Only one of the following equations is an identity. Identify the identity and explain your answer. $(x-1)^{2}-1=x(x-2) \quad(x-1)^{2}=x(x-1)$

Use the regression feature of a graphing utility to find an exponential model $y=a b^{x}$ for the data and identify the coefficient of determination. Use the graphing utility to plot the data and graph the model in the same viewing window. $(−3, 102.2), (0, 80.5), (3, 67.8), (6, 58.2), (10, 55.0)$

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. When the teacher returned to find a docile class, he knew that...

How did the policies of the United States government affect the relationship between settlers in the West and Native Americans?

Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer(s) using a graphing utility. $\ln (x+5)=\ln (x-1)+\ln (x+1)$

You are given the value of $\tan \theta$. Is it possible to find the value of $\sec \theta$ without finding the measure of $\theta$? Explain.

Use a calculator to find each value. Round your answers to the nearest thousandth. $\sec 195^{\circ}.$

Find the indicated sets. $\mathscr{P}(\{1,2\} \times\{3\})$

Write a recursive definition and an explicit formula for your sequence.

Use a graphing utility to graph f and g in the same viewing window. Approximate the point of intersection of the graphs of f and g. Then solve the equation $f(x)=g(x)$ algebraically. $f(x)=64^{x}$ $g(x) = 8$

Use a graphing calculator to graph each function the interval from 0 to $2 \pi .$ Then sketch each graph. $y=\sin x+2 x$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $|x-3| \geq 4$

What is the inverse of $y=\sqrt{x-5}?$

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.)

$$\begin{matrix} \text{Task} & \text{Mean Time (minutes)} & \text{Standard Deviation}\\ \text{Task 1: Descriptive Analysis of Data} & \text{11.4} & \text{5.0}\\ \text{Task 2: Standardizing Scores} & \text{11.9} & \text{9.0}\\ \text{Task 3: Poisson Probability Table} & \text{7.3} & \text{3.9}\\ \text{Task 4: Areas under Normal Curve} & \text{9.1} & \text{5.5}\\ \end{matrix}$$

Find the probability that a student will take at least 10 minutes to complete Task 1.