108 divided by 12 is 9 Maexus needs Nine Feet Of Wood
The Karger's algorithm relates to graph theory where G=(V,E) is an undirected graph with |E| edges and |V| vertices. The objective is to find the minimum number of cuts in edges in order to separate G into two disjoint graphs. The algorithm is randomized and will, in some cases, give the minimum number of cuts. The more number of trials, the higher probability that the minimum number of cuts will be obtained.
The Karger's algorithm will succeed in finding the minimum cut if every edge contraction does not involve any of the edge set C of the minimum cut.
The probability of success, i.e. obtaining the minimum cut, can be shown to be ≥ 2/(n(n-1))=1/C(n,2), which roughly equals 2/n^2 given in the question.Given: EACH randomized trial using the Karger's algorithm has a success rate of P(success,1) ≥ 2/n^2.
This means that the probability of failure is P(F,1) ≤ (1-2/n^2) for each single trial.
We need to estimate the number of trials, t, such that the probability that all t trials fail is less than 1/n.
Using the multiplication rule in probability theory, this can be expressed as
P(F,t)= (1-2/n^2)^t < 1/n
We will use a tool derived from calculus that
Lim (1-1/x)^x as x->infinity = 1/e, and
(1-1/x)^x < 1/e for x finite.
Setting t=(1/2)n^2 trials, we have
P(F,n^2) = (1-2/n^2)^((1/2)n^2) < 1/e
Finally, if we set t=(1/2)n^2*log(n), [log(n) is log_e(n)]
P(F,(1/2)n^2*log(n))
= (P(F,(1/2)n^2))^log(n)
< (1/e)^log(n)
= 1/(e^log(n))
= 1/n
Therefore, the minimum number of trials, t, such that P(F,t)< 1/n is t=(1/2)(n^2)*log(n) [note: log(n) is natural log]
<span>To find out how much Newton would pay you take the cruise cost of $1920.96 and divide by $720 to find out it would take 3 months for Newton to pay off the balance at $720 per month. The cost of the cruise would be $1920.96 + ($1920.96-$720)*0.186+ ($1920-$1440)*0.186)</span>
Answer:
Factoring
Step-by-step explanation:
(x+4)² = 15
x² + 8x + 16 = 15
x² + 8x + 1 = 0
I hope this helps you :)
9514 1404 393
Answer:
-140 feet
Step-by-step explanation:
The relation between speed, distance, and time can be written ...
distance = speed × time
distance = (28 ft/s)(5 s) = 140 ft
In 28 seconds, the skydiver changed position by 140 feet. Since the direction is presumed to be down (falling), the change in altitude is -140 feet.
