Determine the number of vectors (x1,... ,xn), such that

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

University Physics 13
Problem 12DQ A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point charge outside the conductor affect the electric field insid

Classical Mechanics 0
By evaluating their dot product, find the values of the scalar s for which the two vectors b = x + s'Sr and c = x sS7 are orthogonal. (Remember that two vectors are orthogonal if and only if their dot product is zero.) Explain your answers with a sketch.

Physics: Principles with Applications 6
(II) In a Rotor-ride at a carnival, people are rotated in a cylindrically walled room. (See Fig. 535.) The room radius is 4.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down

Physics: Principles with Applications 6
(II) The roller-coaster car shown in Fig. 6-41 is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4. Figure 6-41

Human Anatomy & Physiology 9
Blockage of the scleral venous sinus might result in (a) a sty, (b) glaucoma, (c) conjunctivitis, (d) a cataract.

Genetics: Analysis and Principles 6
What is an operon? a. A site in the DNA where a regulatory protein binds b. A group of genes under the control of a single promoter c. An mRNA that encodes several genes d. All of the above

Human Biology 11
Jogging is considered aerobic exercise because the cardio-vascular system (heart and blood vessels) can adjust to supply the oxygen needs of working cells. In contrast, sprinting the 100-meter dash might be called anaerobic (lacking oxygen) exercise, and golf non aerobic exercise. Explain these last