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2 years ago

How to solve x=6y-11 and 3x-2y=-1 by substitution

Mathematics

1 answer:

vagabundo [1.1K]2 years ago

7 0

Substitute x into the second equation:
3(6y-11)-2y=-1
18y-33-2y=-1
16y=32
y=2
Then put the y value into the first equation to get x:
x=6(2)-11
x=1
There you go!

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2 years ago

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A researcher is exploring the notion that there is an economy of scale in raising children. While having one child might add to

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Answer:

The probability is $G = 85%$

Step-by-step explanation:

From the question we are told that

The percentage of parents that have one child under 18 in their homes is k = 15%

The percentage of parents that have two children is T = 65%

The percentage of parents that have three or more children is Y = 20%

Generally the probability that any given family who is selected have two or more children at home is mathematically evaluated as

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2 years ago

given the points a (-1,2) and (7,14), find the coordinates of the point p on directed line segment ab that partitions ab in the

Vinvika [58]

Check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
a(-1,2)\qquad b(7,14)\qquad
\qquad 1:3
\\\\\\
\cfrac{aP}{Pb} = \cfrac{1}{3}\implies \cfrac{a}{b} = \cfrac{1}{3}\implies 3a=1b\implies 3(-1,2)=1(7,14)
\\\\
-------------------------------\\\\
{ P=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}$

$\bf -------------------------------\\\\
P=\left(\cfrac{(3\cdot -1)+(1\cdot 7)}{1+3}\quad ,\quad \cfrac{(3\cdot 2)+(1\cdot 14)}{1+3}\right)
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2 years ago

A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swim

Vitek1552 [10]

If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.

<u>Given the following data:</u>

Width of rectangle = 6 meters

Length of rectangle = 8 meters

To determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.

Note: The diagonal side of the rectangular pool represents the hypotenuse.

Mathematically, Pythagorean's theorem is given by the formula:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

Substituting the given parameters into the formula, we have;

$Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}$

Hypotenuse = 10 meters.

Read more here: brainly.com/question/18890335

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1 year 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 $Z = 1.175$ .