Answer:
Expected value E = $0.45
Step-by-step explanation:
Expected value E = P×w - P'×l
Where;
P = probability of making the next 2 throw.
P = 223/406 × 223/406 = 0.3017
P' = probability of not making a throw.
P' = 1 - P = 1 - 0.3017
P' = 0.6983
w = expected win = $20
l = Expected loss = $8
Substituting the values;
E = 0.3017 × $20 - 0.6983 × $8
E = $0.4476
Expected value E = $0.45
Answer:
The answer is 3
Step-by-step explanation:
7-8-(-5)-1
-1-(-5)-1
-1 + 5 - 1
4 - 1
3
Answer:
![REF= \left[\begin{array}{ccc}5&-1&1\\0&\frac{-7}{5} &\frac{-18}{5}\end{array}\right]](https://tex.z-dn.net/?f=REF%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26%5Cfrac%7B-7%7D%7B5%7D%20%26%5Cfrac%7B-18%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
![RREF=\left[\begin{array}{ccc}1&0&\frac{5}{7} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=RREF%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cfrac%7B5%7D%7B7%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The augmented matrix of the system is: ![\left[\begin{array}{ccc}5&-1&1\\3&-2&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C3%26-2%26-3%5Cend%7Barray%7D%5Cright%5D)
First we find the stepped form of A (REF):
1. We subtract 3/5 from row 1 to row 2 (R2-
R1) and get the matrix
![\left[\begin{array}{ccc}5&-1&1\\0&\frac{-7}{5} &\frac{-18}{5}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26%5Cfrac%7B-7%7D%7B5%7D%20%26%5Cfrac%7B-18%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
Note that this matrix is in echelon form.
Now we find the reduced row echelon form of the augmented matrix (RREF)
2. From the previous matrix, we multiply the first row by 1/5 and the second row by -5/7 and obtain the matrix:
![\left[\begin{array}{ccc}1&\frac{-1}{5} &\frac{1}{5} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cfrac%7B-1%7D%7B5%7D%20%26%5Cfrac%7B1%7D%7B5%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
3. From the previous matrix, to row 1 we add 1/5 of row 2 (R1 +
R2) and we obtain the matrix
![\left[\begin{array}{ccc}1&0&\frac{5}{7} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cfrac%7B5%7D%7B7%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
which is the reduced row echelon form of the augmented matrix.
Answer:
Not equivalent
Step-by-step explanation:
Let,
3(x-2) + 5 = 3x + 1
By Multiplying
3x - 6 + 5 = 3x + 1
3x - 1 = 3x + 1
So, the expressions are not equal