What types of functions are $f(x)=e^x$ and $g(x)=x^e$ ? Compare the differentiation formulas for $f$ and $g$.

Solve the inequality and mark the solution set on a number line.
$x^2(x − 3)(x + 4)^2 > 0$.

Samuelson and Solow reasoned that when aggregate demand was low, unemployment was

a. high, so there was upward pressure on wages and prices.

b. high, so there was downward pressure on wages and prices.

c. low, so there was upward pressure on wages and prices.

d. low, so there was downward pressure on wages and prices

Use the appropriate form of the percentage formula. Round division to the nearest hundredth if necessary.

$1.5 \%$ of what number is $20$ ? Round to the nearest hundredth.

Determine whether the quadratic function has a maximum or minimum value. Then find the value. $y = - 4 x ^ { 2 } + 8 x + 12$

Insert a question mark if the sentence is interrogative or an exclamation point if the sentence is exclamatory. Are you ready

An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) period, (b) frequency, (c) angular frequency, (d) amplitude, and (e) maximum speed of the glider?

Insert a question mark if the sentence is interrogative, or an exclamation point if the sentence is exclamatory.
Is this oboe yours

A certain viral infection causes a fever that typically lasts 6 days. A model of the fever $\left( \text{in}^{\circ} \mathrm{F}\right)$ on day $x, 1 \leq x \leq 6$ is

$$F(x)=-\frac{2}{3} x^{2}+\frac{14}{3} x+96$$

According to the model, on what day should the maximum fever occur? What is the maximum fever?

If a = i + j + k, b = 2i − j + 3k and c = i − 2j + k, find a unit vector parallel to the vector 2a – b + 3c.

The $80-\mathrm{cm}$-tall, $65-\mathrm{cm}$-wide tank shown in Figure mentioned is completely filled with water. The tank has marks every $10 \mathrm{~cm}$ along one wall, and the $0 \mathrm{~cm}$ mark is barely submerged. As you stand beside the opposite wall, your eye is level with the top of the water.

a. Can you see the marks from the top of the tank (the $0 \mathrm{~cm}$ mark) going down, or from the bottom of the tank (the $80 \mathrm{~cm}$ mark) coming up? Explain. b. Which is the lowest or highest mark, depending on your answer to part a, that you can see?

A meteorologist is assembling a weather balloon. The balloon's envelope has a volume of $60000 \mathrm{~L}$ and a mass of $4.0 \mathrm{~kg}$. The balloon must lift $20.0 \mathrm{~kg}$ of instruments in addition to its own mass. When properly inflated, the balloon must have a pressure of $90 \mathrm{kPa}$ at a temperature of $15^{\circ} \mathrm{C}$. The mass that the balloon can lift is the mass of the air it displaces minus the mass of the gas inside its envelope. The meteorologist wants to use methane, $\mathrm{CH}_4(\mathrm{~g})$, to fill the balloon. His colleague, however, believes that helium, despite its greater cost, is the only gas that will work. Assuming that the average molar mass of air is $28.90 \mathrm{~g} / \mathrm{mol}$, which gas is better: methane or helium? Show calculations to support your answer.

Does factoring, completing the square, or using the quadratic formula seem to you the easiest method for solving the given equation?

$x^2-14 x-736=0$

Based on the following information, compute cash flows from financing activities.

$$\begin{array} {lrrrrr} \text{Purchase of short-term investments}& \hspace{10pt}\text{\$\hspace{10pt}500}&\\ \text{Dividends paid }& \hspace{10pt}\text{900}&\\ \text{Interest paid}& \text{300}&\\ \text{Additional short-term borrowing from bank}& \hspace{10pt}\text{950}&\\ \end{array}$$