Choose the correct answer: $\frac{d}{d x} \ln f(x)=$ a. $\frac{f(x)}{f^{\prime}(x)}$ b. $\frac{f^{\prime}(x)}{f(x)}$ c. $\frac{f^{\prime}(x)}{f^{\prime}(x)}$

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minute s and a standard deviation of 1.7 minutes. For a randomly received emergency call, what is the probability that the response time will be more than 10 minutes?

Why is there a brief period at the beginning of ventricular contraction where there is no change in volume?

Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the point on the line. Data for this problem are based on information taken from Prehistoric New Mexico: Background for Survey (by D.E. Stuart and R.P. Gauthier, University of New Mexico Press) It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico:

$$\begin{array}{c|ccccc} \hline x & 5.25 & 5.75 & 6.25 & 6.75 & 7.25 \\ \hline y & 19 & 13 & 33 & 37 & 62 \\ \hline \end{array}$$

Given $\Sigma x=31.25, \Sigma y=164, \Sigma x^{2}=197.813$, $\Sigma y^{2}=6832, \Sigma x y=1080, \text { and } r=0.913$.

The total number y(t) of cases of AIDS (acquired immunodeficiency syndrome) diagnosed in a certain region after t years satisfies $y^{\prime}-\frac{3}{t} y=0$ (for $t \geq 1$). $y(1) = 125$ (125 cases after 1 year) a. Solve this differential equation and initial condition. (Your solution will show that AIDS does not spread logistically, as do most epidemics, but like a power. This means that AIDS will spread more slowly, which seems to result from its being transmitted at different rates within different subpopulations. b. Use your solution to predict the number of AIDS cases in the region by the year $t = 15.$

A retirement plan pays $1000 at retirement and every month thereafter for a total of 12 years. Find the sum of the present values of these payments (at an interest rate of 6% compounded monthly) by summing the series$1000+$\frac{1000}{1.005}$+$\frac{1000}{(1.005)^{2}}$+\cdots+$$\frac{1000}{(1.005)^{143}}$

What is the most powerful stimulus that influences respiration?

Show that finding $\sqrt{N}$ by applying Newton’s method to the equation $x^{2}-N=0$ leads to the iteration formula $x_{n+1}=\frac{1}{2}\left(x_{n}+\frac{N}{x_{n}}\right)$ This formula is known as the Mechanic’s Rule.

The article “Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings” presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand placed on a structure by an earthquake. A sample of 18 measurements had a mean error of 457.8 kNm with a standard deviation of 317.7 kNm. An engineer claims that the method is unbiased, in other words, that the mean error is 0. Can you conclude that this claim is false?

An aircraft company estimates its marginal revenue function for helicopters to be $M R(x)=(x+40) \sqrt{x^{2}+80 x}$ thousand dollars, where x is the number of helicopters sold. Find the total revenue from the sale of the first 10 helicopters.

Find the absolute extreme values of each function on the given interval. $f(x)=2 x^{3}-6 x$ on $[0, 5]$

In an experiment to measure the effect of fluoride "varnish" on the incidence of tooth cavities, thirty-four 10-year-old girls whose parents volunteered them for the study were randomly assigned to two groups. One group was given fluoride varnish annually for 4 years, along with standard dental hygiene; the other group followed only the standard dental hygiene regimen. The mean number of cavities in the two groups was compared at the end of the treatments. Is this experiment subject to the placebo effect? Explain.

A hypothesis that has been rigorously tested can be called a _____ or _____.

Find each integral. $\int \cos 2 t d t$