For each of the following sentences, identify the underlined clause by writing above it ADJ for adjective clause or ADV for adverb clause. Circle the word or words that the underlined clause modifies.

$\underline{\text{Until we learned how to use the compass}}$, we wandered around th ewoods for hours.

A cliff diver drops from rest to the water below. How many seconds does it take for the diver to go from 0 to 60 ; that is, to go from $0 \mathrm{mph}$ to $60 \mathrm{mph}$ ? (For comparison, it takes about $3.5 \mathrm{~s}$ to $4.0 \mathrm{~s}$ for a powerful car to go from 0 to 60 .)

Use the limit comparison test to determine whether the series converges or diverges. $\sum_{n=1}^{\infty} \frac{n+1}{n^{2}+2}$

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

$$\sum_{n=1}^x \frac{1}{n^4+n^2}$$

Complete each comparison with an appropriate expression from the list. Some expressions will be used more than once. más de más grande más pequeña más pequeño mayor menor menos de

Humberto compró cinco aguacates. Rogelio compró diez aguacates.

Rogelio compró________________ cinco aguacates.

Underline the noun clause or clause in each sentence.
What the judges decided was not acceptable to Marcus

Each of the following sentences contains a subordinate clause. Underline the subordinate clause, and identify it by writing above it ADJ for adjective clause, ADV for adverb clause, or N for noun clause.

Example 1. Dana told me $\overset{\textit{\color{#c34632}{N}}}{{\underline{\text{that the exam was postponed}}}}$.

I was looking for a book that has a poem by Emily Dickinson.

Prove that the every-other-term harmonic series $1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\cdots$ diverges. (Hint: Write the series as $\sum_{k=0}^{\infty} \frac{1}{2 k+1}$ and use the Limit Comparison Test.)

A number cube is rolled and the result is a number greater than 2. What is the probability that the result is a 6?

Explain how the meanings of "Five more than a number" and "Five is more than a number" differ.

Find each number. Round to the nearest tenth if necessary. 9 is 45% of what number?

Solve the inequality and graph the solution on the real number line. $\frac{x+6}{x+1}-2<0$

(a) Let G be the group of all 4! permutations of 1, 2, 3, 4. Find $P_G$.

(b) Use part (a) to find the number of ways to paint four identical marbles each one of three colors (check your answer by modeling this problem as a selection-with-repetition problem).

(c) Use part (a) to find the number of ways to put 12 balls chosen from three colors into four indistinguishable boxes with three balls in each box.

Solve each inequality. Graph the solution set on a number line.

$$|3 n-2|-2<1$$