Numerade

AHMAD S.

Viewed Questions

Consider a graph in $G_{n, p}$, with $p=1 / n$. Let $X$ be the number of triangles in the graph, where a triangle is a clique with three edges. Show that $$ \begin{gathered} \operatorname{Pr}(X \geq 1) \leq 1 / 6 \\ \lim _{n \rightarrow \infty} \operatorname{Pr}(X \geq 1) \geq 1 / 7 \end{gathered} $$ and that (Hint: Use the conditional expectation inequality.)

A toumament is a graph on $n$ vertices with exactly one directed edge between each pair of vertices. If vertices represent players, then each edge can be thought of as the result of a match between the two players: the edge points to the winner. A ranking is an ordering of the $n$ players from best to worst (ties are not allowed). Given the outcome of a tournament, one might wish to determine a ranking of the players. A ranking is said to disagree with a directed edge from $y$ to $x$ if $y$ is ahead of $x$ in the ranking (since $x$ beat $y$ in the tournament). (a) Prove that, for every tournament, there exists a ranking that disagrees with at most $50 \%$ of the edges. (b) Prove that, for sufficiently large $n$, there exists a tournament such that every ranking disagrees with at least $49 \%$ of the edges in the tournament.

$In Exercises 25-34, use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists). $\left[ \begin{array}{r} 1 & 2 & -1 \\ 3 & 7 & -10 \\ -5 & -7 & -15 \end{array} \right]$$

In Exercises 25-34, use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists). $\left[ \begin{array}{r} 1 & 2 & -1 \\ 3 & 7 & -10 \\ -5 & -7 & -15 \end{array} \right]$

Matrices and Determinants

The Inverse of a Square Matrix

TyeDye Lights makes two products: Party and Holiday. It takes 80,900 direct labor hours to manufacture the Party Line and 93,500 direct labor hours to manufacture the Holiday Line. Overhead consists of $\$ 225,000$ in the machine setup cost pool and $\$ 149,960$ in the packaging cost pool. The machine setup pool has 52,000 setups for the Party product and 98,000 setups for the Holiday product. The packaging cost pool has 26,000 parts in the Party product and 39,200 parts for the Holiday product. Using the traditional cost method of direct labor hours, what is the predetermined overhead rate? A. $\$ 1.50$ per direct labor hour B. $\$ 2.15$ per direct labor hour C. $\$ 2.30$ per direct labor hour D. $\$ 3.80$ per direct labor hour

Activity-Based, Variable, and Absorption…

Calculate Predetermined Overhead and…

Questions asked

INSTANT ANSWER

- Find the BDD model for the following fault tree and evaluate the system reliability given that the failure probabilities of components are: \( \operatorname{Pr}\{A\}=0.01, \operatorname{Pr}\{B\}=0.05, \operatorname{Pr}\{C\}=0.075 \) and that all failures are \( s \)-independent B C

INSTANT ANSWER

2. Consider a computer system called \( 3 \mathrm{P} 2 \mathrm{M} \) in the following figure. The \( 3 \mathrm{P} 2 \mathrm{M} \) system consists of three processors and two shared memories communicating over a shared bus, as shown in the following Figure. The system is operational as long as at least two processors can communicate with at least one of the two memories over the bus. a) Construct the fault tree model of this system b) Find all the minimal cut sets c) Assume all the components fail exponentially with the following failure rates: processors (P1, P2, P3): 0.0001/hour; memories (M1, M2): 0.0001 /hour; bus: 0.000001 /hour. Find the system reliability at mission time \( t=100 \) hours.

INSTANT ANSWER

2. Consider a computer system called \( 3 \mathrm{P} 2 \mathrm{M} \) in the following figure. The \( 3 \mathrm{P} 2 \mathrm{M} \) system consists of three processors and two shared memories communicating over a shared bus, as shown in the following Figure. The system is operational as long as at least two processors can communicate with at least one of the two memories over the bus. a) Construct the fault tree model of this system b) Find all the minimal cut sets c) Assume all the components fail exponentially with the following failure rates: processors (P1, P2, P3): 0.0001/hour; memories (M1, M2): 0.0001 /hour; bus: 0.000001 /hour. Find the system reliability at mission time \( t=100 \) hours.

INSTANT ANSWER

A component with time to failure T has failure rate z(t)= 2.0*10-6 t/hour for t>0 1) Determine the probability that the component survives 200 hours 2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours Note that the failure rate in this problem is not constant, but a function of time t.