Answer:
A number, when divided by 119, leaves a remainder of 19. If it is divided by 17, it will leave a remainder of 2
Step-by-step explanation:
Well in area you multiply and perimeter you add, so right now you are multiplying the measures of the triangle, So you can either write out the problem and solve it or use a calculator to get you answer, but I would say to solve it because you never if the calculator could be wrong, so if you wanna write it out then you write 9 then put the 14 under it and put the 5 under 14 but under the 4 of 14, so basically you are just going to multiply 9 by 14 to get 126 then multiply 126 by 5 to get 630, so now 630 is your final answer
Answer:
x = √(14²-7²) = 7√3
Step-by-step explanation:
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:
49 hamburguers (of 3/4 pound)
Step-by-step explanation:
3/4 pound is equal to 0.75 pound
37 1/3 pounds of meat is equal to
37 + 1/3 pound = 37.3333 pounds
To find how much hamburguers can be made, we need to divide
37.3333 pounds/ 0.75 pounds
37.3333 pounds/ 0.75 pounds = 49.777777
(We need to round to the lowest number)
This means that 49 hamburguers could be made
