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Question

For sets H and K, we define the intersection H n K by H n K = {xI

X E H and X € K%. Show that if H ≤ G and K < G, then H n K < G.

(Remember: ≤ denotes "is a subgroup of," not "is a subset of.")


A consumer consuming two commodities X and Y has the following utility function U=XY+2X. If the price of the two commodities are 4 and 2 respectively and his/her




budget is birr 60. (2pts)




A. Find the quantities of good X and Y which will maximize utility.




B. Find the MRSxy at optimum.

Aconsumer consuming two commodities x and y has the following utility functions U= xy + 2z. If the price of the two commodities are 4 and 2 respectively and his/her budget is birr 60.





Find the quantities of good x and y which with miximize utility





Find the MRSxy at optimum

Minimal Absolute Difference

There are N pyramids in a line.You are given their heights as a list of integers.Write a program to find the minimum absolute difference between the heights of any two different pyramids.


Input

The input is a single line containing space-separated integers.


Output

The output should be a single line containing the minimum absolute difference of any two different pyramid heights.


Explanation

Given Pyramid heights are 7 1 5.

The absolute difference between the heights of any two different pyramids are


given an object person containing a person details, write a JS program to log the name, address & nicknames count

input

{ 'name':'Pranay', 'address':{'city':'Mumbai','state':'maharastra'}, 'nicknames':['nani','chanti']}

output

pranay is from mumbai,maharastra

pranay has 2 nicknames


"use strict";

process.stdin.resume();

process.stdin.setEncoding("utf-8");

let inputString = "";

let currentLine = 0;

process.stdin.on("data", (inputStdin) => {

 inputString += inputStdin;

});

process.stdin.on("end", (_) => {

 inputString = inputString

  .trim()

  .split("\n")

  .map((str) => str.trim());

 main();

});

function readLine() {

 return inputString[currentLine++];

}

function main() {

 let person = JSON.parse(readLine().replace(/'/g, '"'));

 /* Write your code here and log the output */

}


Answer the next question (s) on the basis of the following domestic supply and demand schedules for a product. Suppose that the world price of the product is $1.



Quantity supplied (domestic) 12,10,7,4,1. Price $5,4,3,2,1



Quantity demanded (domestic) 2,4,7,11,16



I) referring to the above data, if this nation were entirely closed to international trade, what is the equilibrium price and quantity?

The following data show the different combinations of coffee and cars that can be produced by an economy, given a particular amount of resources, and a particular state of technology. Draw the corresponding production possibility frontier to answer the questions below:



Type of Production Production Alternatives



A B C D E F



Coffee (tons) 100 80 60 40 20 0



Cars (units) 0 8 12 15 17 18



1.Given the production possibility frontier above,can the economy produce the combination of 50 tons of coffee and 5 units of cars?What does this combination suggest about the use of the resources?Are they fully utilized?



2.Given the production possibility frontier above,can the economy produce the combination of 80 tons of coffee and 12 units of cars,and why?



3.What is the opportunity cost of increasing coffee production from 40 to 60 tons per year,assuming that resources are fully utilized?














Mention and explain each field of IPv4 header in detail, by taking suitable examples.

Find the first address, last address and the number of addresses of a network whose one



of the IP addresses is 50.28.22.75 / 25.

A satellite orbits the earth at a speed of 8*10∆3m/s.calculate the period of orbit of the satellite if the distance between the centre of the earth and satellite is 6400km

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