You can use estimation to find the product of two decimals by rounding both the decimal’s so the nearest tenth or tens place (depending on how long it is) and then multiplying the decimals.
for example, if you had 4.6 and 8.9, you have to round the 4.6 and 8.9. you round the 4.6 up to 5 because the 6 bumps the 4 up to 5) and then round 8.9 to 9 (because the 9 bumps the 8 up to 8.) then, multiply 5 and 9 and you get 45!
-15x=-4x
We know that adding zero wouldn’t change the value
-15x=-4x+0
Now we can add 4x (since that’s the opposite of the negative sign) to the other side
-11x=0
0 divided by 11 is 0
x=0
Discounted price before sales tax = 75/100 x (40 + 24 + 18 x 3) = 3/4 x (64 + 54) = 3/4 x 118 = $88.5
Total price inclusive of sales tax = 107/100 x 88.5 = $94.69
Answer:
The probability of the system being down in the next hour of operation is 0.3.
Step-by-step explanation:
We have a transition matrix from one period to the next (one hour) that can be written as:
![T=\left[\begin{array}{ccc}&R&D\\R&0.7&0.3\\D&0.2&0.8\end{array}\right]](https://tex.z-dn.net/?f=T%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26R%26D%5C%5CR%260.7%260.3%5C%5CD%260.2%260.8%5Cend%7Barray%7D%5Cright%5D)
We can represent the state that system is initially running with the vector:
![S_0=\left[\begin{array}{cc}1&0\end{array}\right]](https://tex.z-dn.net/?f=S_0%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D)
The probabilties of the states in the next period can be calculated using the matrix product of the actual state and the transition matrix:
That is:
![S_1=S_0\cdot T= \left[\begin{array}{cc}1&0\end{array}\right]\cdot \left[\begin{array}{cc}0.7&0.3\\0.2&0.8\end{array}\right]= \left[\begin{array}{cc}0.7&0.3\end{array}\right]](https://tex.z-dn.net/?f=S_1%3DS_0%5Ccdot%20T%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5C%5C0.2%260.8%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5Cend%7Barray%7D%5Cright%5D)
With the inital state as running, we have a probabilty of 0.7 that the system will be running in the next hour and a probability of 0.3 that it will be down.
Answer:
$67.25
Step-by-step explanation:
52.60 x 8% = 52.60 x 0.08 = 4.21
52.60 x 20% = 52.60 x 0.20 = 10.44
52.60 + 4.21 + 10.44 = 67.25
