Answer:
The larger number is 67 and the smaller number is 13
Step-by-step explanation:
y=5x+2
x+y=80
-5x+y=2
6x=78
x=13
y=65+2
y=67
______________________________________
Answer:
24 : 28 = 42 : 49
Step-by-step explanation:
49/28=1.75
42/__=1.75
__=42/1.75
__=24
Answer:
Here we have the matrix:
![M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right]](https://tex.z-dn.net/?f=M%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D)
And we want to find its inverse.
The inverse of a 2x2 matrix A is:
(1/det(A))*adj(A)
where det(A) is the determinant of the matrix.
Such that for a matrix:
![A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B11%7D%26a_%7B12%7D%5C%5Ca_%7B21%7D%26a_%7B22%7D%5Cend%7Barray%7D%5Cright%5D)
The determinant is:
det(A) = a₁₁*a₂₂ - a₁₂*a₂₁
in the case of our matrix M, the determinant is:
det(M) = 1*3 - 0*0 = 3
and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.
Then for our matrix A we would have:
![adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right]](https://tex.z-dn.net/?f=adj%28A%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B22%7D%26-a_%7B12%7D%5C%5C-a_%7B21%7D%26a_%7B11%7D%5Cend%7Barray%7D%5Cright%5D)
Then for our matrix M, we have:
![adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right]](https://tex.z-dn.net/?f=adj%28M%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-0%5C%5C-0%261%5Cend%7Barray%7D%5Cright%5D)
Then the inverse of the matrix M is:
![M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right]](https://tex.z-dn.net/?f=M%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7Bdet%28M%29%7D%20%2Aadj%28M%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%2F3%5Cend%7Barray%7D%5Cright%5D)
Answer:
23%
Step-by-step explanation:
If in any year there is a 12% chance that a mutual fund will outperform the market, that is in a mutually exclusive situation where the previous years performance is not considered. In this situation where trying to calculate the probability of a mutual fund outperforming the market 2 years in a row, the answer will be 23% as according to the calculations done by the financial analyst where the probability is calculated in a situation dependent on the previous years performance.
