Alarge high school has a row of 500 numbered lockers, which the custodians have left unlocked and closed before the students arrive. they have also cleaned them so there are no fingerprints on them. on the first day of school, the first student rushes down the hall and opens all of the lockers. the second student follows behind, closing every other locker starting with second locker. starting with the third locker, the third student changes the state of every third locker. this pattern continues until 500 students have gone down the hall, changing the state of the lockers as they go. how many students will have left fingerprints on locker number 378?

Profits from using currency options and futures.on july 2, the two-month futures rate of the mexican peso contained a 2 percent discount (unannualized). there was a call option on pesos with an exercise price that was equal to the spot rate. there was also a put option on pesos with an exercise price equal to the spot rate. the premium on each of these options was 3 percent of the spot rate at that time. on september 2, the option expired. go to the oanda.com website (or any site that has foreign exchange rate quotations) and determine the direct quote of the mexican peso. you exercised the option on this date if it was feasible to do so. a. what was your net profit per unit if you had purchased the call option? b. what was your net profit per unit if you had purchased the put option? c. what was your net profit per unit if you had purchased a futures contract on july 2 that had a settlement date of september 2? d. what was your net profit per unit if you sold a futures contract on july 2 that had a settlement date of september 2

Rachel died in 2014 and her executor is finalizing her estate tax return. the executor has determined that rachel’s adjusted gross estate is $10,120,000 and that her estate is entitled to a charitable deduction in the amount of $500,000. using 2014 rates, calculate the estate tax liability for rachel’s estate.

Ahospital purchases a $500,000 magnetic resonance imaging (mri) machine that has a useful life of 9 years. the salvage value at the end of 9 years is $77,000. (a) write a linear equation that describes the value y (in dollars) of the mri machine in terms of the time t (in years), 0 ≤ t ≤ 9. (b) find the value, in dollars, of the machine after 6 years. $ (c) find the time, in years, when the value of the equipment will be $140,000. (round your answer to two decimal places.) yr