Solve the equation for the indicated variable :

Mathematics

1 answer:

sveta [45]3 years ago

8 0

Y = 3/8(x + 4)....multiply both sides by 8/3, eliminating the 3/8 o the right
8/3y = x + 4....now subtract 4 from both sides
8/3y - 4 = x <==

n = m^2 - (n + 3)
n = m^2 -n - 3...add n to both sides
n + n = m^2 - 3
2n = m^2 - 3...add 3 to both sides
2n + 3 = m^2...take sqrt of both sides, eliminating the ^2
sqrt (2n + 3) = m or m = - sqrt (2n + 3) <==

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Ludmilka [50]

Answer:

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Find a side of an equilateral triangle with a 12 inch altitude

saveliy_v [14]

Since the triangle is an equilateral triangle we know all of it's sides must be the same length, with that in mind the angles that make up the triangle must be equal as well. Knowing that a triangle's three interior angles make up 180 degrees we know that the size of each angle must be one third of this (as each angle must be equal).

180/3 = 60

then we may split the triangle along it's altitude into two special right triangles
more specifically two 30-60-90 triangles.

this means that the side with 30 degrees will be some value "x" where the side for 60 degrees will be related as it is "x*sqrt(3)" and the hypotenuse (which would be the side of the triangle) would be proportionally "2x"

this would mean that the altitude is the side associated with the 60 degree angle as such we can solve for "x" using this.

12= x*sqrt(3)
12/sqrt(3)=x
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now we may solve for the side length of the triangle which is "2x"

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3 years ago

The U.S. Bureau of Labor Statistics reports that of persons who usually work full-time, the average number of hours worked per w

alukav5142 [94]

Answer:

The standard deviation of number of hours worked per week for these workers is 3.91.

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

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem we have that:

The average number of hours worked per week is 43.4, so $\mu = 43.4$ .

Suppose 12% of these workers work more than 48 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for these workers.

This means that the Z score of $X = 48$ has a pvalue of 0.88. This is Z between 1.17 and 1.18. So we use $Z = 1.175$ .