Mathematics, 20.01.2021 05:20 HyperZ

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Answer from: bcaughman6885

(a) check explanation

(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.

(d) the fraction of boys who chose geometry as their favourite is ¹/₆

(e) the fraction of students who chose statistics that were boys is ²/₃

Step-by-step explanation:

From the given statement;

Total number of boys = 60

Total number of girls = 80

Total number of students who chose Number = 60, number of boys = 20, number of girls = 40

Total number of students who chose Algebra = 30, number of boys = ?, number of girls = ?

Total number of students who chose geometry = 20, number of boys = 10, number of girls = 10

number of boys who chose statistics = 20, number of girls = ?

let the number of boys who chose algebra = x

20 boys(number) + x boys(algebra) + 10 boys (geometry) + 20 boys (statistics) = 60

50 + x = 60

x = 60 - 50

x = 10 boys

Thus, 10 boys chose algebra, then (30 - 10) girls chose algebra, i.e 20 girls.

Let the number of girls who chose statistics = y

40 girls(number) + 20 girls(algebra) + 10 girls(geometry) + y girls (statistics) = 80

70 + y = 80

y = 80 - 70

y = 10 girls

Thus, 10 girls chose statistics

Now complete the two-way table as follows;

(a) Two-way table

Boys Girls Total

Algebra 10 20 30

Geometry 10 10 20

Number 20 40 60

Statistics 20 10 30

Total 60 80 140

(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.

$= \frac{number \ of \ girls \ who \ chose \ statistics }{Total \ number \ of \ girls} \\\\= \frac{10}{80} \\\\= \frac{1}{8}$

(d) the fraction of boys who chose geometry as their favourite;

$= \frac{number \ of \ boys \ who \ chose \ geometry }{Total \ number \ of \ boys} \\\\= \frac{10}{60} \\\\= \frac{1}{6}$

(e) the fraction of students who chose statistics that were boys is calculated as;

$= \frac{number \ of \ boys \ who \ chose \ statistics }{Total \ number \ of \ students \ who \ chose \ statistics} \\\\= \frac{20}{30} \\\\= \frac{2}{3}$

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