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3 years ago

Solve by the substitution method 2x + 9y=41 - 4x + y=13

Mathematics

1 answer:

melisa1 [442]3 years ago

6 0

Answer:

x=-2, y=5. (-2, 5).

Step-by-step explanation:

2x+9y=41

-4x+y=13

---------------

2(2x+9y)=2(41)

-4x+y=13

-----------------------

4x+18y=82

-4x+y=13

------------------

19y=95

y=95/19

y=5

2x+9(5)=41

2x+45=41

2x=41-45

2x=-4

x=-4/2=-2

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The following six independent length measurements were made (in feet) for a line: 736.352, 736.363, 736.375, 736.324, 736.358, a

horrorfan [7]

Answer:

Assuming population data

$\sigma = \sqrt{0.000354}=0.0188$

Assuming sample data

$s = \sqrt{0.000425}=0.0206$

Step-by-step explanation:

For this case we have the following data given:

736.352, 736.363, 736.375, 736.324, 736.358, and 736.383.

The first step in order to calculate the standard deviation is calculate the mean.

Assuming population data

$\mu = \frac{\sum_{i=1}^6 X_i}{6}$

The value for the mean would be:

$\mu = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

And the population variance would be given by:

$\sigma^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6}$

And we got $\sigma^2 =0.000354$

And the deviation would be just the square root of the variance:

$\sigma = \sqrt{0.000354}=0.0188$

Assuming sample data

$\bar X = \frac{\sum_{i=1}^6 X_i}{6}$

The value for the mean would be:

$\bar X = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

And the population variance would be given by:

$s^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6-1}$

And we got $s^2 =0.000425$

And the deviation would be just the square root of the variance:

$s = \sqrt{0.000425}=0.0206$

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3 years ago

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konstantin123 [22]

Answer:

$a=\sqrt{7}$

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Step-by-step explanation:

Please find the attachment.

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To find the side length a, we will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle.

$a^2+b^2=c^2$

Upon substituting our given values in Pythagoras theorem, we will get:

$a^2+3^2=4^2$

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$a^2+9-9=16-9$

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Take square root of both sides:

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Therefore, the length of side 'a' is $\sqrt{7}$ units.

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Step-by-step explanation:

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