Answer: c) About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.

e) The correlation coefficient, r, is 0.397.

Step-by-step explanation:

Given that:

Coefficient of determination (r²) between two variables, age of car (x) and value of car (y) = 0.158

Correlation of determination (r²) of 0.158 = (0.158 × 100% = 15.8% of the variation between the two variables can be explained by the regression line). Hence, about 16% of the variation between age and value of car can be explained by the linear relationship.

Coefficient of correlation (r) = sqrt(r²) = sqrt(0.158) = 0.397

A constant is any number, anywhere on the number line.

A variable is an unknown, x y z n etc

One way to look at this is to make 2 equations and treat it as a set of equations. We will make the cost of a donut equal to x, and the cost of a coffee equal to y.

Harold's order:

4x + 2y = 4.08

Melinda's order:

2x + 3y = 3.92

To combine these equations, we need to cancel out either x or y:

4x + 2y = 4.08

<span>2x + 3y = 3.92

</span>

4x + 2y = 4.08

<span>4x + 6y = 7.84

</span>

4x + 2y = 4.08

<span>-4x - 6y = -7.84

</span>

We can now combine these equations:

4x + 2y = 4.08

<span>-4x - 6y = -7.84

</span>

-4y = -3.76

y = 0.94

Therefore the cost of a large coffee is $0.94. We can plug this into either original equation to find the cost of a donut.

<span>4x + 2y = 4.08

</span>4x + 2(0.94) = 4.08

4x + 1.88 = 4.08

4x = 2.20

x = 0.55

The cost of a donut is $0.55, and the cost of a large coffee is $0.94.