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Eduardwww [97]
3 years ago
7

A gemstone is cut in the shape of a triangular pyramid. The area of the base of the pyramid is 42 square millimeters. The height

of the pyramid is 4 millimeters. What is the volume of the gemstone? (Recall the formula V = one-third B h.)
Mathematics
1 answer:
never [62]3 years ago
7 0

Answer:

the volume of the gemstone is 56 millimeters^3

Step-by-step explanation:

The computation of the volume of the gemstone is shown below:

As we know that

The volume of the triangular pyramid is

= (1 ÷ 3) × (base area) × h

Now put the given values to the above formula

= 1 ÷ 3 × 42 × 4

=  56 millimeters^3

Hence, the volume of the gemstone is 56 millimeters^3

The above formula should be used and the same should be considered

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7 0
2 years ago
How is this proportional?
Alja [10]

Answer:

you are subtracting 1.40 everytime to get the number at the bottom

Step-by-step explanation:

2 - 1.40 = 1.40

3 - 1.40 = 2.40

6 - 1.40 = 5.40

7 - 1.40 = 6.40

4 0
2 years ago
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.

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3 years ago
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lukranit [14]

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8)525+3w because you have to add his original total to the amount of cds he will get and if he gets 3 every week that's 3w and then you add them to get the new total.

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3 years ago
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Answer:

8.88 dollars so D

Step-by-step explanation:

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