Answer:
Solution given:
9x-4=8+7x[Vertically opposite angle]
9x-7x=8+4
2x=12
x=12/2
x=6
:.<u>8</u><u>+</u><u>7</u><u>x</u><u>=</u><u>8</u><u>+</u><u>7</u><u>×</u><u>6</u><u>=</u><u>5</u><u>0</u><u>°</u>
Answer:
46, 55, 58, 63, and 66
Step-by-step explanation:
These points are where each line is at, beginning marked at 46, next line at 55, next at 58, next 63, and ends at 66.
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]
Answer:
Step-by-step explanation:
The figure is a cube
The surface area of a cube is equal to
where
b is the length side of the cube
In this problem we have
substitute
Answer:
He needs $1.64 he has to pay $26.64
Step-by-step explanation:
$25 is what Edwin has
5.95 x 2 = $11.19
$2.50 x 3 = $7.50
11.19 + 7.50 + 7.95 = $26.64
