Let b = {(1, 3), (−2, −2)} and b' = {(−12, 0), (−4, 4)} be bases for r2, and let a = 0 2 3 4 be the matrix for t: r2 → r2 relative to b.

(a) find the transition matrix p from b' to b. p =

(b) use the matrices p and a to find [v]b and [t(v)]b, where [v]b' = [−2 4]t. [v]b = [t(v)]b =

(c) find p−1 and a' (the matrix for t relative to b'). p−1 = a' = (

(d) find [t(v)]b' two ways. [t(v)]b' = p−1[t(v)]b = [t(v)]b' = a'[v]b' =

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)

Arestaurant offers delivery for their pizzas. the total cost the customer pays is the price of the pizzas, plus a delivery fee. one customer pays $23 to have 2 pizzas delivered. another customer pays $59 for 6 pizzas. how many pizzas are delivered to a customer who pays $86?