Prove the result in Result 4.5: For every positive integer n, 12 + 22 + + n2 =

Chemistry: A Molecular Approach 3
The cyanate ion (OCN-) and the fulminate ion (CNO-) share the same three atoms but have vastly different properties. The cyanate ion is stable, while the fulminate ion is unstable and forms explosive compounds. The resonance structures of the cyanate ion were explored in Example 9.8 . Draw Lewis stru

Introductory Chemistry 5
Classify each change as physical or chemical. (a) Sugar dissolves in hot water. (b) Sugar burns in a pot. (c) A metal surface becomes dull because of continued abrasion. (d) A metal surface becomes dull on exposure to air.

University Physics 13
Problem 109P Compute the ratio of the rate of heat loss through a single-pane window with area 0.15 m2 to that for a double-pane window with the same area. The glass of a single pane is 4.2 mm thick, and the air space between the two panes of the double-pane window is 7.0 mm thick. The glass ha

Probability and Statistical Inference 9
In a smoking survey among boys between the ages of 12 and 17, \(78 \%\) prefer to date nonsmokers, \(1 \%\) prefer to date smokers, and \(21 \%\) dont care. Suppose seven such boys are selected randomly. Let \(X\) equal the number who prefer to date nonsmokers and \(Y\) equal the number who prefer to

Organic Chemistry 7
Problem 21P For each of the following compounds, indicate the aldehyde or ketone from which it would be formed by an aldol addition: a. 2-ethyl-3-hydroxyhexanal b. 4-hydroxy-4-methyl-2-pentanone c. 2,4-dicyclohexyl-3-hydroxybutanal d. 5-ethyl-5-hydroxy-4-mcthyl-3-heptanone

Myers' Psychology for AP 2
Cognitive neural prosthetics are placed in the brain to help control parts of the a. motor cortex. b. auditory cortex. c. somatosensory cortex. d. visual cortex. e. parietal lobe.

Principles of Economics 6
Consider a monopolistically competitive market with N firms. Each firms business opportunities are described by the following equations: Demand: Q = 100/N P Marginal Revenue: MR = 100/N 2Q Total Cost: TC = 50 + Q2 Marginal Cost: MC = 2Q a. How does N, the number of firms in the market, affect each

Concepts of Biology 1
Among other bones, the axial skeleton includes the ________. a. thoracic cage and vertebral column b. thoracic cage and pectoral girdle c. skull and pelvic girdle d. pectoral and pelvic girdles