All categories

3 years ago

Can anyone help me wit this!!

Mathematics

1 answer:

dybincka [34]3 years ago

3 0

Answer:

See attachment for table values
y₁ = y₂ for x = 6

Step-by-step explanation:

In each case, put the x-value in the formula and do the arithmetic. If you're allowed, you can save some time and effort by realizing that the solution (x) will have to be an even number.

y₁ is an integer value for all integer values of x. y₂ is an integer value for even values of x only. y₁ and y₂ will both be integers (and possibly equal) only when x is even.

For example, for x = 6, we have

... y₁ = 3·6 - 8 = 18 -8 = 10

... y₂ = 0.5·6 +7 = 3 +7 = 10

That is, for x = 6, both columns of the table have the same number (10). That is, y₁ = y₂ for x = 6. The solution to the equation

... y₁ = y₂

... x = 6.

You might be interested in

The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The siderea

BartSMP [9]

Answer:

(a) See below

(b) r = 0.9879

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is

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

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

x y xy x² y²

36 0.22 7.92 1296 0.05

67 0.62 42.21 4489 0.40

93 1.00 93.00 20164 3.46

433 11.8 5699.4 233289 139.24

887 29.3 25989.1 786769 858.49

1785 82.0 146370 3186225 6724

2797 163.0 455911 7823209 26569

3675 248.0 911400 13505625 61504

9965 537.81 1545776.75 25569715 95799.63

(ii) Calculate the correlation coefficient

$r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}$

(c) Regression line

The equation for the regression line is

y = a + bx where

$a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}$

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

x y Estimated Residual

36 0.22 -10 10

67 0.62 -8 9

93 1.00 -7 8

142 1.86 -3 5

433 11.8 19 - 7

887 29.3 45 -16

1785 82.0 104 -22

2797 163.0 170 - 7

3675 248.0 228 20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

4 0

3 years ago

PLEASE HELP 15 points!! Todd has created the following diagram to prove the Pythagorean theorem. He drew right ABC with leg leng

masya89 [10]

Answer:

c^2 = a^2 + b^2. Hope this helps!

7 0

3 years ago

Read 2 more answers

Factor. z^2 -6z -16 simplify

leva [86]

(z-8) (z+2)
What I do to factor is find _x_=-16 and _+_=-6. -8x2=-16 and -8+2=-16. The coordinates for z if you were to graph this would be (8,0) and (-2,0)

3 0

3 years ago

Help please 9 and 10

DIA [1.3K]

9 is obtuse isosceles 10 is scalene,right

7 0

3 years ago

Finley's pumpkin had a mass of 6.5 kilograms before he carved it. After carving it, the pumpkin had a mass of 3.9 k.g.

Zarrin [17]

I believe the answer is 20%

3 0

3 years ago

Read 2 more answers