a group of 60 adults were surveyed on the ways on how they cope with stress. and the following are the results 34 said they tend to go for a vacation 27 said they would go for a smoke break 41 answered they listen to music 13 tend to go for a vacation and smoke 16 said go for a smoke and listen to music 20 go for a cation and listen to music 28 said two of the coping mechanism how many adults said exactly one of the coping mechanisms

The number of adults that said exactly one coping mechanism are 25 adults

Step-by-step explanation:

Total number of adult in the group = 60 adults

The number that go on vacation vacation = 34

The number that go for a smoke break = 27

The number that listen to music = 41

The number that go for a vacation and smoke = 13

The number that smoke and listen to music = 16

The number that go for a vacation and listen to music = 20

The number that said two of the coping mechanism = 28

Set theory

We have;

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

Given that the following relations;

n(A∪B∪C) = 60

n(A) = 34

n(B) = 27

n(C) = 41

n(A∩B) = 13

n(A∩C) = 20

n(B∩C) = 16

Therefore;

60 = 34 + 27 + 41 -13 -  20 - 16 + n(A∩B∩C)

∴ n(A∩B∩C) = 60 - (34 + 27 + 41 -13 -  20 - 16) = 7

Given that 28 said exactly 2, we have;

Total number of respondents = Those that said exactly 1 + Those that said exactly 2 + Those that said exactly 3

Total number of respondents = 60

Those that said exactly 2 = 28

Those that said exactly 3 = n(A∩B∩C) = 7

Therefore;

60 = Those that said exactly 1 + 28 + 7

Those that said exactly 1 = 60 - (28 + 7) = 25

Alternatively, we have;

Those that said exactly one = n(A) -(n(A∩B) + n(A∩C) - n(A∩B∩C))  + n(B) - (n(B∩C) + n(A∩B) - n(A∩B∩C)) + n(C) - (n(A∩C) + n(B∩C) - n(A∩B∩C))  

= 34 - (13 + 20 - 7) + 27 - (16 + 13 - 7) + 41 - (20 + 16 - 7) = 25

60 - 28 - 7 = 25

The number of adults that said exactly one coping mechanism = 25.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet