Recent content by JOhnJDC

I think the answer is to construct the 90% confidence interval using the data given. Because this interval will be centered on the observed sample mean x, only 5% of averages will be above the upper bound of this interval. Therefore, I can be 95% confident that the upper bound is the value v...

Homework Statement I know the sample size n, the observed sample mean x, and the observed sample standard deviation s. I need to determine a value v such that I'm 95% confident that the average is v or less.The Attempt at a Solution If I calculate the 95% confidence interval, then I know...

That clears it up. Thanks, guys.

Homework Statement \int(3x3-4x2-3x+2)/(x4-x2) Homework Equations P(x)/Q(x)=A1/(x-r1)+A2/(x-r2)+... if x-r occurs with multiplicity m, then A/(x-r) must be replaced by a sum of the form: B1/(x-r)+B2/(x-r)2+... I think this second equation is the source of my confusion. The Attempt at a...

I see it now. Thanks for your help. \int(a2-u2)-1/2udu Substitute v=a2-u2, dv=-2udu, udu=-dv/2 = -1/2\intv-1/2dv = -v-1/2 = -sqrt(a2-u2)

Are you saying that I should substitute u=a sin theta to obtain: \intudu/sqrt(a2-u2) = \int(a sin theta)(a cos theta)(d theta)/(a cos theta) = a cos theta So, u = a cos theta and cos theta = u/a, but u/a doesn't equal -sqrt(a2-u2) What am I missing?

Homework Statement Find \int(x+2)dx/sqrt(3+2x-x2) Homework Equations \intdu/sqrt(a2 - u2) = sin-1u/aThe Attempt at a Solution I began by completing the square: 3+2x-x2 = 4 -(x2-2x+1) So, 4-(x-1)2 = a2-u2 and a=2 and u=(x-1) Further, since x=(u+1), dx=du and (x+2)=(u+3) Substituting, I...

Other than finding a quotient, I've never had to manipulate/simplify factorials. Thinking about this again, since the number (n-k+1) is 1 greater than the number (n-k), (n-k)! times (n-k+1) must equal (n-k+1)!.

Homework Statement If k people are seated in a random manner in a row containing n seats (n>k), what is the probability that the people will occupy k adjacent seats in the row? I realize that there are n choose k sets of k seats to be occupied, and that there are n-k+1 sets of k adjacent...

Thanks, Dick. Any ideas on my proof question from above (my 2nd post)?

I'm not so strong in trig, but did you mean to say 1-cos(theta)=2*sin2theta/2? If 1-cos2theta = 2sin2theta, then 1-cos theta = 2sin2theta/2 because we halved the angle cos2theta on the left side?

I have a separate, basic question related to arc lengths of polar curves. I'm trying to derive the formula ds2=r2dtheta2+dr2, which enables me to compute arc lengths of polar curves by integration, from the rectangular equation for the differential element of arc length, namely ds2=dx2 + dy2...

Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...

Thanks, EvilKermit. I used a graphing calculator to find the intersection at (-2,-8). I just wanted to do it algebraically. I'll check out the link you provided. y=x3 and y=3x-2 do not intersect at any point when x=0; nor is the area between the curves symmetrical about the y-axis. The...

Homework Statement What is the area between y=x3 and its tangent at x=1The Attempt at a Solution The first derivative of y=x3, which is 3x2, tells me that the slope of the tangent at x=1 is 3. That (1,1) is a point on the tangent line tells me that the equation of the tangent line is y=3x-2...