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:
Days can Stefan feed
Coco with the oats he has left is 5 days
Step-by-step explanation:
Total Oats = 4 1/2 cups
He uses 3 1/4 cups to make granola bars for
a camping trip
Remaining oats after making granola bars = Total oats - oats used for granola bars
= 4 1/2 - 3 1/4
.= 9/2 - 13/4
= 18-13/4
= 5/4 cups
Remaining oats after making granola bars is 5/4 cups
Coco needs 1/4 of a cup of oats each day, how many days can Stefan feed
Coco with the oats he has left?
Days can Stefan feed
Coco with the oats he has left = Remaining oats / 1/4 cups
= 5/4 cups ÷ 1/4 cups
= 5/4 × 4/1
= 20/4
= 5 days
Days can Stefan feed
Coco with the oats he has left is 5 days
Answer:
- make sure calculator is in "radians" mode
- use the cos⁻¹ function to find cos⁻¹(.23) ≈ 1.338718644
Step-by-step explanation:
A screenshot of a calculator shows the cos⁻¹ function (also called arccosine). It is often a "2nd" function on the cosine key. To get the answer in radians, the calculator must be in radians mode. Different calculators have different methods of setting that mode. For some, it is the default, as in the calculator accessed from a Google search box (2nd attachment).
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The third attachment shows a graph of the cosine function (red) and the value 0.23 (dashed red horizontal line). Everywhere that line intersects the cosine function is a value of A such that cos A = 0.23. There are an infinite number of them. You need to know about the symmetry and periodicity of the cosine function to find them all, given that one of them is A ≈ 1.339.
The solution in the 4th quadrant is at 2π-1.339, and additional solutions are at these values plus 2kπ, for any integer k.
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Also in the third attachment is a graph of the inverse of the cosine function (purple). The dashed purple vertical line is at x=0.23, so its intersection point with the inverse function is at 1.339, the angle at which cos(x)=0.23. The dashed orange graph shows the inverse of the cosine function, but to make it be single-valued (thus, a <em>function</em>), the arccosine function is restricted to the range 0 ≤ y ≤ π (purple).
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So, the easiest way to answer the problem is to use the inverse cosine function (cos⁻¹) of your scientific or graphing calculator. (<em>Always make sure</em> the angle mode, degrees or radians, is appropriate to the solution you want.) Be aware that the cosine function is periodic, so there is not just one answer unless the range is restricted.
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I keep myself "unconfused" by reading <em>cos⁻¹</em> as <em>the angle whose cosine is</em>. As with any inverse functions, the relationship with the original function is ...
cos⁻¹(cos A) = A
cos(cos⁻¹ a) = a
(5/8)+(2/5)=
so you need a common den so in this case its 40
so we multiply to get 40 like
(5/5)(5/8)+ (2/5)(8/8)=
25/40 + 16/ 40 = 41/40
