# Lesson 6Towers and CylindersSolidify Understanding

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).