Answer the following questions about each of the words from the Underlined word. Then, write an original sentence for each word. Check your original sentences with a partner or small group. How did Lyndon Johnson's actions demonstrate a $\underline{manipulation}$ of events during the Tonkin Gulf crisis?

Solve the equation. Give the exact solution and an approximate solution to four decimal places, when appropriate.

$$\left( \frac { 3 } { 2 } \right) ^ { 6 x + 2 } = \frac { 27 } { 8 }$$

Use the table, which shows the age groups of students in a college sociology class.

$$\begin{matrix} \text{Age} & \text{Number of students}\\ \text{18–19} & \text{11}\\ \text{20–21} & \text{18}\\ \text{22–30} & \text{2}\\ \text{31– 40} & \text{1}\\ \end{matrix}$$

A student from the class is randomly chosen for a project. Find the probability that the student is the given age. Older than 21 years old

A single-pass, cross-flow heat exchanger with both fluids unmixed is being used to heat water $\left(\dot{m}_{c}=2 \mathrm{kg} / \mathrm{s}\right.\left.c_{p}=4200 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ from $20^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ with hot exhaust gases $\left(c_{p}=1200 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ entering at $320^{\circ} \mathrm{C}$. What mass flow rate of exhaust gases is required? Assume that UA is equal to its design value of 4700 W/K, independent of the gas mass flow rate.

Your classmate uses a calculator to evaluate $\tan (\pi / 2)$ and gets a result of 0.0274224385. Describe the error.

Use the tables below. One student from each school is chosen at random to be on a committee. Find each probability. $$ \begin{matrix} \text{School A}\\ \text{Freshman} & \text{Sophomore} & \text{Junior} & \text{Senior}\\ \text{30\\%} & \text{27\\%} & \text{25\\%} & \text{18\\%}\\ \end{matrix} $$ $$ \begin{matrix} \text{School B}\\ \text{Freshman} & \text{Sophomore} & \text{Junior} & \text{Senior}\\ \text{28\\%} & \text{28\\%} & \text{24\\%} & \text{20\\%}\\ \end{matrix} $$ two juniors

Which of the following statement is not true? (a) Simple interest is to be used only in simple decision situations. (b) Compounded interest involves computing interest on top of interest. (c) Simple interest is rare in practical situations of borrowing and loaning. (d) If the interest is not stated as being simple or compounded, we assume the latter.

What is a mutation?

The complex carbohydrate found in the cell walls of most fungi is ____ A. chitin. B. cellulose. C. glycogen. D. starch.

Expand each binomial. $(4+9 x)^{3}$

Gerald Corporation entered a public-private partnership using a DBOM contract with the state of Massachusetts 10 years ago for railroad system upgrades. Determine the profitability index for the financial results listed below using a MARR of 8% per year. Investments: Year 0 $-4.2 million Year 5$-3.5 million, Net savings: Years 1-5 $1.2 million per year Years 6-10$2.5 million per year

Determine whether each equation is true for all real numbers x. Explain your reasoning. 2x + 3x = 5x

Multiply. (x-3)(x+6)(x+1)

Use the Empirical Rule. The mean rate for satellite television for a sample of households was $72.50 per month, with a standard deviation of$12.50 per month. Estimate the percent of satellite television rates between $60.00 and$85.00. (Assume the data set has a bell-shaped distribution.)