Patients who are addicted to cocaine are sometimes using the drug to combat depression. as such, sometimes addicts are given antidepressant medications to prevent relapse. a three-year study compared the effects of two such medications, lithium and desipramine, along with a placebo for 72 cocaine users wishing to break the habit. the patients were put into 3 groups of 24, and given 1 of the 3 treatments at random. this two-way table illustrates the results. treatment relapse no relapse total desipramine 10 14 24 lithium 18 6 24 placebo 20 4 24 total 48 24 72 give a conditional relative frequency for relapse among patients who took lithium. a. 18/72 = 25% b. 27/72 = 33.33% c. 18/24 = 75% d. 48/72 = 66.67%

Option C, 18/24 = 75%

Step-by-step explanation:

Patients who were addicted to cocaine were divided into 3 groups of 24.

Each group was treated with three different drugs. One group of 24 patients were put on Lithium for treatment out of 24 patients who relapsed were 18.

So conditional relative frequency for relapse among patients who took Lithium would be :

Relative frequency of patients = (patients relapsed) / (total number of patients)

Relative frequency = = 75%

Option C, 18/24 = 75% would be the answer.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: