Question

1. in a random survey, 20 seventh graders and 32 eighth graders are asked their preference on playing tennis. of the students surveyed, 18 students prefer to play tennis, and there are 12 seventh graders who do not prefer to play tennis. which two - way frequency table could represent the data? a, b, c, d (tables as shown) 38. consider the five equations.

Explanation:

Step1: Analyze Grade 7 Data

Seventh graders: total 20, prefer tennis 18? Wait no, wait the problem says: 20 seventh graders, 18 students prefer tennis (wait no, "18 students prefer to play tennis, and there are 12 seventh graders who do not prefer to play tennis." Wait, let's re-express:

Total seventh graders: 20. Number of seventh graders who do not prefer tennis: 12. So seventh graders who prefer tennis: \( 20 - 12 = 8 \).

Total eighth graders: 32. Number of students who prefer tennis: 18. So eighth graders who prefer tennis: \( 18 - 8 = 10 \)? Wait no, wait the problem: "18 students prefer to play tennis, and there are 12 seventh graders who do not prefer to play tennis."

Wait, let's parse the problem again:

"In a random survey, 20 seventh graders and 32 eighth graders are asked their preference on playing tennis. Of the students surveyed, 18 students prefer to play tennis, and there are 12 seventh graders who do not prefer to play tennis. Which two - way frequency table could represent the data?"

So:

• Seventh graders (Grade 7) total: 20.
• Seventh graders who do not prefer tennis: 12. So seventh graders who prefer tennis: \( 20 - 12 = 8 \).
• Total students who prefer tennis: 18. So eighth graders (Grade 8) who prefer tennis: \( 18 - 8 = 10 \).
• Eighth graders total: 32. So eighth graders who do not prefer tennis: \( 32 - 10 = 22 \).
• Total students who do not prefer tennis: (20 - 8)+(32 - 10)=12 + 22 = 34.
• Total students: 20 + 32 = 52.

Now let's check each table:

Table A:

• Prefer Tennis: Grade 7:8, Grade 8:10, Total:18.
• Do Not Prefer Tennis: Grade 7:12, Grade 8:22, Total:34.
• Total: Grade 7:20, Grade 8:32, Total:52. Perfect match.

Let's check other tables:

Table B: Prefer Tennis Grade 7:8, Grade 8:18, Total:26≠18. So no.

Table C: Prefer Tennis Grade 7:8, Grade 8:14, Total:22≠18. No.

Table D: Prefer Tennis Grade 7:9, Grade 8:9, Total:18. But Grade 7 total should be 20, 9 + 11 = 20, but Grade 7 prefer tennis should be 8, not 9. So no.

Step2: Confirm Table A

Table A has Grade 7 Prefer Tennis:8, Do Not:12 (8 + 12 = 20), Grade 8 Prefer Tennis:10, Do Not:22 (10 + 22 = 32), Prefer Tennis Total:8 + 10 = 18, Do Not Total:12 + 22 = 34, Grand Total:20 + 32 = 52. All match the given data.

Answer:

A. The two - way frequency table with Prefer Tennis: Grade 7 (8), Grade 8 (10), Total (18); Do Not Prefer Tennis: Grade 7 (12), Grade 8 (22), Total (34); Total: Grade 7 (20), Grade 8 (32), Total (52)