Apple products have become a household name in america with 51% of all households owning at least one apple product (cnn, march 19, 2012). the likelihood of owning an apple product is 61% for households with kids and 48% for households without kids. suppose there are 1,200 households in a representative community, of which 820 are with kids and the rest are without kids. are the events "household with kids" and "household without kids" mutually exclusive and exhaustive?

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Fast! find the length of cu. the triangles are similar. show your work.

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.)