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3 years ago

15

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. x y 32 24 16 8 8

6 A. yes; y = 0.5x B. yes; y = 2x C. yes; y = 1.5x D. no; y does not vary directly with x.

1 answer:

densk [106]3 years ago

3 0

Direct variation is modeled by an equation of y = kx.
If all the pairs of values in the table give us a constant proportion, then that's a direct variation.

As we can see, 8/32 = 1/4 ≠ 8/24 = 1/3. So that's not a direct variation.

The answer choice is D.

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Solving systems of equations using substitution p=q+2<br> 4p+3q= -27

GREYUIT [131]

Ok, so you are given the value of P=q+2

The substitution method tells us that we must insert the value we know, into the second equation, 4P+3q= -27

Doing so will give us 4(q+2)+3q= -27

For right now, lets just focus on the first part, 4(q+2)

We can simplify this by distributing(multiplying) the 4 to whats inside the variables.

This will give us 4q+8

now lets add this back to the rest of the equation >>> 4q+8+3q = -27

We can further simplify by adding like terms >>> 7q+8 = -27

subtract the 8 from both sides >>> 7q = -35

now divide both sides by 7 >>> q = -35/7

Therefor q = -5

EDIT*

now that we know q = -5 we can put q into the equation for P !

we know that p=q+2

so lets put q in now >>> p=(-5)+2

and simplify>>> p = -3

I hope this helps:)

6 0

4 years ago

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p

ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

5 0

3 years ago

If parallelogram RSTV has diagonals then RSTV must also be a _______. square and a rectangle rhombus and a rectangle rhombus rec

andrew11 [14]

<span>a rectangle rhombus(parallelogram) since even a parallelogram has diagonals</span>

5 0

3 years ago

PLEASE HELP!!!!!!!!! WILL GIVE BRAINLIEST!!!!!!!

n200080 [17]

12 dimes and 48 nickles is the correct answer to the problem

6 0

3 years ago

Read 2 more answers

I need help on Area plz

nydimaria [60]

Answer:139 cm squared

Step-by-step explanation:

First separate it:

10x3

7x7

4x15

These are the 3 rectangles that make up this shape

Then multiply

10x3=30

7x7=49

4x15=60

Then add your answers

30+49+60=139cm squared

8 0

3 years ago