A utility company charges a base rate for water usage of $19.50 per month, plus$4.58 for every additional 1000 gal of water used over a 2000-gal base. (A) Write a formula for the monthly charge C for a household that uses n thousand gallons over the 2000-gal base. (B) Compute the cost for a family that uses a total of 6000 gal of water for a given month.

Anna and Julia each take a bicycle trip. Anna rides 20 miles in

$$1 \frac { 1 } { 3 }$$

hours. Julia rides 246 miles in 16 hours. Which rider has the slower unit rate? By how much?

If n > 0, then -|n| = _

Find the slope of the line through the points (6, 4) and (-4, -1).

Jonas has a personal music player with 80 gigabytes of memory (80 gigabytes is approximately 8 x 10^10 bytes). If each song requires an average of 4 megabytes of memory (approximately 4 x 10^6 bytes), how many songs can Jonas store on the device?

If n < 0, then n-|n|=_.

Let

$$f, g: \mathbb{R}\rightarrow\mathbb{R}$$

be continuous at a point c, and let h(x) := sup {f(x), g(x)} for

$$x\ \in\mathbb{R}.$$

Show that

$$h\left(x\right)=\frac{1}{2}\left(f\left(x\right)+g\left(x\right)\right)+\frac{1}{2}\left|f\left(x\right)-g\left(x\right)\right|$$

for all

$$x\ \in\mathbb{R}.$$

Use this to show that h is continuous at c.

For the system

$$\begin{array}{l}{x^{\prime}=4 x-x^{3}-x y^{2}} \\ {y^{\prime}=4 y-x^{2} y-y^{3}}\end{array}$$

determine the type and stability of each real equilibrium point by calculating the Jacobian matrix at each equilibrium .

$f(x)=\frac{3 x}{x-2},\ g(x)=2 x+1.$ Find: The function $g^{-1}$ and its domain

Show that $A\neq B$. A={1,3,5}, B=$\{n|n\in\textbf{Z}^+\text{ and }n^2-1\leq n\}$

A certain star is 4.3 × 10^2 light years from Earth. One light year is about 5.9 × 10^12 miles. How far from Earth (in miles) is the star? Express your answer in scientific notation.

A power company charges one household $0.12 per kilowatt-hour (kWh) and$14.89 in monthly taxes. (A) Write a formula for the monthly charge C for this household if it uses k kilowatt-hours. (B) Compute the monthly charge if the house uses 1200 kWh.

Find the matrix products, if they exist.

$$\left[\begin{array}{lll}{4} & {1} & {3}\end{array}\right]\left[\begin{array}{l}{2} \\ {7} \\ {5}\end{array}\right]$$

A 0.73-kg magnetic target is suspended on a string. A 0.025-kg magnetic dart, shot horizontally, strikes the target head-on. The dart and the target together, acting like a pendulum, swing 12.0 cm above the initial level before instantaneously coming to rest. Sketch the situation and choose a system.