(Factorials) Factorials are used frequently in probability problems. The factorial of a positive integer n (written n! and pronounced “n factorial”) is equal to the product of the positive integers from
1 to n. Write an application that calculates the factorials of 1 through 20. Use type long. Display the
results in tabular format. What difficulty might prevent you from calculating the factorial of 100?

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

Which of these options are the correct sequence of actions for content to be copied and pasted? select content, click the copy button, click the paste button, and move the insertion point to where the content needs to be inserted. click the copy button, select the content, move the insertion point to where the content needs to be inserted, and click the paste button. select the content, click the copy button, move the insertion point to where the content needs to be inserted, and click the paste button. select the content, move the insertion point to where the content needs to be inserted, click the copy button, and click the paste button.

You can apply several different worksheet themes from which tab?