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Bezzdna [24]
2 years ago
14

The volume of this cylinder is 32π yd2. Find the height.

Mathematics
1 answer:
Arturiano [62]2 years ago
6 0
The radius of the can is
4 inches.

Explanation:
The formula for volume of a cylinder is:
V=πr2h

Since we know the volume and the height of the can, we can determine the radius.
32
π
=
π
r
2
×
2
Cancelling the similar terms on either side, we get.
32
π
=
π
r
2
×
2
32
=
r
2
×
2
Divide both sides by
2
.
16
=
r
2
Square both sides, remembering that the result has to be a positive integer.
4
=
r
Hence the radius of the cylindrical can is
4
inches.
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The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probab
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Answer:

(a) 0.6579

(b) 0.2961

(c) 0.3108

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Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable <em>X</em> thus follows a Poisson distribution with parameter, <em>λ</em> = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.  

The mean of the approximated distribution of X is:

μ = λ  = 250

The standard deviation of the approximated distribution of X is:

σ = √λ  = √250 = 15.8114

Thus, X\sim N(250, 250)

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

P(235

                             =P(-0.95

Thus, the value of P (235 < <em>X</em> < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

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(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

                             =P(-0.40

Thus, the value of P(48.

(d)

Let the sample size be <em>n</em>.

P(48

                             0.95=P(-z

The value of <em>z</em> for this probability is,

<em>z</em> = 1.96

Compute the value of <em>n</em> as follows:

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Thus, the sample selected must be of size 240.

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