Lesson 11 So, You Say There’s a Chance? Practice Understanding

Ready

1.

Solve this equation by factoring. $5 x^{2} + 17 x - 12 = 0$

2.

Solve for $u$ . $a = \frac{v - u}{t}$

This is the formula for acceleration.

$u$ = initial velocity

$v$ = final velocity

$t$ = elapsed time

3.

Multiply. $\sqrt[5]{2} \cdot \sqrt[5]{4} \cdot 4$ .

Write your answer as a base of $2$ using a rational exponent.

4.

Solve. $x^{2} + 7 x + 13 = 0$

5.

Explain why the quadratic equation in problem 4 had $2$ complex solutions.

6.

Given: $(x^{4} + x^{3} - 7 x^{2} - x + 6) \div (x + 2) = (x^{3} - x^{2} - 5 x + 9) R (- 12)$

If $P (x) = x^{4} + x^{3} - 7 x^{2} - x + 6$ , what is the value of $P (- 2)$ ?

7.

Subtract. $\frac{x - 5}{(x + 1)} - \frac{11}{(x - 3)}$

Set

A local newspaper releases results of a poll of residents to see what proportion approve of the job the city mayor is doing. The article reports that $99$ of a sample of $187 residents$ , or $53 %$ , approve of the job the mayor is doing.

8.

Can you conclude that $53 %$ of all residents approve of the job the mayor is doing? Why or why not?

9.

Identify the margin of error for this poll, then interpret the meaning of the margin of error.

A company of several thousand employees is interested in the average wage it is paying. After sampling $125$ of these employees, it finds the average wage of the employees in this sample is $$47,000$ with a standard deviation of $$1,200$ .

10.

Find the margin of error, then interpret the meaning of the margin of error.

11.

The CEO of the company is wondering how competitive its wages are with a competing company. He finds a report online that says a sample of $30$ employees had an average salary of $$44,000$ with a standard deviation of $$4,000$ . Is there evidence that his company is paying its workers more on average than its competitor? Give evidence for your answer.

Go

Predict the number and potential type of solutions for each function. Justify your answer.

12.

$f (x) = x^{2} - 25$

13.

$g (x) = x^{3} - 27$ , $(x = 3)$ is a solution.

14.

$h (x) = - x^{4} - 2 x^{3} + 7 x^{2} - 2 x + 8$

The graph of $h (x)$ is shown.

15.

$p (x) = (x^{2} - 4) (x^{2} + 9) (x - 7) (x + 2)$