Asurvey of 100 people asked if they have a dog or a cat. the answers were: 56 people answered yes for dog and 51 people answered yes for cat. some people may own neither and some people may own both animals. what is the maximum number of people who could answer yes for both, cat and dog?

 The maximum number of people who could answer yes for both cat and dog is 7.

Step-by-step explanation:  Given that a survey of 100 people asked if they have a dog or a cat.

Out of those 100 people, 56 people answered yes for dog and 51 people answered yes for cat. Some people may own neither and some people may own both animals.

We are to find the maximum number of people that could answer yes for both cat and dog.

Let A and B represents the set of people that answered Yes for dog and Yes for cat respectively.

Then, according to the given information, we have

From Set Theory, we have

Since the total number of people is 100, so we get

Therefore, from equation (i), we get

Thus, the maximum number of people who could answer yes for both cat and dog is 7.

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q

3 4 7 12 19

+1 +3 +5 +6

i would guess 26 because this isnt a sequential pattern or its to short to know