Question

Meg used this table to track the average attendance from month to month at her theater for five months.

A 5-column table with 1 row is titled Percent Increase and Decrease. Column 1 is labeled October with entry negative 1. Column 2 is labeled November with entry 0.5. Column 3 is labeled December with entry negative 0.9. Column 4 is labeled January with entries three-fourths. Column 5 is labeled February with entry one-half. A number line going from negative 1 to positive 1 in increments of 0.25.

Graph the numbers on the number line. Choose the inequality symbol that makes each comparison true.

Nov.
Feb.
Oct.
Dec.
Jan.
Nov.

Answer 1

To analyze Meg's table and the provided values carefully, we need to convert the entries into a more usable form for the inequality comparisons.

The entries are:
- October: -1
- November: 0.5
- December: -0.9
- January: 0.75
- February: 0.5

Now, we can graph these numbers on the number line:

- October (-1) is at the far left.
- December (-0.9) is slightly to the right of October.
- November (0.5) is towards the right side of the number line.
- February (0.5) is at the same position as November.
- January (0.75) is to the right of both November and February.

Next, we will compare the values using inequality symbols:

1. **November (0.5) vs. February (0.5)**:
- \(0.5 = 0.5\)
- Thus, we can write: **November = February** or \( \text{Nov.} \equiv \text{Feb.} \)

2. **November (0.5) vs. October (-1)**:
- \(0.5 > -1\)
- Thus, we can write: **November > October** or \( \text{Nov.} > \text{Oct.} \)

3. **October (-1) vs. December (-0.9)**:
- \(-1 < -0.9\)
- Thus, we can write: **October < December** or \( \text{Oct.} < \text{Dec.} \)

4. **December (-0.9) vs. January (0.75)**:
- \(-0.9 < 0.75\)
- Thus, we can write: **December < January** or \( \text{Dec.} < \text{Jan.} \)

5. **January (0.75) vs. February (0.5)**:
- \(0.75 > 0.5\)
- Thus, we can write: **January > February** or \( \text{Jan.} > \text{Feb.} \)

6. **November (0.5) vs. December (-0.9)**:
- \(0.5 > -0.9\)
- Thus, we can write: **November > December** or \( \text{Nov.} > \text{Dec.} \)

Here are the summarized comparisons:
- **Nov. = Feb.**
- **Nov. > Oct.**
- **Oct. < Dec.**
- **Dec. < Jan.**
- **Jan. > Feb.**
- **Nov. > Dec.**

This should help complete your analysis of the average attendance data.