The average age of teaching staff in a certain institution is 51.0 years old. Assume that the distribution of ages is normal and has a standard deviation of 8.0 years. If 9 teaching staff are chosen at random for a committee, find the probability that the average age of those teaching staff is less than 52.9 years.

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Now ray has had the tires for two months and he notices that the tread has started to pull away from the tire. he has already contacted the place who sold the tires and calmly and accurately explained the problem. they didn’t him because they no longer carry that tire. so he talked with the manager and he still did not get the tire replaced. his consumer rights are being violated. pretend you are ray and write a letter to the company’s headquarters. here are some points to keep in mind when writing the letter: include your name, address, and account number, if appropriate. describe your purchase (name of product, serial numbers, date and location of purchase). state the problem and give the history of how you tried to resolve the problem. ask for a specific action. include how you can be reached.

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.