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Harlamova29_29 [7]
3 years ago
15

A town has two fire engines operating independently. The probability that a specific engine is available when needed is 0.96. (a)

What is the probability that neither is available when needed? (b) What is the probability that a fire engine is available when needed?
Mathematics
1 answer:
o-na [289]3 years ago
8 0

Answer:

Answer is

a. P (both pumps not available) = 0.016

b. P (both pumps available) = 0.984

Step-by-step explanation:

a. Probability of neither pump is available.

We know that P1 + P2 = 1

P1 = Probability of one pump is available = 0.96

P2 = Probability of a pump not available = 1-0.96 = 0.04

Now the probability of both pump not available will be = P2 x P2

=0.04 x 0.04 = 0.016

b. Probability of both pumps available will be.

Using the equation of probability

P (both pumps available) + P (both pumps unavailable) = 1

P (both pumps available) = (1- P (both pumps unavailable))

P (both pumps available) = 1-0.016

P (both pumps available) = 0.984

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Step-by-step explanation:

We are given that:

f'(0) = 5 \text{ and } F(x) = f(3x)

And we want to find F'(0).

First, find F(x):

\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]

From the chain rule:

\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}

Then:

\displaystyle \begin{aligned} F'(0) & = 3f'(3(0)) \\ \\ & = 3f'(0) \\ \\ & = 3(5) \\ \\ & = 15\end{aligned}

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Answer:

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Step-by-step explanation:

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