Assume a penicillin dose of $9000$ units per kilogram of body weight, taken every $6$ hours, is prescribed for the treatment of a bacterial infection. For penicillin, $400,000$ units are equal to $250 \mathrm{mg}$. a. Express the dose in milligrams per kilogram ( $\mathrm{mg} / \mathrm{kg})$ of body weight. b. How many milligrams of penicillin would a $20$-kilogram child take in one day?

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean $\mu=7500$ and estimated standard deviation $\sigma=1750$. test result of x< 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. What is the probability that, on a single test, x is less than 3500?

Determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; infection points; symmetry; and those intercepts that can be obtained conveniently. Then sketch the graph. $y=-2+12 x-x^{3}$

Find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region enclosed by the curves. $y=1 / x^2, \quad y=3 x-x^2$

Identify the level curves $f(x, y)=c$ and sketch the curves corresponding to the indicated values of $c$.

$$f(x, y)=\frac{\ln y}{x^2} ; \quad c=-2,-1,0,1,2$$

Match given key term to the appropriate definition.

__________ curvatures is the cervical and lumbar curves of the spine.

A patient has an indwelling urinary catheter. Why does an indwelling urinary catheter present a risk for urinary tract infection? (Select all that apply.)

1. It allows migration of organisms into the bladder.
2. The insertion procedure is not done under sterile conditions.
3. It obstructs the normal flushing action of urine flow.
4. It keeps an incontinent patient's skin dry.
5. The outer surface of the catheter is not considered sterile.

The time between infection and the display of symptoms for streptococcal sore throat is a random variable whose probability density function can be approximated by

$$f(t)=\frac{\mathrm{i}}{15.676} t^{2} e^{-0.05 t}$$

if $0 \leqslant t \leqslant 150$ and f(t) = 0 otherwise (t measured in hours). What is the probability that an infected patient will display symptoms within the first 48 hours?

Use the graphing utility of your calculator to draw the graphs of the curves $y=x^2 e^{-x}$ and $y=\frac{1}{x}$ on the same screen. Use ZOOM and TRACE or some other feature of your calculator to find where the curves intersect and then compute the area of the region bounded by the curves.

Consider the given curves.

Compute the curvature.

In $2014$ there were $1.2$ million people in the United States who had been infected with HIV. At that time the infection rate was $44,000$ people per year.

(a) Write a formula for a linear function $f$ that models the total number of people in millions who were living with HIV/AIDS $x$ years after $2014$ .

(b) Estimate the number of people who may have been infected by the year $2018$.

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^{2} )$ and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. $f(x)=x^{2}+4$

a. List the defense mechanisms that reduce the risk of infection in the oral cavity. b. State the locations of resident (normal) flora in the digestive tract. c. State the approximate pH of gastric secretions and two purposes served by this pH level.