The port operations staff in Izmir Port tries to make loading schedule of a ship that will arrive on Monday. There are 6 container yards in the port. The containers first must be picked up from each yard to shipment lane by a dedicated forklift. Secondly containers must be loaded on board from shipment lane by a specific crane. The required times (in minutes) for each operation is as follows; Yards Forklift Crane 1 15 45 2 55 60 3 26 75 4 9 50 5 22 20 6 19 10 Determine how the loading of container at each yard should be scheduled in order to minimize the total makespan. Please draw the Gantt chart to show the optimal schedule and calculate the makespan.

I know the answer for A is 155 and B is 102, please show work how to to get there especially after finding 13(208)- 53 (51) for A. And For b same thing please show work step by step.

A) Find the multiplicative inverse of 51 (mod 208). justify your answer and leave it as number between 0 and 207.

B) solve the following linear congruence. Justify your work and leave your answer as a number between 0 and 207 : 51x - 1 = 1 (mod 208)

Please illustrate the difference between circumscription and default logic

How many​ 7-digit telephone numbers are possible if the first digit cannot be

eight and

​(a) only even digits may be​ used?

​(b) the number must be a multiple of 10​ (that is, it must end in​ 0)?

​(c) the number must be a multiple of 1,000?

​(d) the first 2 digits are 92?

​(e) no repetitions are​ allowed?

prove or disprove .if n is a non negative integer, then 5 divides 2 ⋅ 4^n + 3⋅9^n.

Using the digits 0 through 8, find the number of different 5-digit numbers such that:

a. Digits can be used more than once.

b. Digits cannot be repeated, but can come in any order.

c. Digits cannot be repeated and must be written in increasing order.

d. Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense.

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a matrix sized m × n and b is a vector sized m × 1, with the component values of matrix A and vector b known. The x vector is n × 1 and the component values are unknown. Explain how the possible solution of SPL Ax = b.

i want answer for the question , and what he mean by (the component values of matrix)

S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation an equivalence relation on S?

S = Z (integers), R = {(a,b) : a = b mod 3}. Is this relation an equivalence relation on S? If so, what are the equivalence classes?

Reflect on the concept of exponential and logarithm functions. What concepts (only the names) did you need to accommodate these new concepts in your mind? What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? In your day to day, is there any occurring fact that can be interpreted as exponential or logarithmic functions? What strategy are you using to get the graph of exponential or logarithmic functions? Provide a graph from Desmos graphing calculator of this function. Show your work.

5.       Find the general solution to the equation

y^'’ + 9y = 9sec² 3t

How do you use mathmatical induction to show that the coefficient of x^2 in the expansion of (1+x+x^2+...x^n)^n is (1+2+...n).