# Equation of an Ellipse, Interest and Lotto Probability

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Several state and federal government spokespersons who use linear equations in a variety of ways.

1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse. Because the President officiates at this event, the Secret Service makes calculations which they use in planning security.

The Ellipse is actually an ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse.

2. The Board of Governors at the Federal Reserve Bank set the prime interest rate. These rates trickle down through the economy at various rates and affect consumer spending and saving habits. The economists at the Federal Reserve follow sample households in order to extrapolate information which they use in forecasting. For example, in one household they studied, the family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the interest would have been the same. Find the principal and the rate.

3. Another family in the Federal Reserve study group borrowed $120,000. The loan is to be repaid in 13 years at 12% interest, compounded annually. How much will be repaid at the end of 13 years?

4. Twice a week, the State of Michigan runs a 6 out of 49 number lotto that pays at least $2 million. The State needs to know the probabilities of winning in order to ensure that the lottery has ample reserves for the payouts. You purchase a card for $1 and pick any 6 numbers from 1 to 49. If your numbers match those that the state draws, you win. How many 6-number combinations are there for the drawing? If you buy one ticket, what is your probability of winning (6 out of 6)?

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##### Solution Summary

Equation of an Ellipse, Interest and Lotto Probability are investigated.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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