Because the image is congruent to the original figure, then it undergoes a congruent transformation which can be a reflection, a rotation, or a translation. So, the answer is D.

Question

asked 2021-07-02

An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.

Certificate of deposit

Office complex

Land speculation

Technical school

amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500

amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000

Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

Certificate of deposit

Office complex

Land speculation

Technical school

amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500

amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000

Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

asked 2021-08-15

The game of Clue involves 6 suspects, 6 weapons, and 9 rooms.

One of each is randomly chosen and the object of the game is to guess the chosen three.

(a) How many solutions are possible? In one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards.

Let S, W, and R be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. Also, let X denote the number of solutions that are possible after that player observes his or her three cards.

(b) Express X in terms of S, W, and R.

(c) Find E[X]

One of each is randomly chosen and the object of the game is to guess the chosen three.

(a) How many solutions are possible? In one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards.

Let S, W, and R be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. Also, let X denote the number of solutions that are possible after that player observes his or her three cards.

(b) Express X in terms of S, W, and R.

(c) Find E[X]

asked 2021-08-22

The seller of a loaded die claims that it will favor the outcome 6. We don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.

a) There's a 3% chance that the die is fair.

b) There's a 97% chance that the die is fair.

c) There 's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.

d) There's a 3% chance that a fair die could randomly produce the results we observed, so it's reasonable to conclude that the die is loaded.

a) There's a 3% chance that the die is fair.

b) There's a 97% chance that the die is fair.

c) There 's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.

d) There's a 3% chance that a fair die could randomly produce the results we observed, so it's reasonable to conclude that the die is loaded.

asked 2021-08-15

Consider n independent sequential trials, each of which is successful with probability p. If there is a total of k successes, show that each of the

\(\displaystyle{n}\frac{!}{{{k}!{\left({n}−{k}\right)}!}}\)

possible arrangements of the k successes and n-k failures is equally likely.

\(\displaystyle{n}\frac{!}{{{k}!{\left({n}−{k}\right)}!}}\)

possible arrangements of the k successes and n-k failures is equally likely.