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3 years ago

The sum of 5 consecutive integers is 110

Mathematics

1 answer:

nikdorinn [45]3 years ago

3 0

Answer:

Step-by-step explanation:

Let the five consecutive integers be (x - 2 ) , (x - 1) , (x) , (x + 1) , (x + 2)

(x - 2 ) + (x - 1) + (x) + (x + 1) + (x + 2) = 110

x - 2 + x -1 + x + x +1 + x + 2 = 110

5x = 110

x = 110/5

x = 22

The consecutive numbers are: 20,21,22,23,24

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(a) See below

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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

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

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(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

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(c) Regression line

The equation for the regression line is

y = a + bx where

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(d) Residuals

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

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

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