Math Answers

Given f(x)=x^7 -x^5 -x^4 +2x +1 on interval [-1,1] show that there's at least one critical point on this interval.

D and E are points on sides of AB and BC respectively of ∆ABC such that AD:DB= 2:3 and BE=4÷3 EC. If DK||AE and AE and CD intersect at P, Find the ratio of CP:PD

If p(A) = 0.6 and k is the number of successes of A in n trials

(A) Show that p {550<= k <= 650} = 0.999 , for n = 1000

(B) Find n such that p{0.59n <= k <= 0.61n} = 0.95

Solve the following initial value problem using Laplace transform. y''+16y = 2 sin 4t, y(0)=-1/2; y'(0)=0 

Does the sequence 3+ (-1)^n converge to 2. Justify

1.Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the

a) reflexive closure of R.

b) symmetric closure of R.

The life expectancy at birth y for females born in a certain country is given by the equation y=0.13x+74.6​, where x is the number of years after 1950.

a. Find the life expectancy for a female born in 1990.

b. Find and interpret the slope of the equation.

c. Find and interpret the​ y-intercept of the equation.

Construct the truth table of the following proposition.

1. (p∧q)→(p∨q)

2. ~(p→q)

3. (p∨q)∧~p

Using the number 1,2,3,4,5 and 6 as the element of the population

a. find the mean of the sample of size 3 without replacement

b.construct the sampling distribution of the sample mean

I. The mean

II.The variance

III. The standard deviation of the sampling of the sample means

The demand function for a commodity is Q=6000−30P

Q=6000−30P. Fixed costs are R72000

R72000 and the variable cost is R60 per unit produced. What are the equations for total revenue and total cost in terms of P

P?