Draw a plausible mechanism for the following transformation: OH O O O O O HO H3O+

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

Campbell Biology 9
In mitochondria, exergonic redox reactions a. are the source of energy driving prokaryotic ATP synthesis. b. are directly coupled to substrate-level phosphorylation. c. provide the energy that establishes the proton gradient. d. reduce carbon atoms to carbon dioxide. e. are coupled via phosphorylated

Campbell Biology in Focus - Standalone book 1
Fossilized stromatolites a. more than 2.8 billion years old have not been discovered. b. formed around deep-sea vents. c. resemble structures formed by bacterial communities that are found today in some shallow marine bays. d. provide evidence that plants moved onto land in the company of fungi aroun

College Physics for AP® Courses 1
A number of amusement parks have rides that make vertical loops like the one shown in Figure 6.33. For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What other

Human Anatomy & Physiology 9
Osteocytes residing in lacunae of osteons of healthy compact bone are located quite a distance from the blood vessels in the central canals, yet they are well nourished. How can this be explained?

Principles of Economics 6
Consider the following cost information for a pizzeria: Quantity Total Cost Variable Cost 0 dozen pizzas $300 $ 0 1 350 50 2 390 90 3 420 120 4 450 150 5 490 190 6 540 240 a. What is the pizzerias fixed cost? b. Construct a table in which you calculate the marginal cost per dozen pizzas using the inf

The Economics of Money, Banking and Financial Markets 12th
Why does the free-rider problem occur in the debt market?

Chemistry 13
The unit troy ounce is often used for precious metals such as gold (Au) and platinum (Pt). (1 troy ounce = 31.103 g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? (1 lb =16 oz; 1 lb = 453.6 g.)