Arthur is testing the effectiveness of a new acne medication. there are 100 people with acne in the study. forty patients received the acne medication, and 60 other patients did not receive treatment. fifteen of the patients who received the medication reported clearer skin at the end of the study. twenty of the patients who did not receive medication reported clearer skin at the end of the study. what is the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin?

a. 15%
b. 33%
c. 38%
d. 43%

 D. 43 %

Step-by-step explanation:

Let M is the event of receiving medicine,

M' is the event of not receiving medicine,

C is the event of clear skin.

Then According to the question,

Total size of the sample space, n(S) = 100

Number of patient who get the medicine, n(M) = 40

Number of patient who do not get the medicine, n(M') = 60

Number of patient  who received the medication reported clearer skin at the end of the study,

Therefore, the probability that patient  who received the medication reported clearer skin at the end of the study,

Number of patient who who did not receive the medication reported clearer skin at the end of the study, n(M\capC) = 20.

Thus, the Number of patient who cleared the skin, n(C) = 15 + 20 = 35

And, the probability that the patient cleared their skin,  

Therefore, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,

⇒

⇒  

⇒   

Thus,   or

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.