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Law Incorporation [45]
3 years ago
6

What is the volume of the prism?

Mathematics
1 answer:
Nikitich [7]3 years ago
7 0

Answer:

24 m³

Step-by-step explanation:

We need to find the volume of the prism. Given that , rectangular prism with cubic units arranged in two rows of two with six total layers . And the volume of each unit is 1 m³ .

<u>Volume</u><u> of</u><u> </u><u>one</u><u> </u><u>unit </u><u>:</u><u>-</u><u> </u>

\rm\implies Volume_{one\ unit } = 1m^3

<u>By </u><u>Unitary</u><u> Method</u><u> </u><u>:</u><u>-</u><u> </u>

Volume of two cubes , will be :-

\rm\implies Volume_{two\ unit } = 2m^3

<u>Volume</u><u> of</u><u> </u><u>one </u><u>layer </u><u>:</u><u>-</u><u> </u>

\rm\implies Volume_{one\ layer } = 4m^3

<u>Volume</u><u> of</u><u> </u><u>six </u><u>layers </u><u>:</u><u>-</u><u> </u>

\rm\implies Volume_{6\ layers } = 4m^3\times 6 \\\\\rm\implies \boxed{\rm Volume_{6\ layers } = 24 \ m^3}

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Answer:

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Step-by-step explanation:

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2 years ago
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7nadin3 [17]
It is 255 cm^2

This is a very basic area problem. You should try refreshing on some of your multiplication and addition skills. Try reading patterns, maybe. Also learning geometric proofs is VITAL.
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3 years ago
Read 2 more answers
A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

Z = \frac{X - \mu}{s}

X = 205

Z = \frac{X - \mu}{s}

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

Z = \frac{X - \mu}{s}

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
{(-3,9), (-2, 4), (0, 0), (1, 1)}<br> Find the inverse
Elena-2011 [213]

Answer:

Step-by-step explanation:

to find the inverse, just switch x and y

so if u have these points : (-3,9) , (-2,4), (0,0), (1,1)

the inverse would be : (9,-3) , (4,-2), (0,0), (1,1)

5 0
3 years ago
Which equation can be used to find 30 percent of 600
agasfer [191]
A/b *100
For example,
30/600.
30/600=0.05
0.05*100=5%
5 0
3 years ago
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