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1 a). In an engineering lab, a cap was cut from a solid ball of radius 2 meters by a plane 1 meter from the center of the sphere. Assume G be the smaller cap, express and evaluate the volume of G as an iterated triple integral in: [Verify using Mathematica] i). Spherical coordinates. ii). Cylindrical coordinates. iii). Rectangular coordinates. [7 + 7 + 6 = 20 marks] which energy change corresponds to the first ionization energy of potassium? Write the domain and range of the function using interval notation. X 10 -10 810 2 -10- Domain: Range: D $(a)={\t if x < 2 if > 2 10 4 - 10 - -6 2 2 TO 3 -90 Read these articles about price collusion. What do you think about firms colluding on prices? What is the governments role in dealing with such firms? Should the government get involved or should it just allow firms to behave as they want? What can the government do to prevent this from happening in the future?Generic-Drug Firms Face Possible Collusion Charges; U.S. Justice Department has sent subpoenas to several drugmakers and to some individual executivesCompanies Admit They Fixed Prices Of Car Parts: (a) does curve 1 or curve 2 better represent the behavior of the gas at the lower temperature? 5.3.12. Let X, X2,..., X be a random sample from a Poisson distribution with mean . Thus, Y = ^n1 X has a Poisson distribution with mean nu. Moreover, X = Y/n is approximately N(, u/n) for large n. Show that u(Y/n) = Y/n is a function of Y/n whose variance is essentially free of . which south korean conglomerate started business as a grocery store How many data were analyzed in total?What is the degree of freedom for the model?What reference group is applied in this model? The number of requests reaching an e-mail server per second has a Poisson distribution with a mean of 2.3. Calculate the followings: 2.1 The probability of receiving no request in the next second? 2.2 The probability of receiving less than 3 requests in the next second? 2.3 The probability of receiving more than 1 request in the next second? 2.4 E(X)? 2.5 Var(X)? The shape of the PPF curve illustrates... O A. Allocative inefficiency O B. Decreasing opportunity cost O C. Increasing opportunity cost O D. Allocative efficiency in temperate oceans of the northern hemisphere during the winter months: A convex mirror has a radius of curvature of 0.50 m. Where must an object be placed in front ofthe mirror such that the image is formed 0.15 m behind the mirror?this is the answer 0.38 m how? The weights of Pedro's potatoes are normally distributed with known standard deviation o =30 grams Pedro wants to estimate the population mean using a 95% confidence interval.He collected a sample of 50 potatoes and found that their mean weight was 152 grams. Which distribution should Pedro use to construct the confidence interval? bHence calculate a 95% confidence interval for [2] [2] True or False or "be true only if "(f) In a Modigliani and Miller (1958) "perfect" world, the firm's weighted average cost of capital depends only on the firm's investment policy and not on how cash flows are shared between its equity using enough experimental units to reduce chance variation is called:___ XYZ Inc. has operating assets of 50, operating liabilities of 30and common equity of 15. ABCs invested capital equals:15.20.35.None of the above, there is not enough information Find the following limit using lim 0 sin sin 0/sin lim x0 tan 3x/ sin 4x Which of the following does not describe a valid comment in Java? Single line comments, two forward slashes O Multi-line comments, start with /* and end with */ Multi-line comments, start with */ and end with /* Documentation comments, any comments starting with /** and ending with Which polar coordinate pair labels the same point as the one shown below? 3,- 4 Select all that apply. . (3) 3, 4 7 . - 3, 4 . (3,-2) 7 4 B. 3, D. -3, 4 What are the advantages and disadvantages of a completely fairscheduler in Linux?