Writing Sentences With Prepositional Phrases. Write five sentences of your own, each containing a prepositional phrase that begins with one of the prepositions listed below. Underline the preposition and circle its object. among

Given that A is a $4 \times 7$ matrix, what is the maximum possible number of leading l's in the reduced row echelon form of A? Why?

Underline the correct pronoun in parentheses. Assume that a third-person pronoun refers to a person, place, or thing already in the sentence.

Angela read to (her, herself) until she fell asleep on the couch.

In this exercise, find all the solutions of the equation. Check your solution(s) in the original equation.

$$x^2-8 x+3=0$$

Polaski Company manufactures and sells a single product called a Ret. Operating at capacity, the company can produce and sell 30,000 Rets per year. Costs associated with this level of production and sales are given below:

$$\begin{array}{lrrrr} &\textbf{Unit}&\textbf{Total}\\[5pt] \text{Direct materials}&\text{\$\hspace{1pt}15}&\text{\$\hspace{8pt}450,000}\\ \text{Direct labor}&\text{8}&\text{240,000}\\ \text{Variable manufacturing overhead}&\text{3}&\text{90,000}\\ \text{Fixed manufacturing overhead}&\text{9}&\text{270,000}\\ \text{Variable selling expense}&\text{4}&\text{120,000}\\ \text{Fixed selling expense}&\underline{\text{\hspace{11pt}6}}&\underline{\text{\hspace{14pt}180,000}}\\ \text{Total cost}&\underline{\underline{\text{\$\hspace{1pt}45}}}&\underline{\underline{\text{\$\hspace{1pt}1,350,000}}}\\ \end{array}$$

The Rets normally sell for $50 each. Fixed manufacturing overhead is constant at$270,000 per year within the range of 25,000 through 30,000 Rets per year.

Required:

1. Assume that due to a recession, Polaski Company expects to sell only 25,000 Rets through regular channels next year. A large retail chain has offered to purchase 5,000 Rets if Polaski is willing to accept a 16% discount off the regular price. There would be no sales commissions on this order; thus, variable selling expenses would be slashed by 75%. However, Polaski Company would have to purchase a special machine to engrave the retail chain’s name on the 5,000 units. This machine would cost $10,000. Polaski Company has no assurance that the retail chain will purchase additional units in the future. Determine the impact on profits next year if this special order is accepted.
2. Refer to the original data. Assume again that Polaski Company expects to sell only 25,000 Rets through regular channels next year. The U.S. Army would like to make a one-time-only purchase of 5,000 Rets. The Army would pay a fixed fee of$1.80 per Ret, and it would reimburse Polaski Company for all costs of production (variable and fixed) associated with the units. Because the army would pick up the Rets with its own trucks, there would be no variable selling expenses associated with this order. If Polaski Company accepts the order, by how much will profits increase or decrease for the year?
3. Assume the same situation as that described in (2) above, except that the company expects to sell 30,000 Rets through regular channels next year. Thus, accepting the U.S. Army’s order would require giving up regular sales of 5,000 Rets. If the Army’s order is accepted, by how much will profits increase or decrease from what they would be if the 5,000 Rets were sold through regular channels?

Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $20=44-8(2-x)$

State the domain of the indicated function below.

$$h(x)=\frac{x^3}{2x^2-8}$$

An electric toothbrush draws $7.0$ watts. If you use it $4.0$ minutes per day and if electric energy costs you $15 \% / \mathrm{kW} \cdot \mathrm{h}$, what do you have to pay to use your toothbrush for one year?

Choose the letter that best describes the question or completes the statement. Which of the following is a unit of work? a. joule b. watt c. horsepower d. newton

The length s of one edge of a cube is given by

$$s = \sqrt { \frac { A } { 6 } },$$

where A represents the cube's surface area. Suppose a cube has an edge length of 9 cm. What is its surface area? Round to the nearest hundredth.

Compute the maximum length of dimension C .

Complete each sentence with the correct indirect object pronoun on the firs line and the correct form of the verb in parentheses on the second line. A Uds. ____ ______ \lparenencantar\rparen hablar por telefono.

Find the force on one side of a cubical container $6.0$ cm on an edge if the container is filled with mercury. The density of mercury is $133$ kN/m$^3$.

Writing Sentences With Prepositional Phrases. Write five sentences of your own, each containing a prepositional phrase that begins with one of the prepositions listed below. Underline the preposition and circle its object. ahead of