Math Answers

Find nth derivative of e^ax cos² xsinx

A survey of 100 students produced the following information: 30 speak English, 45 speak Hindi and 60 speak Marathi. It is found that 10 speak both English and Hindi, 20 speak both Hindi and Marathi, 15 speak both English and Marathi and 5 speak all the three languages. a) How many of these students speak none of the three languages ? b) How many of these students speak exactly two languages ?

Identify the mapping diagram that represents the relation and determine whether the relation is a function(−3,−6),(−1,−6),(5,−6),(8,−6)

Given P(x,y) :y=x+5 ,determine the truth value of each of the following if the universe is the set of real numbers.

x^3y''' + 2x^2y'' = x + sin(lnx)

Show that the set W = {(a, b, 0) : a, b ∈ F} is a subspace of V3(F).

during a mathematics festival, students pay 20 pesos for the chance to put icing of a cake on the face of their favorite math teacher.The stidwnt flip a coin twice, if the results are the same both times (two heada or two tails), the students target flips the.same coin three times.If the teacher does not get the same results three times, the students applies icing on the teacher's face.however,ifthe student does not get the same result on his flips, and the teacher gets the same results on his three flips, the teacher applies icing on the student's face.who is more likely to have an icing on his face, the student or the teacher?

Let g be a finite non abelian group of order n with the property that G has a subgroup of order K for each positive integer K dividing n. prove that G is not a simple group

approximate the real root to four decimal places of x3+5x-3=0 (newton raphson method)

A bottling machine can be regulated so that it discharges an average of µ ounces per bottle. It has been observed that the amount of fill dispensed by the machine is normally distributed with σ = 1 ounce. A sample of n = 9 filled bottles is randomly selected from the output of the machine on a given day (all bottled with the same machine setting) and the ounces of fill measuered for each. 1 i) Find the probability that the sample mean will be within 0.3 ounce of the true mean for that particular setting. [4] ii) How many observations should be included in the sample if we wish X¯ to be within 0.3 ounce of µ with probability 0.95? [4] iii) Suppose we plan to select a random sample of ten bottles and measure the amount of fill in each bottle. If these ten observations are used to calculate S 2 , find numbers b1 and b2 such that P(b1 ≤ S 2 ≤ b2) = 0.90