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17 Rational Expressions Problems : Lowest Terms and LCD

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(See attached file for full problem description)

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Reduce to lowest terms
1. (see attached)

2. (see attached)

3. (see attached)

4. (see attached)

5. Area of a triangle.
If the base of a triangle is 8x +16 yards and it's height is yards, then what is the area of the triangle?

6.Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

7. reduce to LCD

8. Melanie can paint a certain room by herself in x days. Her helper melisse can paint the same room by herself in 2x days. Write a rational expression for the fraction of the room that they complete in one day by working together. Evaluate the expression for x=6.

9. simpilfy

10. (see attached)

11. (see attached)

12. (see attached)

13. commuting students at a well know university, ¼ of the undergraduate students commute, and 1/3 of the graduate students commute. One tenth of the undergraduates drive more than 40 miles daily, and 1/6 of the graduates drive more than 40 miles daily. If there are twice as many undergraduates as there are graduates, then what fraction of the commuters drive more than 40 miles daily?

14. solve for y

15. Catching up. A sailboat leaves port and travels due south at an average speed of 9mph. Four hours later a motorboat leaves the same port and travels due south at an average speed of 21mph. How long will it take the motorboat to catch the sailboat?

16.To estimate the size of the bear population on the peninsula, conservationist captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist estimate of the size of the population?

17. The ancient greeks thought that the most pleasing shape for a rectangle was one for which the ration of the length to the width was 8:5, the golden ration. It the length of a rectangular painting is 2 feet longer than the width, then for what dimensions would the length and width have the golden ration?

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Solution Summary

17 Rational Expressions Problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution provided by:
Changping Wang, MA
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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