Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree. What is the minimum weight spanning tree for the weighted graph in the previous question subject to the condition that edge {d, e} is in the span- ning tree? How would you generalize this idea? Suppose you are given a graph G and a particular edge {u, v} in the graph. How would you alter Prim's algorithm to find the minimum spanning tree subject to the condition that {u, v} is in the tree?

Homework: Section 8.1 Homework Score: 0 of 1 pt 3 of 20 (0 complete) ▼ 8.1.14 A menu offers a choice of 2 salads, 9 main dishes, and 7 desserts. How many different meals consisting of one salad, one main dish, and one dessert are possible? There are different possible meals. (Type a whole number.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All P Type here to search 梦 $

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Psychology 215 – Basic Statistical Methods - Andrzejewski Problem Set #10 Submit a document with the answers to the following questions along with an Excel workbook with the appropriate computations. Be sure to report the appropriate statistics. 1. A cognitive psychologist was interested in the ability to solve puzzles. They selected 24 college sophomores and matched them on the basis of IQ and assigned them, in groups of four, to one of four puzzle conditions (six blocks of four). The psychologist wants to make sure that all the puzzles are equally difficult. The dependent variable was the amount of time it took for a subject to complete the puzzle. The data are presented below. Were there differences in puzzle difficulty at the .05 level? Make sure to complete a 6-step hypothesis test. Block 1 2 3 4 5 -327872 1 25 25 2 34 38 33 32 36 34 Puzzle 3 31 36 30 41 39 40 4 40 37 32 38 46 39

92 CHAPTER 3 The Mathematics of Sharing 13. Karla and five other friends jointly buy the chocolate- strawberry-vanilla cake shown in Fig. 3-18(a) for $30 and plan to divide the cake fairly among themselves. After much discussion, the cake is divided into the six equal-sized slices S1, S2, ..., S6 shown in Fig. 3-18(b). Suppose that Karla values strawberry cake twice as much as vanilla cake and chocolate cake three times as much as vanilla cake. (a) Find the dollar value to Karla of each of the slices s1 through s6. (b) Which of the slices s1 through s6 are fair shares to Karla? S1 S5 S2 S4 S3 (a) (b) Figure 3-18