A dance school has 54 students who learn salsa and 23 of those students also learn ballet. There are 15 students who do not learn salsa but learn ballet and 10 students do not learn either salsa or ballet. Which table best shows the relative frequency of rows for the data?

To determine the table that best represents the relative frequencies of rows for the given data, we need to first understand the information provided.

We know that there are 54 students who learn salsa, and out of those, 23 also learn ballet. This means that 54 - 23 = 31 students only learn salsa.
Furthermore, there are 15 students who do not learn salsa but learn ballet.

Additionally, there are 10 students who do not learn either salsa or ballet.

To construct the table, we need to identify the rows that provide the relative frequencies. Based on the given information, we can categorize the rows as follows:

Row 1: Students who learn both salsa and ballet.
Row 2: Students who only learn salsa.
Row 3: Students who only learn ballet.
Row 4: Students who do not learn either salsa or ballet.

Now, let's construct the table:

| | Relative Frequency |
|-------------|--------------------|
| Row 1 | |
| Row 2 | |
| Row 3 | |
| Row 4 | |

To calculate the relative frequency for each row, we divide the number in each row by the total number of students, which is 54.

Row 1: Students who learn both salsa and ballet. The number of students is 23, so the relative frequency is 23/54 = 0.426.

Row 2: Students who only learn salsa. The number of students is 31, so the relative frequency is 31/54 ≈ 0.574.

Row 3: Students who only learn ballet. The number of students is 15, so the relative frequency is 15/54 ≈ 0.278.

Row 4: Students who do not learn either salsa or ballet. The number of students is 10, so the relative frequency is 10/54 ≈ 0.185.

The final table representing the relative frequencies of rows would be:

| | Relative Frequency |
|-------------|--------------------|
| Row 1 | 0.426 |
| Row 2 | 0.574 |
| Row 3 | 0.278 |
| Row 4 | 0.185 |

Therefore, the table shown above would best represent the relative frequency of rows for the given data.

To determine the relative frequency of rows for the given data, we need to create a table that shows the number of students in each category and calculate the relative frequency.

Let's create a table to visualize the data:

| | Salsa | Ballet | Neither |
|-----------|---------|----------|---------|
| Learn | | | |
| Not Learn | | | |

According to the information provided, there are 54 students in total who learn salsa and 23 of those students also learn ballet. This means that there are 54 - 23 = 31 students who learn salsa but do not learn ballet.

Next, we know that there are 15 students who do not learn salsa but learn ballet. We also know that 10 students do not learn either salsa or ballet.

Filling in the table:

| | Salsa | Ballet | Neither |
|-----------|---------|----------|---------|
| Learn | 54 | 23 | |
| Not Learn | 31 | 15 | 10 |

Now, we can calculate the relative frequency by dividing the values in each category by the total number of students (54 + 31 + 23 + 15 + 10 = 133).

Relative frequency table:

| | Salsa | Ballet | Neither |
|-----------|---------|----------|---------|
| Learn | 54/133 | 23/133 | |
| Not Learn | 31/133 | 15/133 | 10/133 |

Simplifying the fractions:

| | Salsa | Ballet | Neither |
|-----------|-----------|-----------|------------|
| Learn | 0.406015 | 0.172932 | |
| Not Learn | 0.233083 | 0.112782 | 0.075188 |

Hence, the table that best shows the relative frequency of rows for the data is:

| | Salsa | Ballet | Neither |
|-----------|-----------|-----------|------------|
| Learn | 0.406015 | 0.172932 | |
| Not Learn | 0.233083 | 0.112782 | 0.075188 |

None of the above