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3 years ago

Quadrilateral A' B'C'D' is the image of quadrilateral ABCD under a dilation with a scale factor of 3

Mathematics

1 answer:

Shtirlitz [24]3 years ago

8 0

Answer:

Step-by-step explanation:

A'B'C'D' is 3 times bigger than ABCD, so to get back to the original we gotta count the length of B'C' and devide by 3

$9 \div 3 = 3$

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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

Eric drove 113 miles on Monday. On Tuesday, he drove 33 miles less than Monday. How far did he drive both days?

Marat540 [252]

He drove 193 mile you subtract 33 from 113 which is 80 then add 80 and 113 together and you get 193

5 0

3 years ago

Read 2 more answers

Mr. Howard lost money on his investments at a rate of $7 per day. Which expression shows how much money he lost over the course

dalvyx [7]

Answer:

7 x 5 = 35 or the amount lost

Step-by-step explanation:

5 0

3 years ago

What is the value of the x-coordinate that is 9 units to the left of (4, -7)?

mylen [45]

Answer:

-5

Step-by-step explanation:

7 0

3 years ago

Find the greates common factor of the following monomials:2r^4s^2 and 36r^4s^3

ki77a [65]

The greatest common factor is 2 $r^{4} s^{2}$

This is because we start by taking the largest factor that goes into both coefficients. Since the first coefficient is 2, we have to try 2 and 1. Since 2 is larger and goes into 36 evenly, we use that.

Then we use the smallest number of each variable. There are 4 r's in both equations. So, that is the number that we take. There are 2 s's in the first term, so we take that number.

6 0

4 years ago