How can i get the volume??

Write the square of the binomial as a polynomial: (-1 1/3p + 6q)^2

Thepotemich [5.8K]

Answer:

$\frac{16}{9}$ p² -16pq + 36q²

Step-by-step explanation:

Given

(- $\frac{4}{3}$ p + 6q)²

= (- $\frac{4}{3}$ p + 6q)(- $\frac{4}{3}$ p + 6q)

Each term in the second factor is multiplied by each term in the first factor, that is

- $\frac{4}{3}$ p(- $\frac{4}{3}$ p + 6q) + 6q(- $\frac{4}{3}$ p + 6q)

= $\frac{16}{9}$ p² - 8pq - 8pq + 36q² ← collect like terms

= $\frac{16}{9}$ p² - 16pq + 36q²

5 0

4 years ago

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

3 years ago

What number when substituted for the variable, makes the equation 4/5x = 20 true?

ivolga24 [154]

Sent a picture of the solution to the problem (s).

3 0

3 years ago

Read 2 more answers

Consider the equation below.

Eduardwww [97]

Answer:

The equation has no solutions .

Step-by-step explanation:

Given as :

<u>The linear equation is </u>

$\dfrac{3}{4}$ (24 -16 x) = $\dfrac{-2}{3}$ (18 x -27)

Or, $\dfrac{3}{4}$ ×24 - $\dfrac{3}{4}$ × 16 x = $\dfrac{-2}{3}$ × 18 x - $\dfrac{-2}{3}$ × 27

Or, $\dfrac{3}{4}$ ×24 - $\dfrac{3}{4}$ × 16 x = $\dfrac{-2}{3}$ × 18 x + $\dfrac{2}{3}$ × 27

Or, $\frac{3\times 24}{4}$ - $\frac{3\times 16 x}{4}$ = $\frac{-2\times 18 x}{3}$ + $\frac{2\times 27 x}{3}$

Or, 3 × 6 - 3 × 4 x = - 2 × 6 x + 2 × 9

Or, 18 - 12 x = - 12 x + 18

Or, 18 - 18 = - 12 x + 12 x

or, 0 = 0

∵ The linear equation has no variables , so the equation has no solution

Hence,The equation has no solutions . Answer

8 0

3 years ago

How to find circumference of circle? What is formula?

Lapatulllka [165]

C= pi multiplied by diameter

4 0

3 years ago

Read 2 more answers