Amber

I know it means the total amount that you owe on your credit card.

I'm applying for online banking for my debit card & it says Last Statement Balance, but I don't owe money from my debit/checking.

Calculate the probability X < 0.9 when X has the standard uniform distribution

A book has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly located on those pages.

a) Find the probability that a random selection of 50 pages will contain no errors.

b) Find the probability that 50 randomly selected pages will contain at least 2 errors.

Surface finish defects in a small appliance occurs at random with a mean rate of 0.1 defects per unit. Find the probability that a randomly selected unit will contain at least one surface finish defect.

Compute the surface area of the surface generated by revolving the curve

c(t) = (t, e^t )about the x-axis for 0 ≤ t ≤ 1.

1) Express the definite integral as an infinite series.

∫ [0 to 1.9] cos(x^2) dx

The series I got was: [(-1)^n*1.9^(4n+1)]/[(4n+1)(2n)!]

2) Find its value to within an error of at most 10^−4.

A camel is on his way to the University of Cairo to deliver a speech. The university is 200 miles away and the camel walks at 10 miles an hour, planning on walking all night and arriving the following morning. One hour into his journey the desert suddenly expands mysteriously by length of 200 miles.

From his GPS the camel can tell that the expansion with uniform across the desert so that the fraction of the desert which he has traversed has not changed. Still pretty weird, though. An hour later it happens again so the desert is now 600 miles across. On a proportional basis, however, he's still making progress just not as much as planned. Assume that the strange phenomenon contingencies but at the end of each hour the desert expense uniformly (like a giant rubber band) by 200 miles.

a) Find a sequence x_n that gives a fraction of the desert crossed after n hours.

b) Will the camel ever make it to the university? Explain your conclusion.

c) If he doesn't make it give an estimate of how long his journey will take. If he doesn't make it find an upper bound on x_n that's less than 1.

Consider ∫ [4 t0 9] (1/√x) dx

1) Find a value of n for which |Ln − Rn| ≤ 0.01.

What would the shape of distribution be?

Say f(x)= cos(x) and g(x)= 1-(x^2/ 2).

R is the region bounded by the graph of f(x) and the x-axis between x= -π/2 and x= π/2 and S is the region bounded by the graph g(x) and the x-axis.

Rotating R about y-axis:

V = 2π ∫ [0 to π/2] (x cos(x)) dx = π²−2π

Rotating S about y-axis:

V = 2π ∫ [0 to √2] (x(1−x²/2)) dx = π

R has a larger volume because cos(x) is more than 1−x²/2 on the interval.

- Use this comparison to prove something we already know about π

Say f(x)= cos(x) and g(x)= 1-(x^2/ 2).

R is the region bounded by the graph of f(x) and the x-axis between x= -π/2 and x= π/2 and S is the region bounded by the graph g(x) and the x-axis.

- Use the Shell Method to find the volume of the solids generated by rotating R and S around the y-axis.

Say fx= cos(x) and gx= 1-(x^2/ 2).

R is the region bounded by the graph of fx and the x-axis between x= -π/2 and x= π/2 and S is the region bounded by the graph gx and the x-axis.

- Use the Shell Method to find the volume of the solids generated by rotating R and S around the y-axis.