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chubhunter [2.5K]
2 years ago
6

F(x)=sin^5(4x). Find f '(x)

Advanced Placement (AP)
1 answer:
puteri [66]2 years ago
4 0
I got:
f
'
(
x
)
=
10
sin
4
(
2
x
)
cos
(
2
x
)

Explanation:
I would use the Chain Rule starting from the power of
5
then the
sin
and last the
2
x
multiplying each derivative:
f
'
(
x
)
=
5
sin
5
−
1
(
2
x
)
⋅
cos
(
2
x
)
⋅
2

f
'
(
x
)
=
10
sin
4
(
2
x
)
cos
(
2
x
)
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If the wait time is less than 30 minutes for 75% of all patients in the emergency room, what is the probability that the
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The probability that the proportion of patients who wait less than 30 minutes is 0.582 or less is 0.0020

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Probability can be defined as the likelihood of an event to occur. In statistics, the mean of the sample distribution typically shows the probability of the population.

From the parameters given:

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The sample proportion \mathbf{\hat p} can be computed by using the expression:

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\mathbf{\hat p = \dfrac{32}{55}}

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If the percentage of the probability of all patients in the emergency room = 0.75

The probability that the proportion of patients who wait less than 30 minutes is 0.582 or less can be computed as:

\mathbf{( \hat P \leq 0.582) = P \Big( \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}} \leq \dfrac{0.582 - 0.75}{\sqrt{\dfrac{0.75(1-0.75)}{55}}} \Big )}

\mathbf{( \hat P \leq 0.582 )= P \Big( Z \leq \dfrac{-0.168}{\sqrt{0.003409}} \Big )}

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Feudalism allowed the Lords to concentrate a great power and wealth in vast areas, which in time would derive in the creation of powerful states. It also led to constant conflicts and wars among several feuds. Since there was no clear higher power above the feudal lords, it created a fragile and unstable social and political order that paved the way for wars, invasions, and famine.

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