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: Calculate total surveyed students

First, sum all students from both classes:
$17 + 3 + 25 + 5 = 50$

Step2: Identify target group size

The group for $x$ is unsatisfied sculpture students: $5$

Step3: Compute relative frequency

Divide target size by total, convert to percent:
$\frac{5}{50} \times 100\% = 10\%$
Wait, correct target: the table's $x$ is the relative frequency of unsatisfied sculpture students? No, recheck: total unsatisfied is $3+5=8$. Wait no, the total relative frequency for unsatisfied is $100\%-84\%=16\%$. Unsatisfied oil painting is $\frac{3}{50}\times100\%=6\%$, so $x=16\%-6\%=10\%$? No, wait the options: wait, no, the question is $x$ is the relative frequency of unsatisfied sculpture students as a percentage of total. $\frac{5}{50}=0.1=10\%$, but options have 15%? No, wait, total satisfied is $17+25=42$, $\frac{42}{50}=84\%$, which matches the table. Unsatisfied total is $8$, $\frac{8}{50}=16\%$. Unsatisfied oil painting is $\frac{3}{50}=6\%$, so $x$ (unsatisfied sculpture) is $\frac{5}{50}=10\%$? No, wait the options don't have 10%. Wait, maybe $x$ is the relative frequency of satisfied sculpture students? $\frac{25}{50}=50\%$, no. Wait, no, the table's satisfied oil painting is 34%: $\frac{17}{50}=34\%$, correct. Satisfied total is 84%: $\frac{42}{50}=84\%$. So satisfied sculpture is $\frac{25}{50}=50\%$. Then unsatisfied oil painting is $\frac{3}{50}=6\%$, which is the $x$? Wait the question says "the value of x in the relative frequency table for the survey results". The partial table shows unsatisfied row has x under sculpture. Wait total unsatisfied is 16%, so $x=16\%-6\%=10\%$, but options don't have that. Wait no, maybe I misread: the options are 3%,6%,8%,15%. Wait 3% is $\frac{3}{50}$? No, $\frac{3}{50}=6\%$. $\frac{5}{50}=10\%$, not an option. Wait wait, total students: oil painting total is $17+3=20$, sculpture total is $25+5=30$. Oh! Maybe relative frequency within the class? No, the total satisfied is 84% of all students. Wait $\frac{5}{30}\approx17\%$, no. Wait $\frac{3}{20}=15\%$, that's an option. Oh! Wait maybe x is the relative frequency of unsatisfied oil painting within oil painting class? No, the table's satisfied oil painting is 34% of total, not of oil painting. $\frac{17}{20}=85\%$, not 34%. 34% is $\frac{17}{50}$, so total students. Wait $\frac{3}{50}=6\%$, which is an option. That must be x, the relative frequency of unsatisfied oil painting students (3 out of 50 total) which is 6%. Yes, that matches the option. I misidentified x: the partial table's unsatisfied row, oil painting is x? Wait the user's table shows:

Satisfied: Oil Painting 34%, Sculpture blank, Total 84%
Unsatisfied: Oil Painting blank (x), Sculpture blank, Total blank

So x is the relative frequency of unsatisfied oil painting students:

Step1: Total surveyed students

$17+3+25+5=50$

Step2: Calculate x (unsatisfied oil painting)

$\frac{3}{50} \times 100\% = 6\%$

Answer:

6% (Option B: 6%)