Answer:
95% Confidence interval for the variance:
95% Confidence interval for the standard deviation:
Step-by-step explanation:
We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².
The sample, of size n=8, has a standard deviation of s=2.89 miles.
Then, the variance of the sample is
The confidence interval for the variance is:
The critical values for the Chi-square distribution for a 95% confidence (α=0.05) interval are:
Then, the confidence interval can be calculated as:
If we calculate the square root for each bound we will have the confidence interval for the standard deviation:
Answer:
-2(x+2)(4x-35)
Step-by-step explanation:
Factor out the 2 and by grouping.
Two ratios are 3:4 and 18:24
Answer:
x-intercepts: -2; 1; 5
Average rate of change: 1.8
Step-by-step explanation:
<u>x- intercepts as per graph are:</u>
<u>Average rate of change over the interval (-1, 4) is:</u>
- Δy/Δx = (y(4) - y(-1))/(4 - (-1)) = (3 - (-6))/5 = 9/5 = 1.8
Answer:
f(x) = (x+10)^2 - 4
Step-by-step explanation:
vertex form is y = a(x-h)^2+k
to complete the square, we want to add a number on both sides so x^2+20x+whatver the number is, is the square of something
to find that number take 20, divide by 2, and then square it to get 100.
so, you would get f(x)+100 = x^2+20x+100+96
subtract 96 on both sides: x^2+20x+100 = f(x) + 4
factor: f(x) = (x+10)^2 - 4
