6- Use induction to prove the following identity for integers n1 - i-1.docx

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6. Use induction to prove the following identity for integers n 1 : i = 1 n ( 2 i 1 ) ( 2 i + 1 ) 1 = 2 n + 1 n .

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7.One of the most dramatic changes in connectivity and communications in the past five years or so hasbeen a) mobile or wireless telephones b) public and private discussion c) satellite uplinks d) running programs on remote computers 8.The four basic elements of any communication system include a)peer-to-peer, videoconferencing, online photo-conferencing, net optical b)sending and receiving devices, communication channel, connection device, and data transmission specifications c)telephone lines, coaxial cables, fiber-optics cables, and communication channel d)software, hardware, communication channel, network .

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7. What is the dominant generation of ALL vascular plants? Individuals of the dominant generation are 8. What is an immature fern leaf called? (haploid/diploid). 9. A cluster of sporangia located on the underside of a fern frond is known as a 10. What is the function of an indusium? 11. With regard to the true ferns: a. The heart-shaped gametophyte is called a b. This gametophyte is (haploid/diploid). c. Fern gametophytes produce (gametes/spores). d. Reproductive structures called (archegonia/antheridia) are located nearest the "notch" (indentation) of the heart-shaped gametophyte. 12. What is the name of the cone-shaped, spore-producing structures observed in lycophytes and horsetails? 13. What substance is responsible for the abrasive texture of horsetail stems? 14. Place each of the following organisms in their appropriate group. Staghorn A. Lycophyte Cyrtomium B. Fern Bird's nest C. Horsetail Selaginella D. Moss Lemon button Equisetum Rabbit's foot Haircap .

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7. After graduation, you and 19 of your closest friends (lets say 10 males and 10 females) charter a plane to go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted island. No one finds you and you start a new population totally isolated from the rest of the world. Two of your friends carry (i.e. are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does not change as the population grows, what will be the incidence of cystic fibrosis on your island? .

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6. It is Halloween evening and Nick and Rachel have just returned home after trick-or-treating. They have been dividing up the candy and are now down to four candy bars: Snickers, Milky Way, Kit Kat, and Baby Ruth. The allocation procedure is that Nick gets to choose one of the four candy bars, then Rachel can choose one of the three remaining candy bars, then Nick chooses one of the two remaining candy bars, and finally Rachel gets the remaining candy bar. Nick's preferences are that he most likes Snickers (assigning it a payoff of 5) then Milky Way (payoff of 4), then Kit Kat (payoff of 3), and lastly Baby Ruth (payoff of 1). Rachel most likes Milky Way (payoff of 6), then Kit Kat (payoff of 5), then Baby Ruth (payoff of 4), and finally Snickers (payoff of 2). Using SPNE, how are the candy bars allocated between Nick and Rachel? .

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