Answer:4654 square yards
Step-by-step explanation:
13 x 358 = 4654
Answer:
The sample of 15 pieces of colored fruit snacks
Step-by-step explanation:
The sample of 15 pieces of colored fruit snacks. The 60 pieces are from ONE day which means it can be heavily biased. It might be like "BLUE RASPBERRY SPECIAL DAY!" or "PRESIDENTS DAY!! RED BLUE AND WHITE!!". However, 15 pieces, whilst having less of a population, is probably more spaced out.
We're looking for the two values being subtracted here. One of these values is easy to find:
<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
The other value we find by taking a Left Riemann Sum, which means that we divide the interval [1,15] into the intervals listed above and find the area of rectangles over those regions:
</span><span>Each integral breaks down like so:
(3-1)*f(1)=4
(6-3)*f(3)=9
(10-6)*f(6)=16
(15-10)*f(10)=10.
So, the sum of all these integrals is 39, which means g(15)=39.
Then, g(15)-g(1)=39-0=39.
</span>
I hope my answer has come to your help. God bless and have a nice day ahead!
The given system of equations in augmented matrix form is
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\-6&1&2&4&-12\\1&-3&-3&5&-20\\-2&5&6&0&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C-6%261%262%264%26-12%5C%5C1%26-3%26-3%265%26-20%5C%5C-2%265%266%260%2612%5Cend%7Barray%7D%5Cright%5D)
If you need to solve this, first get the matrix in RREF:
- Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%2611%265%26-13%2637%5C%5C0%2619%2610%264%26-10%5Cend%7Barray%7D%5Cright%5D)
- Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%26-164%26132%26-1052%5Cend%7Barray%7D%5Cright%5D)
- Add 164(row 3) to -91(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&13080&-39240\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%260%2613080%26-39240%5Cend%7Barray%7D%5Cright%5D)
- Multiply row 4 by 1/13080:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add -153(row 4) to row 3:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&0&-364\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%260%26-364%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add 6(row 3) and -8(row 4) to row 2:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%260%260%26-10%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add -2(row 2), 4(row 3), and -2(row 4) to row 1:
![\left[\begin{array}{cccc|c}3&0&0&0&3\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%260%260%260%263%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}1&0&0&0&1\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D1%260%260%260%261%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
So the solution to this system is 
.
