Between​ 12:00 PM and​ 1:00 PM, cars arrive at a local​ bank's drive-thru at the rate of cars per hour ​( car per​ minute). The formula below from probability can be used to determine the probability that a car will arrive within t minutes of​ 12:00 PM. Use this information to answer the questions given below in parts ​(a)​(e).

Complete question :

Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. F(t)=1−e^−0.1t

Determine how many minutes are needed for the probability to reach 80%.

16.09 minutes

Step-by-step explanation:

Given the function :

F(t)=1−e^−0.1t

To attain 80% probability ; 80% = 0.8

0.8 = 1 - e^-0.1t

0.8 - 1 = - e^-0.1t

-0.2 = - e^-0.1t

Take the In of both sides

In(0.2) = In( e^-0.1t)

−1.609437 = - 0.1t

Divide both sides by - 0.1

−1.609437 / -0.1 = - 0.1t / 0.1

16.09 = t

Hence, the time it'll take will be 16.09 minutes

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0