91Ó°ÊÓ

Work each problem. Small-Business Loan The probability that a bank with assets greater than or equal to \(\$ 30\) billion will make a loan to a small business is \(0.002 .\) What are the odds against such a bank making a small-business loan? (Source: The Wall Street Joumal analysis of CAl Reports.)

Evaluate each expression. Do not use a calculator. $$C(8,1)$$

Describe in your own words how you would determine the binomial coefficient for the fifth term in the expansion of \((x+y)^{8}\)

Find \(a_{1}\) and \(r\) for each geometric sequence. $$a_{2}=-6, a_{7}=-192$$

Decide whether each sequence is finite or infinite. $$a_{1}=1 ; a_{2}=3 ; \text { for } n \geq 3, a_{n}=a_{n-1}+a_{n-2}$$

Determine the positive integer values of \(n\) for which the given statement is not true. $$3^{n}>2 n+1$$

Find \(a_{8}\) and \(a_{n}\) for each arithmetic sequence. $$a_{3}=\pi+2 \sqrt{e}, a_{4}=\pi+3 \sqrt{e}$$

Work each problem. In a recent year there were 51.277 people waiting for an organ transplant. The following table lists the number of patients waiting for the most common types of transplants. \begin{tabular}{c|c} \hline Organ Transplant & Patients Waiting \\ \hline Heart & \(3,774\) \\ Kidney & \(35,025\) \\ Liver & \(7,920\) \\ Lung & \(2,340\) \end{tabular} Assuming that none of these people needs two or more transplants, approximate the probability that a transplant patient chosen at random will need A. a kidney or a heart. B. neither a kidney nor a heart.

Evaluate each expression. Do not use a calculator. $$C(12,4)$$

Find \(a_{1}\) and \(r\) for each geometric sequence. $$a_{4}=-\frac{1}{4}, a_{9}=-\frac{1}{128}$$