Aman has n keys on a key ring, one of which opens the door to his apartment. having celebrated a bit too much one evening, he returns home only to find himself unable to distinguish one key from another. resourceful, he works out a fiendishly clever plan: he will choose a key at random and try it. if it fails to open the door, he will discard it and choose at random one of the remaining n−1 keys, and so on. clearly, the probability that he gains entrance with the first key he selects is 1/n. show that the probability the door opens with the third key he tries is also 1/n.

Anew firm is developing its business plan. it will require $615,000 of assets, and it projects $450,000 of sales and $355,000 of operating costs for the first year. management is reasonably sure of these numbers because of contracts with its customers and suppliers. it can borrow at a rate of 7.5%, but the bank requires it to have a tie of at least 4.0, and if the tie falls below this level the bank will call in the loan and the firm will go bankrupt. what is the maximum debt ratio the firm can use? (hint: find the maximum dollars of interest, then the debt that produces that interest, and then the related debt ratio.)a. 41.94%b. 44.15%c. 46.47%d. 48.92%e. 51.49%

1. what is the lowest balance during this period? 2. lily just received her bank statement below. a. what does the bank think her ending balance is? b. how much more does the bank think lily has? c. what transactions are missing? 3. what is the danger of not balancing your bank account? lily’s bank statement deposits: 2/25 $35 2/26 $20 3/1 $256.32 checks: 2/24 ck #301 $25 2/26 #302 $150 debit card: 2/24 american eagle $75.48 2/25 chick fa la $4.67 2/27 mcdonalds $3.56 2/28 chevron $34.76 withdrawal: 2/27 $40 beginning balance $423.34 deposits $311.32 total debits $333.47 ending balance $401.19

The new york times (nov. 30, 1993) reported that “the inability of opec to agree last week to cut production has sent the oil market into turmoil . . [leading to] the lowest price for domestic crude oil since june 1990.” why were the members of opec trying to agree to cut production? so they could save more oil for future consumption so they could lower the price so they could raise the price why do you suppose opec was unable to agree on cutting production? because each country has a different production capacity because each country experiences different production costs because each country has an incentive to cheat on any agreement the newspaper also noted opec’s view “that producing nations outside the organization, like norway and britain, should do their share and cut production.” what does the phrase “do their share” suggest about opec’s desired relationship with norway and britain? opec would like norway and britain to keep their production levels high. opec would like norway and britain to act competitively. opec would like norway and britain to join the cartel.