6.25 (Prime Numbers) A positive integer is prime if it’s divisible by only 1 and itself. For example, 2, 3, 5 and 7 are prime, but 4, 6, 8 and 9 are not. The number 1, by definition, is not prime. a) Write a method that determines whether a number is prime. b) Use this method in an application that determines and displays all the prime numbers less than 10,000. How many numbers up to 10,000 do you have to test to ensure that you’ve found all the primes? c) Initially, you might think that n/2 is the upper limit for which you must test to see whether a number n is prime, but you need only go as high as the square root of n. Re- write the program, and run it both ways.

Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. purchases at stock exchanges--what’s being bought-- are one source of data with a natural ordering in time. given a long sequence s of such events, your friends want an efficient way to detect certain "patterns" in them--for example, they may want to know if the four events buy yahoo, buy ebay, buy yahoo, buy oracle occur in this sequence s, in order but not necessarily consecutively. they begin with a collection of possible events (e.g., the possible’ transactions) and a sequence s of n of these events. a given event may occur multiple times in s (e.g., yahoo stock may be bought many times in a single sequence s). we will say that a sequence s’ is a subsequence of s if there is a way to delete certain of the events from s so that the remaining events, in order, are equal to the sequence s’. so, for example, the sequence of four events above is a subsequence of the sequence buy amazon, buy yahoo, buy ebay, buy yahoo, buy yahoo, buy oracle their goal is to be able to dream up short sequences and quickly detect whether they are subsequences of s. so this is the problem they pose to you: give an algorithm that takes two sequences of even~s--s’ of length m and s of length n, each possibly containing an event more than once--and decides in time o(m n) whether s’ is a subsequence of s

When is an original work considered public domain? a. when posted via social media b. when it is posted on the internet c. when a copyright symbol is not included with the piece of work d. when explicit permission is given by the author / owner

Which activity should be part of a long-term plan to positively affect yourhealth? oa. wearing regular clothing when handling toxinsob. not worrying about secondhand smokeoc. avoiding excessive exposure to sunlightod. drinking only well water