What does it mean to have a / chance?

Probability is the measure of how likely an event will occur. Probabilities are written as fractions or decimals from to , or as percentages from to .

2.

The sun will come up tomorrow.

3.

You will roll an even number on a standard -sided die.

4.

The month of February will have days.

5.

Carlos guesses the correct number between and .

6.

The football team has won of its last games. The team will win the next game.

8.

You get a citation for driving your car in a school zone.

Set

You have masonry tiles that you plan to lay out in your backyard to create a rectangular patio, but you haven’t decided on the dimensions of the patio. The tiles are square. You begin by laying each tile out in a really long line so you can make sure each one is clean and not damaged.

This makes a rectangle that measures by . You know you don’t want a patio with these dimensions, but you decide to methodically explore the dimensions you may want by next creating a rectangle that measures by . You continue on making rectangles until you’ve tried all of the possibilities. Since it’s hard to keep all of the dimensions in your head, you decide to make a table that organizes all of the widths, lengths, and the fixed area you want.

9.

Complete the table to show the dimensions of the rectangles until they repeat. Then sketch a graph from the ordered pairs and draw a smooth curve through the points.

 Width Length Area $1$ $2$ $3$ $4$ -- $6$ -- $8$ $9$ -- -- $12$ $144$ $72$ $144$ $144$ $144$ $144$ $144$ $144$ $144$ $144$ $144$ $144$ $144$ $144$

10.

What happens to the length as the width increases? Why? Would the graph change if the width became the dependent variable and the length became the independent variable? Explain.

11.

This type of relation is called an inverse variation. Explain why it is called that.

12.

For each ordered pair in the table, what does equal?

Solve the equation you just wrote for length.

13.

What is the value of , the constant of variation, in this story?

14.

When you solve for in the general formula for inverse variation, what is the location of in the equation?

Go

Solve the following equations. Show each step in your solution process. Check your solution(s).