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kolbaska11 [484]
3 years ago
15

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the p

ool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14
A cylinder with a radius of 12 feet and a height of 4.5 feet.
Mathematics
1 answer:
KIM [24]3 years ago
3 0

Answer:

<em>1885.5 m^3 of water</em>

<em></em>

Step-by-step explanation:

I'll assume this is the complete question

<em>Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14 </em>

<u><em>The pool forms</em></u><em> a cylinder with a radius of 12 feet and a height of 4.5 feet.</em>

<em></em>

height of pool = 4.5 ft

radius of pool12^{2} = 12 ft

height of water is 4 inches below pool top

<em>12 inches make 1 ft</em>

4 inches = 4/12 ft = 0.33 ft

Therefore, height of water = 4.5 - 0.33 = 4.17 ft

<em>volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed</em>

volume of cylinder formed by the water = volume of water = πr^{2}h

volume = 3.14  x 12^{2} x 4.17 = <em>1885.5 m^3 of water</em>

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Step-by-step explanation:

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A confidence interval (CI) is desired for the true average stray-load loss u (watts) for a certain type of induction motor when
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Answer:

A) CI = (57.12 , 59.48)

B) CI = (57.71 , 58.89)

C) CI = (57.53 , 59.07)

D) n = 239.63

Step-by-step explanation:

a)

given data:

mean, \bar X = 58.3

standard deviation, σ = 3

sample size, n = 25Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025,

Zc = Z(α/2) = 1.96

ME = Zc * σ \sqrt{n}

ME = 1.96 * 3 \sqrt{25}

ME = 1.18

CI = (\bar X - Zc * s\sqrt{n}  , \barX + Zc * s\sqrt{n})

CI = (58.3 - 1.96 * 3\sqrt{25} , 58.3 + 1.96 * 3\sqrt{25})

CI = (57.12 , 59.48)

b)

Given data:

mean, \bar X = 58.3

standard deviation, σ = 3

sample size, n = 100

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ \sqrt{n}

ME = 1.96 * 3\sqrt{100}

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CI = (\bar X - Zc * s\sqrt{n}  , \barX + Zc * s\sqrt{n})

CI = (58.3 - 1.96 * 3\sqrt{100} , 58.3 + 1.96 * 3\sqrt{100})

CI = (57.71 , 58.89)

c)

sample mean, \bar X = 58.3

sample standard deviation, σ = 3

sample size, n = 100

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

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Significance Level, α = 0.01,

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The critical value for α = 0.01 is 2.58.

for calculating population mean we used

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n = (2.58 * 3/0.5)^2

n = 239.63

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