ohwow!

A certain insurance agent is trying to assess the probabilities of clients making claims over the next few months. She decides that if the probability of a client making n claims is p_n where n is >/= (greater than or equal to) 0, then the probability p_n+1 of a client making one more claim, namely n+1 claims, is 1/7 p_n. (When n=0, p_0 is the probability that the client makes no claims.) What is the probability that a client will make at least two claims over the next couple of months?

Urn I contains 4 red balls and 6 blue balls. Urn II contains 16 red balls and an unknown number b of blue balls. One ball is chosen at random from each urn. If it is known that the probability that the 2 chosen balls have the same color is .44, how many blue balls are there in urn II?

Please show me how you got there, I wana make sure I'm doing the right work.

A 52- Card Deck is missing one card. What is the probability that a single card frawn fromt his incomplete deck is a spade?

HINT: Define H: the missing card is a heart. S: Missing card is a Spade, D: missing card is a diamond, and C: the missing card is a club, let P: a spade is chosen from the incomplete deck. Note that {H,S,D,C} is partition of the sample space.

Please let me know how you got this, I greatly appreciate the help thanks!!

One chip is drawn at random from an urn that contains one white chip and one black chip. If the white chip is selected, we simply return it to the urn; if the black chip is drawn, that chip—together with another black— are returned to the urn. Then a second chip is drawn, with the same rules for returning it to the urn. Calculate the probability of drawing two whites followed by three blacks.

I need some help would you mind showing the formula etc you used!

Suppose that two numbers are chosen from the set {1,2,....,1000} with replacement (meaning that after a number is chosen, it is put back into the set so that it can be chosen again.) What is the probability that the first number chosen is greater than the second number chosen?

Hint: Let F= first # is greater than the first, S= secont # is greater than the first, E= two numbers are equal. Note that P(F) + P(S) + P(E) = 1 and P(F) = P(S).

A fair coin is tosses 10 times. What is the probability of the event E that two hands or two tails occur successively exactly once. For example HTHTH T T HTH. (Hint: the total number of sequences of Hs and Ts is 2^10 = 1024.

Let A be the 3x3 matrix:

[2 0 0]

[-3 5 -3]

[-6 6 -4]

Find a diagonal matrix D and an invertible matrix P such that A=PDP^-1.

Find a 3x3 matrix whose null space is

1.a point

2. a line

3. a plane

I'm not sure how to go about starting this, please explain how to get the answer if you answer! Thank you I really appreciate it

Find a subset of the vectors that forms a basis for the space spanned by the vectors; then express each vector that is not in the basis as a linear combination of the basis vectors.

a) v1= (1,-2,0,3), v2= 2,-4,0,6), v3=(-1,1,2,0), v4=(0,-1,2,3)

Consider the double integral cos((x+y)^2)dA (the inside integral starts at the boundary R) Where R is the region bounded by the 2 axes and te line y=2-x.

a) Write this as a double integral in retangular coordinates.

b)Make the substitution u=x+y, v=x-y, and write this as a iterated integral in u and v (using the Jacobian).

c) evaluate the integral

Thank you so much for the help!

Find the coordinate vector of w relative to the basis S={u1,u2} of R^2.

(a) u1= (2,-4), u2= (3,8); w=(1,1)

People often define the dot product on P2 (or more general vector spaces of functions) by: f(x) "dot" g(x)= the integral from 0 to 1 f(x)g(x) dx. This should seem reasonable from calculus: When you change from finite things (like the coordinants of a vector in R^n) to infinite things (like the graph of a polynomial f(x)), sums become integrals. So instead of summing UiVi over the coordinates i, we integrate f(x)g(x) over the possible values of x. But one problems shows up: the 'standard' basis {1,x,(x^2)} is not orthonormal!

1. Find (x^2) "dot" (x+1) for this inner product.

2. Find a non-zero polynomial in P2 which is orthogonal to (x^2) for this dot product.

3. Find an orthogonal basis for P2 (you may want to use Gram-Schmidt on the standard basis {1,x,(x^2)}).

Prove why all of these are false, as in with examples or any other explanation.

a) If V= span{v1,....,vn} then {v1,...,vn} is a basis for V.

b) Every linearly independent subset of a vector space V is a basis for V.

c) Every basis for P4 contains at least one polynomial of degree 3 or less.

Which of the following form a bases for P2, (does this form a bases for P2).

a) 1+x+(x^2), x+(x^2), (x^2)

Please explain and justify the answer so I can better understand it!!! THANK YOU

Consider the bases B= {x+2,x-1} and C={2x-1,3x+1} for P1. Let p be the polynomial suthat [p]_B= the 2x1 matricie [2]. Find [p]_C.

[1]

Give vector v= [2,-2,3] & vector w=[2,-1,2]

Find a way to write v as a sum v=x+y where x is parallel to w and y is perpendicular to w.

If you don't want to solve it through, thats fine, please try giving the steps!

I understand if the dot product of y and w=0 it's perpendicular but how would I manipulate that to give me the actual vector. And for x, would I just do x cross w=0 to get parallel?

Thank you so much for the help!!

1. When placed a distance d, from a positive point charge, a positively charged particle has a potential energy U due to the electric field created by the point charge. If the positively charged particle is moved to a distance 2d, which of the following represents its potential energy?

A. -U/2

B. U/4

C. U/2

D. 2U

2. A dipole (one positive charge and one negative charge fixed a distance d apart) is placed in a uniform electric field as show in problem 1. The magnitude of the net force on the dipole is...

A. 0

B. qE

C. 2qE

D. 2qEd

3. For the dipole in problem 2, the magnitude of the net torque on the dipole is...

A. 0

B. qEd

C. 2qEd

D. 4qEd

A dipole (one positive charge and one negative charge a fixed distance, d, apart) is placed in a uniform electric field as shown above. The magnitude of the net force on the dipole is

A. 0

B. qE

C. 2qE

D. 2qEd

When placed a distance d from a positive point charge, a positively charged particle has a potential energy U due to the electric field created by the point charge. If the positively charged particle is moved to a distance 2d, which of the following represent its potential energy?

A. -U/2

B. U/4

C. U/2

D. 2U

Diagram for problem- https://docs.google.com/open?id=0B3h69Alvd6ggMEhfV...

1. If the particles begin and end at rest, and all are positively charged, the same amount of work was done by which particles?

A. W & Y

B. W,Y & Z

C. Y & Z

D. W,X,Y &Z

2. If all particles started from rest, and all are positively charged, which particles must have been acted upon by a force other than that produced by the electric field?

A. W & Y

B. X & Z

C. X,Y, & Z

D. W,X,Y & Z

3. Suppose particle Z has a charge of +2C, and it begins and ends at rest. If E is 5 N/C, how much work is done on particle Z?

A. 10J

B. 20J

C. 40J

D. 80J