Family income in the United States has increased steadily for many years (primarily due to inflation). In 1980, the median family income was about $21,000 per year. In 2003, it was about$52,700 per year. Find the average rate of change of median family income to the nearest dollar over that period.

Factor using complex numbers. $3 x^{2}+27$

a. Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning. b. Write the negation of the quantified statement. (The negation should begin with “all,” “some,” or “no.”). There are no seniors who did not graduate.

The volume of a sphere is given by the equation

$$V = \frac { 1 } { 6 \sqrt { \pi } } S ^ { 3 / 2 }$$

, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for

$$\pi$$

.

If f(x)=4x+11, find f(-2).

Solve each inequality algebraically. $x^{3}-9 x \leq 0$

If a walkway rises 2 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.) A. 0.2, B. $\frac{2}{10}$, C. $\frac{1}{5}$, D. 20%, E. 5, F. $\frac{20}{100}$, G. 500%, H. $\frac{10}{2}$, I. -5.

Solve the system of equations by using the row-reduction method.

$$\left\{\begin{array}{l}{3 x+4 y=1} \\ {8 x+11 y=4}\end{array}\right.$$

Use the statements below and the given logic statement to write compound sentences in English. p: I go to the math learning center. q: I complete my math homework.

$$q\Rightarrow p$$

In 1897 the Swedish explorer Andree tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is

$$\mathrm { Fe } ( s ) + \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 } ( a q ) \longrightarrow \mathrm { FeSO } _ { 4 } ( a q ) + \mathrm { H } _ { 2 } ( g )$$

The volume of the balloon was

$$4800\ m^3,$$

and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 98% (by mass)

$$H_2SO_4$$

were needed to ensure the complete filling of the balloon? Assume a temperature at

$$0^\circ C,$$

a pressure of 1.0 atm during filling, and 100% yield.

Explain briefly why the brightness of a bulb doesn’t change noticeably when you use longer copper wires to connect it to the battery.

Let

$$f(x)=\left\{\begin{array}{l}{x^{2}-3 \text { for } x \leq 2} \\ {5-x \text { for } x>2}\end{array}\right.$$

Evaluate the following limits. If the lumit does not exist, explain why it does not exist. a. $\lim _{x \rightarrow 2^{+}} f(x)$ b. $\lim _{x \rightarrow 2^{-}} f(x)$ c. $\lim _{x \rightarrow 2} f(x)$

Find the indicated sides of the right triangle. b = 5600, c = 6500, a = ?

True or False. Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.