What phases or states of matter are present in a glass of bubbling carbonated beverage that contains ice cubes?

Given the region bounded by the graphs of $y=x \sin x, y=0, x=0$, and $x=\pi$, find

the volume of the solid generated by revolving the region about the $x$-axis.

Suppose a microscope's resolution is diffraction limited. Which one of the following changes would provide the greatest improvement to its resolution? Observing at a longer wavelength through a smaller aperture.

Identify where gold is mined in the United States, and describe the type of gold deposits in each region.

Approximate the definite integral using the Trapezoidal Rule and Simpson’s Rule with $n=4$ Compare these results with the approximation of the integral using a graphing utility.

$$\displaystyle\int_{0}^{\pi/4}x \tan x \ dx$$

How did manifest destiny lead the United States to annex Texas and fight the Mexican War?

Total income minus exemptions and deductions _____

Invent a game that illustrates radioactive decay.

The function $T(g)=1670+0.15(g-16,700)$ represents the 2009 federal income tax T (in dollars) due for a “married filing jointly” filer whose modified adjusted gross income is g dollars, where $16,700 \leq g \leq 67,900.$ Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this function?

What is the formula for the income elasticity of demand?

After a 20% price reduction, a cordless phone sold for $48. What was the phone's price before the reduction?

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If all payoffs of a matrix game are zero, then the game is fair.

Make a decision as to whether or not each is a statement.

Grover Cleveland was president of the United States in $1885$ and $1897$.

Match the terms with the definitions.

a. adjusted gross income

b. dependent

c. exemption

d. filing status

e. gross income

f. itemized deductions

g. standard deduction

h. tax credit

i. taxable income

__ An amount subtracted directly from the tax owed