In a report issued by the Economist Intelligence Unit in 2013, the number of commercial vehicle registrations in the United States (in thousands) by year from 2010 through 2015 is approximated by the function $N(t)=1.3926 t^{3}-9.2873 t^{2}+74.719 t+228.3$ $(0 \leq t \leq 5)$ where t is measured in years with t = 0 corresponding to 2010. If the projection holds up, what would the approximate average commercial vehicle registration per year be in the period from 2010 through 2015?

Determine a polynomial of degree 7 whose Galois group is cyclic of order 7.

Prove that the discriminant of

$$x^{n}+n x^{n-1}+n(n-1) x^{n-2}+\cdots+n(n-1) \dots(3)(2) x+n !$$

is $(-1)^{n(n-1) / 2}(n !)^{n}$.

If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 6%/year.

Evaluate each expression. $36 \div 6+7-6$

Find the area of the region under the graph of the function f on the interval [a, b]. $f(x)=2 x+3 ;[-1,2]$

Copy and complete each function table. Then state the domain and range of the function. Each ticket cost $7.$

$$\begin{matrix} \text{Number of Tickets} & \text{Total Cost(\$)}\\ \text{4} & \square\\ \text{8} & \square\\ \text{15} & \square\\ \text{20} & \square\\ \end{matrix}$$

$

The percentage of high school students who drink and drive stood at 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011. a. Find a linear function f(t) giving the percentage of high school students who drink and drive in year t where t = 0 corresponds to the beginning of 2001. b. At what rate was the percentage of students who drink and drive dropping between 2001 and 2011? c. If the trend continues, what will the percentage of high school students who drink and drive be at the beginning of 2014?

Define the average value of a function f over an interval [a, b]. Give a geometric interpretation.

The return on assets using borrowed money, called leveraged return, is given by $L=\frac{Y-(1-D) R}{D}$ where Y is the return of the asset, R is the cost of borrowed money, and D is the percentage of money the investor must put down to secure the loan. Leanne wants to buy a bond returning 6%/year using borrowed money. The bank required her to pay 20% in cash with the remaining 80% borrowed at an interest rate of 5%/year. What is the leveraged return?

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by $G(x)=400+4 x+0.0001 x^{2}$. Each racket can be sold at a price of p dollars, where p is related to x by the demand equation p=10-0.0004x. If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.

For each of the initial value problems use a numerical solver to plot the solution curve over the indicated interval. Try different display windows by experimenting with the bounds on y. Note: Your solver might require that you first place the differential equation in normal form. $y^{\prime}+(\cos t) y=\sin t$, y(0)=0, $t \in[-10,10]$

An efficiency study conducted by Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker t hr after starting work at 8 A.M. is $-t^{3}+6 t^{2}+15 t, \ (0 \leq t \leq 4)$ Factor the expression.