For the following paired data, (1) Calculate the correlation coefficient, r, and (2) at the 0.05 significance level, determine whether there exists a linear correlation. x | 2 4 5 6y | 6 9 8 10

Linear correlation exists

Step-by-step explanation:

Given the data :

X : | 2 4 5 6

Y : | 6 9 8 10

Using technology to fit the data and obtain the correlation Coefficient of the regression model,

The Correlation Coefficient, r is 0.886

To test if there exists a linear correlation :

Test statistic :

T = r / √(1 - r²) / (n - 2)

n = number of observations

T = 0.886 / √(1 - 0.886²) / (4 - 2)

T = 0.866 / 0.3535845

T = 2.449

Comparing Pvalue with α

If Pvalue < α ; Reject H0

Pvalue = 0.1143

α = 0.05

Pvalue > α ; We reject the null and conclude that linear correlation exists

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.