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EastWind [94]
3 years ago
6

SHOW YOUR WORK AND PLEASE DON'T GUESS THANX!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
Leno4ka [110]3 years ago
5 0
Here: Mean = 55 + 62 + 61 + 54 + 68 + 72 + 59 + 61 + 70 + 15 / 10
= 57.7

Range = Greatest - Lowest = 72 - 15 = 57

In short, Your Mean is 57.7 & Range is 57

Hope this helps!
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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

5 0
3 years ago
Use the information given in the table on the right to complete each of the following statements.
tino4ka555 [31]

.5

46

16%

Step-by-step explanation:

Still stuck? Get 1-on-1 help from an expert tutor now.

6 0
2 years ago
In the figure, m<2 = 83, and m<21 = 68. Find the measure of each angle
zhuklara [117]

Answer:

m<1 = 97

m<2 = 83

m<3 = 112

m<4 = 68

m<5 = 112

m<6 = 68

m<7 = 97

m<8 = 83

m<9 = 97

m<10 = 83

m<11 = 112

m<12 = 68

m<13 = 112

m<14 = 68

m<15 = 97

m<16 =  83

Step-by-step explanation:

8 0
3 years ago
The set of ordered pairs represents a functuon. Write a rule represents the function. (0,0),(1,6),(2,24),(3,54),(4,96)
Lubov Fominskaja [6]
It’s super self explanatory it’s right there
3 0
3 years ago
A group of friends was working on a student film. They spent $330 on costumes, which was 55% of their total budget. What was the
wariber [46]

Answer:

$600

Step-by-step explanation:

Let "x" represent their total budget for the film.

Amount spent on costumes = $330

Percent spent on costumes = 55%

Therefore:

55% of x = $330

55/100 × x = 330

55x/100 = 330

Cross multiply

55x = 100 × 330

55x = 33,000

Divide both sides by 55

x = 33,000/55

x = 600

Total budget = x = $600

7 0
2 years ago
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