The grover cleveland cinema is conducting a mathematical study. in its theater, there are 200 seats. adult tickets, , cost $12.50 and child tickets, , cost $7.50. the cinema's goal is to sell at least $1500 worth of tickets for the theater. write a system of linear inequalities that can be used to find the possible combinations of adult tickets and child ticket that would satisfy the cinema's goal.

Atorch and a battery cost 2.50 altogether.the torch costs 1.50 more than the battery.what fraction of the total price is the torch? give your answer in its simplest form.

(05.02)a farmer has decided to divide his land area in half in order to plant soy and corn. calculate the area of the entire area so he knows how much soil is needed. a parallelogram with a height of 6 yards and side length 9 yards. the height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. rhombus is split into a soy half and a corn half. each bag of soil covers 40 square yards. how many bags should the farmer purchase?

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→∞.