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3 years ago

Plz help me idk what t0o do

Mathematics

1 answer:

77julia77 [94]3 years ago

5 0

Answer:

$y = - \frac{1}{2} x + 2$

Step-by-step explanation:

According to the chart for the values of x (input) the corresponding values of y (output) are given.

The slope of the equation is constant and given by $m = - \frac{1}{2}$ .

If we want to check the slope to be constant then we can use the table and the values of x and y.

The first point ( $x_{1},y_{1}$ ) ≡ (-2,3)

The second point ( $x_{2},y_{2}$ ) ≡ (8,-2)

The third point ( $x_{3},y_{3}$ ) ≡ (10,-3)

The fourth point ( $x_{4},y_{4}$ ) ≡ (20,-8)

Now, we can check that slope of the straight line is constant for all those values.

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 2 - 3}{8 - (- 2)} = - \frac{1}{2}$

$\frac{y_{3} - y_{2}}{x_{3} - x_{2}} = \frac{- 3 - (- 2)}{10 - 8} = - \frac{1}{2}$

$\frac{y_{4} - y_{3}}{x_{4} - x_{3}} = \frac{- 8 - (- 3)}{20 - 10} = - \frac{1}{2}$

Now, Let us assume that the equation of the straight line is $y = - \frac{1}{2} x + c$ ....... (1)

Now, we have to find the value of c.

This straight line passes through ( $x_{1},y_{1}$ ) ≡ (-2,3) point.

So, the value of c can be calculated from the equation (1) as, c = 3 - 1 = 2

Therefore, $y = - \frac{1}{2} x + 2$ is the required equation. (Answer)

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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 :

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

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2 years ago

If AM = 7, MB = 6, and CM = 8, find CD.

geniusboy [140]

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3 years ago

Factor the polynomial. x2 - 5xy + 6y2 A) (x - 3)(x - 2) B) (x - 6y)(x + y) C) (x - 3y)(x - 2y) D) (x + 3y)(x + 3y)

Elden [556K]

X^2 - 5xy + 6y^2 = <span>(x - 3y)(x - 2y)

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hope that helps</span>

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2 years ago

The volume of a shampoo filled into a container is uniformly distributed between 370 and 385 milliliters. (a) What are the mean

Olenka [21]

Answer:

(a) mean = 377.5ml. standard deviation = 4.33

(b) 0.333

Step-by-step explanation:

(a)The mean:

$\mu = \frac{385 + 370}{2} = 377.5 ml$

The standard deviation:

$\sigma = \frac{385 - 370}{\sqrt{12}} = 4.33$

(b)

$P(x < 375) = \frac{375 - 370}{385 - 370} = \frac{1}{3} \approx 0.333$

(c)P(x > m) = 0.95

$\frac{m - 370}{385 - 370} = 0.95$

$m - 370 = 14.25$

$m = 384.25ml$

So the volumn of shampoo should be 384.25ml to exceed 95% of containers.

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3 years ago

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