Answer:
True
Step-by-step explanation:
Considering the above definition of Pooled Variance, the correct answer is TRUE.
This is because Pooled variance is used to determine the reasonable estimates of variance, where several repeated tests are expected at each value.
This helps to provide greater precision estimates of variance.
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
.
Answer:
12 sec
Step-by-step explanation:
After 1 sec distance between the deer and the bear = (8 + 5) = 13 feet.
After x sec distance is 13x.
13x = 156
x= 156/13=12 sec
Answer:
(1, - 3 )
Step-by-step explanation:
Using the translation rule (x, y ) → (x + 2, y + 1 ), then
B(- 1, 2 ) → (- 1 + 2, 2 + 1) → (1, 3 )
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
(1, 3 ) → (1, - 3 )