Given f (x) = 4x2 – 8x + 14 and g(x) = 5x + 3: Find (gºf)(4)

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 is 3 = 5x - 12?

zepelin [54]

Answer:

x = 3

Step-by-step explanation:

3=5x-12

Rearrange the Equation.

5x - 12 = 3

Add 12 to both sides.

5x - 12 + 12 = 3 + 12

Simplify

5x = 15

Divide both sides by 5

5x/5 = 15/5

x = 3

5 0

4 years ago

Lewis is 0.9 metres tall. Tim is 0.15 metres taller than Lewis. How tall is Tim?

Luda [366]

Answer:

D33Z NUTZ

Step-by-step explanation:

BAHHAHAHAHHAH louis is 5'8

7 0

3 years ago

Read 2 more answers

(1/3)•(-2) = ? Please answer ASAP!! :)

Andre45 [30]

Answer:

-.6 repeating

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Mr.V's trail mix uses 1/2cup of peanuts, 2 1/4 cups raisins, and he uses 2 times more sunflower seeds than raisins.How many tota

ladessa [460]

Answer:

The total number of cups is 9 1/2 cups

Step-by-step explanation:

Here, we are interested in calculating the total cups of trail mix that Mr V can make.

From the question, we are told that he used 1/2 cups of peanuts, 2 1/4 cups of raisins and 2 times more sunflower seeds than raisins.

So basically, we need to find the number of cups of sunflower seeds used.

The information we have here is that he used 2 times more of raisins;

Thus, the number of cups of sunflower would be 2 * 2 1/4 = 2 * 9/4 = 9/2. But practically is 9/2 , two times more than 2 1/4? NO!

What we should do here is to add 9/2 to 2 1/4. In that case, the difference between the two will be 2 times the cups of raisins;

So 9/2 + 9/4 = (18 + 9)/4 = 27/4

So the total number of cups of trail mix that can be made will be;

1/2 + 27/4 + 9/4 = (2 + 27 + 9)/4 = 38/4 = 19/2 = 9 1/2 cups

7 0

3 years ago