Show that if a tree has a vertex of degree K, then there are at least K vertices in the

Chemistry: The Central Science 12
Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in Si and Cl atoms is \(4.29+\) and \(6.12+\), respectively. (a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both \(\mathrm{Si}\) and \(\mathrm{Cl}\) by assum

Introductory Chemistry 5
Consider the reaction: \(\mathrm{Mg}(s)+2~\mathrm{HCl}(aq) \longrightarrow \mathrm{MgCl_2}(aq)+\mathrm{H_2}(g)\) What minimum amount of 1.85 M HCl is necessary to produce 28.5 L of \(\mathrm H_2\) at STP? Equat

Physics: Principles with Applications 7
A pendulum consists of a mass M hanging at the bottom end of a massless rod of length which has a frictionless pivot at its top end. A mass m, moving as shown in Fig. 735 with velocity v, impacts M and becomes embedded. What is the smallest value of v sufficient to cause the pendulum (with embedded m

Sears and Zemansky's University Physics with Modern Physics 13
A narrow, U-shaped glass tube with open ends is filled with \(25.0 \mathrm{~cm}\) of oil (of specific gravity 0.80) and \(25.0 \mathrm{~cm}\) of water on opposite sides, with a barrier separating the liquids (Fig. P12.58). (a) Assume that the two liquids do not mix, and find the final heights of the

Myers' Psychology for AP 2
The way we explain negative and positive events is called a. personal control. b. reciprocal determinism. c. positive psychology.d. attributional style.e. situational assessment

Principles of Economics 6
The residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2010, they buy 100 heads of cauliflower for $200, 50 bunches of broccoli for $75, and 500 carrots for $50. In 2011, they buy 75 heads of cauliflower for $225,80 bunches of broccoli for $120, and 500 carrots f

The Practice of Statistics 5
Cereal A companys cereal boxes advertise 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean m = 9.70 ounces and standard deviation s = 0.03 ounces. (a) What is the probability that a randomly selected box of the cereal contains less

Urban Economics 8
Migration to Portland In the last several months, the number of cars driving in Portland with Washington State license plates has increased dramatically. Suppose this refl ects migration from Seattle to Portland. Use two utility curves, one for Portland and a second for Seattle, to represent this mig