Assume that 140 surveys are completed. of those surveyed, 71 responded positively to effectiveness, 60 responded positively to side effects, and 65 responded positively to cost. also, 33 responded positively to both effectiveness and side effects, 31 to effectiveness and cost, 28 to side effects and cost, and 21 to none of the items. how many responded positively to all three?

15

Step-by-step explanation:

Let n(T) denotes total surveys done i.e. n(T)=140

Let n(A) be the no. of responses to positively to effectiveness i.e. n(A)=71

Let n(B) be the no. of side effects i.e.n(B) =60

Let n(C) be the no. of responses to cost i.e. n(C)= 65

33 responded positively to both effectiveness and side effects

So, n(A∩B)=33

31 to effectiveness and cost

n(A∩C)=31

28 to side effects and cost

n(B∩C)=28

21 to none of the items

So, n(A∪B∪C)=140-21 = 119

we are supposed to find ow many responded positively to all three i.e. n(A∩B∩C)

Formula:

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

119=71+60+65-33-31-28+ n(A∪B∪C)

119=104+ n(A∪B∪C)

119-104= n(A∪B∪C)

15= n(A∪B∪C)

Hence 15 responded positively to all three

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

b.   e = 7.5h

hope this , lovely!