Underline the prepositional phrases in the following sentence. Then, circle the object of each preposition. Hint: Some sentences have more than one prepositional phrase.

. Then, the idea is sent to the postmaster general.

Write a short paper in your own words explaining the meaning of each of the following concepts to a classmate. coterminal angles

Mass and Weight
Scientists measure an object's mass in kilograms and its weight in newtons. If you know the amount of mass that an object has, you can calculate its weight, in newtons, with the following formula:

Weight = mass x 9.8

Write a program that asks the user to enter an object's mass, and then calculates and displays its weight. If the object weighs more than 1,000 newtons, display a message indicating that it is too heavy. If the object weighs less than 10 newtons, display a message indicating that the Object is too light.

Sketch a ray diagram to show that when an object is placed more than twice the focal length away from a converging lens, the image formed is inverted, real, and diminished in size.

Reimplement the example given in Previous Section using the Lock and Condition concepts presented in Previous Section.

What problem-solving technique helps to understand concepts that cannot be observed directly, such as the molecules in a gas?

Use concepts from this chapter to explain how a juggler is able to juggle balls with perfect timing.

Aerogel is the substance with the lowest known density of any solid. Aerogel has some remarkable properties, for example, it is the best known insulator of any solid. NASA recently used aerogel to capture dust particles from the tail of a comet, returning these particles safely to earth in its Stardust mission. Determine the mass in kilograms of a cubic meter of aerogel, which has a density of $1.5 \mathrm{mg} \cdot \mathrm{cm}^{-3}$.

Make a drawing, based on the kinetic-molecular theory and the ideas about atoms and molecules presented in this chapter, of the arrangement of particles in each of the cases listed here. For each case, draw 10 particles of each substance. It is acceptable for your diagram to be two-dimensional. Represent each atom as a circle, and distinguish each different kind of atom by shading.
a homogeneous mixture of water vapor and helium gas (which consists of helium atoms)

Use the extension of set-builder notation concepts and the roster method to write the sets E = {$2x^2-x | x\in N$ and x<5} .

The steps of the algebraic proof below are correct. However, the justifications for each step are out of order. Determine the correct order for the justifications.

$$\begin{array}{|l|l|} \hline \text{Statements} & \text{Reasons} \\ \hline 1.9 x=3(2 x+3) & 1. \text{Simplify} \\ \hline 2.9 x=6 x+9 & 2. \text{Division Property of Equality} \\ \hline 3.9 x-6 x=6 x+9-6 x & 3. \text{Given} \\ \hline 4.3 x=9 & 4. \text{Simplify} \\ \hline 5 . \frac{3 x}{3}=\frac{9}{3} & 5. \text{Subtraction Property of Equality}\\ \hline 6 . x=3 & 6. \text{Distributive Property} \\ \hline \end{array}$$

Air at $45^{\circ} \mathrm{C}$ (dry bulb) and 10% relative humidity is to be humidified adiabatically to 70% relative humidity. a) Use the psychrometric chart to estimate the adiabatic saturation temperature of the air. b) Estimate the final temperature of the air and the rate at which water must be added to humidify 15 kg/min of the entering air. c) What have you assumed in carrying out this calculation?

What is the time value of money? Why should accountants have an understanding of compound interest, annuities, and present value concepts?

Represent the situation using the mathematical content, concepts, and skills from this topic. Use your representation to answer the Main Question.