Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

a) The customers surveyed purchased only mysteries =12

b) The customers purchased mysteries and science fiction, but not romance novels=10

c) The customers purchased mysteries or science fiction=46

d) The customers purchased mysteries or science fiction, but not romance novels=44

e) The customers purchased  exactly two types of books=21

Step-by-step explanation:

Given: n(S)=57

n(M)=33

n(S)=25

n(R)=18

n(M∩S)=12

n(R∩M)=9

n(S∩R)=6

n(R∩S∩M)=2

From the Venn diagram,

d=2

n(M∩S)=a+d=12

⇒a=10

n(R∩M)=b+d=9

⇒b=7

n(S∩R)=c+d=6

⇒c=4

Now, the customers surveyed purchased only mysteries=n(M)-a-b-d=33-10-7-4=12

The customers purchased mysteries and science fiction, but not romance novels=a=10

The customers purchased mysteries or science fiction=n(M∪S)=n(M)+n(S)-n(M∩S)=33+25-12=46

The customers purchased mysteries or science fiction, but not romance novels=n(M∪S)-d=46-2=44

The customers purchased  exactly two types of books= a+b+c=10+7+4=21

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.