A group of 100 students were asked if they study French or Spanish in school. The results are shown in this two-way table.

| | French | Not French | Total |
| :---------- | :----- | :--------- | :---- |
| Spanish | 5 | 63 | 68 |
| Not Spanish | 30 | 2 | 32 |
| Total | 35 | 65 | 100 |

Which statements are correct? Check all that apply.

A. 5 students study both French and Spanish.
B. 63 students study French.
C. 2 students study neither French nor Spanish.
D. 30 students study French, but not Spanish.
E. 63 students study Spanish.

The correct statements from the survey results are that 5 students study both French and Spanish, 2 students study neither language, and 30 students study French but not Spanish. Statements regarding the number of students studying only French or Spanish are inaccurate. Thus, the validated statements are A, C, and D.
;

Answered by Anonymous | 2025-07-08

5 students study both French and Spanish.
2 students study neither French nor Spanish.
30 students study French, but not Spanish.
The correct statements are: 5 students study both French and Spanish, 2 students study neither French nor Spanish, and 30 students study French, but not Spanish. 5 , 2 , 30 ​

Explanation

Analyze the problem and data We have a two-way table showing the results of a survey about French and Spanish studies among 100 students. We need to verify each statement against the data in the table to determine which ones are correct.

Verify statement 1 Statement 1: 5 students study both French and Spanish. Looking at the table, the intersection of 'French' and 'Spanish' shows 5 students. So, this statement is correct.

Verify statement 2 Statement 2: 63 students study French. The 'Total' for French is 35, not 63. So, this statement is incorrect.

Verify statement 3 Statement 3: 2 students study neither French nor Spanish. Looking at the table, the intersection of 'Not French' and 'Not Spanish' shows 2 students. So, this statement is correct.

Verify statement 4 Statement 4: 30 students study French, but not Spanish. Looking at the table, the intersection of 'French' and 'Not Spanish' shows 30 students. So, this statement is correct.

Verify statement 5 Statement 5: 63 students study Spanish. The 'Total' for Spanish is 68, not 63. So, this statement is incorrect.

Conclusion Based on the analysis, the correct statements are:



5 students study both French and Spanish.
2 students study neither French nor Spanish.
30 students study French, but not Spanish.

Examples
Two-way tables are commonly used in surveys and data analysis to understand relationships between different categories. For example, a company might survey its employees to understand the relationship between job satisfaction and years of experience. The table helps visualize how many employees fall into each category, such as 'satisfied with less than 5 years of experience' or 'dissatisfied with more than 10 years of experience'. This information can then be used to make informed decisions about employee benefits and company policies.

Answered by GinnyAnswer | 2025-07-08