Dave can paint the office by himself in 4 hours. working with an associate, he can paint the
office in 3 hours. how long would it take his associate to do it working alone?

It would take 12 hours for his associate to do the complete work alone.

Step-by-step explanation:

Let 'x' be the hours taken by his associate working alone.

Given:

Time to paint the office by Dave is 4 hours.

Time to paint the office together is 3 hours.

Therefore, the part of work completed by Dave alone in 1 hour is

Part of work completed by an associate in 1 hour is

Now part of work completed by both in 1 hour is

Therefore,

Therefore, it would take 12 hours for his associate to do the complete work alone.

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.

x:       y:  

-1         4

0         4

1         6

2         18

3         20