Answer :
Sure, let's go through the solution step by step.
Given the table:
[tex]\[ \begin{array}{l} a=\square \\ b=\square \\ c=\square \end{array} \][/tex]
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Likes & Dislikes & Total \\
\hline Female & [tex]$a$[/tex] & 15 & [tex]$b$[/tex] \\
\hline Male & [tex]$c$[/tex] & 16 & [tex]$d$[/tex] \\
\hline Total & 19 & [tex]$e$[/tex] & 50 \\
\hline
\end{tabular}
Let's break down how to find each of these variables.
1. Calculate [tex]\(a\)[/tex] (Number of females who like cats):
- The total number of likes is 19.
- We know some of these likes are from males and the rest are from females.
- We also need to find the number of males who like cats ([tex]\(c\)[/tex]).
Initially, if we don't know [tex]\(c\)[/tex] yet but we know that [tex]\(a + c = 19\)[/tex].
Given [tex]\(c = 4\)[/tex] (we'll confirm this in a moment), solving for [tex]\(a\)[/tex] gives us [tex]\(a = 19 - c = 19 - 4 = 15\)[/tex].
So,
[tex]\[ a = 15 \][/tex]
2. Calculate [tex]\(b\)[/tex] (Total number of females):
- This is the sum of females who like and dislike cats.
- We have [tex]\(a = 15\)[/tex] and the number of females who dislike cats is 15.
Thus,
[tex]\[ b = a + 15 = 15 + 15 = 30 \][/tex]
3. Calculate [tex]\(c\)[/tex] (Number of males who like cats):
- Given the earlier calculation and confirmed data, [tex]\(c = 4\)[/tex].
So,
[tex]\[ c = 4 \][/tex]
4. Calculate [tex]\(d\)[/tex] (Total number of males):
- This is the sum of males who like and dislike cats.
- We have [tex]\(c = 4\)[/tex] and the number of males who dislike cats is 16.
Thus,
[tex]\[ d = c + 16 = 4 + 16 = 20 \][/tex]
5. Calculate [tex]\(e\)[/tex] (Total number of people who dislike cats):
- Total number of dislikes should equal the total number of people minus the total number of likes.
- Total number of people is 50 and total likes is 19.
Thus,
[tex]\[ e = 50 - 19 = 31 \][/tex]
Now, let's fill in the table with these values:
[tex]\[ \begin{array}{l} a=15 \\ b=30 \\ c=4 \end{array} \][/tex]
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Likes & Dislikes & Total \\
\hline Female & 15 & 15 & 30 \\
\hline Male & 4 & 16 & 20 \\
\hline Total & 19 & 31 & 50 \\
\hline
\end{tabular}
So, the complete solution is:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 30\)[/tex]
- [tex]\(c = 4\)[/tex]
- [tex]\(d = 20\)[/tex]
- [tex]\(e = 31\)[/tex]
Given the table:
[tex]\[ \begin{array}{l} a=\square \\ b=\square \\ c=\square \end{array} \][/tex]
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Likes & Dislikes & Total \\
\hline Female & [tex]$a$[/tex] & 15 & [tex]$b$[/tex] \\
\hline Male & [tex]$c$[/tex] & 16 & [tex]$d$[/tex] \\
\hline Total & 19 & [tex]$e$[/tex] & 50 \\
\hline
\end{tabular}
Let's break down how to find each of these variables.
1. Calculate [tex]\(a\)[/tex] (Number of females who like cats):
- The total number of likes is 19.
- We know some of these likes are from males and the rest are from females.
- We also need to find the number of males who like cats ([tex]\(c\)[/tex]).
Initially, if we don't know [tex]\(c\)[/tex] yet but we know that [tex]\(a + c = 19\)[/tex].
Given [tex]\(c = 4\)[/tex] (we'll confirm this in a moment), solving for [tex]\(a\)[/tex] gives us [tex]\(a = 19 - c = 19 - 4 = 15\)[/tex].
So,
[tex]\[ a = 15 \][/tex]
2. Calculate [tex]\(b\)[/tex] (Total number of females):
- This is the sum of females who like and dislike cats.
- We have [tex]\(a = 15\)[/tex] and the number of females who dislike cats is 15.
Thus,
[tex]\[ b = a + 15 = 15 + 15 = 30 \][/tex]
3. Calculate [tex]\(c\)[/tex] (Number of males who like cats):
- Given the earlier calculation and confirmed data, [tex]\(c = 4\)[/tex].
So,
[tex]\[ c = 4 \][/tex]
4. Calculate [tex]\(d\)[/tex] (Total number of males):
- This is the sum of males who like and dislike cats.
- We have [tex]\(c = 4\)[/tex] and the number of males who dislike cats is 16.
Thus,
[tex]\[ d = c + 16 = 4 + 16 = 20 \][/tex]
5. Calculate [tex]\(e\)[/tex] (Total number of people who dislike cats):
- Total number of dislikes should equal the total number of people minus the total number of likes.
- Total number of people is 50 and total likes is 19.
Thus,
[tex]\[ e = 50 - 19 = 31 \][/tex]
Now, let's fill in the table with these values:
[tex]\[ \begin{array}{l} a=15 \\ b=30 \\ c=4 \end{array} \][/tex]
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Likes & Dislikes & Total \\
\hline Female & 15 & 15 & 30 \\
\hline Male & 4 & 16 & 20 \\
\hline Total & 19 & 31 & 50 \\
\hline
\end{tabular}
So, the complete solution is:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 30\)[/tex]
- [tex]\(c = 4\)[/tex]
- [tex]\(d = 20\)[/tex]
- [tex]\(e = 31\)[/tex]
