Question

Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced Algebra and Physics in a particular high school. From a sample of 50 students, it is found that 39 are taking Algebra, 16 are taking Physics, and 7 are enrolled in both. How many students are enrolled in either Algebra or Physics? (4 points)

Algebra Not in Algebra Total
Physics 7 16
Not in Physics
Total 39 50
a
41

b
2

c
48

d
7

Some please help me

Answer 1

Answer:

48 students

Step-by-step explanation:

Represent algebra with A and physics with P

Given

Total = 50

n(A) = 39

n(P) = 16

n(Both) = 7

Required

Determine students taking Algebra or Physics

This is calculated using

n(A or P) = n(A) + n(P) - n(Both)

n(A or P) = 39 + 16 - 7

n(A or P) = 48

Answer 2

A total of 48 students are enrolled in either physics or algebra.

Number of students taking algebra n(A)= 39

Number of students taking physics n(B)= 16

Number of students taking both subjects n(A∩B)= 7

So, the number of students taking either physics or algebra will be the union of sets i.e. n(A∪B)

What does the union of sets represent?

The union of two sets is a set containing all elements that are in A or in B (possibly both).

As we know,

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 39+16-7

n(A∪B) = 48

Therefore, A total of 48 students are enrolled in either physics or algebra.

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