Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).
Hence, the answer is (D).
I had 32 cookies and I wanted to give 14 of my friends a cookie each, how many cookies are left?
I went to the pet store with $32 and i bought a $15 for my dog, how much money do I have left?
My friend (insert any random name here) was biking a 32 mile race, he/she has gone 15 miles so far, how many more miles does (their name here) have to bike?
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.
What we Know: 3 box have some counters. There are 63 counters when they are all combined.
A and B counters = 36
The difference between A and C is 10.
Since we already know A and B we can subtract them from 63 to get C
C= 63- 36 = 27
Now we have to find A by looking for what number gives us the difference of 10 when subtracted from C.
36 = 18+ 18 or 19+ 17
18 and 18 wont work because it does not give us the difference of 10.
So A = 17 counters and B = 19 counters.
Identify the opposite, adjacent, and hypotenuse based on the 15 degree angle. From there plug in the variable x and 14 into your tangent equation which would be tan15=x/14. Solve for x using a calculator and your answer would be rounded to 3.8.
