Consider the function defined by $f(x)=\sqrt[3]{2 x-7}$.

Explain why $f^{-1}$ exists.

The weekly demand for the Pulsar 25 color LED television is

$$p=600-0.05 x \quad(0 \leq x \leq 12,000)$$

where $p$ denotes the wholesale unit price in dollars and $x$ denotes the quantity demanded. The weekly total cost function associated with manufacturing the Pulsar 25 is given by

$$C(x)=0.000002 x^3-0.03 x^2+400 x+80,000$$

where $C(x)$ denotes the total cost incurred in producing $x$ sets.

Compute $C^{\prime}(2000), R^{\prime}(2000)$, and $P^{\prime}(2000)$ and interpret your results.

What is $36 \frac{1}{2} \%$ as a decimal?

Find $\lim _{x \rightarrow 1} \dfrac{x^2+2 x-3}{x^2-1}$, if it exists.

What's the difference between an independent variable and a dependent variable?

The power at Ice Station Lion is supplied via solar cells. Once a year, a plane flies in and sells solar cells to the ice station at a price of $20 per cell. Because of uncertainty about future power needs, the ice station can only guess the number of cells that will be required during the coming year (see probability distribution in Table 6). If the ice station runs out of solar cells, a special order must be placed at a cost of$30 per cell. a. Assuming that the news vendor problem is relevant, how many cells should be ordered from the plane? b. In part (a), what type of cost is being ignored? TABLE 6:

$$\begin{matrix} \text{No. of Cells} & \text{Probability}\\ \text{50} & \text{.20}\\ \text{60} & \text{.15}\\\text{70} & \text{.30}\\ \text{80} & \text{.10}\\ \text{90} & \text{.15}\\\text{100} & \text{.10}\\ \end{matrix}$$

Based on the things Carlos and hisfriends like,

what activities do you think they like to do?

MODELO: A Roberto le gustan las peliculas. Le gusta ir al cine.

$$\begin{array}{lll} \text{ir al cine}& \text{ ver televisión}& \text{ escuchar música}\\ \text{jugar al tines}& \text{ comer comida italian }& \text{ jugar a los videojuegos }\\ \end{array}$$

A mis amigos les gustan los deportes.

Consider the number $N$ to be located anywhere in the given array. By checking several locations in the array, determine how $N$ is related to the sum of all entries in the shaded cells. Describe the relationship in words.

Write as a decimal.

$$1\dfrac{5}{8}$$

state the domains and ranges of f and f^-1. f(x) = √x+1.

Find the limit (if it exists), $\lim\limits_{x \to 2}\frac{\vert x-2\vert}{x-2}$.

Solve. If no solution exists, state this.

$$\dfrac{t}{10}+\dfrac{t}{15}=1$$

Wendy and Peter each made up a new "Guess My Decimal" game just for you. Use their clues to determine the number. a. Wendy gives you this clue: "My decimal is seven-tenths greater than 46%. What is my decimal?" Show your work. b. Peter continues the game with the following clue: "My decimal is sixhundredths less than five-tenths." Use pictures and/or words to show your thinking.

A plastic injection molding process is often used in manufacturing because of its ability to mold complicated shapes. An experiment was conducted on the manufacture of a television remote part, and the warpage (mm) of the part was measured and stored in TV Remote.

Two factors were to be considered, the filling time $(1,\ 2, \text{or}\ 3\ \text{sec})$ and the mold temperature $(60,\ 72.5,\ \text{or}\ 85 \degree \text{C})$.

At the $0.05$ level of significance, (a) is there an interaction between filling time and mold temperature?