( pls help me :( )

Nsider the following system of equations y=6x^2+1, y=x^2+4

sp2606 [1]

The given equations are y= 6x^2+1 and y=x^2+4

Both the equations equal y so we can make them equal

6x^2+1=x^2+4

To bring x term on one side we subtract x^2 both sides

6x^2-x^2+1=4

5x^2+1=4

To isolate x term we subtract 1 both sides

5x^2=4-1

5x^2=3

Dividing by 5 both sides

X^2=3/5

Taking root of both sides we have:

X=±√⅗

Substituting x value to find y

When x=+√⅗=0.7745

Y= 6x^2+1

Y=6(3/5)+1

Y= 18/5+1

Y=23/5 =4.6

When x= -√⅗=-0.7745

Y= 6(3/5)+1

Y=23/5=4.6

Point of intersections are ( 0.7745,4.6) and (-0.7745,4.6)

7 0

3 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

A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defe

denis-greek [22]

By definition of conditional probability,

$P(A_2\mid A_1)=\dfrac{P(A_1\cap A_2)}{P(A_1)}$

The inclusion-exclusion principle tells us

$P(A_1\cap A_2)=P(A_1)+P(A_2)-P(A_1\cup A_2)=0.12+0.08-0.14=0.06$

Then

$P(A_2\mid A_1)=\dfrac{0.06}{0.12}=0.5000$

8 0

4 years ago

Please help. Geometry circles 20 points!

slavikrds [6]

See the attached pictures:

7 0

3 years ago

Write an equation for 15 is 15% of what number? Use x for your variable

iVinArrow [24]

Reading through the problem, we have "15 is",

that's "15 =", 15%, 15/100, "of", times, "what number", x.

So our equation reads 15 = 15/100 · x.

5 0

3 years ago