Consider seven integers selected from the first 10 positive integers. Rank these steps to their corresponding step numbers to show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. a. Group the first ten positive integers into five subsets of two integers each, each subset adding up to 11.
b. Hence, pairs of integers from groups are obtained. In each case, these pairs of integers have a sum of Il, as desired.
c. Select seven integers from these sets. By the pigeonhole principle at least four of them come from the same subset
d. Leave the two integers in the same subset (group). Then there are five more integers and four groups. Again, by the pigeonhole principle, there are at
least two integers in the same group.
e. Select seven integers from these sets. By the pigeonhole principle at least two of them come from the same subset

Leave the two integers in the same subset (group). Then there are six more integers and five groups. Again, by the pigeonhole principle, there are at least two integers in the same group.

There is a simple pattern for determining if a binary number is odd. what is it and why does this pattern occur? how many bits would you need if you wanted to have the ability to count up to 1000? how high could you count in binary if you used all 10 of your fingers as bits? (finger up means 1, finger down means 0)

When creating a budget, log fixed expenses before income. after income. after savings. at the top.

File account. java (see previous exercise) contains a definition for a simple bank account class with methods to withdraw, deposit, get the balance and account number, and return a string representation. note that the constructor for this class creates a random account number. save this class to your directory and study it to see how it works. then write the following additional code: 1. suppose the bank wants to keep track of how many accounts exist. a. declare a private static integer variable numaccounts to hold this value. like all instance and static variables, it will be initialized (to 0, since it’s an int) automatically. b. add code to the constructor to increment this variable every time an account is created. c. add a static method getnumaccounts that returns the total number of accounts. think about why this method should be static - its information is not related to any particular account. d. file testaccounts1.java contains a simple program that creates the specified number of bank accounts then uses the getnumaccounts method to find how many accounts were created. save it to your directory, then use it to test your modified account class.