Find the area of triangle ABC. A. 35.92 units²
B. 43.79 units²
C. 21.39 units²
D. 22.91 units²

Step-by-step explanation:

The area of a triangle with sides and and angle between them is given by .

Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as . Assign values:

Substituting these values into our area formula, we get:

The value of the appropriate z test statistic to test this claim is 0.48.

Step-by-step explanation:

We are given that a potential competitor has been conducting blind taste tests on its blend and finds that 48% of consumers strongly prefer its French Roast to yours.

After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend.

Let p = proportion of consumers who prefers new blend.

So, Null Hypothesis, : p 48%     {means that the new blend is preferred by less than or equal to 48% of consumers}

Alternate Hypothesis, : p > 48%     {means that the new blend is preferred by more than 48% of consumers}

The test statistics that would be used here One-sample z proportion statistics;

                      T.S. =    ~ N(0,1)

where, = sample proportion of tasters prefer new blend = = 0.50

           n = sample of tasters = 144

So, test statistics  =  

                              =  0.48

Hence, the value of the appropriate z test statistic to test this claim is 0.48.