Encuestas a los estudiantes sobre si tienen un perro o un gato. Ciento cuarenta y tres de los estudiantes tienen un perro y respondieron que no tienen gato. Ciento cincuenta y uno de los estudiantes no ten\'ian perro, y $70$ de ellos respondieron que ten\'ian un gato. Organiza los resultados en una f\'abula de dos v\'ias. Incluir las frecuencias marginales.

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Algebra 1

Evaluate expressions using exponent rules

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Q. Encuestas a los estudiantes sobre si tienen un perro o un gato. Ciento cuarenta y tres de los estudiantes tienen un perro y respondieron que no tienen gato. Ciento cincuenta y uno de los estudiantes no ten\'ian perro, y

70

de ellos respondieron que ten\'ian un gato. Organiza los resultados en una f\'abula de dos v\'ias. Incluir las frecuencias marginales.

Identify Categories: Identify the categories for the two-way table. $\newline$ We have two categories: students with dogs and students with cats. We will create a table with these categories and include the number of students who have neither a dog nor a cat.
Fill Information: Fill in the given information. $\newline$ We know that $143$ students have a dog and do not have a cat. We also know that $151$ students do not have a dog, and among those, $70$ have a cat. We will place these numbers in the appropriate cells of the table.
Calculate No Dog No Cat: Calculate the number of students who do not have a dog and do not have a cat. Since $70$ of the $151$ students who do not have a dog have a cat, the remaining number of students who do not have a dog and do not have a cat is $151 - 70 = 81$ .
Create Two-Way Table: Create the two-way table with the information we have. $\newline$ Let's denote $D$ for dog and $C$ for cat. The table will have rows for ＂Has Dog＂ and ＂No Dog,＂ and columns for ＂Has Cat＂ and ＂No Cat.＂ We will also include a row and a column for the marginal frequencies (totals). $\newline$ | | Has Cat | No Cat | Total | $\newline$ |---------|---------|--------|-------| $\newline$ | Has Dog | ? | $143$ | ? | $\newline$ | No Dog | $70$ | $81$ | $151$ | $\newline$ | Total | ? | ? | ? |
Calculate Total Cat: Calculate the total number of students who have a cat. $\newline$ We know that $70$ students do not have a dog but have a cat. We do not have the information directly about how many students have both a dog and a cat, so we cannot fill in this cell yet. We will leave it as a question mark for now.
Calculate Total Dog: Calculate the total number of students who have a dog. We know that $143$ students have a dog and do not have a cat. We do not have the information directly about how many students have both a dog and a cat, so we cannot fill in this cell yet. We will leave it as a question mark for now.
Calculate Total Students: Calculate the total number of students surveyed. $\newline$ We cannot calculate the total number of students surveyed without knowing how many students have both a dog and a cat. Since this information is not provided, we cannot complete the two-way table accurately. We will leave the total number of students as a question mark.
Complete Two-Way Table: Complete the two-way table as much as possible with the given information. $\newline$ | | Has Cat | No Cat | Total | $\newline$ |---------|---------|--------|-------| $\newline$ | Has Dog | ? | $143$ | ? | $\newline$ | No Dog | $70$ | $81$ | $151$ | $\newline$ | Total | ? | $224$ | ? | $\newline$ We can fill in the ＂No Cat＂ column total as $143$ (students with a dog and no cat) + $81$ (students with no dog and no cat) = $224$ .