An automobile insurance company has compiled the information summarized below on its policy-holders. Suppose someone calls to file a claim. To which age group does he or she most likely belong?

$$\scriptstyle\begin{array}{lcc} \hline & \% \text { of } & \% \text { Involved in } \\ \text { Age Group } & \text { Policyholders } & \text { Accidents Last year } \\ \hline \text { young }(<30) & 20 & 35 \\ \text { Middle-aged }(30-64) & 50 & 15 \\ \text { Elderly }(65+) & 30 & 25 \\ \hline \end{array}$$

Determine (a) the before-tax ROR, and (b) approximate after-tax ROR for a project that has a first cost of $750,000, a salvage value of 25% of the first cost after 3 years, and annual (GI-OE) of$260,000. Assume the company has a $T_{e}$ of 37%.

Complete each step. Find the value of each model at x=25.

$$\begin{array}{|c|c|} \hline x & and \\ \hline 0 & 50 \\ \hline 2 & 67 \\ \hline 4 & 80 \\ \hline 6 & 89 \\ \hline 8 & 94 \\ \hline 10 & 97 \\ \hline 12 & 98 \\ \hline 14 & 99 \\ \hline \end{array}$$

Match each equation of an ellipse in Column I with the appropriate intercepts in Column II.

$$\begin{matrix} \text{I} & \text{II}\\ \text{(a) }{36 x^{2}+9 y^{2}=324} & \text{A. (-3, 0), (3, 0), (0, -6), (0, 6)}\\ \text{(b) }{ 9 x^{2}+36 y^{2}=324} & \text{B. ( - 4, 0), ( 4, 0), (0, - 5), (0, 5)}\\ \text{(c) }{ \frac{x^{2}}{25}+\frac{y^{2}}{16}=1} & \text{C. ( - 6, 0), (6, 0), (0, - 3), (0, 3)}\\ \text{(d) }{ \frac{x^{2}}{16}+\frac{y^{2}}{25}=1} & \text{D. (- 5, 0), (5, 0), (0, - 4), (0, 4)}\\ \end{matrix}$$

When dealing with sound intensities and decibel levels, a convenient approximation (accurate to 2 significant figures) is: For every doubling of the intensity, the decibel level increases by 3.0. Suppose the sound level at some location is 85 dB. Find the decibel levels if the sound intensity is increased by factors of 2.0.

Solve the equation. Approximate the result to three decimal places. $2^{4 x}=21$

Harris International currently pays a dividend of $3.24 per share on its preferred stock that sells for$54 per share. In order to raise capital to purchase a smaller competitor, the company plans to issue 2.7 million shares of preferred stock at a 10% discount to its current price. Determine (a) the amount of funding that Harris will realize through the stock offering, and (b) the cost of equity financing.

Find each quotient. Write answers in standard form. $\frac{-3+4 i}{2-i}$

An industrial robot with a controller, teach pendants, and job-specific peripherals has an initial cost of $85,000 now, and the future cost will increase exactly by the inflation rate. The cost of a similar robot 3 years from now at a market interest rate of 10% per year and inflation rate of 4% per year is closest to: (a)$95,610 (b) $102,414 (c)$125,931 (d) $127,261

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. $4 t^{-2}+8 t^{-4}$

A force of 30.0 N is app lied in the positive x-direction to a block of mass 8.00 kg, at rest on a frictionless surface. What is the block's acceleration?

Write an equation for each line described. Give answers in standard form and in slope-intercept form (if possible). m=-2, b=12

(A) Find $f^{\prime}(x)$ using the quotient rule, and (B) Explain how $f^{\prime}(x)$ can be found easily without using the quotient rule. $f(x)=\frac{1}{x}$

A group of laboratory animals is infected with a particular form a bacteria, and their survival time is found to average 32 days, with a standard deviation of 36 days. a. Visualize the distribution of survival times. Do you think that the distribution is relatively mound-shaped, skewed right, or skewed left? Explain. b. Within what limits would you expect at least 3/4 of the measurements to lie?