91Ó°ÊÓ

Find the term in the expansion of \(\left(x^{2}+y^{2}\right)^{5}\) containing \(x^{4}\) as a factor.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In the sequence \(21,700,23,172,24,644,26,116, \ldots,\) which term is \(314,628 ?\)

Use a calculator's factorial key to evaluate each expression. $$\left(\frac{300}{20}\right) !$$

Use the formula for the value of an annuity to solve.\( Round answers to the nearest dollar. To offer scholarship funds to children of employees, a company invests \)\$ 15,000\( at the end of every three months in an annuity that pays \)9 \%$ compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest.

Prove that $$ \left(\begin{array}{l} n \\ r \end{array}\right)=\left(\begin{array}{c} n \\ n-r \end{array}\right) $$

Use a calculator's factorial key to evaluate each expression. $$\frac{20 !}{300}$$

Graph the piecewise function: $$ f(x)=\left\\{\begin{array}{lll} 2 x-4 & \text { if } & x \neq 3 \\ -5 & \text { if } & x=3 \end{array}\right. $$

determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the Fundamental Counting Principle to determine the number of five- digit ZIP codes that are available to the U.S. Postal Service.

Use a calculator's factorial key to evaluate each expression. $$\frac{20 !}{(20-3) !}$$

Show that $$ \left(\begin{array}{l} n \\ r \end{array}\right)+\left(\begin{array}{c} n \\ r+1 \end{array}\right)=\left(\begin{array}{l} n+1 \\ r+1 \end{array}\right) $$ Hints: $$ \begin{array}{l} (n-r) !=(n-r)(n-r-1) ! \\ (r+1) !=(r+1) r ! \end{array} $$