The decision version of the knapsack problem is as follows: given a set of n items {1, 2, …, n}, where each item j has a value v(j) and a weight w(j), and two numbers v and w, can we find a subset x of {1, 2, …, n} such that σj∈x v(j) ≥ v and σj∈x w(j) ≤ w? prove formally that the knapsack problem is np-complete (you can use any known np-problem discussed in the class).

Alex’s family members live in different parts of the world. they would like to discuss the wedding plans of one of their distant relatives. however, alex wants all the family members to talk to each other simultaneously so that they can make decisions quickly. which mode of internet communication should they use? a. blog b. email c. wiki d. message board e. instant messaging

Ramona enjoys her job because she is able to kids in an after school program. the work value ramona feels strongest about is a. leadership b. risk c. independence d. work with people select the best answer from the choices provided a b c d

Use a software program or a graphing utility with matrix capabilities to solve the system of linear equations using an inverse matrix. x1 + 2x2 − x3 + 3x4 − x5 = 6 x1 − 3x2 + x3 + 2x4 − x5 = −6 2x1 + x2 + x3 − 3x4 + x5 = 3 x1 − x2 + 2x3 + x4 − x5 = −3 2x1 + x2 − x3 + 2x4 + x5 = 5