Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1 , a2 , ak , where a1 = 1, ak = n, and aⱼ < aⱼ ₊ ₁ for j = 1, 2, . . , k − 1.

Miguel bought a movie ticket that cost $5. he also bought popcorn and a bottle of water. how much did miguel spend altogether?

You have $600,000 saved for retirement. your account earns 5.5% interest. how much, to the nearest dollar, will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

Joel wants to buy a new tablet computer fram a store having a 20% off sale on all tablets. the tablet he wants has an original cost of $190. he also wants to make sure he has enough money to pay the 5% sales tax. part one joel uses the incorect expression 0.95(190)(0.8) to calculate that the tablet will cost him a total of $144.40. describe his error and write the correct expression part two how much will joel pay for the tablet show your work if you answer this question correctly you will receive a prize of 99 points good luck