Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solutions or infinitely many solutions.

$$x=4-8 y$$

$$3 x+24 y=12$$

Brightly colored $_______________$ attract pollinators to flowers.

Identify the underlined word or word group in each sentence by writing above it ADV for adverb or PREP for preposition.

Our star party will last from dusk $\underline{\text{till}}$ dawn.

Use a depth-first search in the previous example to show that any amount between 0 and 10 quarts can be obtained in one of the pitchers.

Graph each linear function. Give the domain and range. G(x)=2x

Explain why the given groups are not isomorphic. $U_{10} \text{ and } U_{12}$

Show that there are no simple groups of order

$$p^rm$$

, where p is a prime, r is a positive integer, and m < p.

Find the unit rate.

$$\frac { 32 \text { students } } { 4 \text { groups } }$$

For the beam shown, select the lightest wide-flange steel beam that can safely support the loads. For beams in U.S. customary units, the allowable stresses in bending and shear are $24\ \mathrm{ksi}$ and $14.5\ \mathrm{ksi}$, respectively, and in SI units the allowable stresses in bending and shear are $165\ \mathrm{MPa}$ and $100\ \mathrm{MPa}$, respectively.

A substance has a half-life of $2.045$ minutes. If the initial amount of the substance was $132.8$ grams, how many half-lives will have passed before the substance decays to $8.3$ grams? What is the total time of decay?

How did society and the legal system in England evolve after 1066?

"Statement of retained earnings Hayes Enterprises began 2015 with a retained earnings balance of $928,000. During 2015, the firm earned$377,000 after taxes. From this amount, preferred stockholders were paid $47,000 in dividends. At year-end 2015, the firm’s retained earnings totaled$1,048,000. The firm had 140,000 shares of common stock outstanding during 2015.

a. Prepare a statement of retained earnings for the year ended December 31, 2015, for Hayes Enterprises. (Note: Be sure to calculate and include the amount of cash dividends paid in 2015.)"

Explain how society resolves the conflict among goals which conflict.

Use the given function f to: Find the domain and the range of $f ^{-1}$. $f (x) = 2 + ln x$