Match the reasons with the statements in the proof. Given: m 1 = m 3 m 2 = m 3 Prove: l | | m 1. m∠1 = m∠3 and m∠2 = m∠3 Substitution 2. m∠1 = m∠2 Definition of alternate interior angles 3. ∠1 and ∠2 are alternate interior angles Given 4. l||m If alternate interior angles are equal, then the lines are parallel.

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.)

Student representatives surveyed their classmates on their preference of a school mascot for a new school. the results are shown in the table below. which pair of samples seems most representative of student preference?

At a cost of 200, your club bought 175 frisbees to sell at the pep rally. you plan on selling them for $5 each. what is the domain of the function?