Avending machine dispensing books of stamps accepts only one-dollar coins, $1 bills, and $5 bills. a) find a recurrence relation for the number of ways to deposit n dollars in the vending machine, where the order in which the coins and bills are deposited matters. b) what are the initial conditions? c) how many ways are there to deposit $10 for a book of stamps?

Yael decides that she no longer enjoys her job, and she quits to open a gluten-free, dairy-free kosher bakery. she pays a monthly rent for her store of $2,000. her labor costs for one month are $4,500, and she spends $6,000 a month on nut flours, sugar, and other supplies. yael was earning $2,500 a month working as a bank teller. these are her only costs. her monthly revenue is $14,000. which of the following statements about yael’s costs and profit are correct? correct answer(s) an accountant would say she is earning a monthly profit of $1,500. her implicit costs are $2,500 a month. an economist would tell her that she is experiencing a loss. her total costs are $12,500 a month. her explicit costs include the labor, rent, and supplies for her store. her economic profit is $1,500 a month.

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

You speak to a business owner that is taking in almost $2000 in revenue each month. the owner still says that they are having trouble keeping the doors open. how can that be possible? use the terms of revenue, expenses and profit/loss in your answer