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

Question

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.