Math Answers

Trace the curve x=a(theta - sin theta), y = a(1-cos theta). State the properties you use for tracing it also.

According to the Sleep Foundation, the average night's sleep is 7.6 hours. Assume the standard deviation is .6 hours and that the probability distribution is normal.

a) What is the probability that a randomly selected person sleeps more than 8 hours?

b) What is the probability that a randomly selected person sleeps 6 hours or less?

c)Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

Luis Mahla purchases a Porsche Boxster for $46,800 and finances the entire amount at an annual interest rate of 5.4% for 8 years. Find the monthly payment. Assume the sales tax is 6% of the purchase price and the license fee is 1% of the purchase price. (Round your answer to the nearest cent.)

The average price of a gallon of unleaded regular gasoline was reported to be $2.75 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $.20.

a. What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean?

b. What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean?

c. What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean?

d. Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to have at least a .95 probability that the sample mean is within $.03 of the population mean?

Angle between the lines x+3=0 and y+7=0

derive a suitable numerical differentiation formula of 0(h2) to find f''(2. 4) with h =0.1 given the table f(0.1)=3.41, f(1.2) =2.68, f(2.4)=1. 37, f(3.9) =-1. 48.

the position of f(x) of a particle moving in a line at various times xk is given in the following table. estimate the velocity and acceleration of the particle at x =1.2. f(1.0)=2.72, f(1.2)=3.32, f(1.4)=4.06, f(1.6)=4.96, f(1.8)=6.05, f(2. 0)=7.39, f(2.2)=9.02.

determine the constants a, b, c in the differentiation formula y '' (x0) =ay(x0-h) +by(x0) +cy(x0 +h). so that the method of the highest possible order and the error term of the method.

using the classical R-K method of O(h4) calculate approximate solution of the IVP y'=1-x+4y, y(0) =1 at x=0.6, taking h=0.1 and 0.2. use extrapolation technique to improve the accuracy.

Find the volume of a solid obtained by revolving the curve
x=acos³theta, y=asin³theta about the y axis.