Idaho
Society of Professional Engineers
PO Box 170239, Boise, ID 83717-0239 208-426-0636 Fax: 208-426-0639 E-Mail: ispe@idahospe.org
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PO Box 170239, Boise, ID 83717-0239 208-426-0636 Fax: 208-426-0639 E-Mail: ispe@idahospe.org |
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Idaho Society of Professional Engineers Friday Update – 11/05/10
What’s Inside: Lunch & Lead: Sustainable Business Solutions MATHCOUNTS Problem of the Week
In the News: Obama Celebrates Future Engineers
UPCOMING EVENTS:
My Discover-e Resource
Help shape
the future of someone you care about – and then let them discover how they can
shape the world! Find fun activities and events near you that will spark their
imagination and open their eyes to the significance of engineering in their
world.
Lunch & Lead: Sustainable Business SolutionsThe University of Idaho Boise center offers up practical solutions for businesses that want to make a commitment to sustainability and improve their bottom line. It's the focus for monthly brown bag presentations that are part of the Lunch & Lead: Sustainable Business Practices series. The series runs February through December 2010. -------------------------------------------------------------------------------
Thursday, December 2, 2010 ------------------------------------------------------------------------------- All brown bag gatherings are free and open to the public, but RSVPs are required at professionaldev@uidaho.edu or (208) 334-2999. Space is limited. Drinks and cookies are provided; attendees are encouraged to bring their own lunch.
MATHCOUNTS PROBLEM OF THE WEEKCan you solve this MATHCOUNTS problem? The answer will appear in the next edition of the Friday Update!
Botanical Gardens
The landscape of Kelli’s garden is shown. She plans to cover the shaded region of the garden, which measures 2,510 square feet, with stones. Garden Mart sells 50-pound bags of stones each of which contains enough stones to cover a region measuring 4 square feet. Since Garden Mart sells only whole bags of stones (no partial bags), how many pounds of stones need to be purchased in order to have enough stones to cover the shaded region? ------------------------------------------------------------------------------- Garden Mart sells each 50-pound bag of stones for $48.50. The identical type of stones at Garden Wholesaler is not sold in bags, but in bulk by the pound. Garden Wholesaler sells the stones for $1.50 per pound for the first 2 tons, and charges $0.90 per pound for any amount of the stones purchased that exceeds 2 tons. What is the positive difference between the total cost at Garden Mart and at Garden Wholesaler for the quantity of stones which need to be purchased to cover the region of Kelli’s garden from the previous question? -------------------------------------------------------------------------------
The landscape of a different garden is the region shown created from two concentric regular octagons. There are four paths leading to the inner region of the garden. The entrance to each of the four paths is 10 feet wide, which represents 1/3 the side length of the outer regular octagon. These paths lead to a larger pathway that surrounds a circular fountain. The fountain is located in the center of the garden and has a circumference of 20π feet. ------------------------------------------------------------------------------- The shaded region is to be covered with stones. Suppose the distance from the entrance of any of the four paths to the center of the garden (center of the fountain) is 36 feet and the area of the inner octagon is 4/9 the area of the outer octagon. What is the total number of square feet that will be covered in stones? Express your answer to the nearest whole number.
Answer to last week’s problem: Since 62 of the105 championships were won by an American League team, 105 – 62 = 43 championships were won by a National League team. Therefore, the percent of World Series championships won by a National League team is 43/105 = .4095238095 ≈ 41%. ------------------------------------------------------------------------------- Since the Yankees have played in 40 of the 105 World Series, the probability that they will play in the World Series that we will use is 40/105. Since the Yankees have won 27 of those 40 World Series, the probability that they will win the championship is 27/40. The probability that they will appear in the World Series and win the championship is then 40/105 × 27/40 = 27/105 = 9/35.
You can also solve the problem without using dependent events since winning a championship automatically implies that the team is in the World Series. In that case since the Yankees have won 27 of the 105 World Series the probability that they will win the championship is 27/105 = 9/35. ------------------------------------------------------------------------------- Thanks to MATHCOUNTS Coach Troy Deckebach of Wissahickon Middle School, in Amber, Pennsylvania, for recognizing that, as written, there is not enough information provided to solve this problem. Were it written as intended, the problem would read, “Suppose the probability that an American League team will win any individual World Series game is 60%.” With this correction there is now sufficient information to solve the problem.
If the probability that an American League team will win any individual World Series game is 60%, then the probability that a National League team will win any individual game is 100% − 60% = 40%. Suppose a National League team loses the first game, of the series, the probability that they will win the championship with the 5th game is 0.6 × 0.4 × 0.4 × 0.4 × 0.4 = 0.01536. Since a National League team can win 4 out of 5 games in a total of 4 different ways (ANNNN, NANNN, NNANN, NNNAN) we have 0.01536(4) = 0.06144 ≈ 6%.
If you want to see the problem again, click http://mathcounts.org/Page.aspx?pid=1573#
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National Engineers Week - Future City Competition
Board of Professional Engineers and Professional Land Surveyors
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