Answer:
Explanation:
Here is the answer
The correlation coefficient measures the strength of the linear relationship between two variables, and it ranges from -1 to 1. A correlation coefficient of -1 indicates a perfect negative linear relationship between the variables, which means that as one variable increases, the other decreases at a constant rate.
To find the value of A in this scenario, we need to look for a perfect negative linear relationship between the two variables, time (x) and distance from destination (y). The table shows that as time increases, the distance from the destination decreases, but we need to find the exact rate of change.
We can calculate the rate of change by finding the slope of the line that represents the relationship between time and distance. We can use the formula for the slope of a line, which is:
slope = (change in y) / (change in x)
If we choose the first and last points in the table, we get:
slope = (690 - 1060) / (7 - 1) = -70
This means that for every hour of time that passes, the distance from the destination decreases by 70 miles. Therefore, if the correlation coefficient is -1, we should see a perfect negative linear relationship between time and distance, with a slope of -70.
To check if A is the correct value, we can use the formula for the equation of a line in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. We can plug in the values of m and b and solve for A:
y = -70x + b
If we use the first point in the table, where x = 4 and y = 1000, we get:
1000 = -70(4) + b
b = 1220
So the equation of the line is:
y = -70x + 1220
If we plug in the values of x for the remaining points in the table, we get:
y = 1030 when x = 0
y = 880 when x = 2
y = 800 when x = 3
y = A when x = 5
y = 760 when x = 6
To find the value of A, we can plug in the corresponding value of y and solve for A:
1030 = -70(0) + 1220
880 = -70(2) + 1220
800 = -70(3) + 1220
760 = -70(6) + 1220
A = -70(5) + 1220 = 850
Therefore, the value of A should be 850 if the correlation coefficient for the data shown in the table is -1.