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Problem 7 Pigeon Holes: 10 pts Let n>1 be an integer. What is the smallest value of k such that, given any k distinct integers, t1, codots, tk there must be two of them tj and ti that j=j such that either n∣(ti−tj) or n∣(ti+tj)

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According to Searle, the "Chinese room" thought experiment proves that computers cannot have understanding.

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Suppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is $\mu_d = 0$. Use a 0.05 significance level to find the following: $x$ | 61 | 85 | 81 | 73 | 56 | 51 | 77 $y$ | 57 | 76 | 76 | 69 | 86 | 85 | 59 (a) The mean value of the differences $d$ for the paired sample data $d =$ (b) The standard deviation of the differences $d$ for the paired sample data $s_d =$ (c) The $t$ test statistic $t =$ (d) The positive critical value $t =$ (e) The negative critical value $t =$ (f) Does the test statistic fall in the critical region? $\bigcirc$ A. Yes $\bigcirc$ B. No (g) Construct a 95% confidence interval for the population mean of all differences $x - y$. $\langle \mu_d \langle$

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Which of the following statements about rationality is true? Multiple Choice Economists wish to prove that all individuals are rational. Individuals are hardly ever rational. As long as the marginal benefit of an action is positive, the action is rational. Engaging in a behavior for which the marginal costs exceed the marginal benefits is irrational.

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Question 2. If a monopolist uses L workers to produce q units of output, its profit π is given by π(q, L) = q(a - bq) - wL where a, b are positive constants and w is the wage rate. (a) Interpret this equation. (b) Assume a production function q = αL^(1/2). Using the method of Lagrange multipliers, find the firm's optimal employment choice L*. How does employment change as productivity α increases. Why does the sign depend on w? Question 3. Reconsider question 2, but suppose this time that demand is given by p = aq^(-b), where a, b > 0. Note this is an iso-elastic demand function. Hence π(q, L) = aq^(1-b) - wL (a) Assume production function q = αL^(1/2) as before. Find the firm's profit maximising input L* [and obtain a restriction on b so that the second order condition is satisfied]. Find how employment changes with productivity α. (b) Now assume a more general production function q = αF(L), where F is a positive increasing function. Substituting out q in π implies profits can be rewritten as π(L) = a[αF(L)]^(1-b) - wL Obtain a first order condition describing L*. Assuming that F'' < 0, what restriction on b guarantees that the second order condition is satisfied. Using the Implicit Function Theorem, establish that L* always increases with productivity α.

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Customers who participate in a store's free loyalty card program save money on their purchases but allow the store to keep track of their shopping habits and potentially sell these data to third parties. A survey revealed that half (225) of a random sample of 450 US adults would agree to participate in a store loyalty card program, despite the potential for information sharing. Complete parts a through d. a. Estimate the true proportion of all US adults who would agree to participate in a store loyalty card program, despite the potential for information sharing. .5 (Round to three decimal places as needed.) b. Form a 90% confidence interval around the estimate from part a. (.445, .555) (Round to three decimal places as needed.)

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Find y as a function of x if y''' - 13y'' + 40y' = 28e^x, y(0) = 28, y'(0) = 13, y''(0) = 29. y(x) =

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Theories of Emotion For the following situations, identify the theory of emotion being demonstrated. Is it representative of James-Lange Theory or Schachter & Singer Theory? 1. Monica feels as though she is in love because she feels her heart race, is out of breath, and has shaky knees. 2. Bill walks into a room and realizes that the gray shape behind the door is not a shadow but a man with a gun. His heart begins to race at the same time as he experiences the emotion of fear. 3. Rosemary notices that her palms are sweating and her heart is beating quickly. She looks around the room and sees that the teacher is handing out a pop quiz. So, Rosemary concludes that she must be feeling nervous due to the quiz. 4. It was Brenda's birthday, and she thought that nobody had remembered. That night, as she walked into her house and turned on the lights, a crowd of relatives and friends jumped out and yelled "Happy Birthday!" Brenda's heart rate, blood pressure, and breathing increased at about the same time as she experienced the feeling of happiness. 5. Jim recognizes that a fight is about to break out in his favorite restaurant. Consequently, he interprets his heart palpitations as fear. 6. As Bob was walking down the street, a fierce dog came running out from the back of a house and was snarling angrily. His heart began to race until he discovered that the dog was on a long chain. When he noticed how fast his heart was beating, he realized that he was scared.

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Complete Mark 0.75 out of 1.00 Flag question Diet Plan A Diet Plan B Minimum -10 kg -5 kg First Quartile 0 kg 5 kg Median 5 kg 7 kg Third Quartile 10 kg 10 kg Maximum 20 kg 15 kg The table compares two diet plans in terms of kilograms lost over 12 months. NOTE: Negative values indicate WEIGHT GAIN. Which diet plan had a larger percentage of patients losing more than 10 kg? Both the Same Which plan had the larger percentage of patients losing more than 15 kg? Plan A Which diet plan had a greater percentage of people lose weight? Plan B Which diet plan had the larger percentage of patients gain weight? Plan A

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Question 20 Describe the 4 causes of market failure.&nbsp; Why is it safe to assume that the government will continue to provide food stamps to poor people?

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