You want to learn salsa dancing at a fitness center. You have two options; Option A is to pay a $200 registration fee plus $10 per lesson. Option B is to pay $30 for each session you attend. a) Briefly describe what this problem is about. b) Write Let statements for the unknowns. c) How many lessons do you have to attend so it doesn’t matter which option you choose? Show your work.

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

Nikolas calculated the volume of the prism. his work is shown below.

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.