For the answer to the question above,
z=6-(3/4)y-2x
<span>z+(3/4)y+2x=6 </span>
<span>Just by connecting the three points on the graph, I got this equation by isolating each plane to figure it out. This equation only explains the plane bounded by these three points, though, so to draw it just plot the points and connect them.</span>
Answer:
$5.25.
Step-by-step explanation:
That is $7.50 - 30% of 7.50
= 7.50 - 0.30 * 7.50
= $5.25.
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]
You have to derive for a multiplication in both terms:
=e^x+xe^x-(e^x-1 + (x-2)e^x-1) now apply distributive property in the last term:
=e^x+xe^x+e^x-1-xe^x-1 now replace each x by 0 (x=0)
=1 + 0 + e^-1 + 0 = 1+ e^-1 = 1.3679
Answer:
1092
Step-by-step explanation:
Step one:
given data
Ms Lucas has 9 cases of crayon with 52 boxes in each case
total crayon is
9*52= 468
Ms Bruns has 6 cases of crayon with a 104 in each case
total crayon is
6*104= 624
The total crayon is
468+624= 1092
