You invest $180 in a mutual fund today that pays 6.80 percent interest annually. How long will it take to double your money? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to 0 decimal place, e. g. 545)

For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. complete parts (a) through (c) below. x (cash prize, $) p(x) grand prizegrand prize 0.000000008860.00000000886 200,000 0.000000390.00000039 10,000 0.0000016950.000001695 100 0.0001582930.000158293 7 0.0039114060.003911406 4 0.0080465690.008046569 3 0.012865710.01286571 0 0.975015928140.97501592814 (a) if the grand prize is $13 comma 000 comma 00013,000,000, find and interpret the expected cash prize. if a ticket costs $1, what is your expected profit from one ticket? the expected cash prize is $nothing.

You are an employee of an u.s. firm that produces personal computers in thailand and then exports them to the united states and other countries for sale. the personal computers were originally produced in thailand to take advantage of relatively low labor costs and a skilled workforce. other possible locations considered at that time were malaysia and hong kong. the u.s. government decides to impose punitive 100% ad valorem tariffs on imports of computers from thailand to punish the country for administrative trade barriers that restrict u.s. exports to thailand. how do you think your firm should respond? what does this tell you about the use of targeted trade barriers?

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.