Apple products have become a household name in america with 51% of all households owning at least one apple product (cnn, march 19, 2012). the likelihood of owning an apple product is 61% for households with kids and 48% for households without kids. suppose there are 1,200 households in a representative community, of which 820 are with kids and the rest are without kids. are the events "household with kids" and "household without kids" mutually exclusive and exhaustive?

It is mutually exclusive and exhaustive.

Step-by-step explanation:

Since we have given that

                             Owns apple              No apple  Total

With kids                   500.2                       319.8        820

Without kids              182.4                        197.6        380

Total                          682.6                       517.4         1200

P(Households without kids) =

P(Households with kids) =

And P(A∪B) = 0.316+0.683 = 0.999 ≈ 1

Since the two event are disjoint so, the probability of both occurring is 0 and the probability of either occurring is the sum of each occurring.

Hence, it is mutually exclusive and exhaustive.

x=30

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1