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1. Give an example of a set A in R2 which is radial at every point of the interval {(x, 0): |x | 1} but such that this interval is not included in the interior of A.
2. Show that the ellipsoid x 2/a2 + y2/b2 + z2/c2 ≤ 1 is convex. Find a support plane at each point of its boundary and show that it is unique.
3. In R3, which planes through the origin are support planes of the unit cube [0, 1]3? Find all the support planes of the cube.
4. The Banach space c0 of all sequences of real numbers converging to 0 has the norm I{xn }I := supn |xn |. Show that each support hyperplane H at a point x of the boundary ∂ B of the unit ball B := {y: IyI ≤ 1} also contains other points of ∂ B. Hint: See Problem 7 of §6.1.
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation. Find the probability of no accidents in 100,000 flight operations.
the following data look at the association between group membership and whether or not the adolescent has had sexual
What is the maximum amount of money the company could spend to get more information about the market share?
according to the national education association the mean salary of public school teachers was 35819 in 1994. assume
the following data give the time in minutes taken to commute from home to umkc for 20 students.10 50 65 33 48 5 11 23
WNAE, an AM station totally dedicated to deliver news, found that while the Distribution of listeners tune in the station follows the normal Distribution.
john calipari head basketball coach for the 2012 national champion university of kentucky wildcats is th ehighest paid
A statewide real estate company specializes in selling farm property in the state of Nebraska. Their records indicate that the mean selling time of farm property is 90 days.
the theoretical probability of undesirable side effects resulting from taking grebex is 2 in 19. if 570 people take
Describe a problem (real or fictitious) for which it will be appropriate to utilize a hypothesis test. Describe how data will be collected, sample size, assumptions, level of measurement etc.
Think of a major decision you have made. What factors helped you to make that decision? How can you relate a Type I or Type II error to your decision? What were the ramifications of the decision
Illustrate out the term control chart? Critically discuss the grand mean, the UCL and the LCL of a control chart for the mean?
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