The windchill index (revised in 2001) for a temperature of 32 degrees Fahrenheit and wind speed x miles per hour is $W(x)=55.628-22.07 x^{0.16}$. a. Graph the windchill index on a graphing calculator using the window [0, 50] by [0, 40]. Then find the windchill index for wind speeds of x = 15 and x = 30 mph. b. Notice from your graph that the windchill index has first derivative negative and second derivative positive. What does this mean about how successive 1-mph increases in wind speed affect the windchill index? c. Verify your answer to part (b) by defining y2 to be the derivative of $y_1$ (using NDERIV), evaluating it at x = 15 and x = 30, and interpreting your answers.

Match the system in column A with its corresponding function in column B. digestive

The Florida State Center for Health Statistics reported in Women and Cardiovascular Disease Hospitalizations that, for cardiovascular hospitalizations, the mean age of women is 71.9 years. At one hospital, a random sample of 20 female cardiovascular patients had the following ages, in years.

$$\begin{array}{lllll} \hline 75.9 & 83.7 & 87.3 & 74.5 & 82.5 \\ 78.2 & 76.1 & 52.8 & 56.4 & 53.8 \\ 88.2 & 78.9 & 81.7 & 54.4 & 52.7 \\ 58.9 & 97.6 & 65.8 & 86.4 & 72.4 \\ \hline \end{array}$$

a. Round each observation to the nearest year and then construct a stem-and-leaf diagram of the rounded data. b. Truncate each observation by dropping the decimal part, and then construct a stem-and-leaf diagram of the truncated data. c. Compare the stem-and-leaf diagrams that you obtained in parts (a) and (b).

Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 oz and standard deviation 0.2 oz. a. What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz? b. If the population mean fill volume is increased to 12.03 oz, what is the probability that the mean volume of a sample of size 144 will be less than 12 oz?

Casts are sometimes found in a urine sample; what are casts?

Use a graphing calculator trapezoidal approximation program from the Internet to approximate each integral. Use the following values for the numbers of intervals: 10, 50, 100, 200, 500. Then give an estimate for the value of the definite integral, keeping as many decimal places as the last two approximations agree (when rounded). $\int_{0}^{1} \ln \left(x^{2}+1\right) d x$

a. For $f(x)=\sqrt[3]{x}$, find the second Taylor polynomial at x = 1. b. Use your answer from part (a) to approximate $\sqrt[3]{1.3}$. c. Estimate the error by the error formula. [Hint: Find an M such that $\left|f^{(3)}(x)\right| \leq M$ for $1 \leq x \leq 1.3$, using the fact that a decreasing function is maximized at its left-hand endpoint.] d. Restate the approximation and error, rounded appropriately.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company has to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Do the sample data give convincing evidence at the $\alpha=0.05$ significance level that more than 20% of the company's customers are willing to purchase the upgrade?

Given a binomial experiment with probability of success on a single trial p=0.30, find the probability that the first success occurs on trial number n=2.

Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the 50th percentile in the league championship meet. Explain how this is possible. (Remember that lower times are better in this case!)

In this problem, you are asked to solve part of the Focus Problem at the beginning of this chapter. In his book Chances: Risk and Odds in Everyday Life, James Burke says that there is a 72% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 7% chance that the polygraph will falsely accuse someone of lying. Suppose a person answers 10% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?

A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up tails. a. Find the probability mass function of X. b. Find the probability mass function of Y. c. Is it reasonable to assume that X and Y are independent? Why? d. Find the joint probability mass function of X and Y.

Name the organs that help rid the body of waste. What type of waste does each organ remove?

Which of the following terms refers to an increase in cell size? a. Hyperplasia b. Hypertrophy c. Anaplasia d. Atrophy