Math Answers

Twelve different video games showing alcohol use were observed. The duration times of alcohol use were​ recorded, with the times​ (seconds) listed below. What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 ​sec? Are the requirements all​ satisfied?

In the diagram, GB = 2x + 3..



What is GB?

5 units
10 units
15 units
30 units

show that ux =c1eax +c2e-ax is the solution of the difference equation ux +1-2 ux Cosha+ux-1 =0

a line goes through the point (4,7) and is perpendicular to another line with equation y=2x+2. what is the equation of the line?

Suppose that a household generates on average of 28 pounds of garbage each month for recycling.Assume garbage generation is normally distributed with standard deviation of 2 pounds. If a household is selected at random, find the probability of that household generating
a:More than 38 pounds of garbage per month
b:Between 27 and 31 pounds of garbage per month
c:Less than 30 pounds of garbage per month

a golfer hits her ball a distance of 127 m so that it finishes 31 m from the hole, calculate the angle between the line of her shot and direct line to the shot

For a Poisson distributed random variable X, P(X = 4) = P(X = 5). What is the mean and variance of the distribution.

If X is a random variable with E(X) = 3 and E(X^2) = 16, find a lower bound for the probability P[-2 < X < 8).

The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 424 consumers who have owned a ColorSmart-5000 television set for five years. Of these 424 consumers, 326 say their ColorSmart-5000 television sets did not need a repair, whereas 98 say their ColorSmart-5000 television sets did need at least one repair.

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested
for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected
by a technician:

o Gas volume: V = 0.8 m 3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done = 2
1
V
V
pdV

i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m 3 to 0.6 m 3 using:

o integral calculus
o Simpson’s rule
o the mid-ordinate rule.

iii. Comment on the accuracy of the two numerical methods.