Which of the functions below could have created this graph?
1 answer:
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The average rate of change of the function f(x) = over the interval [-3, 3] is 0
The function is
f(x) =
The average rate of change =
First we have to find each values and substitute the values in the equation.
The interval = [-3, 3]
The value of a = -3
The value of b = 3
To find the value of f(-3), substitute the value of x = -3 in the given function
f(-3) =
= 2×9 - 11
= 18-11
= 7
The value of f(b) =
= 2×9 - 11
= 18-11
= 7
The average rate of change =
= 0/6
= 0
Hence, the average rate of change of the function f(x) = over the interval [-3, 3] is 0
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Answer: (a) y = 2.7394x - 118.1368
(b) R² = 0.8215 or 82.15%
Step-by-step explanation: Regression line is the best line that relates the variables in the data.
To calculate the fitted regression equation:
1) Calculate average of x-values () and average of y-values (
);
2) Calculate the slope, b, by doing:
3) Calculate y-intercept, a, by doing:
4) Then, it gives regression equation: y = bx + a
For the data on chemical reactions:
(a)
b = 2.7394
a = -118.1368
y = 2.7394x - 118.1368
<u>The fittest regression equation is </u><u>y = 2.7394x - 118.1368</u>.
(b) R is <u>correlation coefficient</u> and measures the strength of the relationship between the variables. It is calculated as:
For this fit, R = 0.9064
The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.
What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).
For this fit:
0.8215
What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.