Math Answers

A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population.

A. List all the possible samples and the corresponding mean.

B. Construct the sampling distribution of the sample means.

Volume of the Solid (Shell Method)

Given the bounded region is revolved about y axis, find the volume of the solid generated.

The region below the curve y= Inx, above the x-axis, and to the left of the line x=4.

Suppose z is a function of x and y and tan(√x + y) = e^z^2. Determine ∂z/∂x and ∂z/∂y.

1.One-tailed test;variance is known,a=0.05,n=35

(𝑥𝑦²+ 𝑦 − 𝑥)𝑑𝑥 + 𝑥(𝑥𝑦 + 1)𝑑𝑦 = 0

A 9N force F1 and a 10N force F2 act in the same direction 2i+j-2k and 4i-3j respectively.

a) Find the resultant of the two forces

b)find the total work done if the forces make the object move 2m along the vector S=i+j+k

c)what is the maximum work done that can be achieve if the forces displace the object by 1m?

d)what is unit vector along which the object will move to achieve maximum work done?

f) find F1.F2

g) find F1*F2

In a company having 80 employees, 60 earn 10.00 per hour and 20 earn $13.00 per hour. Determine the mean earning per hour.b would the answer in part (a) be the same if the 60 employees earn a mean hourly wage.

A 9N force F1 and a 10N force F2 act in the same direction 2i+j-2k and 4i-3j respectively.

a) Find the resultant of the two forces

b)find the total work done if the forces make the object move 2m along the vector S=i+j+k

c)what is the maximum work done that can be achieve if the forces displace the object by 1m?

d)what is unit vector along which the object will move to achieve maximum work done?

f) find F1.F2

g) find F1*F2

The owner of a restaurant that serves continental food wants to study characteristics of his customers. He decides to focus on two variables: the amount of money spent by customers and whether customers order dessert. The results from a sample of 60 customers are as follows: • Amount spent: X=$38.54, S= $7.26 • 18 customers purchased dessert. a. Construct a 95% confidence interval estimate of the population mean amount spent per customer in the restaurant.

Question:1

It is claimed that an automobile is driven in the average less than 20,000 km /year. To test this claim, a random sample of 100 auto-mobiles owners are asked to keep a record of the kilometers, they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deviation of 3900 kilometers. Use a 0.01 level of significance.

Question: 2

Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 litters.

Use a 0.01 level of significance and assume that the distribution is Normal.