Verify the identity by transforming the lefthand side into the right-hand side.

$$\left(1-\sin ^2 \theta\right)\left(1+\tan ^2 \theta\right) = 1$$

You can use the physical properties of matter to separate a mixture. Describe which physical property you would use and how you would take advantage of it to separate the following mixtures: a. a mixture of fine sawdust and iron shavings b. a mixture of gold and sand c. a mixture of cooking oil and sand

Iron oxide ores, commonly a mixture of $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$, are given the general formula $\mathrm{Fe}_3 \mathrm{O}_4$. They yield elemental iron when heated to a very high temperature with either carbon monoxide or elemental hydrogen. Balance the following equations for these processes.

$$\begin{aligned} &\mathrm{Fe}_3 \mathrm{O}_4(s)+\mathrm{H}_2(g) \rightarrow \mathrm{Fe}(s)+\mathrm{H}_2 \mathrm{O}(g) \\ &\mathrm{Fe}_3 \mathrm{O}_4(s)+\mathrm{CO}(g) \rightarrow \mathrm{Fe}(s)+\mathrm{CO}_2(g) \end{aligned}$$

Which of the following is an example of stress? a. Ray is tense and anxious as he has to decide which college to attend. b. Sunga is assigned an extra shift at work. c. Joe’s parents are allowing him to stay home alone while they go away for a weekend. d. Linda remembers to repay a friend the $10 she owes her. e. Enrico learns of a traffic accident on the Interstate.

Most of the given sentences contain an error in subject-verb agreement. Draw a line through the incorrect verb, and write above it the correct form. If a sentence is already correct, write C above the number.

$\lbrack15\rbrack$ Where's the shirts and pants for the dry cleaners?

After being ranked one of the best cities in which to live by a national publication, Northfield Heights experienced a rise in population that could be modeled by $p(t)=\frac{36 t^{3}-12 t+13}{3 t^{3}+90},$ where p is the total rise in population in thousands and t is the number of years after 2006.

$$\begin{array}{|c|c|} \hline \text { Years since 2006 } & \text { Rise in Population } \\ \hline 1 & ? \\ \hline 2 & ? \\ \hline 3 & ? \\ \hline \end{array}$$

What was the total rise in population by 2011?

An aqueous solution contains 3.45 g of iron(III) sulfate, $Fe_2(SO_4)_3$, per liter. What is the molarity of $Fe_2(SO_4)_3$? When the compound dissolves in water, the ${Fe}^{3+}$ ions and ${SO_4}^{2-}$ ions in the crystal go into the solution. What is the molar concentration of each ion in the solution?

Consider an experiment where a single 10 -sided die is rolled with the outcomes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Determine the probability of each event. A number greater than 10 is rolled.

A cartridge for a shotgun, called a shell, contains numerous ball-shaped projectiles, called $\rule{1cm}{1pt}$.

Two strips, one of iron and one of zinc, are riveted together side by side to form a straight bar that curves when heated. Why is the iron on the inside of the curve?

When $25.0 \mathrm{~mL}$ of $0.500 \mathrm{M}$ iron(II) sulfate is combined with $35.0 \mathrm{~mL}$ of $0.332 \mathrm{M}$ barium hydroxide, two different precipitates are formed. (a) Write a net ionic equation for the reaction that takes place. (b) Estimate the mass of the precipitates formed. (c) What are the equilibrium concentrations of the ions in solution?

Find the equation of the surface.

A cylinder of radius $\sqrt{7}$ with its axis along the $y$-axis.

In the absence of friction, explain why the horizontal component of a projectile's velocity is a constant. Which hits the ground first?

The height in feet above the ground of an arrow after it is shot can be modeled by

$$y = - 16 t ^ { 2 } + 63 t + 4$$

. Can the arrow pass over a tree that is 68 feet tall? Explain.