
a. "Chocolate" and "Adults" (whatever those mean) will be independent as long as

"Chocolate" has the marginal distribution given by the second column, with a total probability of

. Similarly, "Adults" has the marginal distribution described by the third row, so that

. Then

Meanwhile, the joint probability of "Chocolate" and "Adults" is given by the cell in the corresponding row/column, with

.
The probabilities match, so these events are indeed independent.
Parts (b) and (c) are checked similarly.
b. Yes;


c. Yes;

Answer:
C. 6.9
Step-by-step explanation:
Pretend this is a 2-d diagram and use the Pythagorean theorem.
Pythagorean theorem: a^2 + b^2 = c^2
a = 6 mm
b = 7/2 = 3.5 mm
c = x
6^2 + 3.5^2 = x^2
36 + 12.25 = x^2
48.25 = x^2

x = 6.9
Answer: C.(z^3+1)^2
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