The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is:
Given that:
Let the number of months be t. So, the function C(t) is calculated as follows:
The range is calculated as follows:
The smallest possible value of t is 0 i.e. when no monthly subscription is done.
So, we have:
And the highest is i.e. for a large value of t
So, we have:
Hence, the range of the function is:
Read more about range of functions at:
Answer:
The line of best fit
y = 0.633x + 0.561
Step-by-step explanation:
The coordinates that the dart hit include
(–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6)
The x and y coordinates can be written as
x | y
-5|0
1 | -3
4|5
-8|-6
0|2
9|6
So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.
Σxᵢ = sum of all the x variables.
Σyᵢ = sum of all the y variables.
Σxᵢyᵢ = sum of the product of each x variable and its corresponding y variable.
Σxᵢ² = sum of the square of each x variable
Σyᵢ² = sum of the square of each y variable
n = number of variables = 6
The scatter plot and the line of best fit is presented in the second attached image to this solution
Then the regression analysis is then done
Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]
Intercept b: = [Σyᵢ - m×(Σxᵢ)] / n
Mean of x = (Σxᵢ)/n
Mean of y = (Σyᵢ) / n
Sample correlation coefficient r:
r = [n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}
And -1 ≤ r ≤ +1
All of these formulas are properly presented in the third attached image to this answer
The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.
Hope this Helps!!!
Answer:
Step-by-step explanation:
Answer:
a = -1
Step-by-step explanation:
The line of symmetry for the parabola given by ...
y = ax² +bx +c
is
x = -b/(2a)
Using the given values, we have ...
-2 = -(-4)/(2a)
Multiplying by -a/2, we get ...
a = (4/2)(-1/2) = -1
The value of "a" is -1.
