Question

mr. capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes. he also noted which class each student had taken.
oil - painting
satisfied: 17
not satisfied: 3
sculpture
satisfied: 25
not satisfied: 5
art classes

	oil painting	sculpture	total
satisfied	34%		84%

what is the value of x in the relative frequency table for the survey results? round the answer to the nearest percent.
○ 3%
○ 6%
○ 8%
○ 15%

Explanation:

Step1: Find total number of students

First, calculate the total number of students in oil - painting: \(17 + 3=20\)
Then, calculate the total number of students in sculpture: \(25 + 5 = 30\)
The total number of students surveyed is \(20+30 = 50\)

Step2: Find the number of not - satisfied students

The number of not - satisfied students in oil - painting is 3 and in sculpture is 5. So the total number of not - satisfied students is \(3 + 5=8\)

Step3: Calculate the relative frequency of not - satisfied students (x)

The relative frequency \(x=\frac{\text{Number of not - satisfied students}}{\text{Total number of students}}\times100\%\)
Substitute the values: \(x=\frac{3}{50}\times100\% = 6\%\) (Wait, let's re - check. Wait, maybe we made a mistake. Wait, the total number of students: oil - painting has 17 satisfied and 3 not, so 20. Sculpture has 25 satisfied and 5 not, so 30. Total students: 20 + 30=50. The number of not - satisfied in oil - painting is 3. So the relative frequency of not - satisfied in oil - painting (if x is for oil - painting not satisfied) is \(\frac{3}{50}\times100\%=6\%\). Let's verify with the satisfied row. The satisfied in oil - painting is 17, \(\frac{17}{50}\times100\% = 34\%\) (which matches the table). The satisfied in sculpture is \(\frac{25}{50}\times100\% = 50\%\), and 34%+50% = 84% (which matches the total satisfied percentage). Then the not - satisfied total is \(100\% - 84\%=16\%\). The not - satisfied in sculpture is \(\frac{5}{50}\times100\% = 10\%\). So the not - satisfied in oil - painting is \(16\% - 10\% = 6\%\). So x (the relative frequency of not - satisfied in oil - painting) is 6%.

Answer:

6%