First, distribute to cancel out brackets
= m-n+p-2m+2p-3n-n+m-2p
Collect like terms
= -5n+p
Your answer: -5n + p
Hope this helped :)
The seventh number would have to be 11
I can’t solve them all for you, but I can teach you how repeating decimals work!
For example, 1. 0.3 with a line over the three means that the three repeats forever, so it’s equivalent to 0.333333333333….
Another example is 4, since it only repeats the number that has the line over it, it is equal to 0.025555555…
Hope this helps ☺️
All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If

is the component for state

, then you have

which means

. So the state vector is

.