a. Recall that
For , we have
By integrating both sides, we get
If , then
so that
We can shift the index to simplify the sum slightly.
b. The power series for can be obtained simply by multiplying both sides of the series above by .
c. We have
G(x)= -8x H(x)=x^2 +3x+2
1 answer:
You might be interested in
Functions are used to represent graphs, and vice versa.
The function represented by the graph is
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
Where
The vertex is the minimum or the maximum point on the graph.
So, we have:
The function becomes
The function also passes through the point (-1,0).
So, we have:
Remove the absolute bracket
Subtract 3 from both sides
Divide both sides by 3
Substitute -1 for (a) in
Hence, the function represented by the graph is
Read more about absolute value graphs at:
Answer:
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.7531
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 23.29 - 0.34 = 22.95 mpg
The upper end of the interval is the sample mean added to M. So it is 23.29 + 0.34 = 23.63 mpg
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.