Use mathematical induction to prove that each conjecture is valid for all positive integers n. 1/3+2/3+3/3+...+n/3=n(n+1)/6

Kevin is an insurance salesman. when he sells a policy, he makes 20 percent of the policy premium (p) up front; then each year the policy is active, he receives 15 percent of the original premium. which equation could be used to figure his total commission on a policy that has been active for five years? c=0.80p c=0.20p + 0.15p c=0.35p + 4(0.15) c=0.95p

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.

The diagram represents the polynomial 4x2 + 23x – 72. what is the factored form of 4x2 + 23x – 72? (4x + 8)(x – 9) (4x – 8)(x + 9) (4x + 9)(x – 8) (4x – 9)(x + 8)