Part 1: Answer the following question:
In a survey of students about favorite sports, the results include 22 who like tennis, 25
who like football, 9 who like tennis and football, 17 who like tennis and baseball, 20 who like football and baseball, 6 who like all three sports, and 4 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
Part 2: Create a Venn diagram to reflect the information in the question. You will not be able to post your Venn diagram in the discussion thread itself, but you should describe your Venn diagram and be certain to address the following questions:
•How can a Venn diagram help you solve the problem?
•How many circles will you need in your diagram
•Where will you place the students who like all 3 sports
•Where will you place the students who like none of the sports?
Steve or Reiny could you help plz??
Part 1: To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football from the total number of students who like football.
Total number of students who like tennis and football: 9
Total number of students who like football: 25
Number of students who like only tennis and football: 25 - 9 = 16
Similarly, to find the number of students who like only tennis and baseball, we need to subtract the number of students who like both tennis and baseball from the total number of students who like tennis.
Total number of students who like tennis and baseball: 17
Total number of students who like tennis: 22
Number of students who like only tennis and baseball: 22 - 17 = 5
To find the number of students who like only baseball and football, we need to subtract the number of students who like all three sports from the total number of students who like baseball and football.
Total number of students who like all three sports: 6
Total number of students who like baseball and football: 20
Number of students who like only baseball and football: 20 - 6 = 14
Part 2: A Venn diagram can help visualize the overlapping relationships between different groups or categories. In this case, it can help us see the number of students who like only specific sports, as well as those who like multiple sports or none at all.
We will need three circles in the Venn diagram to represent the three sports: tennis, football, and baseball. Each circle will represent the students who like that specific sport.
The circle for students who like all three sports (tennis, football, and baseball) will overlap with all three circles.
The students who like none of the sports will be placed outside of all three circles, indicating that they do not belong to any of the sports categories.
Part 1:
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football (9) and the number of students who like all three sports (6) from the total number of students who like football (25). So, the number of students who like only tennis and football is 25 - 9 - 6 = 10.
Similarly, to find the number of students who like only tennis and baseball, we need to subtract the number of students who like both tennis and baseball (17) and the number of students who like all three sports (6) from the total number of students who like tennis (22). So, the number of students who like only tennis and baseball is 22 - 17 - 6 = -1. However, since we cannot have a negative number of students, we assume that there are 0 students who like only tennis and baseball.
To find the number of students who like only baseball and football, we need to subtract the number of students who like both football and baseball (20) and the number of students who like all three sports (6) from the total number of students who like baseball (0). Since there are 0 students who like baseball, there cannot be any students who like only baseball and football.
Part 2:
A Venn diagram can help solve the problem by visually organizing the information about the different sports and the students' preferences. It allows us to see the overlapping regions between different sports and determine the number of students who like each combination of sports.
To create the Venn diagram, you will need three circles, one for each sport: tennis, football, and baseball. The circles should overlap with each other in different combinations.
The students who like all three sports (tennis, football, and baseball) should be placed in the overlapping region where all three circles intersect.
The students who like none of the sports should be placed outside of all three circles, in a separate region.
By analyzing the regions of the Venn diagram, you can determine the number of students who like only tennis and football, only tennis and baseball, and only baseball and football.