Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $7+3 \ln x=5$

Factor completely. See the discussed examples.

$$3 n^2+20 n+5$$

Solve the given equation. See the examples in this chapter.

$$(x-6)(x-7)=0$$

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

The used-car salesman sometimes used chicanery to...

Solve the exponential equations exactly and then approximate your answers to three decimal places.

$$e^{x^2}=73$$

Students in two basic Spanish classes were required to learn 50 new vocabulary words. One group of 45 students received the list on Monday and studied the words all week. Statistics summarizing this group's scores on Friday's quiz are given. The other group of 25 students did not get the vocabulary list until Thursday. They also took the quiz on Friday, after "cramming" Thursday night. hen, when they returned to class the following Monday, they were retested without advance warning. Both sets of test scores for these students are shown.

$$\begin{align*} &\text{Group 1}\\ \hline &\text{Fri.}\\ &\text{Number of students = 45}\\ &\text{Mean = 43.2 (of 50)}\\ &\text{StDev = 3.4}\\ &\text{Students passing (score $\ge$ 40) = 33\\\%} \end{align*}$$

$$\begin{array}{c} \begin{array}{c} \text{Group 2} \end{array} \\ \begin{array}{c|c|c|c} \text { Fri. } & \text { Mon. } & \text { Fri. } & \text { Mon. } \\ \hline 42 & 36 & 50 & 47 \\ 44 & 44 & 34 & 34 \\ 45 & 46 & 38 & 31 \\ 48 & 38 & 43 & 40 \\ 44 & 40 & 39 & 41 \\ 43 & 38 & 46 & 32 \\ 41 & 37 & 37 & 36 \\ 35 & 31 & 40 & 31 \\ 43 & 32 & 41 & 32 \\ 48 & 37 & 48 & 39 \\ 43 & 41 & 37 & 31 \\ 45 & 32 & 36 & 41 \\ 47 & 44 & & \end{array} \end{array}$$

Was there a significant difference in the percentages of students who passed the quiz on Friday?

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $\ln x-\ln 5=4$

Find $y^{\prime \prime}$. $y=3 \sin u+4 \cos u$

Relaciona cada oración con el significado apropiado de por. A. 1.Hay paisajes bonitos por la costa. 2.No voy al parque por las mañanas. 3.Puedes ir por esa calle. 4.Voy a pasear por una hora. 5.Vengo por el jarabe.

B. a.cause or reason. b.approximate place. c.movement within an area. d.time periods during the day. e.approximate time.

Relaciona cada oración con el significado apropiado de para. A. 1.Para mí, esto es complicado. 2.Yo lo uso para escribir las tareas. 3.Para mañana, escribes el informe. 4.El regalo es para Josefa. 5.Vamos para el hospital.

B a.deadline b.purpose c.movement toward a place d.recipient of an action e.opinion

In this exercise, use a calculator to approximate the value. Round your answer to two decimal places.

$$\arcsin (-0.39)$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $\ln x+\ln (x-2)=1$

A manufacturer has determined that the cost C of producing x items is given by $C(x)=200+35 x+0.02 x^{2}$ dollars. Each item produced can be sold for $\$ 78$. How many items should she produce to maximize profit?

Evaluate the trigonometric function. Round your answer to four decimal places. $\tan \frac{\pi}{3}$

Find the domain of each function. See the examples in this chapter.

$$g(x)=|x+1|$$