Complete the two-way frequency table. Interpret the meaning of the number in the starred cell of the table.

$$\begin{array}{c} \\ \qquad \qquad\text{Preferred Mode of Transportation} \\ \begin{array}{|c|c|c|c|c|} \hline \text { Age } & \text { Bike } & \text { Car } & \text { Bus } & \text { Total } \\ \hline \text { Adults } & 25 & 3 & 12 & \\ \hline \text { Teenagers } & 5 & 28 & 12 & \\ \hline \text { Total } & & & & \\ \hline \end{array} \end{array}$$

A researcher surveyed 135 people, 85 females and 50 males. The researcher asked each person which of the following types of movies they preferred: action, comedy, or drama. Complete the table.

$$\begin{array}{c}\\ \text{Favorite Type of Movie} \\ \begin{array}{|c|c|c|c|c|} \hline \text { Gender } & \text { Action } & \text { Comedy } & \text { Drama } & \text { Total } \\ \hline \text { Female } & 35 & & 18 & \\ \hline \text { Male } & 12 & 28 & & \\ \hline \text { Total } & & & 28 & \\ \hline \end{array} \end{array}$$

Kristi feels that since she can find the product of any two binomials using FOIL, she needn't study the other special products. What advice would you give her ?

Transportation For groups of $80$ or more people, a charter bus company determines the rate per person according to the formula

Rate $=8-0.05(n-80), \quad n \geq 80$

where the rate is given in dollars and $n$ is the number of people.

(b) Use the function in part (a) to complete the table. What can you conclude?

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline n & 90 & 100 & 110 & 120 & 130 & 140 & 150 \\ \hline R(n) & & & & & & & \\ \hline \end{array}$$

Explain why the container of water must be inverted when a gas is collected by displacement of water.

• At year-end, Barr Co. had shipped $12,500 of merchandise FOB destination to Lee Co. Which company should include the$12,500 of merchandise in transit as part of its year-end inventory?

• Parris Company has shipped $20,000 of goods to Harlow Co., and Harlow Co. has arranged to sell the goods for Parris. Identify the consignor and the consignee. Which company should include any unsold goods as part of its inventory?

Determine the vertical and horizontal asymptotes of the graph of the function

$$f(x)=\frac{3x^2}{x^2-1}$$

For the following exercise,

Prove the identity.

The displacement $h(t)$ in centimeters of a mass suspended by a spring is modeled by the function $h(t)=\frac{1}{4} \sin (120 \pi t)$, where $t$ is measured in seconds. Find the amplitude, period, and frequency of this displacement.

A vocabulary word appears in italics in the sentence or short passage below. Find the root in the vocabulary word and choose the letter for the correct definition.

Although his team was far behind, the coach hoped his half-time speech would $regenerate$ the players' enthusiasm.
(A) give new life to
(B) put an end to
(C) reduce or remove
(D) explain

Escribe una pregunta.

1. Juan fue al restaurante.
2. Juan fue al restaurante.
3. El mesero trabajaba en el restaurante.
4. Juan pidió un menú.
5. El mesero era de México.
6. El mesero era muy simpático.
7. Todos comieron muy bien.
8. Todos comieron mucho.
9. Juan volvió a casa en bus.
10. Juan volvió tarde.

The special products can be used to perform selected multiplications. On the left, we use $(x+y)(x-y)=x^{2}-y^{2}$. On the right, $(x-y)^{2}=x^{2}-2 x y+y^{2}$.

$$\begin{aligned} 51 \times 49 &=(50+1)(50-1) & 47^{2} &=(50-3)^{2} \\ &=50^{2}-1^{2} & &=50^{2}-2(50)(3)+3^{2} \\ &=2500-1 & &=2500-300+9 \\ &=2499 & &=2209 \end{aligned}$$

. Use special products to evaluate each expression. $99 \times 101$

A body moves in a straight line with a velocity whose square decreases linearly with the displacement between two points $A$ and $B$, which are $300 \mathrm{ft}$ apart as shown. Determine the displacement $\Delta s$ of the body during the last 2 seconds before arrival at $B$.

A skater glides along a circular path of radius $5.00 \mathrm{~m}$. If he coasts around one half of the circle, find (a) the magnitude of the displacement vector and (b) how far the person skated. (c) What is the magnitude of the displacement if he skates all the way around the circle?

Solve the following variation problems.

Determine the approximate distance between the Earth, with a mass of approximately $6.0 \times 10^{24} \mathrm{~kg}$, and an object which has a mass of $6.42 \times 10^{22} \mathrm{~kg}$ if the gravitational force equals approximately $4.95 \times 10^{21} \mathrm{~N}$. Remember $F=\frac{k m_1 m_2}{d^2}$ and the Universal Gravitational Constant equals $6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2$.