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trapecia [35]
3 years ago
12

A cylinder has a radius of 12m and a height of 30m. Find the surface area and volume

Mathematics
1 answer:
Anastasy [175]3 years ago
4 0

Answer:

Surface Area: 1008π OR 3166.73

Volume: 4320π OR 13,571.68

Step-by-step explanation:

Surface Area Equation:

2πrh+2πr^2

Work:

2π (12) (30) + 2π12^2

2π(360) + 2π(144)

720π + 288π

1008π OR 3166.73

Volume Equation:

πr^2h

Work:

π12^2 (30)

π144 (30)

4320π OR 13,571.68

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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and
egoroff_w [7]

Answer:

a) P(140

P(0.036

P(0.036

b) P(140< \bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(139,28.1)  

Where \mu=139 and \sigma=28.1

We are interested on this probability

P(140

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(140

And we can find this probability like this:

P(0.036

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(0.036

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)

And the new z score would be:

Z=\frac{\bar X -\mu}{\sigma_{\bar x}}

P(140< \bar X

P(140< \bar X

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Sindrei [870]

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What are the factors in the expression (a+b)12
BlackZzzverrR [31]
Solution:

1) Distribute
12a+12b

Done!
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