Let A be the event and B be the vent
. Since the intersection of the events
, the events A and B are mutually exclusive.
The number is either odd or even. Since , the events are mutually exclusive and exhaustive.
Correct choice is "the number is either odd or even".
Let = amount of salt (in pounds) in the tank at time
(in minutes). Then
.
Salt flows in at a rate
and flows out at a rate
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
which I'll solve with the integrating factor method.
Integrate both sides. By the fundamental theorem of calculus,
After 1 hour = 60 minutes, the tank will contain
pounds of salt.