Find the value of $10,000 invested for 8 years at 8% interest if the compounding is done: a. quarterly. b. continuously.

Use your graphing calculator to graph each function on a window that includes all relative extreme points and inflection points, and give the coordinates of these points (rounded to two decimal places). [Hint: Use NDERIV once or twice with ZERO.] (Answers may vary depending on the graphing window chosen.) $f(x)=\frac{x^{4}}{e^{x}}$

Find the area bounded by the given curves. $y=3 x^{2}-12 x$ and $y=0$

Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of lima beans (in tons/acre).

$$\scriptscriptstyle\begin{array}{c|cccccccccccc} \hline \text {Method A} & 1.83 & 2.34 & 1.61 & 1.99 & 1.78 & 2.01 & 2.12 & 1.15 & 1.41 & 1.95 & 1.25 & \\ \hline \text {Method B} & 2.15 & 2.17 & 2.11 & 1.89 & 1.34 & 1.88 & 1.96 & 1.10 & 1.75 & 1.80 & 1.53 & 2.21 \\ \hline \end{array}$$

Use a 5% level of significance to test the hypothesis that there is no difference between the yield distributions. What is the level of significance? State the null and alternate hypotheses.

For each data set use the specified grouping method to a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on your result from part (a). d. construct a relative-frequency histogram based on your result from part (b). According to the News Generation, Inc. Web site’s Radio Facts and Figures, which has as its source Arbitron Inc., the mean number of radios per U.S. household was 5.6 in 2008. A random sample of 45 U.S. households taken this year yields the following data on number of radios owned. Use single-value grouping.

$$\begin{array}{lclllllll} \hline 4 & 10 & 4 & 7 & 4 & 4 & 5 & 10 & 6 \\ 8 & 6 & 9 & 7 & 5 & 4 & 5 & 6 & 9 \\ 7 & 5 & 3 & 4 & 9 & 5 & 4 & 4 & 7 \\ 8 & 4 & 9 & 8 & 5 & 9 & 1 & 3 & 2 \\ 8 & 6 & 4 & 4 & 4 & 10 & 7 & 9 & 3 \\ \hline \end{array}$$

Suppose you want to eat lunch at a popular restaurant. The restaurant does not take reservations, so there is usually a waiting time before you can be seated. Let x represent the length of time waiting to be seated. From past experience, you know that the mean waiting time is $\mu=18$ minutes with $\sigma=4$ minutes. You assume that the x distribution is approximately normal. What is the probability that the waiting time will exceed 20 minutes, given that it has exceeded 15 minutes? Hint: Compute P(x>20|x>15).

Two populations have mound-shaped, symmetric distributions. A random sample of 16 measurements from the first population had a sample mean of 20, with sample standard deviation 2. An independent random sample of 9 measurements from the second population had a sample mean of 19, with sample standard deviation 3. Test the claim that the population mean of the first population exceeds that of the second. Use a 5% level of significance. Estimate the P-value of the sample test statistic.

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n=6 professional baseball players gave the following information.

$$\begin{array}{|l|llllll|} \hline x & 0.328 & 0.290 & 0.340 & 0.248 & 0.367 & 0.269 \\ \hline y & 3.2 & 7.6 & 4.0 & 8.6 & 3.1 & 11.1 \\ \hline \end{array}$$

Use a 5% level of significance to test the claim that $\beta \neq 0$.

Show that the rectangle of fixed area whose perimeter is a minimum is a square.

Name the arches that form the foot and explain their significance.

Find the following limits without using a graphing calculator or making tables. $\lim _{x \rightarrow 3}\left(4 x^{2}-10 x+2\right)$

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of $\bar{x}=37.5 \mathrm{m} 1 / \mathrm{kg}$ (milliliters plasma per kilogram body weight). Assume that $\sigma=7.50 \mathrm{ml} / \mathrm{kg}$ for the distribution of blood plasma. What conditions are necessary for your calculations?

Use the technology of your choice to do the following tasks. a. Obtain individual normal probability plots and the standard deviations of the samples. b. Perform a residual analysis. c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so, also do parts (d) and (e). d. Use a one-way ANOVA test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken. e. Interpret your results from part (d). The Federal Bureau of Prisons publishes data in Statistical Report on the times served by prisoners released from federal institutions for the first time. Independent simple random samples of released prisoners for five different offense categories yielded the data on time served, in months, shown on the WeissStats CD.

Three machines-A, B, and C-are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts, respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C. Suppose we randomly select a part produced by one of these three machines at random. Draw a tree diagram to represent this chance process.