If A and B are independent events with P( A) = 0.60 and P( A| B) = 0.60, then P( B) is: a. 0.60 b. cannot be determined with the information given c. 0.36 d. 1.2

Step-by-step explanation:

For two events A and B to be independent, it means they can occur at the same time i.e the occurrence of one does not affect the other occurring. It is represented as P(A∩B) = P(A)P(B)

Given P( A) = 0.60 and P( A| B) = 0.60, to find P(B), we will use the formula for the conditional probability P( A| B) = P(A∩B) /P(B)

P( A| B) = P(A)P(B) /P(B)

P( A| B) = P(A)

Since  P( A| B) = 0.60, therefore P(A) is also equal to 0.60 and P(B) cannot be determined since they cancelled out already

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°