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• Let P(x, y) be the statement “student x has taken class y”, where the domain for x consists of all students and y consists of all computer engineering courses at your school.


• Express each of the quantification in English sentences


1. ∀x ∀y P(x,y)


2. ∀x Ǝy P(x,y)


3. Ǝx ∀y P(x,y)


4. Ǝx Ǝy P(x,y)


How much will mollys monthly payment be is she makes 36 monthly payments


I need each answer please I am only getting one answer if not can you separate the answers. Thank you. Consider a firm with the following production function 𝑸 = 𝟓𝟎𝟎𝟎𝑳 − 𝟐𝑳 𝟐 


a. How many units of labor are needed at that point.


b. Obtain the function of marginal product of labor (𝑀𝑅𝐿).


c. Graph the production function and the 𝑀𝑅𝐿.



If cost = 1500 + 200Q - Q2 + Q3, then how much is TFC?

For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3 + 4 + 3 10 which is even.) Find the answer and explain why it is correct in at least two different ways.


We can expect that the amount of money that a bank creates will decrease when…

a.

the South African Reserve Bank increases the repo rate.

b.

more bank clients choose to deposit their funds at the bank.

c.

the bank borrows from the South African Reserve Bank.

d.

the bank's clients choose to hold a smaller part of their money in the form of cash.


Write a java program to find the sum of all odd numbers between 1 to n - using do...while loop

In a farming community, 30% of the farmers grow oranges only, 10% grow lemons only and 4% grow both oranges and lemons.

1.1) What proportion of farmers in the community grow either oranges or lemons? [3 marks]

1.2) If a farmer is chosen randomly from these in the community, what is the probability that he grows neither oranges nor lemons? [2 marks]

1.3) Of all the farmers who grow oranges, what proportion grow lemons also?  [2 marks]

When supply shifts to the right and demand stays constant, the equilibrium price


A. decreases and the equilibrium quantity decreases.

B. decreases and the equilibrium quantity increases.

C. increases and the equilibrium quantity decreases.

D. increases and the equilibrium quantity increases.


If c>0, then the following equality holds,


the integral from a to b dx/x equals to the integral from ac to bc dx/x.


Show your work and an explanation for each step.


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