Amigo Mobility, which manufactures battery-powered mobility scooters, has $700,000 to invest. The company is considering three different battery projects that will yield the following rates of return:$ $\text{Deep cycle = 28\\%} \\ \text{Wet/flooded = 42\\%} \\ \text{Lithium ion = 19\\%}$ $The initial investment required for each project is$200,000, $100,000, and$400,000, respectively. If Amigo’s MARR is 15% per year and it invests in all three projects, what rate of return will the company make?

What rate of return per month will an entrepreneur make over a $2 \frac{1}{2}$-year project period if he invested $150,000 to produce portable 12-volt air compressors? His monthly costs are$27,000 and his revenues are $33,000.

You have been asked to evaluate two alternatives, X and Y, that may increase plant capacity for manufacturing high-pressure hydraulic hoses. The parameters associated with each alternative have been estimated. Which one should be selected on the basis of a present worth comparison at an interest rate of 12% per year? Why is yours the correct choice?

$$\begin{array}{lcc} \text { Alternative } & \mathrm{X} & \mathrm{Y} \\ \hline \text { First cost, } \$ & -45,000 & -58,000 \\ \text { Maintenance cost, } \$ \text { /year } & -8,000 & -4,000 \\ \text { Salvage value, } \$ & 2,000 & 12,000 \\ \text { Life, years } & 5 & 5 \end{array}$$

Two quantities (A and B) co-vary such that Quantity A changes at a constant rate with respect to Quantity B. Suppose the change in the value of Quantity A is always 6.5 times as large as the change in the value or Quantity B. Suppose also that the value of Quantity A is 5 when the value of Quantity B is 12. a. What is the value of Quantity A when the value of Quantity B is 19? b. What is the value of Quantity A when the value of Quantity B is -1? c. What is the value of Quantity B when the value of Quantity A is 7?

If a 3D printer increased in cost at exactly the inflation rate, what was the inflation rate if the printer costs exactly twice as much now as it did 10 years ago?

Find the value of each element in

$$A=\left[\begin{array}{rrrr} {-3} & {45} & {28} & {-19} \\ {24} & {36} & {-22} & {5} \\ {8} & {-11} & {54} & {17} \\ {-15} & {4} & {29} & {-9} \end{array}\right]$$

. $a_{32}$

Find a functions other than f(x)=x such that the following are true. $[f \circ f](x)=x$

Graph each function. $f(x)=\frac{2}{3}(x-2)^{2}$

Calculate the perpetual equivalent annual cost (years 1 to $\infty)$ of $1,000,000 now and$1,000,000 three years from now at an interest rate of 10% per year.

When a 60% acetic acid solution is added to 10 liters of a 20% acetic acid solution in a 100-liter tank, the concentration of the total solution changes. Find the relevant domain of f (a) and the vertical or horizontal asymptotes, if any.

A contact lens with the appropriate depth ensures proper fit and oxygen permeation. The depth of a lens can be calculated using the formula $S=r-\sqrt{r^{2}-\left(\frac{d}{2}\right)^{2}}$, where S is the depth, r is the radius of curvature, and d is the diamter, with all units in millimeters. If the depth of the contact lens is increased by 0.1 millimeter and the diameter of the lens is 8.2 millimeters, what radius of curvature would be requred?

Find the domain of each expression. $\sqrt[3]{\frac{x}{36-x^{2}}}$

Lifetime Savings Accounts, known as LSAs, allow people to invest after-tax money without being taxed on any of the gains. If an engineer invests $10,000 now and$10,000 each year for the next 20 years, how much will be in the account immediately after the last deposit, provided the account grows by 10% per year?