In a survey of 269 college students, it is found that
69 like brussels sprouts,
90 like broccoli,
59 like cauliflower,
28 like both brussels sprouts and broccoli,
20 like both brussels sprouts and cauliflower,
24 like both broccoli and cauliflower, and
10 of the students like all three vegetables.

a) how many of the 269 college students do not like any of these three vegetables?

b) how many like broccoli only?

c) how many like broccoli and cauliflower but not brussels sprouts?

d) how many like neither brussels sprouts nor cauliflower?

a) 83, b) 28, c) 14, d) 28.

Step-by-step explanation:

Since we have given that

n(B) = 69

n(Br)=90

n(C)=59

n(B∩Br)=28

n(B∩C)=20

n(Br∩C)=24

n(B∩Br∩C)=10

a) How many of the 269 college students do not like any of these three vegetables?

n(B∪Br∪C)=n(B)+n(Br)+n(C)-n(B∩Br)-n(B∩C)-n(Br∩C)+n(B∩Br∩C)

n(B∪Br∪C)=

So, n(B∪Br∪C)'=269-n(B∪Br∪C)=269-156=83

b) How many like broccoli only?

n(only Br)=n(Br) -(n(B∩Br)+n(Br∩C)+n(B∩Br∩C))

n(only Br)=

c) How many like broccoli AND cauliflower but not Brussels sprouts?

n(Br∩C-B)=n(Br∩C)-n(B∩Br∩C)

n(Br∩C-B)=

d) How many like neither Brussels sprouts nor cauliflower?

n(B'∪C')=n(only Br)= 28

Hence, a) 83, b) 28, c) 14, d) 28.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925