Solve the following
Z = 22 +
27
-X 5
44 + 27
(a) 22.90
(b) 23.90
(c) 21.90
(d) 24.90
Answers
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☆ Answer :
Option 3) 39 ⩽ x ⩽63
___________________________
☆ Given :
A Survey Concluded :-)
%of Americans who like CHEESE = 63%
% of Americans who like APPLES = 76%
% of Americans who like BOTH = x %
___________________________
☆ To Find :
% of American who like both i.e. value of x
___________________________
☆ Solution :
Let A and B denote the set of Americans who like Cheese and Apple respectively.
n(A) = 63 and n(B) = 76
According to De-Morgan's Law
n(A U B ) = n(A) + n(B) - n(A∩B)
⟹ n(A U B ) = 63 + 76 - n(A ∩ B)
⟹ n(A ∩ B) = 139 - n(A U B)
But, n(A U B) ⩽ 100
⟹ -n(A U B) ⩾ -100
⟹ 139 - n(A U B) ⩾ 139 - 100 = 39
⟹ 39 ⩽ n(A ∩ B) . . . (i)
Again ,
A ∩ B ⊆ A and A ∩ B ⊆ B
∴ n(A ∩ B) ⩽ n(A) = 63
and n(A ∩ B) ⩽ n(B) = 76
∴ n(A ∩ B) ⩽ 63 . . . (ii)
Combining eq (i) And (ii)
39 ⩽ n(A ∩ B) ⩽ 63
\red{ \huge\underline{\boxed{ \bf 39 \leqslant x \leqslant 63} }}
39⩽x⩽63
\large\mathfrak{ \text{W}hich \: \: is \: \: the \: \: required \: \: \text{ A}nswer.}Whichistherequired Answer.
Answer:
23.90
Explanation:
answer is 23.90
hope it helped you