Based on the scatterplot and the value of the correlation coefficient, it would make sense to test the significance of this observed linear relationship between latitude and melanoma mortality rate. The appropriate hypotheses are:

a. H0: melanoma mortality rate is related to latitude
Ha: melanoma mortality rate is not related to latitude
b. H0: melanoma mortality rate is not related to latitude
Ha: melanoma mortality rate is related to latitude
c. H0: melanoma mortality rate is linearly related to latitude
Ha: melanoma mortality rate is not linearly related to latitude
d. H0: melanoma mortality rate is not linearly related to latitude
Ha: melanoma mortality rate is linearly related to latitude

d. H0: melanoma mortality rate is not linearly related to latitude

   Ha: melanoma mortality rate is linearly related to latitude

Step-by-step explanation:

The linear regression equation is

y=α+βx where α=intercept and β=slope.

β=slope demonstrates the change in dependent variable due to unit change in independent variable.

If the slope is zero then we can say that Y and X are not linearly related.

Thus, the hypothesis for testing significance of linear relationship two variables can be written as

Null hypothesis: The two variables are not linearly related i.e. β=0

Alternative hypothesis : The two variables are linearly related i.e. β≠0.

Thus, in the given scenario the hypothesis are

H0: melanoma mortality rate is not linearly related to latitude

Ha: melanoma mortality rate is linearly related to latitude.

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option