Which of the following relationships is NOT​ valid? A. When marginal cost is above average variable​ cost, AVC is rising. B. Rising marginal cost implies that average total cost is also rising. C. When marginal cost is below average total​ cost, the latter is falling. D. None of the above

The total value of your portfolio is $10,000: $3,000 of it is invested in stock a and the remainder invested in stock b. stock a has a beta of 0.8; stock b has a beta of 1.2. the risk premium on the market portfolio is 8%; the risk-free rate is 2%. additional information on stocks a and b is provided below. return in each state state probability of state stock a stock b excellent 15% 15% 5% normal 50% 9% 7% poor 35% -15% 10% what are each stock’s expected return and the standard deviation? what are the expected return and the standard deviation of your portfolio? what is the beta of your portfolio? using capm, what is the expected return on the portfolio? given your answer above, would you buy, sell, or hold the portfolio?

Read the following scenario and answer the question in 5-10 sentences. you are the owner of a small business that is a defendant in a lawsuit in federal court. you received bad news from your lawyer that the judge did not allow certain documents to be admitted as evidence in court and that the jury reached a $50,000 verdict in favor of the plaintiff. your lawyer tells you that it is within your legal right to hire him to file an appeal with the united states court of appeals. if the appellate court rules in your favor, you may be able to avoid paying part or all of the $50,000. evaluate your lawyer’s suggestion about appealing the decision.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.