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1.Show that the following compound propositions are logically equivalent using truth table. ¬p → (q → r) and q → (p ...

q → r) and q → (p ∨ r). Q2. Write the converse, inverse and contrapositive of the statement: “I will score marks whenever I will study”. Q3. Convert the following compound propositions into English sentences for given p: It is below freezing. q: It is snowing. (i) ¬q → ¬p (ii) ¬q ∨ (¬p ∧ q ) (iii) p ↔ ¬q (iv) p ∨ q (v) ¬q ∧ ¬p Q4. Determine whether each of the statements is true or false. (i) If 1 + 1 = 2, then 2 + 2 = 5. (ii) If 1 + 1 = 3, then 2 + 2 = 4. (iii) If 1 + 1 = 3, then dogs can fly. (iv) Monkeys can fly if and only if 1 + 1 = 3. (v) A number is prime if and only if it is divisible by 1 and itself.
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2.2)Two books are accelerating to the right on a frictional surface and the coefficient of kinetic friction between the floor ...

ction between the floor and book is µk. Using the information given in the figure: (a) draw free body diagrams for both the books, and also for the combined system (of mass m1+m2), (b) find acceleration of the books along horizontal direction, and (c) find the magnitude and direction of the force exerted by the left book on the right book. 3.A car of mass 1500-kg enters a circular path at point P and leaves at point Q (see the figure) at constant speed of 5.0m/s, and the frictional force acting on its tires is 2500-N. a) how long it takes to reach point Q from point P, and b) what should be the minimum value of the coefficient of static friction between the tires and the road? 4)In an elevator which is accelerating downward at 2.5ms−2 , a 25-kg block hangs from a spring attached to the ceiling of the elevator. If spring gets stretched by 0.15m, find its spring constant.
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3.You make very good pizzas, so you decide to sell your pizzas on campus. Since the set up for making ...

pizza is already available to you, the only cost involved is that of making the pizza, which you calculate to be $ 5 per pizza. a. What is the cost function? If 10 pizzas are available in a day, the market offers a price of $ 11 per pizza. If 50 pizzas are available in a day, the market offers a price of $ 7 per pizza. b. Assuming a linear relationship between price and quantity, find the price that the market offers as a function of the number of pizzas available. You start selling the pizzas. c. What is revenue as a function of the quantity you sell? What is the profit function? d. What quantity will maximize your profit? Call it q ∗ 1. What is the maximum profit? e. If somebody is already supplying 5 pizzas every day, What is the maximum profit that you can make?
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4.Suppose that Wegboys has a supermarket with a downward sloping demand curve in Pilgrim City. It purchases frozen turkeys ...

chases frozen turkeys at a constant wholesale price of $1/turkey, which is its full marginal cost for supplying turkeys. During July, only a small number of wealthy people are interested in buying turkeys in Pilgrim. Their demand curve is P = 10 – .02 Q, where P is Wegboys’ retail price for turkeys during the month and Q is the quantity of turkeys purchased. The demand curve for these wealthy people is constant – it is the same curve in both November and July. During November, a large number of less wealthy people enter the market to purchase turkeys for Thanksgiving. Their demand curve for Wegboys’ turkeys is P = 4 – .0005Q. In other months of the year, they do not purchase turkeys at any price. a. (5 points) What price should Wegboys charge in July to maximize its profits? Calculate its profits from turkey sales. b. (5 points) Demonstrate that Wegboys can earn a higher profit if it lowers its retail price for turkeys during November (you can do this without finding the optimal price). Explain the basic economic intuition.
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5.1. For this question, you will review a process, identify problem areas ( such as wastes, cycle time inefficiencies, etc), ...

inefficiencies, etc), and suggest an improved process. Open and read the Process Improvement (Final Q 1) document which describes the process steps in words and also includes a process map as a visual tool for understanding what's going on in each step. You will need to respond to the following three sub-questions: FINAL Q1: 3 Attachments are the Q1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ I need the 3 part question answered. This is everything in the question.. Understand that there is NOTHING INCOMPLETE, I have added everything that was sent to us. ------------------------------------------------------------------------------------------------------------------------------------------------------------------ a. Of the 9 process steps in the Process Improvement (Final Q 1) document, which specific steps in that process are experiencing lean wastes and/or process cycle time issues (please note, there is more than one step experiencing issues). In your response, name the process step, and/or the transfer interface between steps, and what waste(s) or cycle time issue is involved. Be sure to use standard lean/six sigma terminology that we used in the course when referring to any of the quality concepts; e.g., transportation waste when referring to situations involving a lot of moving around from one place to another. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- b. Which of the process steps you identified in part a do you believe could benefit from process improvement and why? --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- c. What changes would you institute in the process to improve the steps you cited in part b of this question and describe how those changes improves the process. Be specific about which process step(s) your improving and thoroughly describe the improvement to that step. [Note: This question ties to what you decided was important in part b question above.] Also, when answering how you would improve a given process step, assume you have an unlimited budget and personnel resources and you can do mostly anything you want as long as it doesn't violate the laws of physics or the judicial system. Be cautious though because process improvement is designed to save time, money, and resources in doing the needed work.For example, automation is good, and also potentially expensive, so is it worth it for the improvement? - you will have to be the judge of that.
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6.The supply for a particular item is given by the function S ( x ) = 15 + 7 x . Find the producer's surplus if the equilibrium ...

producer's surplus if the equilibrium price of a unit $ 99 .A retailer anticipates selling 7600 units of its product at a uniform rate over the next year. Each time the retailer places an order for x units, it is charged a flat fee of $ 100 . Carrying costs are $ 38 per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost? For a particular commodity, the demand function is q = 1 4 ( 400 − p 2 ) . a . Find ε when p = 8 .A hotel rents 240 rooms at a rate of $ 60 per day. For each $ 1 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics