9. in how many ways can a 5-question true/false quiz be answered if
it is okay to leave questions unanswered?

  243

Step-by-step explanation:

Each of the 5 questions can be answered 3 ways: t/f/(blank). So, the 5 questions can be answered 3·3·3·3·3 = 3^5 = 243 ways.

We know that 1 gallon is equal to 16 cups.
So 9 gallons is 144 cups.
each guest eats 2.5 cups, and there are 34 guests,
2.5 times 34 = 85, the amount eaten by the guests.
So to figure out whats left, subtract the eaten from the total.
144-85=59
59 is the answer. 
hope it helped :)