A local kids play sold 8 adult tickets and 9 child tickets for a total of $205. On day two they sold only 4 adult tickets and 3 child tickets for a total of $83. What was the price of each kind of ticket?

In the field of thermodynamics, rankine is the unit used to measure temperature. one can convert temperature from celsius into rankine using the formula , what is the temperature in celsius corresponding to r degrees rankine? a. 9/5(c - 273) b. 9/5(c + 273) c. 5/9( c - 273) d. 5/9( c + 273)

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.)

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.