Question

Last year 45 percent of the total number of complaints made to a telephone company were about billing errors. In which of the following circle graphs does the shaded area represent the fraction of the total number of complaints made that were about billing errors last year?

1) The graph has one-quarter of the circular region shaded.
2) The graph has approximately one-third of the circular region shaded.
3) The graph has three-quarters of the circular region shaded.
4) The graph has slightly less than half of the circular region shaded.
5) The graph has slightly more than half of the circular region shaded.

Answer 1

The graph has slightly more than half of the circular region shaded. The correct answer is (option 5)

Step-by-step explanation:

In a circle graph, the shaded area represents the proportion of the whole. Since 45 percent of the total complaints were about billing errors last year, we need (option 5) a graph where the shaded area is slightly more than half to accurately reflect this percentage.

To validate this, let's consider the other options:

1) One-quarter shaded is too small.

2) Approximately one-third shaded is too small.

3) Three-quarters shaded is too large.

4) Slightly less than half shaded is too small.

Now, let's calculate the percentage of the circular region shaded in (option 5) to ensure it aligns with the given information. If we consider "slightly more than half" as 51 percent, this aligns with the 45 percent of complaints about billing errors. Therefore, option 5) is the correct choice.

In conclusion, the shading in option 5) accurately represents the fraction of total complaints related to billing errors last year. This choice aligns with the given percentage, making it the most suitable representation in a circle graph.