A car drives over the top of a hill that has a radius of

Probability and Statistical Inference 9
(Michigan Mathematics Prize Competition, 1992, Part II) From the set \(\{1,2,3, \ldots, n\}\), \(k\) distinct integers are selected at random and arranged in numerical order (from lowest to highest). Let \(P(i, r, k, n)\) denote the probability that integer \(i\) is in position \(r\). For example, ob

Chemistry 11
Calculate the number of C, H, and O atoms in 1.50 g of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\), a sugar.

Organic Chemistry 9
For each pair of ions, determine which ion is more stable. Use resonance forms to explain your answers. (a) CH3 CH CH3 + CH3 CH OCH3 + or (b) + 3 CCH CH3 3 NCH CH3 + 3 CCH CH3 3 CHCH CH3 or (c) CH2 CH CH+ CH3 or CH2 CH CH2 + CH2 (d) CH2 CH3 or 2 NCCH (e) CH2 + CH2 + or (f) O O

Principles of Economics 6
Suppose the federal government requires beer drinkers to pay a $2 tax on each case of beer purchased. (In fact, both the federal and state governments impose beer taxes of some sort.) a. Draw a supply-and-demand diagram of the market for beer without the tax. Show the price paid by consumers, the pri

Principles of Macroeconomics 6
Bill and Hillary produce food and clothing. In an hour, Bill can produce 1 unit of food or 1 unit of clothing, while Hillary can produce 2 units of food or 3 units of clothing. They each work 10hours a day. a. Who has an absolute advantage in producing food? Who has an absolute advantage in producing

Human Biology 11
You are a living organism. Which characteristics of life do you exhibit?

Principles of Economics 9
Fredo loves watching Downton Abbey on his local public TV station, but he never sends any money to support the station during its fund-raising drives. a. What name do economists have for people like Fredo? b. How can the government solve the problem caused by people like Fredo? c. Can you think of wa

Introductory Chemistry: A Foundation 9
Write the complete orbital diagram for each of the following elements, using boxes to represent orbitals and arrows to represent electrons. a. aluminum, Z 5 13 b. phosphorus, Z 5 15 c. bromine, Z 5 35 d. argon, Z 5 18