This symbol means that you have to evaluate the generic term
at n=1,2,3,4,5, and then sum all the terms. Here's the table:
![\begin{array}{c|c}n&-4n+1\\1&-3\\2&-7\\3&-11\\4&-15\\5&-19\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7Dn%26-4n%2B1%5C%5C1%26-3%5C%5C2%26-7%5C%5C3%26-11%5C%5C4%26-15%5C%5C5%26-19%5Cend%7Barray%7D)
So, their sum is
![-3-7-11-15-19=-55](https://tex.z-dn.net/?f=-3-7-11-15-19%3D-55)
Alternatively, you manipulate the expression to get
![\displaystyle \sum_{n=1}^5(-4n+1) = \sum_{n=1}^5(-4n) + \sum_{n=1}^5 1 = -4\sum_{n=1}^5 n + \sum_{n=1}^5 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5E5%28-4n%2B1%29%20%3D%20%5Csum_%7Bn%3D1%7D%5E5%28-4n%29%20%2B%20%5Csum_%7Bn%3D1%7D%5E5%201%20%3D%20-4%5Csum_%7Bn%3D1%7D%5E5%20n%20%2B%20%5Csum_%7Bn%3D1%7D%5E5%201)
For the first sum you can use the formula
![\displaystyle \sum_{n=1}^k n = \dfrac{k(k+1)}{2} \implies \sum_{n=1}^5 n = \dfrac{5\cdot 6}{2} = 15](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5Ek%20n%20%3D%20%5Cdfrac%7Bk%28k%2B1%29%7D%7B2%7D%20%5Cimplies%20%5Csum_%7Bn%3D1%7D%5E5%20n%20%3D%20%5Cdfrac%7B5%5Ccdot%206%7D%7B2%7D%20%3D%2015)
The second sum is simply 1 summed 5 times with itself: 1+1+1+1+1=5.
So, we have
![-4\cdot 15 + 5 = -60+5 = -55](https://tex.z-dn.net/?f=-4%5Ccdot%2015%20%2B%205%20%3D%20-60%2B5%20%3D%20-55)
Answer:
rational interger whole and natural.
Step-by-step explanation:
It's all of them
This is exactly like the last question you posted. First you have to change the 3 and 2/3 mixed fraction into a pure fraction. 3 and 2/3 = 9/3 and 2/3 = 11/3 "eleven thirds." You now just need to divide (11 / 3) by (2/3.) (11 / 3) / (2 / 3) = (11 / 3) * (3 / 2) = 11 / 2 = 5 and 1/2 pieces. So if Mae cuts the ribbon into pieces that are 2/3 yard long, Mae will end up with 5 and 1/2 pieces. Checking our work, 5 pieces would be 5 * (2/3) = 10 / 3 = 3 and 1/3 yard long, leaving us with an extra 1/3 yard of ribbon, which is the "half piece" we got. Depending on the phrasing of the question, the answer could be "Mae makes 5 and a half pieces." or "Mae can make 5 pieces, and will have 1/3 yard of ribbon left over."
the answer is C. 9 1/3
Hope this helps!
Answer:
its commutative property. you just switch the letters and they will still have the same value
Step-by-step explanation: