Answer:
False. See te explanation an counter example below.
Step-by-step explanation:
For this case we need to find:
for all 
and for 
in the Markov Chain assumed. If we proof this then we have a Markov Chain
For example if we assume that 
then we have this:
Because we can only have if we have this:
, from definition given 
With 
we have that 
So based on these conditions 
would be 1 with probability 1/2 from the definition.
If we find a counter example when the probability is not satisfied we can proof that we don't have a Markov Chain.
Let's assume that 
for this case in order to satisfy the definition then 
But on this case that means 
and on this case the probability 
, so we have a counter example and we have that:
for all 
so then we can conclude that we don't have a Markov chain for this case.
Answer:
1.
Anya could find out her volume by multiplying 1.5*1.5*4 and then subracting that from 11*8.5.
Terrence could find out his volume by multiplying 3*3*4 and then subtracting that from 11*8.5
Anya's suggestion would maker a larger volume.
There can be 2 different volumes because someone might cut out more than the other person.
2.
I think there's something missing from this question.
Answer:
Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
- The vertex is the point at which the graph changes direction as we go from left to right.
- Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
- Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
- Now the answers:
- Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so <em>minimum</em>
- vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so <em>minimum</em>
- vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is <em>maximum</em>
- Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is <em>maximum</em>
- vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is <em>minimum</em>
- vertex is (0.5,5) because it was getting big then changed and started getting smaller so <em>maximum</em>
