Describe two advantages of using credit cards.

Sketch the curves of the given functions by addition of ordinates. $y=3-2 \cos x$

A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 $k g \cdot m ^ { 2 }$ is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

What three variables influence the speed of stream flow?

Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.

$$\begin{gather*} (x + 3)y'' + xy' + (\ln |x|)y = 0, \,\,\, y(1) = 0, \,\,\, y'(1) = 1 \end{gather*}$$

Variations in members of a population help ____.

Find the inner surface area A of a cylindrical 250.0 cubic cm cup as a function of the radius r of the base. Then if A = 175.0 square cm, solve for r. Write one or two paragraphs explaining your method for setting up the function, and how you used a graphing calculator to solve for r with the given value of A.

$f(x)=\sin x, g(x)=\cos x, h(x)=2 x,$ and $p(x)=\frac{x}{2}.$ Find the value of each of the following: $(f-g)\left(60^{\circ}\right)$

The life span of the lightbulbs manufactured by a certain company is measured by a random variable X with probability density function

$$f(x)=\left\{\begin{matrix} 0.01e^{-0.01x}, &\text{ if }x\geq 0 \\ 0, &\text{ if }x<0 \end{matrix}\right.$$

where x denotes the life span (in hours) of a randomly selected bulb. a. What is the probability that the life span of a randomly selected bulb is between 50 and 60 hours? b. What is the probability that the life span of a randomly selected bulb is no greater than 60 hours? c. What is the probability that the life span of a randomly selected bulb is greater than 60 hours?

Describe a real-world situation that can be modeled by the equation 15x = 135. Solve the equation and explain what the solution means in this situation.

The flow rate of water in a 6-m-wide rectangular channel is to be measured using a 1.1-m-high sharp-crested rectangular weir that spans across the channel. If the head above the weir crest is 0.60 m upstream from the weir, determine the flow rate of water.

Use your calculator to write the following in the form $10^{x}$ where x is correct to 4 decimal places: 6

Determine whether 97 divides $n^{2}-85$ for some choice of $n \geq 1$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Credit reports contain bankruptcy information.