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Chapter 0: Problem 21
Find the intersection of the sets. $$\\{1,2,3,4\\} \cap\\{2,4,5\\}$$
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a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-7 x+4, \text { for } x=8$$
$$\text { factor completely.}$$ $$x^{2 n}+6 x^{n}+8$$
A large number can be put into perspective by comparing it with another number. For example, we put the \(\$ 15.2\) trillion national debt (Example 12 ) and the \(\$ 2.17\) trillion the government collected in taxes (Exercise 115 ) by comparing these numbers to the number of U.S. citizens. For this project, each group member should consult an almanac, a newspaper, or the Internet to find a number greater than one million. Explain to other members of the group the context in which the large number is used. Express the number in scientific notation. Then put the number into perspective by comparing it with another number.
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-3(x-y), \text { for } x=8 \text { and } y=2$$
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