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

Find $\lim _{x \rightarrow-1} \dfrac{x^2-x-2}{x^2+4 x+3}$, if it exists.

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.

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.

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:

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

Air enters the compressor of a Brayton refrigeration cycle at $100\ \mathrm{kPa}, 260 \mathrm{~K}$, and is compressed adiabatically to $300\ \mathrm{kPa}$. Air enters the turbine at $300\ \mathrm{kPa}, 300 \mathrm{~K}$, and expands adiabatically to $100\ \mathrm{kPa}$. For the cycle (a) determine the net work per unit mass of air flow, in $\mathrm{kJ} / \mathrm{kg}$. and the coefficient of performance if the compressor and turbine isentropic efficiencies are both $100 \%$. (b) plot the net work per unit mass of air flow, in $\mathrm{kJ} / \mathrm{kg}$, and the coefficient of performance for equal compressor and turbine isentropic efficiencies ranging from $80$ to $100 \%$.

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?

Write as a decimal. 4$\frac{1}{4}$

Find the sum of each infinite geometric series, if it exists. $\\$$0.27+0.0027+0.000027+\cdots$

Match the property of A with the corresponding property of the graph of f. Assume f is differentiable. Area function A: (a) A is decreasing. (b) A has a local maximum. (c) A is concave up. (d) A goes from concave up to concave down. Graph of f: (i) Lies below the x-axis. (ii) Crosses the x-axis from positive to negative. (iii) Has a local maximum. (iv) f is increasing.

Lamprino Appliance uses a perpetual inventory system. The following are three recent merchandising transactions:
June 10 Purchased 10 televisions from Mitsu Industries on account. Invoice price, $\$ 300$ per unit, for a total of $\$ 3,000$. The terms of purchase were $2 / 10, \mathrm{n} / 30$.
June 15 Sold one of these televisions for $\$ 450$ cash.
June 20 Paid the account payable to Mitsu Industries within the discount period.

Instructions
a. Prepare journal entries to record these transactions assuming that Lamprino records purchases of merchandise at:

1. Net cost
2. Gross invoice price

Write as a decimal.

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

Approximate to three decimal places

$$\cos 0.68$$

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

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