Acertain person goes for a run each morning. when he leaves the house for his run, he is equally likely to go out either the front or the back door and similarly when he returns, he is equally likely to go to either the front or the back door. the runner owns 3 pairs of running shoes which he takes off after the run at whichever door he happens to be. if there are no shoes at the door from which he leaves to go running, he runs barefoot. we are interested in determining the proportion of time that he runs barefoot. 1. set this problem up as a discrete time markov chain. give the states and the one-step transition probability matrix. 2. determine the proportion of days that he runs barefoot.

At the end of year 2, retained earnings for the baker company was $3,550. revenue earned by the company in year 2 was $3,800, expenses paid during the period were $2,000, and dividends paid during the period were $1,400. based on this information alone, retained earnings at the beginning of year 2 was:

Verizon communications, inc., provides the following footnote relating to its leasing activities in its 10-k report. the aggregate minimum rental commitments under noncancelable leases for the periods shown at december 31, 2010, are as follows: years (dollars in millions) capital leases operatingleases 2011 $97 $1,898 2012 74 1,720 2013 70 1,471 2014 54 1,255 2015 42 1,012 thereafter 81 5,277 total minimum 418 $ 12,633 rental commitments less interest and (86) executory costs present value of 332 minimum lease payments less current (75) installments long-term obligation $257 at december 31, 2010 (a) confirm that verizon capitalized its capital leases using a rate of 7.4 %. (b) compute the present value of verizon's operating leases, assuming an 7.4% discount rate and rounding the remaining lease term to 3 decimal places. (use a financial calculator or excel to compute. do not round until your final answers. round each answer to the nearest whole number.)

Ajax corp's sales last year were $435,000, its operating costs were $362,500, and its interest charges were $12,500. what was the firm's times-interest-earned (tie) ratio? a. 4.72b. 4.97c. 5.23d. 5.51e. 5.80