Prove that if W is a subspace of a vector space V and w\, w2, , wn are in W, then a\W\ +

Introductory Chemistry 5
Write a balanced chemical equation for the photosynthesis reaction in which gaseous carbon dioxide and liquid water react in the presence of chlorophyll to produce aqueous glucose (\(C_{6} H_{12} O_{6}\)) and oxygen gas.

A First Course in Probability 9
Problem 33P A newsboy purchases papers at 10 cents and sells them at 15 cents. However, he is not allowed to return unsold papers. If his daily demand is a binomial random variable with n = 10, p = , approximately how many papers should he purchase so as to maximize his expected profit?

Physics: Principles with Applications 7
(III) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at \(90^{\circ}\). (a) At what angle does the target particle move after the collision? (b) What are the final speeds of the two particles? (c) What fra

Chemistry 11
The following Lewis structures for (a) HCN, (b) \(\mathrm{C_2H_2}\), (c) \(\mathrm{SnO_2}\), (d) \(\mathrm{BF_3}\) (e) HOF, (f) HCOF. and (g) \(\mathrm{NF_3}\) are incorrect. Explain what is wrong with each one and give a correct structure for the molecule. (Relative positions of atoms are shown corr

Organic Chemistry 8
Identify the most electronegative element in each of the following molecules: (a) CH2FCl (b) FCH2CH2CH2Br (c) HOCH2CH2NH2 (d) CH3OCH2Li

Consumer Behavior 6
What is perception, and what methods do we use to perceive stimuli?

Chemistry for today : general, organic, and biochemistry 9
Explain why the rate of chemical reactions is generally slow for organic compounds and usually fast for inorganic compounds.