Answer :
Let's determine the values in the two-way table using the provided information.
1. Total Number of People:
- The total number of people surveyed is 50.
2. Total People who Like Cats (Total Row, Likes Column):
- The total number of people who like cats is 19.
3. Total People who Dislike Cats (Total Row, Dislikes Column):
- The total number of people who dislike cats can be found by subtracting the number of people who like cats from the total number of people.
- [tex]\( e = 50 - 19 = 31 \)[/tex]
4. Females:
- Females who dislike cats are provided directly: 15.
5. Males:
- Males who dislike cats are provided directly: 16.
6. Total Females (Total Column, Female Row):
- The total number of females ([tex]\( b \)[/tex]) can be found by summing the number of females who like cats and those who dislike cats.
- Let [tex]\( a \)[/tex] be the number of females who like cats.
- Therefore, [tex]\( b = a + 15 \)[/tex]
7. Total Males (Total Column, Male Row):
- The total number of males ([tex]\( d \)[/tex]) can be found by summing the number of males who like cats and those who dislike cats.
- Let [tex]\( c \)[/tex] be the number of males who like cats.
- Therefore, [tex]\( d = c + 16 \)[/tex]
8. Sum of Total Females and Males:
- The total number of people is also the sum of the total number of females and males.
- [tex]\( b + d = 50 \)[/tex]
9. Solving for [tex]\( a \)[/tex] and [tex]\( c \)[/tex]:
- From the total row for people who like cats, we know [tex]\( a + c = 19 \)[/tex].
Now, putting all the equations together:
1. [tex]\( e = 31 \)[/tex]
2. [tex]\( b + d = 50 \)[/tex]
3. [tex]\( a + 15 + c + 16 = 50 \)[/tex]
4. [tex]\( a + c = 19 \)[/tex]
5. [tex]\( b = a + 15 \)[/tex]
6. [tex]\( d = c + 16 \)[/tex]
Substitute [tex]\( b \)[/tex] and [tex]\( d \)[/tex] in the sum equation:
- [tex]\( a + 15 + c + 16 = 50 \)[/tex]
- [tex]\( a + 15 + c + 16 = 50 \rightarrow a + c + 31 = 50 \rightarrow a + c = 19 \)[/tex]
Now, we can resolve the following step:
- Since [tex]\( a + c = 19 \)[/tex], we already have the equation correct, confirming [tex]\( a + c = 19 \)[/tex].
Next, use individual equations:
7. From [tex]\( b + d = 50 \)[/tex]:
- Substitute: [tex]\( (a + 15) + (c + 16) \)[/tex]
- Simplification: [tex]\( a + c + 31 = 50 \rightarrow a + c = 19 \)[/tex]
Thus, all calculations are consistent with initial requirements:[tex]\[ \begin{array}{|c|c|c|c|} \hline Female & a & 15 & b=a+15\\\hline Male & 19-\text{Female Like} & 16 & 50-(a+15)\\\hline\end{array} \][/tex]
So, we can solve it independently unchanged with following values confirming through correctly calculated steps.
1. [tex]\( a + c = 19 \)[/tex]
So, the values are:
[tex]\( a = 3 \)[/tex] since it fits by [tex]\( x of 15 - a = 16 default \\ Similar next value remains \( 19 > confirm: -16=3 \text {finales})\)[/tex]
[tex]\( a =3 \)[/tex] will display next as:
[tex]\[ b = 3 + 15 = 18 \][/tex]
Finally all boxed steps valuated fitting constants.
So:
[tex]\[c = \boxed{16} \][/tex]
Thus final comprehensive overall boxed are\x values solves:[
\\ ]
1. Total Number of People:
- The total number of people surveyed is 50.
2. Total People who Like Cats (Total Row, Likes Column):
- The total number of people who like cats is 19.
3. Total People who Dislike Cats (Total Row, Dislikes Column):
- The total number of people who dislike cats can be found by subtracting the number of people who like cats from the total number of people.
- [tex]\( e = 50 - 19 = 31 \)[/tex]
4. Females:
- Females who dislike cats are provided directly: 15.
5. Males:
- Males who dislike cats are provided directly: 16.
6. Total Females (Total Column, Female Row):
- The total number of females ([tex]\( b \)[/tex]) can be found by summing the number of females who like cats and those who dislike cats.
- Let [tex]\( a \)[/tex] be the number of females who like cats.
- Therefore, [tex]\( b = a + 15 \)[/tex]
7. Total Males (Total Column, Male Row):
- The total number of males ([tex]\( d \)[/tex]) can be found by summing the number of males who like cats and those who dislike cats.
- Let [tex]\( c \)[/tex] be the number of males who like cats.
- Therefore, [tex]\( d = c + 16 \)[/tex]
8. Sum of Total Females and Males:
- The total number of people is also the sum of the total number of females and males.
- [tex]\( b + d = 50 \)[/tex]
9. Solving for [tex]\( a \)[/tex] and [tex]\( c \)[/tex]:
- From the total row for people who like cats, we know [tex]\( a + c = 19 \)[/tex].
Now, putting all the equations together:
1. [tex]\( e = 31 \)[/tex]
2. [tex]\( b + d = 50 \)[/tex]
3. [tex]\( a + 15 + c + 16 = 50 \)[/tex]
4. [tex]\( a + c = 19 \)[/tex]
5. [tex]\( b = a + 15 \)[/tex]
6. [tex]\( d = c + 16 \)[/tex]
Substitute [tex]\( b \)[/tex] and [tex]\( d \)[/tex] in the sum equation:
- [tex]\( a + 15 + c + 16 = 50 \)[/tex]
- [tex]\( a + 15 + c + 16 = 50 \rightarrow a + c + 31 = 50 \rightarrow a + c = 19 \)[/tex]
Now, we can resolve the following step:
- Since [tex]\( a + c = 19 \)[/tex], we already have the equation correct, confirming [tex]\( a + c = 19 \)[/tex].
Next, use individual equations:
7. From [tex]\( b + d = 50 \)[/tex]:
- Substitute: [tex]\( (a + 15) + (c + 16) \)[/tex]
- Simplification: [tex]\( a + c + 31 = 50 \rightarrow a + c = 19 \)[/tex]
Thus, all calculations are consistent with initial requirements:[tex]\[ \begin{array}{|c|c|c|c|} \hline Female & a & 15 & b=a+15\\\hline Male & 19-\text{Female Like} & 16 & 50-(a+15)\\\hline\end{array} \][/tex]
So, we can solve it independently unchanged with following values confirming through correctly calculated steps.
1. [tex]\( a + c = 19 \)[/tex]
So, the values are:
[tex]\( a = 3 \)[/tex] since it fits by [tex]\( x of 15 - a = 16 default \\ Similar next value remains \( 19 > confirm: -16=3 \text {finales})\)[/tex]
[tex]\( a =3 \)[/tex] will display next as:
[tex]\[ b = 3 + 15 = 18 \][/tex]
Finally all boxed steps valuated fitting constants.
So:
[tex]\[c = \boxed{16} \][/tex]
Thus final comprehensive overall boxed are\x values solves:[
\\ ]
