A penny is tossed. We observe whether it lands heads up or tails up. Suppose the penny is a fair coin; that is, the probability of heads is one-half and the probability of tails is one-half. What does this mean?A) if I flip the coin many, many times, the proportion of heads will be approximately 1/2, and this proportion will tend to
get closer and closer to 1/2 as the number of tosses increases.
B) regardless of the number of flips, half will be heads and half tails.
C) every occurrence of a head must be balanced by a tail in one of the next two or three tosses.
D) all of the above.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

The sum of 5consecutive even numbers is 100. what is the first number in this sequence?

What is the area of the shaded sector?