Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2
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Explanation:
For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval
In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank
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To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.
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Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4
This is why f(-4) = -3
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We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.
From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]
We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3
Doing those replacements and simplifying leads to...
[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2
So the average rate of change is 2
Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.
This is a simple consequence of the Zero-sum problem: https://en.wikipedia.org/wiki/Zero-sum_problem
Answer:
The 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].
Step-by-step explanation:
Given information:
Sample size = 10
Sample mean = 12.2 mph
Standard deviation = 2.4
Confidence interval = 95%
At confidence interval 95% then z-score is 1.96.
The 95% confidence interval for the true mean speed of thunderstorms is
Where, 
is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.
![CI=[12.2-1.488, 12.2+1.488]](https://tex.z-dn.net/?f=CI%3D%5B12.2-1.488%2C%2012.2%2B1.488%5D)
![CI=[10.712, 13.688]](https://tex.z-dn.net/?f=CI%3D%5B10.712%2C%2013.688%5D)
Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].
Your answer is 85.555,hope this helped or 85.5 with - over it
