Answer: The description are as follows:
Step-by-step explanation:
Correlation coefficients is a statistical measure that measures the relationship between the two variables.
(a) r = 1, it means that there is a Perfect positive relationship between the two variables. If there is positive increase in one variable then other variable also increases with a fixed proportion.
(b) r = -1, it means that there is a perfect negative relationship between the two variables. If there is positive increase in one variable then other variable decreases with a fixed proportion.
(c) r = 0, this is a situation which shows that there is no relationship between the two variables.
(d) r = 0.86, this is a situation which shows that there is a fairly strong positive relationship between the two variables.
(e) r = 0.06, it is nearly zero which represents that either there is a very minor positive relationship between the two variables or there is no relationship between them.
(f) r = -0.89, this is a situation which shows that there is a fairly strong negative relationship between the two variables.
Assuming that the label only covers the body of the cylinder and not the circular faces on the top and bottom.
Answer:
Spongebob Square Pants!
Step-by-step explanation:
Answer:
5½ inches
Step-by-step explanation:
7⅔ - 2 1/6 = 7 4/6 - 2 1/6 = 5 3/6 = 5½
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
![S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}](https://tex.z-dn.net/?f=S_n%3Da%2Bar%2Bar%5E2%2B%5Ccdots%2Bar%5E%7Bn-2%7D%2Bar%5E%7Bn-1%7D)
Multiply both sides by <em>r</em> :
![rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n](https://tex.z-dn.net/?f=rS_n%3Dar%2Bar%5E2%2Bar%5E3%2B%5Ccdots%2Bar%5E%7Bn-1%7D%2Bar%5En)
Subtract the latter sum from the first, which eliminates all but the first and last terms:
![S_n-rS_n=a-ar^n](https://tex.z-dn.net/?f=S_n-rS_n%3Da-ar%5En)
Solve for
:
![(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}](https://tex.z-dn.net/?f=%281-r%29S_n%3Da%281-r%5En%29%5Cimplies%20S_n%3D%5Cdfrac%20a%7B1-r%7D-%5Cdfrac%7Bar%5En%7D%7B1-r%7D)
Then as gets arbitrarily large, the term
will converge to 0, leaving us with
![S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}](https://tex.z-dn.net/?f=S%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7DS_n%3D%5Cfrac%20a%7B1-r%7D)
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18