Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 160 workers can produce 32 cars in 2 hours, find the number of cars that 220 workers can produce in 3 hours.

They'll build 66 cars in those conditions.

Step-by-step explanation:

In this case we can use a compounded rule of three to solve the problem. We need to set it up as shown bellow:

160 workers -> 32 cars -> 2 hours

220 workers -> x cars -> 3 hours

If the number of workers rise, then we expect the number of cars to rise aswel, so they're directly proportional. If the number of hours worked increase we can expect the number of cars to increase aswell, so they're directly proportional. We can now set the fractions:

(160*2)/(220*3) = 32/x

320/660 = 32/x

x = (32*660/320) = 66 cars

They'll build 66 cars in those conditions.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x