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1. What is an unbiased estimator? Why is this concept important? Give an example of an unbiased estimator and an example of a biased estimator. You can use reading 12.1 as a guide but answer in your own words. 2. Based on a sample of 100 leatherback sea turtles, researchers conclude that the average amount of time a leatherback sea turtle can hold its breath is about 73 minutes, with a 95% confidence interval of (70,76). a. Which of these is the best description of what that means? i. 95% of leatherback sea turtles can hold their breath for between 70 minutes and 76 minutes. ii. Given a random leatherback sea turtle, we have 95% confidence that it can hold its breath for between 70 minutes and 76 minutes. iii. We have 95% confidence that among the turtles in the researchers' sample, the average amount of time one of those turtles can hold its breath is between 70 minutes and 76 minutes. iv. We have 95% confidence that among all leatherback sea turtles, the average amount of time a leatherback sea turtle can hold its breath is between 70 minutes and 76 minutes. b. Explain your answer to part a. Current postal regulations do not permit a package to be mailed if the combined length, width, and height exceeds 72 in. What are the dimensions of the largest permissible package with length twice the length of its square end? (Hint: A square has area 2 .) The general manager is recognizing the exceptionally good contribution of employee by choosing the best employee of the month and issuing a recognition certificate. Specify the source of power that this manager has? 1. What is the number of pure strategies that each player has: 1 Left Right 2 2 Right Left, Right 1,0 2,2 1 Left 2,2 a) Both have 2 strategies. b) Both have 4 strategies. c) Player 1 has 2, and player Tor FA cost managem ent system provides informatio n for strategic managem ent decisions and financial reporting. The wages of the janitor in the factory are indirect costs for a manufact ured product. Find Aut(Z 20). Use the Fundamental Theorem of Abelian Groups to express this group as an external direct product of cyclic groups of prime power order. This question refers to the population growth problem in section 3.9 of the lecture notes. Suppose that bacteria growth is modelled by the DE given in the notes. Suppose that the number of bacteria is observed to double after 4 days, and the estimated carrying capacity is 19 times the initial population. What is the estimated population, as a multiple of the initial population, after 18 days? (For example an answer of 3.5 would indicate a population 3.5 times the initial population). Give the answer accurate to 2 decimal places. Number Solve the following equations. a) +=(Hint: use the quadratic formula) b) log (x + 5) - log (x - 1) = log 10 - log 2 c) x + 27 = 2 + x-5 d) 3x+1-3x = 162 (Hint: use exponent rules) e) y x-10 (Hint: First, simplify the system) y+10 2. (10 points): Given the function, f(x)=x57x + 12x a) Find the stationary points of f(x). b) Characterize the stationary points of f(x). point(s) possible The vector v has initial point P and terminal point Q. Write v in the form ai + bj+ck. That is, find its position vector. P= (1, -2,-5); Q=(4,-4,1) v=ai + bj+ck where a= -0, b= =. an Jenna paid foreign income tax of $5,158 on foreign income of $25,788. Her worldwide taxable income was $167,000, and her U.S. tax liability was $41,000. Required: a. What is the amount of the foreign tax credit (FTC) allowed? b. What would be the allowed FTC if Jenna had paid foreign Income tax of $11,400 instead? Note: Do not round intermediate calculations. Round your final answer to the nearest whole dollar amount. Amounts a Foreign tax credit allowed b. Foreign tax credit allowed In a random sample of 50 men, 40% said they preferred to walk up stairs rather than take the elevator. In a random sample of 40 women, 50% said they preferred the stairs. The difference between the two sample proportions (men - women) is to be calculated. What is the standard error for the difference between the two sample proportions? By the definition given in lecture, a model is ( ) A. an abstract representation of reality. B. logical structure and collection of ideas for thinking about a problem or answering a question C. not the best model for a situation unless it is the most accurate model available. D. best if it is as realistic as possible. E. no other answer is the best one. Students in Math 221 were asked about the number of classes they are taking this semester. We got the following answers along with the probability of each:Number of courses2345 or moreProbability0.10.15??0.2Part 1: What is the probability that a student selected at random from Math 221 is taking 4 classes? Question 1If the projects are independent, the AW at the MARR is calculated. All the projects with AW equal or greater than zero are acceptable.Question 1 options:TrueFalse 2. We want to test if our portfolio of investment grew by 2% since we started investing in it. Since our portfolio includes 5000 different types of investments, we select a simple random sample of 20. Our t statistic computed from this sample is 1.99. Use the two different procedures below to determine whether you would reject or not the Null Hypothesis above (the two-sided hypothesis that our overall portfolio grew by 2%). Use a level of statistical significance of 5%. (a) Use the procedure to reject/do not reject the Null Hypothesis based on the critical values t*. Show/discuss the steps you take and state your conclusions. (5 marks) (b) Use the procedure to reject/do not reject the Null Hypothesis based on the probability using p values. Show/discuss the steps you take and state your conclusions. (5 marks) Find the total area under the curve f(x) = 2x from x = = 0 and x = 5. 3 4. Find the length of the curve y = 7(6+ x)2 from x = 189 to x = 875. if the bonding in [mno4]- is 100% ionic, what would the charges on the mn and o atoms a. Discuss the effectiveness of using subsidies to promote a switch of travelers from private cars to public transport. (15 marks)b. Discuss how THREE strategies that the Caribbean or sub-Caribbean region can undertake to sustain or increase its demand in cruise tourism in the post-COVID-19 era (10 marks) Requirements 1. Journalize any required 2018 entries for the bond investment. Remote Down & Co. owns vast amounts of corporate bonds. Suppose Remote Down buys $1,200,000 of AzCo bonds at face value on Consider an economy without private banks where the money demand is determined by Md = $Y A [+ i' with A = 0.0575. The supply of money is controlled by the central bank according to MS M, = = $20,000 and M = $1,000. Using where M is constant for any given level of the interest rate. Initially $Y this information answer the following questions. (a) (2 points) Write down the equilibrium condition in the money market. (b) (3 points) Use your previous answer to find the equilibrium interest rate.