Going from 107 to 98 is (minus 9)
going from 98 to 90 is (minus 8)
going from 90 to 83 is (minus 7)
going from 83 to 77 is (minus 6)
following this pattern, the number after 77
is 77 minus 5 = 72
therefore your answer is 72
you have 10 fish and 3 died (must not have been taking very good care of them ?), but it didnt say that you cleaned them out ...
so you still have 10 fish in the tank
8 more got put in, so 10 + 8 = 18 fish
2 died but you STILL didnt take them out, so you have 18 fish in the tank now.
Answer:
Variance of the given data = 31.143
Explanation:
Variance, 
, where n is the number of observations, μ is the mean and 
is the observations made.
Number of observations, n = 7
Mean, μ = 
So variance of the given data = 31.143
f(1) = -8, simply is a way of saying, the 1st value in the arithmetic sequence is -8.
f(n) = f(n-1) - 3, is another way of saying, following values are just, the previous minus -3.
so in short, -3 is the common difference, since that is what we're "adding" to get the new value in the sequence.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d = -3\\ a_1 = -8 \end{cases} \\\\\\ a_n=-8+(n-1)(-3)\implies a_n=-8-3n+3\implies \stackrel{f(n)}{a_n}=\stackrel{\stackrel{explicit}{\downarrow }}{-3n-5}](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%20%5C%5C%5C%5C%20a_n%3Da_1%2B%28n-1%29d%5Cqquad%20%5Cbegin%7Bcases%7D%20a_n%3Dn%5E%7Bth%7D%5C%20term%5C%5C%20n%3D%5Ctextit%7Bterm%20position%7D%5C%5C%20a_1%3D%5Ctextit%7Bfirst%20term%7D%5C%5C%20d%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20d%20%3D%20-3%5C%5C%20a_1%20%3D%20-8%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20a_n%3D-8%2B%28n-1%29%28-3%29%5Cimplies%20a_n%3D-8-3n%2B3%5Cimplies%20%5Cstackrel%7Bf%28n%29%7D%7Ba_n%7D%3D%5Cstackrel%7B%5Cstackrel%7Bexplicit%7D%7B%5Cdownarrow%20%7D%7D%7B-3n-5%7D)
Base on the question that ask to calculate the sine, cosine, and tangent of 5pi/3 radians and base on my further calculation, I would say that the answer would be <span>sin Θ = -sqrt 3/2; cos Θ = -1/2; tan Θ = -sqrt 3. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification </span>
