Which of the following is the best example of a functional modification? a) campbell's puts more of a higher-grade chicken in its classic chicken noodle soup. b) a smoke alarm is modified to be more sensitive to smoke at farther distances. c) motorola uses a battery that allows its cell phones to charge back up more quickly. d) the manufacturer of the primer and sealer, kilz, introduces an odorless variety. e) friskies changes the ingredients in its cat food to a taste that is preferred by most cats.

Stocks a, b, and c are similar in some respects: each has an expected return of 10% and a standard deviation of 25%. stocks a and b have returns that are independent of one another; i.e., their correlation coefficient, r, equals zero. stocks a and c have returns that are negatively correlated with one another; i.e., r is less than 0. portfolio ab is a portfolio with half of its money invested in stock a and half in stock b. portfolio ac is a portfolio with half of its money invested in stock a and half invested in stock c. which of the following statements is correct? a. portfolio ab has a standard deviation that is greater than 25%.b. portfolio ac has an expected return that is less than 10%.c. portfolio ac has a standard deviation that is less than 25%.d. portfolio ab has a standard deviation that is equal to 25%.e. portfolio ac has an expected return that is greater than 25%.

Cooper sues company a in state court in south carolina, where he lives, for negligence alleging personal injury and property damage of $100,000 after a truck driven by an employee of company a rear-ended his pickup truck. company a is incorporated in delaware, has its headquarters in new york, but does a substantial amount of business in south carolina. claiming diversity of citizenship, company a seeks removal to federal district court, but cooper opposes the motion. which of the following is true regarding whether the case may be properly removed to federal district court? the amount in controversy satisfies diversity requirements; and if company a's nerve center is in a state other than south carolina, then the case may be properly removed to federal court.the amount in controversy satisfies diversity requirements; and because company a is incorporated and has its headquarters in a state other than south carolina, the case may be properly removed to federal court.because the amount in controversy satisfies diversity requirements and company a is incorporated in a state other than south carolina, the case may be properly removed to federal court regardless of where company a's headquarters, nerve center, or principal place of business is located.because the amount in controversy satisfies diversity requirements and company a is headquartered in a state other than south carolina, the case may be properly removed to federal court regardless of where company a is incorporated and regardless of the location of its nerve center.because the amount in controversy fails to satisfy jurisdictional requirements, regardless of the location of company a, the case may not be removed to federal court.

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.