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Alex Ar [27]
3 years ago
7

A triangular pyramid has a height of 18 yards and base with an area of 330 square yards. What is the volume of the pyramid?

Mathematics
1 answer:
Zanzabum3 years ago
5 0
18*330
multiply thats your answer

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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random
yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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.

For sums, we have that the mean is \mu*n and the standard deviation is s = \sigma \sqrt{n}

In this problem, we have that:

\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

Z = \frac{4000 - 3500}{160}

Z = 3.13

Z = 3.13 has a pvalue of 0.9991

X = 3000

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

Z = \frac{3000 - 3500}{160}

Z = -3.13

Z = -3.13 has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

5 0
3 years ago
A square is cut into three equal rectangles. How does the area of the square compare to the sum of the areas of the three rectan
ludmilkaskok [199]

Answer:

A?

Step-by-step explanation:

If the square was split into 3 rectangles the 3 rectangles sum up to the square.

4 0
3 years ago
Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of
Lubov Fominskaja [6]

length = 8ft
height = 4 in
width = w ft --> u looking for this

convert in to ft for the height:

4 in (1 ft / 12 in) = 1/3 ft

You know that:
1 cubic yard = $ 98
? cubic yard = $58.07

Solve for ? cubic yard:
? cubic yard = 58.07/98 = 0.592551

convert this in cubic feet:
1 yard = 3 feet
0.59255 cubic yard (27 cubic ft/1 cubic yard) = 15.99887755 cubic ft

Now solve for the width:
length x width x height = ? cubic ft.
width = ? cubic ft / (length x height) =15.99887755 cubic ft/[(8ft)(1/3 ft )] = 5.999579082 ft

approx 6 ft
4 0
3 years ago
Please, I need help with this math question.
kondaur [170]

Step-by-step explanation:

Indeed the brainliest is t

8 0
2 years ago
If a bottle rotates through 270 degrees in 3 seconds,how degrees does it rotate in 2 seconds?
makkiz [27]
It rotates 180 degrees because its like 90 +90+180
 180+90=270
7 0
3 years ago
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