Luis leans a 25.0 foot ladder against the side of his house to hang his Christmas lights. If the angle of elevation to the top of the ladder is 64o, what is the horizontal distance from the ladder to the base of the house?

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

There are two major tests of readiness for college: the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores in recent years has been roughly normal with mean µ = 20.9 and standard deviation s = 4.8. sat scores are reported on a scale from 400 to 1600. sat scores have been roughly normal with mean µ = 1026 and standard deviation s = 209. reports on a student's act or sat usually give the percentile as well as the actual score. the percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. tanya scores 1260 on the sat. what is her percentile (± 1)?

On which number line are -3 and its opposite shown