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2 years ago

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Mathematics

1 answer:

Firlakuza [10]2 years ago

7 0

Though these segments aren't marked congruent in the diagram, the two lines inside the circle making up the bases of the triangles are congruent as all radii are congruent. So the triangles are congruent by SAS.

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A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

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

Where:

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

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

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

2 years ago

1. A professional basketball used for league play has a diameter of 25 cm. Which of the following is closest to the volume of th

yKpoI14uk [10]

Answer:

V = 8,181.23 $cm^{3}$

Step-by-step explanation:

Unfortunately, we are not given any answer choices to choose from but using the information provided we can find the actual volume of the basketball. A basketball is made in the shape of a sphere and the formula for the volume of a sphere is the following...

V = $\frac{4}{3} * \pi * r^{3}$

radius of a circle/sphere is half of it's diameter. Since we are provided the diameter size we simply divide it by 2 which would give us 12.5cm. Now we simply plug this value into the formula and solve for V.

V = $\frac{4}{3} * \pi * 12.5^{3}$

V = $\frac{4}{3} * \pi * 1953.125$

V = 8,181.23 $cm^{3}$

5 0

2 years ago

How many days in the month

iren2701 [21]

January : 31 days.

February : February is the second and shortest month of the year in the Julian and Gregorian calendar with 28 days in common years and 29 days in leap years, with the quadrennial 29th day being called the leap day. It is the first of five months to have a length of less than 31 days, and the only month to have less than 30 days

March : 31 days.

April : 30 days.

May : 31 days.

June : 30 days.

July : 31 days.

August : 31 days.

Septembers : 30 days.

October : 31 days.

November : 30 days.

December : 31 days.

Hope this helps!

7 0

3 years ago

G (x)=x-3 and h(x)= square root of x, find(g o h) (25)

nevsk [136]

H(25) = sqrt25 = 5

g(5) = 5 - 3 = 2

answer is 2

7 0

2 years ago

I need help anyone please

liraira [26]

Answer:

Step-by-step explanation:

The slope is 2/4=1/2

The y-intercept is 3

Given the shaded area, y is going to be less than or equal to.

So B is correct

7 0

3 years ago