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Mathematics

2 answers:

mart [117]3 years ago

5 0

The first one because it’s the actual formula for a sphere and it has pie at the end because we are solving for a sphere

pychu [463]3 years ago

5 0

Archimedes solved this in his famous book Sphere and Cylinder in 225 BC. The result is reportedly on his tombstone.

The ratio of the volume of the radius r sphere to the cylinder radius r, height 2r is

$\dfrac 2 3$

The same ratio is the ratio of the surface area of the sphere to that of the cylinder (including the ends).

Answer: Last choice

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The breaking strength of a cable is assumed to be lognormally distributed with a mean of 75 and standard deviation of 20. • If t

son4ous [18]

Answer:

If the load of magnitude 50 is hung from the cable, determine the probability of failure of the cable?

There is a 10.56% probability of failure of the cable.

If the load can take values 30, 50, and 70 with probabilities 0.2, 0.35, and 0.45 respectively, determine the probability of failure of the cable?

There is a 15.87% probability of failure of the cable.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

The breaking strength of a cable is assumed to be lognormally distributed with a mean of 75 and standard deviation of 20. This means that $\mu = 75, \sigma = 20$ .

If the load of magnitude 50 is hung from the cable, determine the probability of failure of the cable?

This is the pvalue of Z when $X = 50$ .

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

$Z = \frac{50 - 75}{20}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056.

There is a 10.56% probability of failure of the cable.

If the load can take values 30, 50, and 70 with probabilities 0.2, 0.35, and 0.45 respectively, determine the probability of failure of the cable?

Now we have that

$X = 0.2(30) + 0.35(50) + 0.45(70) = 55$