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CHALLENGE

At a school of 500 students, there are 125 students enrolled in Algebra, 257 students who play sports, and 52 students who are enrolled in Algebra and play sports. Create a Venn diagram to illustrate this information.

Sagot :

Dashataranidn

Step-by-step explanation:

To create the Venn diagram, follow these steps:

 1.  Define Sets:

  • Let A represent the students enrolled in Algebra.
  • Let S represent the students who play sports.

 2.  Write the given information:

  • Total number of students, n(U) = 500
  • Number of students enrolled in Algebra, n(A) = 125
  • Number of students who play sports, n(S) = 257
  • Number of students enrolled in both Algebra and sports, n(A ∩ S) = 52

 3.  Calculate number of students in each groups:

    [tex]\bullet\ \text{Students only in algebra: $n_o(A)=n(A)-n(A\cap S)=125-52=73$}[/tex]

    [tex]\bullet\ \text{Students only in sports: $n_o(S)=n(S)-n(S\cap A)=257-52=205$}[/tex]  

    [tex]\bullet\ \text{Students in both Algebra and sports: $n_o(A\cap S)=52$}[/tex]

    [tex]\bullet\ \text{Students in neither Algebra nor sports: $n_o(AUS)'=n(U)-n(AUS)$}[/tex]

       [tex]\text{First, we need to find $A\cup S$ using the formula:}\\n(AUS)=n_o(A)+n_o(S)+n(A\cap S)=73+205+52=330[/tex]

       [tex]\text{Therefore, $n(A\cup S)'=500-330=170$}[/tex]

 4.  Venn Diagram Data:

  • Students only in Algebra: 73
  • Students only in sports: 205
  • Students in both Algebra and sports: 52
  • Students in neither Algebra nor sports: 170
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