Math Answers

Use Descartes’ Rule of Signs to determine the possible number of positive, negative and

imaginary zeros of P (x).

(i) P (x) = 2x^5+x^4+x^3-4x^2-x-3.

Use Descartes’ Rule of Signs to determine the possible number of positive, negative and

imaginary zeros of P (x).

(i) P (x) = 2x

5 +x

4 +x

3 −4x

2 −x −3.

Let P be the property “is a prime number” and O be the property “is an odd integer.” Consider the sets A = {x ∈ N : P(x)} and B = {x ∈ N : O(x)}. 1. Examine A and B with respect to the subset relation. What can you conclude? Justify your answer. 2. Are A and B equal? Justify your answer.

Find the angle nearest to the whole number between the surfaces x2+y2+z2=9 and z=x2+y2-3 at the point (2, -1, 2).

8. Let (x1, x2, ..., xn) be independent measurements of a random variable X with density function

f(x) = e−(x−α), x > α. Find an estimator, ˆ

α, of α by method of moments.

Sally can paint a room in 8 hours while it takes steve 9 hours to the same room. How long would it take them to paint the room if they worked together?

type an integer or a decimal round to one decimal place as needed

in 205 14.9 out of every 50 employees at a company were women. if there are 43,030 total company employees, estimate the number of women

At what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec

The number of automobile accidents a driver will be involved in during a one-year period is a random variable Y having a Poisson distribution with parameter X, where X depends on the driver. Suppose a driver is chosen at random from some population and hence X itself is a

continuous random variable with p.d.f f(x) , 0 < x < ∞

(a) Show that P(Y=k)= int o ^ infty P(Y=k|X=x)f(x)dx

(b) Suppose that x has an exponential distribution with mean 1/c where c is a

positive constant. Obtain the distribution of Y, hence find the expectation of Y.

The random variable X_{1} , X 2 ,.......,Xn , are independent and each has a poisson distribution with mean 1. Let Y=X 1 +X 2 +........+Xn . find the conditional distribution of X mathcal N given Y.