What relationship do the ratios of sin x° and cos y° share? the ratios are both identical (12 over 13 and 12 over 13) the ratios are opposites (negative 12 over 13 and 12 over 13) the ratios are reciprocals (12 over 13 and 13 over 12) the ratios are both negative (negative 12 over 13 and negative 13 over 12)?

*let m∠cob = 50°30’, m∠aob = 70° and m∠aoc = 20°30’. could point c be in the interior of ∠aob? why?

Atype of plant is introduced into an ecosystem and quickly begins to take over. a scientist counts the number of plants after mmonths and develops the equation p(m)= 19.3(1.089)^m to model the situation. most recently, the scientist counted 138 plants.assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants werefirst introduced? a)o 6.1b)0.6.6c)10 72d)o 23.1

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.)