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3 years ago

Which two lines are parallel 3x+y=-2 2y-6x=4 2y=-6x-8

1 answer:

5 0

To start, solve each equation for y.
1st equation) 3x+y=-2, subtract 3x, y=-3x-2
2nd equation) 2y-6x=4, add 6x, 2y=6x+4, divide by 2, y=3x+2
3rd equation) 2y=-6x-8, divide by 2, y=-3x-4
Now, for lines to be parallel, their slope must be the same. Using the equation y=mx+b where m is slope, you can determine the slope of each line.
1st line) y=-3x-2, slope of -3
2nd line) y=3x+2, slope of 3
3rd line) y=-3x-4, slope of -3
Comparing these lines, you can see that only lines 1 and 3 have the same slope, making those your parallel lines.

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seraphim [82]

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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 $Z = 1.175$ .

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

$1.175 = \frac{48 - 43.4}{\sigma}$

$1.175\sigma = 4.6$

$\sigma = \frac{4.6}{1.175}$

$\sigma = 3.91$

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

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3 years ago

Lisa's store collects 5% sales tax on every item sold. If she collected $22.00 in sales tax, what was the cost of the items her

Ede4ka [16]

Since we are looking for the principal amount, then all we have to do is reverse the process of getting the amount of tax. In order to get the principal, you just have to divide 22 with 0.05. The answer is 440 so that is the principal amount you are looking for.

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3 years ago