The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows:

Machine Breakdowns Per Week Probability
0 0.10
1 0.20
2 0.15
3 0.30
4 0.15
5 0.10
1.00

a. Simulate the machine breakdowns per week for 20 weeks.
b. Compute the average number of machines that will break down

Answer is given below.

Step-by-step explanation:

Machine Breakdown   Probability      Cumulative-Distribution-Rang         Rang

Per week    

0                                     0.10                              0.10                                    0-9

1                                     0.10                             0.20                                   10-19

2                                     0.20                             0.40                                  20-39

3                                     0.25                              0.55                                   40-64

4                                    0.30                             0.95                                      65-94

5                                       0.5                              1.0                                      95-99

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.