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3 years ago

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The rabbit population on a small island is observed to be given by the function

1 answer:

Ahat [919]3 years ago

5 0

A.) P(t) = 130t - 0.4t^4 + 1200
The population is maximum when P'(t) = 0
P'(t) = 130 - 1.6t^3 = 0
1.6t^3 = 130
t^3 = 81.25
t = ∛81.25 = 4.3 months.

Maximum population P(t)max = 130(4.3) - 0.4(4.3)^4 + 1200 = 1,622

b.) The rabbit population will disappear when P(t) = 0
P(t) = 130t - 0.4t^4 + 1200 = 0
t ≈ 8.7 months

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Answer:

95% Confidence interval: (31.32%,47.04%)

Step-by-step explanation:

We are given the following in the question:

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95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.3918\pm 1.96(\sqrt{\dfrac{0.3918(1-0.3918)}{148}})\\\\ = 0.3918\pm 0.0786\\\\=(0.3132,0.4704)=(31.32\%,47.04\%)$

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Step-by-step explanation:

<u>GIVEN :-</u>

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In the triangle on the right side ,

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In the triangle on the left side ,

Base = 18m

<u>TO FIND :-</u>

Length of the common perpendicular to both triangles.
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<u>FACTS TO KNOW BEFORE SOLVING :-</u>

$Hypotenuse = \sqrt{Base^2 + Perpendicular^2}$ .
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<u>SOLUTION :-</u>

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⇒ Perpendicular of the triangle on right side = Perpendicular of the triangle on left side.

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