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3 years ago

5

The high temperature one day was 30 Fahrenheit. Then the temperature dropped 23 degrees during the night. Does the expression 30

+ (-23) represent the temperature at night? Explain.

1 answer:

erastovalidia [21]3 years ago

5 0

Answer:

This is a single a step problem. When you subtract a positive you can flip the signs.

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PLZZZZZZZ HELP ASAP Figure JKL is reflected about the y-axis to obtain figure J’K’L’: A coordinate plane is shown. Triangle JKL

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A i think

Step-by-step explanation:

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What are the measures of anglss a, b, and c? Show your work and explain your answers.

alexgriva [62]

A is 40

B is 50

C is 115

Explanation, A is the same as the opposite, A + B + 90 = 180, and C + 65 = 180

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3 years ago

Solve: 2x+3y=1<br> y=-2x+11

Sauron [17]

Answer:

(8, -5); x=8; y=-5

Step-by-step explanation:

i'll be solving via substitution

2x+3y=1; y=-2x+11

2x + 3(-2x +11) = 1

2x -6x +33 = 1

-4x = -32

x = 8

2(8) + 3y = 1

16 + 3y = 1

3y = -15

y = -5

(8, -5)

Check:

-5 = -2(8) + 11

-5 = -16 + 11

-5 = -5

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3 years ago

If the divisor is 30, what is the least 3 digit dividend that will give you a remainder of 8?

m_a_m_a [10]

The dividend would be 128 because 128 divided by 30 equals to 4 R 8

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3 years ago

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

(c) y = -12.629 + 0.0654x

(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.

<u> x </u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>

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

<u>3675 </u> <u> 248.0 </u> <u> 911400 </u> <u>13505625</u> <u> 61504 </u>

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.

<u> x </u> <u> y </u> <u>Estimated</u> <u>Residual </u>

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