Lesson 12 So, You Say There’s a Chance? Practice Understanding

Ready

1.

Graph each complex number on the same complex plane. Let the point be the terminal point of a vector with the initial point being at the origin. Label each vector using vector notation.

$\vec{r} = - 9 - 2 i$
$\vec{s} = 10 + 3 i$
$\vec{t} = 3 + 5 i$
$\vec{u} = - 8 + i$
$\vec{v} = - 2 - 4 i$
$\vec{w} = 6 - 7 i$
Find $\vec{v} + \vec{w}$ . Graph the sum on the complex plane.

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.

2.

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

3.

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$ .

4.

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

5.

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

Coordinate Conversion:

The polar coordinates $(r, θ)$ are related to the rectangular coordinates $(x, y)$ as follows:

$x = r \cos θ y = r \sin θ \tan θ = \frac{y}{x} r^{2} = x^{2} + y^{2}$

6.

Graph each point in the rectangular plane.

$(- 8, 0)$
$(0, - 7)$
$(4, 4)$
$(4 \sqrt{3}, 4)$

7.

Convert the points from rectangular to polar coordinates. Then graph the points in the polar plane.

$(- 8, 0) =$ $\underset{―}{}$
$(0, - 7) =$ $\underset{―}{}$
$(4, 4) =$ $\underset{―}{}$
$(4 \sqrt{3}, 4) =$ $\underset{―}{}$

8.

Compare the location of the points in the rectangular plane to the location of the points in the polar plane relative to the $x$ - and $y$ -axes. What do you notice?