Now that you have practiced the basic algorithm, let’s study the stable marriage problem a little bit quantitavely. here we define the following notation: on day j, let pj(m) be the rank of the woman that man m proposes to (where the first woman on his list has rank 1 and the last has rank n). also, let rj(w) be the total number of men that woman w has rejected up through day j − 1 (i. e. not including the proposals on day j). answer the following questions using the notation above.(a) prove or disprove the following claim: ∑m pj(m)−∑w rj(w) is independent of j. if it is true, also give the value of ∑m pj(m)−∑w rj(w). the notation, ∑m and ∑w , simply means that we are summing over all men and all women.(b) prove or disprove the following claim: one of the men or women must be matched to someone who is ranked in the top half of their preference list. you may assume that n is even.

okay, if you need all you need to do is ask, and i'll do my best to assist you.

step-by-step explanation:

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2

a.)the line for function b is steeper

answer:

some responsibilities that come with having a checking account -

1. we have to maintain check register with exactness to avoid checks being returned for insufficient funds which is called bouncing a check.

2. we need to update our check register each time we make a transaction using a convenience card. updating check register will   save   us from   overdrawing of checking account.

3. read the agreement the bank gave you when you signed up for our checking account. this includes all the fees and the minimum balance we need to keep in our account to avoid maintenance charges.  

explanation:

note : -   checking account is a transactional deposit account. we can use it to deposit and withdraw funds. money in a checking account is very liquid. it   can be withdrawn using electronic debits, automated cash machines, or checks among other methods.