Revise the following sentence, correcting any errors.

the drug that could fight staph infections was penicillin discovered by british scientist alexander fleming in $1928$ but it was hard to manufacture and only a small supply existed reserved for the use of the u.s. military forces

Write each expression as a sum and/or difference of logarithms. Express powers as factors. $\ln \left(x e^{x}\right)$

Simplify. Assume that no radicands were formed by raising negative quantities to even powers. $\sqrt{\frac{7 x^3}{36 y^6}}$

In this problem proceed as in Example 6 and use (16) to rewrite the given function in terms of the first powers of cosine functions.

$$\sin ^2 5 x$$

Find power series solution in powers of $x$ of the differential equation

$$y''+xy'+(2x^2+1)y=0$$

Jared seems quiet and reserved, but he is a[n] ______ person once you get to know him.

In this problem proceed as in Example 6 and use (16) to rewrite the given function in terms of the first powers of cosine functions.

$$\cos ^2 2 x$$

A fishing lake has only two kinds of fish: bass and catfish. Management wants to know what percent are bass and what percent are catfish.

How do two colors simulate this situation? What is the population? (Your instructor will supply the objects that represent the population of fish.)

Simplify. Assume that no radicands were formed by raising negative numbers to even powers.

$$\sqrt{27}$$

Use the properties of exponentiation to simplify the expression. Write the answers as products of powers, with no variables in denominators.\

$$\frac{5}{a^{-2}}-\frac{3}{a^{-1}}$$

Some of the following sentences contain misplaced modifiers. In those sentences, underline the modifying clause or phrase that is misplaced. If a sentence is correct, write $C$ next to the item number. All the spaces had been reserved by local students the week before.

Arrange in ascending powers of $x$ :

$$8 x^6 y-7 x^8 y^3+2 x^3-3 x^2$$

Write as powers of 2, 3 and/or 5: $\frac{9^{k}}{10}$

Which lettered pair of words-a, $b, c, d$, or $e-$ most nearly expresses the same relationship as the capitalized pair? Write the letter of your answer

RESTRAINED : FREE

a. enlightened : educated

b. reserved : withdrawn

c. exonerated : guiltless

d. uninvited : welcome

e. contented : satisfied