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Measuring power on a jury. We can consider a 12-person jury as the weighted system
a. What is the Shapley-Shubik index for each person in this system?
b. Explain how you obtained your answer in part (a).
c. How does your answer in part (a) conform with your intuition?
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Chapter 11 Solutions
EBK MATHEMATICS ALL AROUND
- Complete the table. Enter DNE if a quantity doesn't exist or NEI if not enough information is given. f(c) limx-->c- f(x) limx-->c+ f(x) limx -->c f(x) continuity at x=c 2 4arrow_forwardFind the indefinite integral. (Use C for the constant of integration.) 9x arcsin(x) dxarrow_forwardFind the indefinite integral using the substitution x = 5 sin(e). (Use C for the constant of integration.) 1 dx (25-x²)3/2arrow_forward
- Find the indefinite integral using the substitution x = 7 sec(0). (Use C for the constant of integration.) √ ׳ √x² - 49 dxarrow_forwardUse the Cauchy Riemann equations (polar form version). Also, describe what happens at the branch cut.arrow_forwardb. i. Show that the following matrix is orthogonal. A = ドードー ii Find the inverse of matrix A. Show all working in an organized/orderly manner. 2 3 -619 A = 42 3 1 5 B-1127) a. Given D = , decode the following message: 32, 24, 42, 28, 24, 40, 50, 60, 132, 96, 12, 24arrow_forward
- 2 Graph of h 6. The graph of the function h is given in the xy-plane. Which of the following statements is correct? , the graph of h is increasing at an increasing rate. (A) For (B) For (C) For 苏|4 K|4 π π , the graph of h is increasing at a decreasing rate. 2 0 and b>1 (B) a>0 and 01 (D) a<0 and 0arrow_forwardQUESTION 4 Peter says that the following expressions can be simplified into one trigonometric ratio without the use of a calculator. Prove that Peter is correct by simplifying the following expressions into one trigonometric ratio: 4.1 sin 43° + sin 17º (5)arrow_forward3. Consider the sequences of functions fn: [-T, π] → R, sin(n²x) n(2) n (i) Find a function f : [-T, π] R such that fnf pointwise as n∞. Further, show that f uniformly on [-T,π] as n→ ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]? Justify your answer. [10 Marks]arrow_forwardAmong a student group 54% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the rest use Safari. What is the probability that you need to pick 7 students to find 2 students using Google Chrome? Report answer to 3 decimals.arrow_forwardQuestion 3 a. Using Laplace theorem, find the determinant of the following matrix. 3 5 2 4 1 3 7 6 A= 2 48 3 569 7arrow_forwardSamples of rejuvenated mitochondria are mutated (defective) with a probability 0.13. Find the probability that at most one sample is mutated in 10 samples. Report answer to 3 decimal places.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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