To find the joint relative frequency for teachers who teach math and not English, let's follow a series of steps.
### Step-by-Step Solution:
1. Identify the Joint Frequency (Number of Teachers who Teach Math and Not English):
- From the given table, the number of teachers who teach math and not English is the cell corresponding to "Math" (row) and "Not English" (column).
- This value is 22.
2. Determine the Total Number of Survey Responses:
- The total number of survey responses is given at the bottom right cell of the table.
- This value is 104.
3. Calculate the Joint Relative Frequency:
- The joint relative frequency is calculated as:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{\text{Joint Frequency}}{\text{Total Survey Responses}} \right) \times 100
\][/tex]
- Plugging in the values:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{22}{104} \right) \times 100
\][/tex]
4. Convert the Fraction to a Percentage:
- Perform the division and multiplication:
[tex]\[
\left( \frac{22}{104} \right) \times 100 = 21.153846153846153
\][/tex]
5. Round to the Nearest Percent:
- Rounding the result to the nearest whole number gives us:
[tex]\[
21\%
\][/tex]
Thus, the joint relative frequency for teachers who teach math and not English, when rounded to the nearest percent, is 21%.
