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True [87]
2 years ago
8

Question 39/50

Mathematics
1 answer:
KatRina [158]2 years ago
3 0

Using it's concept, it is found that there is a 0.64 = 64% probability that neither flight is delayed.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

In this problem, there are 2 flights, each with a 0.8 probability of being on time. The flights are independent, hence the probability that both are on time is given by:

p = 0.8 x 0.8 = 0.64.

More can be learned about probabilities at brainly.com/question/14398287

#SPJ1

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The range of the equation is y>2

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The given equation is y=2(4)^{x+3}+2

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<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

y=2 \cdot 4^{x+3}+2

This can be written as y=2^{1+2(x+3)}+2

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

x=2^{1+2(y+3)}+2

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x-2=2^{1+2(y+3)}

Applying the log rule, if f(x) = g(x) then \ln (f(x))=\ln (g(x)), then, we get;

\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)

Simplifying, we get;

(1+2(y+3)) \ln (2)=\ln (x-2)

Dividing both sides by \ln (2), we have;

2 y+7=\frac{\ln (x-2)}{\ln (2)}

Subtracting 7 from both sides of the equation, we have;

2 y=\frac{\ln (x-2)}{\ln (2)}-7

Dividing both sides by 2, we get;

y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}

Let us find the positive values for logs.

Thus, we have,;

x-2>0

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The function domain is x>2

By combining the intervals, the range becomes y>2

Hence, the range of the equation is y>2

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