Let V be a vector space, and let x,y be distinct elements of V (i.e. xy. (a) Prove that if x is a scalar multiple of y, then the set {x,y) is linearly dependent. (b) Prove that if {x,y} is linearly dependent, then either x is a scalar multiple of y ory is a scalar multiple of x. (c) Prove that {x,y} is linearly independent if and only if {x-y,x + 2y} is linearly independent.
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- Let A be the set of all integers divisible by 2 and B be the set of all integers divisible by 4. a) Prove/Disprove that B is a subset of A b) Prove/Disprove that A is a subset of B c) Describe the members of the intersection A and B d) Describe the objects of the difference of B and A e) Describe the elements of A union BIf the Poisson's ratio of an elastic material is 0.4, then find the ratio of modulus of rigidity to Young's modulus..If the Poisson's ratio of an elastic material is 0.4, then find the ratio of modulus of rigidity to Young's Modulus If the Poisson's ratio of an elastic material is 0.4, then find the ratio of modulus of rigidity to Young's modulus...?1. Give an example each for the following: * an odd function * an even function
- typing clear urjentIf a convex function is multiplied by a negative constant, the result: A. is concave B. could be either convex or concave, depending on the value of the constant C. is convex D. is linear4. Consider the following argument: If the white flag is flying, then truce has been declared. Truce has not been declared. Therefore, the white flag is not flying. (a) Define statement variables for each component of the above argument, then write the formal argument using your variables.
- Consider a piston-cylinder assembly that operates in isobaric process. Steam undergoes the process from 500°C to reach 1000°C. Select two (2) pressure values in the range of 10< P<45 MPa at which ttypingAssume “Jane” saves $10,000 per year for 10 years starting at age 25. At age 35 she no longer is able to save but leaves her accumulated savings invested until age 65 when she retires. Assume “John” does not begin saving until age 35, but then saves $10,000 per year until age 65 when he also retires. Assume John and Jane invest their entire wealth in the same mutual fund. Who accumulates a larger retirement nest egg? 1. Answer this question by building an Excel spreadsheet that allows you to show the difference in wealth at age 65 assuming an annual rate of return of 8%. Make sure your model allows you to change the assumed rate of return and automatically recalculate the difference in wealth at age 65. 2. At what assumed rate of return are John and Jane’s wealth at age 65 equal? Use “Goal Seek” in order to find this rate of return. 3. Create a graph to clearly show how final wealth for John and Jane depends on the rate of return. Start at 0% and increase the rate of return in…
- Which of the following statements is correct regarding the EMH form? Select one: None of the answers are correct If the market is weak-form efficient, then it is also semistrong and strong-form efficient. If the market is semistrong form efficient, then it is also strong form efficient If a market is strong-form efficient, it is also semistrong and weak form efficient If the market is strong-form efficient, it is also semistrong but not weak-form efficientIn this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?