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3 years ago

I need help with this

Mathematics

1 answer:

OLga [1]3 years ago

3 0

Answer:

121

Step-by-step explanation:

The sum of the angles inside a triangle is always 180. The missing angle in the triangle must then be 180 -74 -47 = 59 degrees. The angles on a straight line add up to 180 degrees so x + 59 = 180. x = 180-59 = 121

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A flower bed is 2 meters wide and 5 meters long. What is the area of the flower bed in square feet? Round intermediate calculati

Troyanec [42]

Answer: 107.58 feet²

<u>Step-by-step explanation:</u>

Area (A) = length (L) x width (w)

Length (L) = 5 meters

width (w) = 2 meters

A = 5 meters x 2 meters

= 10 meters²

Next, convert meters into feet: 1 meter = 3.28 feet

$\frac{10meters^{2}}{} * \frac{(3.28 feet)^{2}}{(1meter)^{2}}}$

= 107.58 feet²

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3 years ago

Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?

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3 years ago

Read 2 more answers

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

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