Suppose that 65% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 75% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

a) 50%, b) 25%.

Step-by-step explanation:

Since we have given that

Probability of all adults regularly consume coffee P(C) = 65%

Probability of all adults regularly consume soda P(S) = 60%

Probability of all adults regularly either one of them P(C ∪S) = 75%

According to question, we get that

(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?

(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

P(C∪S)'=1-P(C∪S)

Hence, a) 50%, b) 25%.

(a) 0.50 or 50%

(b) 0.25 or 25%

Step-by-step explanation:

We are given that;

Probability of adults that regularly consume coffee, P(C) = 0.65

Probability of adults that regularly consume carbonated soda, P(S) = 0.60

Probability of adults that regularly consume at least one of these two products, P(C S) = 0.75

(a) Probability that a randomly selected adult regularly consumes both coffee and soda is given by P(C S) ;

       P(C S) = P(C) + P(S) - P(C S)

           0.75   = 0.65 + 0.60 - P(C S)

         P(C S) = 1.25 - 0.75 = 0.50

Therefore, the probability that a randomly selected adult regularly consumes both coffee and soda is 0.50 or 50%.

(b) Probability that a randomly selected adult doesn't regularly consume at least one of these two products =  P(C S)'

       P(C S)' = 1 -  P(C S) = 1 - 0.75 = 0.25 or 25% .

step-by-step explanation: step 3 should really go to step seven, but anyway never mind.

1 ∠oln ≅ ∠lno

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .