Math Answers

"\\intop" ²_-1 1/ 3√x2 dx=?

"\\intop"₂⁴ e^x cosxdx=?

A company xyz has a labelled mass of 500. It has a mean mass of 550 and standard deviation of 20. Assuming that masses are normally destributed at 550 at 5% significance level.

From past experience, a professor knows that the test score of a student taking her final examination is a random variable with mean 70 and variance 8.  What is the upper bound of the probability that a student will score between 65 and 75

In a communication system each data packet consists of 2000 bits. Due to the noise, each bit may be received in error with probability 0.1. It is assumed bit errors occur independently. Find the probability that there are more than 240 errors in a certain data packet.

Find dp/dq If P= q²+3/(q-1)³+(q+1)³

Given a transportation problem with the following costs, supply, and demand, find the initial solution

using the minimum cell cost method and Vogel’s approximation model. Is the VAM solution

optimal?

To

From 1 2 3 Supply

A 6 7 4 100

B 5 3 6 180

C 8 5 7 200

Demand 135 175 170

A string of iength L is stretched and fastened to two fix points. Find the solution of

the r.{ave equatiorl (vibrating string) ytt = a^2.yxx, when initial displacernent

y(x,0) = f (x) = b sin (pi.x / t).

also find the Fourier cosine transformation of exp(-x^2)

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?

Q2. A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack.

How many packs should be made to maximize book fair profits?

What will the profit be?