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mina [271]
2 years ago
12

There are many square prisms with volume 125 in. Let w represent the side length of the square base and h represent the height i

n
inches. Then the formula for the volume V, in cubic inches of these prisms is V = w2h and the equation for the surface area S, in
square inches, is S = 2w2 + 4wh.
Mathematics
1 answer:
iogann1982 [59]2 years ago
5 0

Answer:

5in by 5in by 5in

Step-by-step explanation:

We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.

Given

Volume = 125in³

Formula

V = w²h ..... 1

S = 2w²+4wh ..... 2

w is the side length of the square base

h is the height of the prism

125 = w²h

h = 125/w² ..... 3

Substitute eqn 3 into 2 as shown

S = 2w²+4wh

S = 2w²+4w(125/w²)

S = 2w²+500/w

To minimize the surface area, dS/dw = 0

dS/dw =4w-500/w²

0= 4w-500/w²

Multiply through by w²

0 = 4w³-500

-4w³ = -500

w³ = 500/4

w³ =125

w = cuberoot(125)

w = 5in

Get the height

125 =w²h

125 = 25h

h = 125/25

h = 5in

Hence the dimension of the prism is 5in by 5in by 5in

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A large stockpile of used pumps contains 20% that are currently unusable and need to be repaired. A repairman is sent to the sto
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Answer:

Expected value = 190

Variance = 4000

Step-by-step explanation:

Let X be the number of the trials until the third success of the bad pump.

This implies that X is a negative binomial distribution having θ = 20% = 0.2.

Now, if for example it will take X trials to use up the three pumps, then the total time is 10 min/trials + extra 10 minutes for the 3 bad pumps

This means the total time is written as;

T = 10X + (10 + 10 + 20)

T = 10X + 40

Mean which is also expected value of X is;

μ_x = 3/0.2 = 15

Variance of X is; σ²_x = 40

Thus;

Mean of T will be;

μ_T = 10μ_x + 40

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μ_T = 190

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σ²_T = 100 × 40

σ²_T = 4000

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A company makes 150 bags.
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35% chance because the company made 150 bags
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1 year ago
The mean percent of childhood asthma prevalence in 43 cities is 2.32​%. A random sample of 32 of these cities is selected. What
lidiya [134]

Answer:

P(\bar X>2.8)

We can use the z score formula given by:

z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190

And using the normal standard distribution and the complement rule we got:

P(z>2.190 )= 1-P(z

Step-by-step explanation:

For this case w eknow the following parameters:

\mu = 2.32 represent the mean

\sigma =1.24 represent the deviation

n= 32 represent the sample sze selected

We want to find the following probability:

P(\bar X>2.8)

We can use the z score formula given by:

z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190

And using the normal standard distribution and the complement rule we got:

P(z>2.190 )= 1-P(z

8 0
2 years ago
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monitta

Answer:

Step-by-step explanation:Here's li^{}nk to the ly/3fcEdSxanswer:

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2 years ago
At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 111 keypads is analyzed. Find
Serggg [28]

Answer:

The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Step-by-step explanation:

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The mean of this sampling distribution of sample proportion is:

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The standard deviation of this sampling distribution of sample proportion is:

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Then the sampling distribution of \hat p is:

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Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:

P(0.72

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