Math Answers

A production facility contains two machines that are used to rework items that are initially defective. Let 𝑋 be the number of hours that the first machine is in use and let 𝑌 be the number of hours that the second machine is in use, on a randomly chosen day. Assume that 𝑋 and 𝑌 have a joint probability density function given by 𝑓(𝑥) = { 3 2 (𝑥 2 + 𝑦 2 ) 0 < 𝑥 < 1 𝑎𝑛𝑑 0 < 𝑦 < 1 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. a. What is the probability that both machines are in operation for less than half an hour?

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply

a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)

Obtain the Conjunctive Normal Form of (x^y) V (-x^y)

The following contingency table represents the voters’ opinion concerning a new tax

reform bill and their level of income.

Levels of Income

Opinion Low Medium High

For 213 203 182

Against 138 110 154

Apply chi-square (χ2

) test to examine whether the opinion of people on new tax bill is

independent from their income level. [Table value of chi- square (χ2

) at 5% level of

significance and for 2 degrees of freedom is 5.99]

The argument is p→~q,~r→p,q|–r in true table in mathematical foundations of computer science

The students of two groups A and B obtained following marks in a test of Mathematics.

Find which group gave more consistent performance, based on coefficient of range.

Marks of Group A 35 47 42 45 40 39 38 46 41 43

Marks of Group B 35 70 55 65 60 42 73 80 53 57

4. The temperatures recorded at the end of every 4 hours during a day at two cities Mumbai

and Pune are given below:

Mumbai 28 30 34 31 28 27

Pune 25 28 34 40 32 26

Use appropriate measure of dispersion and comment on variation.

The plant sent 2,000 thermometers to the pharmacy warehouse. The probability of damage to each thermometer along the way is 0.002. What is the probability that exactly 3 damaged thermometers will arrive at the pharmacy warehouse

There are two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Birr 6/kg and F2 costs Birr 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost? (solve through simplex method)

Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}

R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}

is a relation on set A={1,2,3,4}

A={1,2,3,4}

Suppose a Rn b

means that there is a path of length n from a

to b

Which of the elements are R3?

Find the integral surface of the linear partial differential equation x(x^2+z)p - y(y^2+z)q = (x^2-y^2)z; p, q has their usual meaning , which contains the straight line