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alexandr1967 [171]
3 years ago
5

Question 2 Multiple Choice Worth 10 points)

Mathematics
1 answer:
GuDViN [60]3 years ago
5 0

Answer:

$8,090

Step-by-step explanation:

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A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russ
ElenaW [278]

Answer:

n(S\cap F \cap R)=7

Step-by-step explanation:

The Universal Set, n(U)=2092

n(S)=1232\\n(F)=879\\n(R)=114

n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14

Let the number who take all three subjects, n(S\cap F \cap R)=x

Note that in the Venn Diagram, we have subtracted n(S\cap F \cap R)=x from each of the intersection of two sets.

The next step is to determine the number of students who study only each of the courses.

n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x

These values are substituted in the second Venn diagram

Adding up all the values

2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]

2092=2085+x

x=2092-2085

x=7

The number of students who have taken courses in all three subjects, n(S\cap F \cap R)=7

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3 years ago
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