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3 years ago

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What is the domain of the function represented by the following graph?

1 answer:

Svetllana [295]3 years ago

6 0

Hello!

The domain of the function are the x-values that make the function true.

Since the graph has open circles and filled in circles, the open circles make the function false (written as <) , and the filled in circles make it true (written as ≤).

From the graph, the x value -3, and 2 are open circles. While the value -0.5 are filled in circles. Also, from the interval (-0.5, 2), there is gap, so it is part of the domain.

Therefore, the domain of the function is: {x | -3 < x ≤ -0.5} ∪ {x | 2 < x < ∞}, which is the third choice.

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So, Probability of success = 0.75

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a. What is the probability that exactly 2 of them have never been married?

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b. That at most 2 of them have never been married?

At most two means at x = 0 ,1 , 2

So, $P(X=r) =^{15}C_0 (0.75)^0 (0.25^{15-0}+^{15}C_1 (0.75)^1 (0.25^{15-1}+^{15}C_2 (0.75)^2 (0.25^{15-2}$

$P(X=r) =(0.75)^0 (0.25^{15-0}+15 (0.75)^1 (0.25^{15-1}+\frac{15!}{2!(15-2)!} (0.75)^2 (0.25^{15-2})$

$P(X=r) =9.9439 \times 10^{-6}$

c. That at least 13 of them have been married?

P(x=13)+P(x=14)+P(x=15)

$={15}C_{13}(0.75)^{13} (0.25^{15-13})+{15}C_{14} (0.75)^{14}(0.25^{15-14}+{15}C_{15} (0.75)^{15} (0.25^{15-15})$

$=\frac{15!}{13!(15-13)!}(0.75)^{13} (0.25^{15-13})+\frac{15!}{14!(15-14)!} (0.75)^{14}(0.25^{15-14}+{15}C_{15} (0.75)^{15} (0.25^{15-15})$

$=0.2360$

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