a. Prove the Archimedes result that the area of a section of a parabola equals times the area of the inscribed triangle of the same height. (You may use calculus here.)

b. In what sense can one consider Archimedes to be the inventor of calculus?

c. Find at least five axioms equivalent to the parallel lines axiom. Give the dates when they were proposed and the person that proposed them.

One Hypothesis test is an F test for the equality of the variances of travel Times and the second test is a T-test for the equality of the means of travel times in MINUTES. The F test must be performed first in order to select either Case1 or Case 2 for the T-test as listed in chapter 5. Then perform the Required T-test (either case 1 or 2 depending on your findings of the F-test). Also in the Conclusion and Recommendations section 5, You Must state your findings and the reasons for the existence of differences in the two means and or the existence of differences between the two variances and You Must recommend any future Hypothesis tests and other steps or other ways to collect the data in the future to make an inference about the mean travel times and their variances.

Data from a to b:

Data from B to A:

Sally works as a manager in the gardening section of her local Bunnings Store. Recently, Sally was approached by a customer asking questions about the store’s range of built in kitchens. Although she knew nothing about the products, Sally recommended the deluxe kitchen package which came with free installation. After completing the sale, Sally handed the customer her Bunnings business card (which identified her as a manager), explained that the customer should get his new kitchen professionally installed and to forward her the 3^rd party’s invoice – which Bunnings would pay. A few weeks later, the customer is shocked to learn that Bunnings is refusing to pay his carpenter’s $10,000 invoice and that Sally failed to mention that the offer was capped at $500.

Required:

(a) With reference to Pacific Carriers v Paribas, what is the test for deciding if an agent had apparent authority?

(b) Analyse whether Sally had apparent authority to bind Bunnings Pty Ltd to this $10,000 contract.

(c) How would your answer be different if the customer knew that Sally didn’t have permission to authorise this transaction

Use the Internet to find an environmentally related problem that is happening in your area. Present information about the history behind this problem including the population growth model in the area, what factors led to its occurring and who might be responsible for it. Share what is being done to solve the problem and how effective those efforts are. Present ideas from the textbook about how the problem might be mitigated. Extrapolate your local issue to the global environment. What classes of environmental problems seem to be widespread and recurring across our country and the world. How is population growth related to the problem ?

In your own words, describe each of the four financial statements. Go online and find the most recent set of financial statements for a publicly traded company that you are interested in, and explain what you learned about that company from exploring its financial statements.

In your own words, describe each of the four financial statements. Go online and find the most recent set of financial statements for a publicly traded company that you are interested in, and explain what you learned about that company from exploring its financial statements.

Explain the difference between process capability and statistical control.

Suppose that a process with a normally distributed output has a mean of 50.0 cm. and a variance of 3.61 cm. If the specifications are 51.0 +/- 3.75 cm.,

a. Compute Cp and Cpk

b. What are your conclusions about this process?

In your own words, describe each of the four financial statements. Go online and find the most recent set of financial statements for a publicly traded company that you are interested in and explain what you learned about that company from exploring its financial statements.

Air. Write in reasonable detail, using the macroscopic nature (our experience) and microscopic nature (molecular level) the composition of air, pollutants in air, where pollutants come from, how they impact health and environment, and what steps are being taken to keep air clean. Share your thoughts on this topic.

PLEASE SOLVE ALL PARTS AND EXPLAIN IN DETAIL.

I'M HAVING A DIFFICULT TIME UNDERSTANDING HOW TO FIND/SOLVE THESE TYPES OF PROBLEMS:

In 2017, as reported by ACT Research Service, the mean ACT Math score was μ=20.6 μ=20.6 . ACT Math scores are normally distributed with σ=4.8 σ=4.8 .

1. What is the probability that a randomly selected test taker has an ACT Math score less than 18? Is this result unusual? Explain.
2. Describe the sampling distribution of x ˆ  x^ , the sample mean ACT Math score for a random sample of 40 tests using the N(mean, standard deviation) notation.
3. What is the probability that a random sample of 40 tests has a mean ACT Math score less than 18? Is this result unusual? Explain.
4. What is the difference in part a and c in this question?