Help on this math question. 25 points.
2 answers:
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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 
.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If
which means
Call the amount of pineapple "P', and the amount of gingerale "G".
We know that a mix of pineapple and gingerale makes 200 cups. So:
We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
We can now solve by substitution:
For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]
We know that a mix of pineapple and gingerale makes 200 cups. So:
We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
We can now solve by substitution:
For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]