4. Suppose that a positive integer is written in decimal notation as n = akak–1 … a2a1a0 where 0 ai 9. Prove that n is divisible by 11 if and only if the alternating sum of its digits a0 – ai + … + (–1) kak is divisible by 11.

Einstein office equipment has a rental plan for office machines. a fax machine that lists for $722.98 can be rented for 22% of the price annually. the state imposes a usage charge of 3.2%. if stephen hawking travel decides to rent the fax machine, what will its total monthly rental charge be?