Write the first four terms of each sequence whose general term is given.

$$a _ { n } = ( - 3 ) ^ { n }$$

Convert each improper fraction to a mixed number. $\frac{47}{8}$

Divide where possible. $\frac{-100}{-0.01}$

What is the difference between the product of 1, 2 and 3 and the sum of 1, 2, and 3?

Most users of automatic garage door openers at distances that are normally distributed with a mean of 30 feet and a standard deviation of 11 feet. To minimize interference with other remote-controlled devices, the manufacturer is required to limit the operating distance to 50 feet. What percentage of the time will users attempt to operate the opener outside its operating limit?

Evaluate. Round to three decimal places, if needed. $\log _{8} 4+\log _{8} 16$

345-67

Write each sentence in symbolic form. Represent each simple statement of the sentence with the letter indicated in parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. Today is Monday (m) and it is my birthday (b).

A company selling clothing on the Internet reports that the packages it ships have a median weight of 68 ounces and an IQR of 40 ounces. a) The company plans to include a sales flyer weighing 4 ounces in each package. What will the new median and IQR be? b) If the company recorded the shipping weights of these new packages in pounds instead of ounces, what would the median and IQR be? (1 lb. = 16 oz.)

Involve exponential growth. Suppose a bacterial culture initially has 100 cells. After 2 hours, the population has increased to 400. Find an equation for the population at any time.

Galileo developed a formula for a body’s velocity during free fall by rolling balls from rest down increasingly steep inclined planks and looking for a limiting formula that would predict a ball’s behavior when the plank was vertical and the ball fell freely; see part (a) of the accompanying figure. He found that, for any given angle of the plank, the ball’s velocity t sec into motion was a constant multiple of t. That is, the velocity was given by a formula of the form v = kt. The value of the constant k depended on the inclination of the plank. In modern notation with distance in meters and time in seconds, what Galileo determined by experiment was that, for any given angle theta, the ball’s velocity t sec into the roll was y = 9.8(sin theta)t m/sec. a. What is the equation for the ball’s velocity during free fall? b. Building on your work in part (a), what constant acceleration does a freely falling body experience near the surface of Earth?

What is one conclusion you can draw about the Indus Valley civilization?

(a) Show that the dual of the free Z-module with countable basis is not free. [Use the preceding exercise and Exercise $24,$ Section $3 . ]$ (See also Exercise 5 in Section $11.3 . )$ (b) Show that the dual of the free Z-module with countable basis is also not projective. [You may use the fact that any submodule of a free Z-module is free.]

Using a chart like the one below, analyze the last two paragraphs of "The Harvest" and explain the theme of the story.

$$\begin{array} {|l|l|} \hline \text{Words From the Text} & \text{Insights}\\ \hline \text{ } & \text{ }\\ \hline \text{Theme:} \\ \hline \end{array}$$