There are 54 students in a class. The Venn diagram below shows how many students play a sport, take a foreign language, do both, or do neither. Complete the following two-way frequency table. Plays a sport Does not play a sport Takes a foreign language Does not take a foreign language

To complete the two-way frequency table, we need to determine the number of students who play a sport, take a foreign language, do both, and do neither based on the information provided in the Venn diagram.From the Venn diagram details, we have:- The number of students who take a foreign language only is 21.- The number of students who play a sport only is 12.- The number of students who do both (intersection) is 17.Now, let's calculate the number of students who do neither.First, we calculate the total number of students who play a sport or take a foreign language (or both):Number of students who play a sport or take a foreign language = (Number who play a sport only) + (Number who take a foreign language only) + (Number who do both)= 12 (Sport only) + 21 (Foreign language only) + 17 (Both)= 12 + 21 + 17= 50Now, we subtract this number from the total number of students in the class to find out how many do neither:Number of students who do neither = Total number of students - Number who play a sport or take a foreign language= 54 (Total students) - 50 (Sport or Foreign language)= 54 - 50= 4Now we can complete the two-way frequency table:Plays a sport:- Takes a foreign language: 17 (Both)- Does not take a foreign language: 12 (Sport only)Does not play a sport:- Takes a foreign language: 21 (Foreign language only)- Does not take a foreign language: 4 (Neither)So the completed two-way frequency table is:| | Takes a foreign language | Does not take a foreign language ||-------------------------|--------------------------|----------------------------------|| Plays a sport | 17 | 12 || Does not play a sport | 21 | 4 |Answer:The completed two-way frequency table is as follows:| | Takes a foreign language | Does not take a foreign language ||-------------------------|--------------------------|----------------------------------|| Plays a sport | 17 | 12 || Does not play a sport | 21 | 4 |