During the course of treatment of an illness, the concentration of a drug (in micrograms per milliliter) in the bloodstream fluctuates during the dosing period of 8 hours according to the model

$$C(t)=15.4-4.7 \sin \left(\frac{\pi}{4} t+\frac{\pi}{2}\right), \quad 0 \leq t \leq 8$$

Use an identity to express the concentration $C(t)$ in terms of the cosine function. Note: This model does not apply to the first dose of the medication as there will be no medication in the bloodstream.

In this exercise, determine whether the given statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

To solve $x-9 \sqrt{x}+14=0$, we let $\sqrt{u}=x$.

One hour after x milligrams of a particular drug are given to a person, the change in body temperature T(x), in degrees Fahrenheit, is given by $T(x)=x^{2}\left(1-\frac{x}{9}\right) \quad 0 \leq x \leq 6$ The rate $T^{\prime}(x)$ at which T(x) changes with respect to the size of the dosage x is called the sensitivity of the body to the dosage. (A) When is $T^{\prime}(x)$ increasing? Decreasing? (B) Where does the graph of T have inflection points? (C) Sketch the graphs of T and T$^{\prime}$ on the same coordinate system. (D) What is the maximum value of $T^{\prime}(x)$?

Mrs. Sung gave a test in her trigonometry class. The scores were normally distributed with a mean of 85 and a standard deviation of 3. What percent would you expect to score between 88 and 91?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A doughnut and a compact disc both have genus 1 and are topologically equivalent. ____

Shannon observes two light pulses to be emitted from the same location, but separated in time by $3.00 \mu \mathrm{s}$. Kimmie observes the emission of the same two pulses to be separated in time by $9.00 \mu \mathrm{s}$. (a) How fast is Kimmie moving relative to Shannon? (b) According to Kimmie, what is the separation in space of the two pulses?

How does capitalism differ from socialism and communism?

Find the unique solution of each of the following super increasing knapsack problems:
(a) $118=4 x_1+5 x_2+10 x_3+20 x_4+41 x_5+99 x_6$. (b) $51=3 x_1+5 x_2+9 x_3+18 x_4+37 x_5$. (c) $54=x_1+2 x_2+5 x_3+9 x_4+18 x_5+40 x_6$.

In an experiment, a group of fish was injected with living bacteria. Of those fish maintained at $28^{\circ} \mathrm{C}$, the percentage p that survived the infection t hours after the injection is given in the following table:

$$\begin{array}{llllll} t & 8 & 10 & 18 & 20 & 48 \\ \hline p & 82 & 79 & 78 & 78 & 64 \end{array}$$

Find the linear regression line of p on t.

Give all six trigonometric function values for the angle $\theta$. Rationalize denominators when applicable. $\sin \theta=\frac{\sqrt{3}}{5}$, and $\cos \theta<0$

Who bears the freight when the terms of sale are FOB destination?

Based on the data in table below, assume that ages of moviegoers are normally distributed with a mean of 35 years and a standard deviation of 20 years.

$$\begin{array} { c c c c c c c c }\hline\text{Age}& { 2 - 11 } & { 12 - 17 } & { 18 - 24 } & { 25 - 39 } & { 40 - 49 } & { 50 - 59 } &\text{60 and older}\\ \hline\text{Percent}&{ 7 } & { 15 } & { 19 } & { 19 } & { 15 } & { 11 }&14 \\ \hline \end{array}$$

Find the probability that a simple random sample of 25 moviegoers has a mean age that is less than 30 years.

For August, Lanny Company had 25,000 units in BWIP, 40% complete, with costs equal to $36,000. During August, the cost incurred was$450,000. Using the FIFO method, Lanny had 125,000 equivalent units for August. There were 100,000 units transferred out during the month. The cost of goods transferred out is

a. $500,000.
b.$360,000.
c. $450,000.
d.$400,000.
e. $50,000.

The following data represent the running times of films produced by two motion-picture companies.

$$\begin{matrix} \text{Company} & \text{Time (minutes) }\\ \text{I} & \text{103} & \text{94} & \text{110} & \text{87} & \text{98}\\ \text{II} & \text{97} & \text{82} & \text{123} & \text{92} & \text{175} & \text{88} & \text{118}\\ \end{matrix}$$

Compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. Assume that the running-time differences are approximately normally distributed with unequal variances.