Suppose there are 12-year, 14-year, and 16-year cicadas that all appear this year. after how many years will all three types of cicadas appear together again? how do you know?

Money from an allowance or job is known as .

Job 456 was recently completed. the following data have been recorded on its job cost sheet: direct materials $ 2,418 direct labor-hours 74 labor-hours direct labor wage rate $ 13 per labor-hour machine-hours 137 machine-hours the corporation applies manufacturing overhead on the basis of machine-hours. the predetermined overhead rate is $14 per machine-hour. the total cost that would be recorded on the job cost sheet for job 456 would be: multiple choice $3,380 $5,298 $6,138 $2,622

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.