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3 years ago

Which statement is true? I know it’s not the first one.

Mathematics

1 answer:

agasfer [191]3 years ago

8 0

Answer:

2nd one: AB = 6

Step-by-step explanation:

Because PQ is 4 (Pythagorean triples), you can prove that triangle PBQ is congruent to PAQ by HL. You can then say AQ is equal to 3 becasue of CPCTC. AQ+QB=AB, or 3+3=6. AB=6

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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

the length , breadth and height of a cuboid is 2x^2y cm,5y^2z cm and 4z^2x cm. The volume of the cuboid is ...............

kondor19780726 [428]

For this case we have that by definition, the volume of a cuboid is given by:

$V = L * A * h$

Where:

L: It's the long

A: It is the width

h: It is the height

According to the problem data we have:

$L = 2x ^ 2y \ cm\\A = 5y ^ 2z \ cm\\h = 4z ^ 2x \ cm$

So, the volume of the cuboid is:

$V = (2x ^ 2y) (5y ^ 2z) (4z ^ 2x)\\V = 10x ^ 2y ^ 3z (4z ^ 2x)\\V = 40x ^ 3y ^ 3z ^ 3$

Finally, the volume of the cuboid is: $V = 40x ^ 3y ^ 3z ^ 3$

Answer:

$V = 40x ^ 3y ^ 3z ^ 3$

7 0

3 years ago

One side of triangle is 3 times the shortest side. The third side is 24 feet more than the shortest side. The perimeter is 94 .

Gemiola [76]

Answer: x+3x+X+24=94

5x+24=94

-24. -24

5x=70

X=14

One side is 14 second side 3(14)=42. Third side 14+24= 38

14+42+38=94

Step-by-step explanation:

5 0

3 years ago

I need this, please. I am willing to give brainly

IgorLugansk [536]

Answer:

x=28

Step-by-step explanation:

180= 38 + (4x+30)

142= (4x+30)

112=4x

x=28

4 0

3 years ago

A circular lid on a to-go cup has a diameter of 4 inches. What is the area of the lid to the nearest hundredth? (Use 3.14 as an

77julia77 [94]

Answer:

The answer is A) 12.56 square inches

Step-by-step explanation:

The equation to find the answer is 3.14×r²

r standing for radius. To find the diameter, you simply multiply the radius by 2.

Because they already gave us the diameter, the equation to solve this question is 3.14×4

3.14×4=12.56

3 0

3 years ago