Acertain country taxes the first $20,000 of an individual's income at a rate of 15%, and all income over $20,000 is taxed at 20%. find a piecewise-defined function t that specifies the total tax on an income of x dollars.

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.)

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

The state troopers in one state have a motto, “nine you’re fine; ten you’re mine,” which is the standard that they use for pulling over speeders on the state highways. in other words, if the posted speed limit is 55 mph, drivers can drive at a rate up to 64 mph without fear of getting a ticket. which of the following best describes the ethical culture in the state? a. the troopers are following a standard of positive law. b. the troopers are following a normative standard. c. the troopers are following a headline test. d. the troopers are following the blanchard/peale standard.