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Twisted up (H). Suppose you are given a band of paper with a lot of twists in it. How can you tell without counting whether you have an even number of half twists or an odd number? Can you deduce a general fact about what you would have if there are an odd number of half twists and what you would have if there are an even number of half twists? Try. (Hint: Experiment by drawing on various physical models.)
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- A Ponzi scheme is a fraudulent investment operation in which returns to investors are paid from funds collected from new investors rather than from profit earned by the operator. The scheme takes its name from the notorious operation of Charles Ponzi in 1920. The case of Bernie Madoff is a more recent example.† Suppose the operator of a Ponzi scheme pays an initial return to investors of $24,000. Each month, he must recruit enough new investors to increase the return by 3%. (a)Find a formula that gives the return R, in dollars, that the operator must pay after t months. R(t) = (b) How much must the operator pay to investors at the end of 3 years? (Round your answer to two decimal places.) $__________ (c) Assume that new investors pay $2000 to join the scheme. How many new investors must be recruited at the end of 3 years in order to pay the existing investors? (Enter a whole number of new investors.) _____________ new investorsarrow_forwardA hypothesis test is conducted with H0 : µ = -25 vs. Ha: µ > -25. The hypothesis test sample finds x̅ = -23.6, s = 3, and n = 16 . Within which interval does the tail area P lie? A hypothesis test is conducted with H0 : µ = -25 vs. Ha: µ > -25. The hypothesis test sample finds x̅ = -23.6, s = 3, and n = 16 . Within which interval does the tail area P lie? D. 0.005 < P < 0.010 B. 0.025 < P < 0.050 A. 0.050 < P < 0.100 C. 0.010 < P < 0.025arrow_forwardQuestion 2 The past records of a supermarket show that its customers spend an average of $65 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives points based on the total money spent at the store, and these points can be used to buy products at the store. The management expects that as a result of this campaign, the customers should be encouraged to spend more money at the store. To check whether this is true, the manager of the store took a sample of 12 customers who visited the store. The following data give the money (in dollars) spent by these customers at this supermarket during their visits. 88 69 141 28 106 45 32 51 78 54 110 83 Assume that the money spent by all customers at this supermarket has a normal distribution. Using the 5% significance level, can you conclude that the mean amount of money spend by all customers at this supermarket after the campaign was started is more than $65?arrow_forward
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