Sammy has a rectangular doormat on her porch. the mat is \dfrac45\text{ m} 5 4 mstart fraction, 4, divided by, 5, end fraction, start text, space, m, end text long and \dfrac12\text{ m} 2 1 mstart fraction, 1, divided by, 2, end fraction, start text, space, m, end text wide. what is the area of the doormat?

If the perimeter of the garden is 37 ft. the width is x and the length is 15 ft. what is the width of the garden in feet?

What is the domain of the step function f(x)=[2x]-1?

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?