An open-top box is to be constructed from a 4 in by 14 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. let x denote the length of the side of each cut-out square. assume negligible thickness.(a) find a formula for the volume, v, of the box as a function of x. v(x)=(b) for what values of x does the formula from part (a) make sense in the context of the problem? (inequalities)(c) on a separate piece of paper, sketch a graph of the volume function.(d) what, approximately, is the maximum volume of the box? (include units: (units))

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.)

Jack is considering a list of features and fees for current bank: jack plans on using network atms about 4 times per month. what would be jack’s total estimated annual fees for a checking account with direct paycheck deposit, one overdraft per year, and no 2nd copies of statements? a. $44 b. $104 c. $144 d. $176

(01.03 mc) which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4. select one: a. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1. b. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12. c. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3. d. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.