Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 20 years and over at random. Define two events:

A = the person chosen is obese
B = the person chosen is overweight, but not obese

According to a statistical journal,

P(A) = 0.41and P(B) = 0.33.

Explain why events A and B are disjoint.

(A) Because event B rules out obese subjects.
(B) Because an obese person is certainly overweight.
(C) Because some people may be considered obese and overweight.
(D) Because some people are not obese nor overweight.

(A) Because event B rules out obese subjects.

Step-by-step explanation:

(A) is correct because B doesn't have obese people

(B) is incorrect because we don't know if there are obese person but not overweight.

(C) states a correct fact but that portion doesn't relate to event B (overweight but not obese)

Similarly, (D) also states a correct fact but doesn't relate to event B (overweight but not obese)

Solution:

The two equation given which are in two variables are

1. y = x²-2 x -1 9

2. y + 4 x=5

Writing equation 2 as→y = 5 -4 x

Substituting the value of y in equation 1

⇒ 5 - 4 x = x² - 2 x - 19

⇒x² - 2 x + 4 x -19 -5=0

⇒ x² + 2 x -24=0

⇒x² + 6 x - 4 x - 24=0→→→[Breaking the middle term i.e term containing x]

⇒ x(x+6) -4(x+6)=0

⇒(x-4)(x+6)=0

⇒x-4=0 ∧ x+6=0

⇒x = 4     ∧    x= -6

Put x=4 in equation 2,

y + 4 ×4=5

y + 16=5

y = 5-16

y= -11

As one solution is (-6, 29), The other solution of the system of equation is (4, -11).