What does it mean for a relation is a partial order relation?

20. Consider the following information regarding the operations of Owen Glass Company's South division for last year:

What is the division's gross margin percentage?

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition).

y'y = x + 1

A random number generator produces a sequence of 18 digits (0, 1, ..., 9). What is the probability that the sequence contains at least one 3? (Hint: Consider the probability that it contains no 3's. Round your answer to four decimal places.)

Represent with the language of First Order Predicate Logic the following proposition:

"If S is an arbitrary set of objects for which there is an associative binary operation * (function) with the following two properties: (1) for every pair of objects 'a' and 'b' from S there exists and object 'c' such that a * b = c (left solution property), then there exists in S an object 'e' such that e * x = x for all x in S (S has a left identity).

It is standard in some programming languages for the number zero to represent one of the truth values (either true or false) and for positive numbers to represent the other truth value. If assigned correctly, the operations of addition and multiplication will then correspond to conjunction and disjunction, in some order. Figure out how to make this all work out neatly.

write a MATLAB script that plots the two functions ( y=(2x^2)-(3x)-4 and y=4sin(2Pix) - 1 ) in the same figure for x in [-1,3]. Add a title, x-label, y-label, and legend. ( MATLAB code and graph with all descriptions.)

A product with an annual demand of 900 units has Co = $18.50 and Ch = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 26 and σ = 6. Note: Use Appendix B to identify the areas for the standard normal distribution.

a) What is the recommended order quantity? Round your answer to the nearest whole number.

b) What are the reorder point and safety stock if the firm desires at most a 5% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number.

Record point =

Safety stock =

c ) If a manager sets the reorder point at 32, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places. P(Stockout/cycle) =

The doctor orders a continuous infusion (IV) of morphine for a post-operative teenager of 200 mcg/kg q 3 hr. The teenager weighs 105 lbs. You have 2 mg/mL solution of morphine available for IV injection. STATE THE ANSWER IN SCIENTIFIC NOTATION AND CORRECT NUMBER OF SIGNIFICANT FIGURES

a. What rate of infusion (mL/hr) should you set for the IV drip?

b. The continuous infusion device can only hold a total of 25 mL of morphine solution. How long will it be before you have to replace the morphine solution? Express your answer in hours with the remainder converted to minutes. (i.e. your answer should be something like “in 3 hours and 14 minutes”).