A survey of 2400 people asked them to name their favorite sport to watch. The circle graph summarizes the answers. The central angle for the Basketball slice is $54^\circ$. We need to determine how many people named Basketball as their favorite sport to watch.

1. Problem Description

A survey of 2400 people asked them to name their favorite sport to watch. The circle graph summarizes the answers. The central angle for the Basketball slice is $54^\circ$. We need to determine how many people named Basketball as their favorite sport to watch.

2. Solution Steps

The total number of people surveyed is

2

4

0

0. A full circle has $360^\circ$.

The fraction of people who chose basketball is represented by the ratio of the basketball slice angle to the full circle angle.

Fraction of people who chose basketball = $\frac{54}{360}$

To find the number of people who chose basketball, we multiply the total number of people surveyed by the fraction of people who chose basketball.

Number of people who chose basketball = $2400 \times \frac{54}{360}$

First, simplify the fraction:

$\frac{54}{360} = \frac{27}{180} = \frac{9}{60} = \frac{3}{20}$

Now, multiply the total number of people by the simplified fraction:

Number of people who chose basketball = $2400 \times \frac{3}{20}$

Number of people who chose basketball = $\frac{2400 \times 3}{20} = \frac{7200}{20}$

Number of people who chose basketball = $360$

3. Final Answer

360