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3 years ago

Solve 2x+y=-2 when y=0.5x+3

Mathematics

2 answers:

Tju [1.3M]3 years ago

7 0

That should be the answer if I did it correctly

tester [92]3 years ago

7 0

Answer:

x=-.5

Step-by-step explanation:

y=0.5x+3

2x+.5x+3=-2

2.5x+3=-2

-3 -3

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

2.5x=-5

x=-.5

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Compare properties of squares and rhombi to properties of other quadrilaterals by answering each question. Write a brief explana

GuDViN [60]

Hey there! Hello!

Not sure if you still need these answers, but I'd love to help out if you do!

Now, I want you to go ahead and think of some stuff that's true for squares. To name a few, the opposite sides are going to be parallel to one another, all the angles are 90°, all the sides are the same length, and both diagonals are going to be perpendicular and equal in length. I'm sure there's even more, but I'll leave that to you. (BTW, by diagonals, I mean the lines that go through the the opposite diagonal corners).

What about rectangles? The opposite sides are going to be parallel to one another, the diagonals are going to be equal in length, and the angles are going to be 90°.

Now, rhombi. All sides are going to be equal, opposite sides are going to be parallel, the diagonally opposite angles will be equal to each other, and the diagonals bisect each other at 90°.

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3 years ago

Damon buys lumber worth $562. He gets 20% contractor discount. The sales tax is 6%. his credit card gives him 2% off. How much d

faltersainse [42]

Answer:

$467.05

Step-by-step explanation:

The price is $562

First, 20% off of that:

562 - 20% of 562 = 562 - 0.2(562) = $449.60

Second, he has to pay 6% tax on this amount, so:

6% = 6/100 = 0.06

449.60 + 0.06*449.60 = $476.58

He won't be paying this amount, because paying through credit card will give him 2% discount on this, so:

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4 years ago

You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each nig

brilliants [131]

Answer:

Confidence interval

$8.98-2.2\frac{1.29}{\sqrt{12}}=8.16$

$8.98+2.2\frac{1.29}{\sqrt{12}}=9.80$

And the margin of error would be:

$ME=2.2\frac{1.29}{\sqrt{12}}=0.819$

Step-by-step explanation:

For this case we have the followig dataset:

DATA: 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

We can calculate the mean and the deviation with the following formulas:

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

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$\bar X= 8.98[/tex[tex]s = 1.29$

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by:

$df=n-1=12-1=11$

The Confidence level is 0.95 or 95%, the value of significance is $\alpha=0.05$ and $\alpha/2 =0.025$ , and the critical value would be $t_{\alpha/2}=2.20$

Repplacing the info we got:

$8.98-2.2\frac{1.29}{\sqrt{12}}=8.16$

$8.98+2.2\frac{1.29}{\sqrt{12}}=9.80$ And the margin of error would be:

$ME=2.2\frac{1.29}{\sqrt{12}}=0.819$

7 0

3 years ago

find the area of a parrellelogram whose base is of length 25 cm and the corresponding altitude is of length 8.4 cm

Free_Kalibri [48]

Answer:

Check the above photo and do the sum

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2 years ago

Consider the given data. x 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 8 10 12 12 Use the least-squares regression to fit a straight

levacccp [35]

Answer:

See below

Step-by-step explanation:

By using the table 1 attached (See Table 1 attached)

We can perform all the calculations to express both, y as a function of x or x as a function of y.

Let's make first the line relating y as a function of x.

y as a function of x

(y=response variable, x=explanatory variable)

$\bf y=m_{yx}x+b_{yx}$

where

$\bf m_{yx}$ is the slope of the line

$\bf b_{yx}$ is the y-intercept

In this case we use these formulas:

$\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}$

$\bf b_{yx}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum x^2$ with $\bf (\sum x)^2$

Performing our calculations we get:

$\bf m_{yx}=\frac{(83)(95)^2-(95)(923)}{10*1277-(95)^2}=176.6061$

$\bf b_{yx}=\frac{10*923-(95)(83)}{10(1277)-(95)^2}=0.3591$

So the equation of the line that relates y as a function of x is

In order to compute the standard error $\bf S_{yx}$ , we must use Table 2 (See Table 2 attached) and use the definition

$\bf s_{yx}=\sqrt{\frac{(y-y_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{yx}=\sqrt{\frac{39515985}{10}}=1987.8628$

Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.

So now we have:

x as a function of y

(x=response variable, y=explanatory variable)

$\bf x=m_{xy}y+b_{xy}$

where

$\bf m_{xy}$ is the slope of the line

$\bf b_{xy}$ is the x-intercept

In this case we use these formulas:

$\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}$

$\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum y^2$ with $\bf (\sum y)^2$

Remark: If you wanted to draw this line in the classical style (the independent variable on the horizontal axis), you would have to swap the axis X and Y)

Computing our values, we get

$\bf m_{xy}=\frac{(95)(83)^2-(83)(923)}{10*743-(83)^2}=1068.1072$

$\bf b_{xy}=\frac{10*923-(95)(83)}{10(743)-(83)^2}=2.4861$

and the line that relates x as a function of y is

To find the standard error $\bf S_{xy}$ we use Table 3 (See Table 3 attached) and the formula

$\bf s_{xy}=\sqrt{\frac{(x-x_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{xy}=\sqrt{\frac{846507757}{10}}=9200.5856$

In both cases the correlation coefficient r is the same and it can be computed with the formula:

$\bf r=\frac{\sum xy}{\sqrt{(\sum x^2)(\sum y^2)}}$

Remark: This formula for r is only true if we assume the correlation is linear. The formula does not hold for other kind of correlations like parabolic, exponential,..., etc.

Computing the correlation coefficient :

$\bf r=\frac{923}{\sqrt{(1277)(743)}}=0.9478$

5 0

4 years ago