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Question: Consider a factory operating 24 hours per day consisting of two workstations. Arrivals to the first station occur at a rate of 10 per day. The long-run average time that a job spends at the first workstation is 4.2 hours. After processing at the first workstation, a job is sent directly to the second workstation where it spends an average of 5.3 hours. After processing at the second workstation, the job leaves the system. What is the average work-in-process within the factory?
Prove the theorem of Tinseau, that the orthogonal projection of a space curve onto a plane has a point of inflection (a point where κ(s) = 0) if the plane is perpendicular to the osculating plane of the curve (the plane spanned by T(s) and N(s))
For each case, plot the trajectories of two weights and its corresponding cost with the number of iterations. These two weights should converge to the optimal values as you will give in (a)
A bacterial population experiences exponential growth during a 4-day period. Assume that 200 colonies were present at the beginning of the 1st day, but by the beginning of the 3rd day, the population had grown to 335.
Simplified Blackjack. A game between a "dealer" and a "customer" is played with a (very large) mixed deck of cards consisting of equal numbers of ones, twos.
Suppose N = 10 and r =3. Compute the hypergeometric probabilities for the following values of n and x.
State the appropriate hypotheses for your significance test. Use the sample results to compute the test statistic and the p-value.
Write down the joint pmf (as a table) of X and Y . Are X and Y independent and determine the marginal pmf of X and the conditional pmf of Y given X = 1 - Determine the expectations and variances of X and Y.
The maximum size of a triangle packing in G is denoted ν(G), and the minimum size of a triangle cover in G is denoted τ (G).
Evaluate the indefinite integral.
Create and use an optimization model (preferably linear) of an engineering design - Your model should have 5 to 10 decision variables.
What is the difference between Data and Information - To have an effective communication you need to meet two conditions, mention these conditions.
A farm-implement manufacturer in the Midwest purchases castings from the Omaha Steel foundry. Thirty castings were selected at random and weight!d.
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