and 4 must be men? Show work. 

(c) If the flu virus randomly selects 7 workers from the 15 in the office, what is the probability that 4 are men and 3 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work. 

6.Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work. 

9x−8y= 93 

4x+5y= −10 

7.A freight-hauling firm estimates that it will need a new forklift in six years. The estimated cost of the vehicle is $40,000. The company sets up a sinking fund that pays 8% compounded semiannually, into which it will make semiannual payments to achieve the goal. Calculate the size of the payments. 

8.A recent poll of voters showed that 50% of them support the mayor. What is the probability that in a random sample of 16 voters, exactly 8 of them support the mayor ? Show Work

9.A marketing survey of 2000 randomly-selected convenience store customers found that 1415 of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut yesterday. 180 customers said they bought neither yesterday. 

(a) What is the probability that a single randomly-selected customer bought only a frosted crème-filled donut yesterday? Round answer to nearest hundredth. Show work