Customers arrive at a full-service gas station, with two pumps, at rate of 30 cars per hour. However, customers will go to another station if there are at least four cars in the station: i. e., two being served and two waiting. Suppose that the service time for customers is exponential with mean 5 minutes. Denote by Xt the number of cars at the gas station at time t (both waiting and being served). a) In the long-run, how many cars per hour are served at the station? b) If the gas station is currently empty, what is the expected time until it becomes full?

Determine whether the quadrilateral below is a parallelogram. justify/explain your answer (this means back it up! give specific information that supports your decision. writing just "yes" or "no" will result in no credit.)

Out of $20$ creepy-crawly creatures in a room, $80\%$ are flies and $20\%$ are spiders. if $s\%$ of the total legs belong to spiders, what is $s$?

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true