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Chapter 8: Problem 46
Express each repeating decimal as a fraction in lowest terms. $$0 . \overline{1}=\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10,000}+\cdots$$
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Exercises \(67-72\) are based on the following jokes about books: \(\cdot\) "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." - Groucho Marx \(\cdot\) "I recently bought a book of free verse. For \(\$ 12\)." \- George Carlin \(\cdot\) "If a word in the dictionary was misspelled, how would we know?" - Steven Wright \(\cdot\) "Encyclopedia is a Latin term. It means 'to paraphrase a term paper." - Greg Ray \(\cdot\) "A bookstore is one of the only pieces of evidence we have that people are still thinking." - Jerry Seinfeld \(\cdot\) "I honestly believe there is absolutely nothing like going to bed with a good book. Or a friend who's read one." \(-\)Phyllis Diller In how many ways can people select their two favorite jokes from these comments about books?
Find the term in the expansion of \(\left(x^{2}+y^{2}\right)^{5}\) containing \(x^{4}\) as a factor.
Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{n !}{(n-1) !}-\frac{1}{n-1}$$
Five men and five women line up at a checkout counter in a store. In how many ways can they line up if the first person in line is a woman and the people in line alternate woman, man, woman, man, and so on?
Many graphing utilities have a sequence-graphing mode that plots. the terms of a sequence as points on a rectangular coordinate system. Consult your manual, if your graphing utility has this capability, use it to graph each of the sequences. What appears to be happening to the terms of each sequence as \(n\) gets larger? $$a_{n}-\frac{2 n^{2}+5 n-7}{n^{3}} n:[0,10,1] \text { by } a_{n}:[0,2,0.2]$$
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