The probability for not rolling a five would be 5 out of 6 times (5/6).
Each friend gets $25.50 for only distributing the flyers but, they all have $10.20 worth of copies printed each so, if you want to find out the total amount of money he is really wasting on one friend including the copy money it is $35.70
Answer:
and
Step-by-step explanation:
Consider given system ,
![5x_1-2x_2=-30\\\\\\2x_1-x_2=-13](https://tex.z-dn.net/?f=5x_1-2x_2%3D-30%5C%5C%5C%5C%5C%5C2x_1-x_2%3D-13)
We have to solve for
and
In matrix form,
![\left[\begin{array}{cc}5&-2\\2&-1\end{array}\right]\left[\begin{array}{c}x_1\\x_2\end{array}\right] =\left[\begin{array}{c}-30\\-13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-2%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%5C%5Cx_2%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-30%5C%5C-13%5Cend%7Barray%7D%5Cright%5D)
then this is in form of AX = b,
A=![\left[\begin{array}{cc}5&-2\\2&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-2%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D)
X=![\left[\begin{array}{c}x_1\\x_2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%5C%5Cx_2%5Cend%7Barray%7D%5Cright%5D)
b=![\left[\begin{array}{c}-30\\-13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-30%5C%5C-13%5Cend%7Barray%7D%5Cright%5D)
Pre-multiply by
both side, we get,
..............(1)
First finding inverse of A ,
![\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}](https://tex.z-dn.net/?f=%5Cmathrm%7BFind%5C%3A2x2%5C%3Amatrix%5C%3Ainverse%5C%3Aaccording%5C%3Ato%5C%3Athe%5C%3Aformula%7D%3A%5Cquad%20%5Cbegin%7Bpmatrix%7Da%5C%3A%26%5C%3Ab%5C%3A%5C%5C%20c%5C%3A%26%5C%3Ad%5C%3A%5Cend%7Bpmatrix%7D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B%5Cdet%20%5Cbegin%7Bpmatrix%7Da%5C%3A%26%5C%3Ab%5C%3A%5C%5C%20c%5C%3A%26%5C%3Ad%5C%3A%5Cend%7Bpmatrix%7D%7D%5Cbegin%7Bpmatrix%7Dd%5C%3A%26%5C%3A-b%5C%3A%5C%5C%20-c%5C%3A%26%5C%3Aa%5C%3A%5Cend%7Bpmatrix%7D)
![=\frac{1}{\det \begin{pmatrix}5&-2\\ 2&-1\end{pmatrix}}\begin{pmatrix}-1&-\left(-2\right)\\ -2&5\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B%5Cdet%20%5Cbegin%7Bpmatrix%7D5%26-2%5C%5C%202%26-1%5Cend%7Bpmatrix%7D%7D%5Cbegin%7Bpmatrix%7D-1%26-%5Cleft%28-2%5Cright%29%5C%5C%20-2%265%5Cend%7Bpmatrix%7D)
![\det \begin{pmatrix}5&-2\\ 2&-1\end{pmatrix}=-1](https://tex.z-dn.net/?f=%5Cdet%20%5Cbegin%7Bpmatrix%7D5%26-2%5C%5C%202%26-1%5Cend%7Bpmatrix%7D%3D-1)
Thus, inverse of A is ,
![\frac{1}{-1}\begin{pmatrix}-1&-\left(-2\right)\\ -2&5\end{pmatrix}=\begin{pmatrix}1&-2\\ 2&-5\end{pmatrix}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B-1%7D%5Cbegin%7Bpmatrix%7D-1%26-%5Cleft%28-2%5Cright%29%5C%5C%20-2%265%5Cend%7Bpmatrix%7D%3D%5Cbegin%7Bpmatrix%7D1%26-2%5C%5C%202%26-5%5Cend%7Bpmatrix%7D)
Now substitute
in (1) , we get,
![\left[\begin{array}{c}x_1\\x_2\end{array}=\left[\begin{array}{cc}1&-2\\2&-5\end{array}\right]\left[\begin{array}{c}-30\\-13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%5C%5Cx_2%5Cend%7Barray%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C2%26-5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-30%5C%5C-13%5Cend%7Barray%7D%5Cright%5D)
Multiply , we get,
![=\begin{pmatrix}1\cdot \left(-30\right)+\left(-2\right)\left(-13\right)\\ 2\left(-30\right)+\left(-5\right)\left(-13\right)\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D1%5Ccdot%20%5Cleft%28-30%5Cright%29%2B%5Cleft%28-2%5Cright%29%5Cleft%28-13%5Cright%29%5C%5C%202%5Cleft%28-30%5Cright%29%2B%5Cleft%28-5%5Cright%29%5Cleft%28-13%5Cright%29%5Cend%7Bpmatrix%7D)
![\left[\begin{array}{c}x_1\\x_2\end{array}\right]=\left[\begin{array}{c}-4\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%5C%5Cx_2%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Thus,
and
The answer to your question is 9.5
Answer:
I think it is 26 and 2
Step-by-step explanation:
39÷6=6.5
4×6.5=26
13÷6.5=2