Need answer has soon has posible

Element x decays radioactively with a half life of 8 minutes. if there are 450 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 37 grams?

21 type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the solution set of n2 - 14n = -45 is { (separate the solutions with a comma)

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.)