?You put some ice cubes in a glass, fill the glass with cold water, and then let the

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

Mathematical Statistics with Applications 7
The joint distribution of amount of pollutant emitted from a smokestack without a cleaning device \(\left(Y_{1}\right)\) and a similar smokestack with a cleaning device \(\left(Y_{2}\right)\) was given in Exercise 5.10 to be \(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} 1, & 0 \leq y_{1} \l

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 3
Problem 84CP A cannon on a train car fires a projectile to the right with speed v0, relative to the train, from a barrel elevated at angle ?. The cannon fires just as the train, which had been causing to the right along a level track with speed vtrain, begins to accelerate with acceleration a. Find

Principles of General Chemistry 2
Consider the following reaction energy \(diagram\): (a) How many elementary steps are in the reaction mechanism? (b) Which step is rate limiting? (c) Is the overall reaction exothermic or endothermic? Equation Transcription: Text Transcription: diagram

Chemistry: The Central Science 13
(a) A cube of osmium metal 1.500 cm on a side has a mass of 76.31 g at 25 C. What is its density in g>cm3 at this temperature?

Classical Mechanics 0
Consider the rapid steady precession of a symmetric top predicted in connection with (10.112). (a) Show that in this motion the angular momentum L must be very close to the verti-cal. [Hint: Use (10.100) to write down the horizontal component Lhor of L. Show that if is given by the right side of (10.

Chemistry 11
Calculate the vapor pressure of a solution made by dissolving 82.4g of urea (molar mass = 60.06 g/mol)in 212 mL of water at 35C. What is the vapor-pressure lowering?

Inquiry into Physics 7
A 0.1-kg ball is attached to a string and whirled around in a circle overhead. The string breaks if the force on it exceeds 60 N. What is the maximum speed the ball can have when the radius of the circle is 1 m?