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Mathematics Senior High

なぜ赤線の記述を書いているのかよく分かりません。 教えてほしいです🙇‍♀️

指針> n=k+1の場合に (k+1)°が現れるが, この展開には二項定理 (数学IⅡ)を利用する。 フェルマの小定理に関する証明 重要 例題139 OOOO0 救学的帰納法によって証明せよ。 【類茨城大) 基本136 カーk+1の場合に (k+1)”が現れるが, この展開には二項定理(数学I)を利用する。 (k+1)°=k°+C,ke-1+Cake-?+… .Cp-ポ+,Cp-ik+1 (k+1)°-(k+1)= Cike-1+Cake-2+ +Cp-k+,Cp-k+l°-k nーkのときの仮定より, kピーkはかで割り切れるから, ,Ci, Ca, , C-iすなわち よって C,(1Srsp-1) がpで割り切れる ことを示す。 解答 4合同式(チャート式基礎からの数学 A)を 利用してもよい(解答編 p.427 参照)。 「n°ーnはpの倍数である」 を①とする。 [1] n=1のとき 1°-130 よって,① は成り立つ。 のとおける。 [2] n=k のとき①が成り立つと仮定すると, k"ーk=pm (mは整数) n=k+1のときを考えると, ②から (R+1)°-(k+1)=k°+,Cik-1+CakP-2+… +Cp-sk?+,Cp-e+1ー(k+1) =CkP-1+,Ck-2+… +Cp-k+,Cp-k+pm p. 3 (カ-1)! r(rー1)! (カーア)! 2.n.Cr-1 p! ACr=(カーr)! %D D ア 1Srsp-1のとき pは素数であるから, rとかは互いに素であり, Crはpで割り切れる。 ゆえに,3から,(k+1)°ー(k+1) はpの倍数である。 したがって、n=k+1 のときにも①は成り立つ。 「1「21 から、すべての自然数nについて、 n°ーnはpの倍数である。 よって r. C,=DかCrー

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English Senior High

どなたか英語の得意な方この問題問いてくださいませんか、、 先日受験して不安で眠れません

6. 次の英文を読み, 以下の設問に答えよ。 legally as a *trophy. In 2003, a lone hunter killeda rhino on a legal safari in South Africa and brought it back to Asia. Dozens of poachers soon followed. The sound of rifles being fired could be heard in the dark forest just as each paying $50,000 for a hunt. It seems like a lot to pay, but poachers can Damien Mander arrived at his campfire after a long day training *game ranger make as much as $200,000 in profits by selling a pair of horns on *the black recruits in Zimbabwe's Nakavango *game reserve. "There, near the eastern market. boundary," he pointed. He and his rangers grabbed their guns, radios, and ull Many officials in Vietnam are fighting back against reports that the country medical kits. They then drove into the night, hoping to stop the shooter. is the main market for rhino horn, stating that rhino horn bound for Vietnam (21) And so goes a night on the front lines of southern Africa's ruthless * rhino is merely in transit for another country. Do Quang Tung, deputy director of war, which has seen more than a thousand rhinos killed since 2006. At the CITES Managing Authority in Vietnam, said the country "could not be the main bloody heart of this conflict is the rhino's horn, a prized ingredient in traditional market for South African rhino horn," claiming that the majority of Vietnamese Asian medicine. Prices range from $33 to $133 a gram, which at the top end is people would not be able to ( 26 ) rhino horn. Even if there is an emerging double the price of gold. group of people who can ( 26 ) it, he thinks it is too small to make the country Although the range of the two African species 一 the white rhino and its a significant consumer. Professor Dang Huy Huynh, chairman of the Vietnam smaller cousin, the black rhino- has been reduced primarily to southern Africa Zoological Society, says that rhino horn has never been a popular ingredient in and Kenya, their populations had shown signs of improvement. In 2007 white traditional medicine. rhinos numbered 17,470, while blacks had nearly doubled to 4,230 since the mid Recently, there has been a renewed interest in the unproven belief that rhino 90s. horn has healing power. For at least 2,000 years, Asian medicine has prescribed For conservationists these numbers represented a triumph. In the 1970s rhino horn to reduce fever and treat a range of illnesses, but the handful of 22 and '80s, *poaching had nearly caused the two species to become extinct. Ther studies which have been conducted on rhino horn have not found any proof that China banned rhino horn from traditional medicine, and Yemen forbade its ust it can reduce fever. The newest rumor is that it cures cancer, but doctors say in ceremonial knife handles. All signs pointed to better days. But in 2008 th the proof is nonexistent一 no research has been published on the horn's efficacy 23) number of poached rhinos in South Africa shot up to 83, from just 13 in 200' as a cancer treatment. But even if rhino horn is not an effective cure for anything, let alone cancer, that doesn't mean it has no effect, says Mary Hardy. By 2010 the figure had soared to 333, followed by over 400 in 2011. Most of th 27) medical director of Simms/Mann UCLA Center for Integrative Oncology. "Belief horn trade was found to lead to Southeast Asia. in a treatment, especially one that is wildly expensive and hard to get, can have *Javan rhinos once lived in Vietnam's forests. ( 24 ) It had a bullet a powerful effect on how a patient feels," she says. its leg and its horn had been removed. In any event, John Hume believes no rhinos need to die to supply the rhino Even with the rhinos gone, rhino horn can still be found in Vietnam. This 28 25 horn to those who want it. The 69-year-old * entrepreneur has acquired one of because South African law, which complies with the Convention on Internatio the largest privately-owned rhino herds in the world, and currently has more Trade in Endangered Species (CITES), allowS a rhino's horn to be expor ○M3(45)

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Mathematics Senior High

解説が分かりにくいので、⑶⑷⑸の解き方を教えていただきたいです‥

《【4】~【6] はいずれか 1 題を選んで解答すること、》 ※[4J [s]。 とちうかを用く (4) 1から4までの数字が1つずつ書かれたカードが2枚ずつ,合計8枚ある。 2ドC |3d ト4 a 11 この中から無作為に4枚のカードを取り出し; 次の操作 A, Bをこの順に行う 8枚のカードをすべて区別して考えるとして, 次の各問いに答えよ. (1)は結果のみを 記入せよ、(2)~(5)は結果のみではなく,考え方の筋道も記せ *操作 A:取り出されたカードに書かれた数字の小さい順に, 左から1列に並べる. 同じ数字が書かれたカードがある場合は, それらのカードを重ねて並べ る。 操作B:2枚重なっているカードを取り除く. (1Xi) 4枚のカードの取り出し方は全部で何通りあるか. (i)取り出した4枚のカードが,1||2||2||3|となる場合は何通りあるか. ()(i)の4枚について操作 A, 操作Bを行った結果,どのようにカードが残って、 いるかを記せ、 (2) 操作Aの終了後,4枚のカードが|1||2||3|||4| と並んでいる確率を求めよ。 (3) 操作Aの終了後, 並んでいるカードに書かれた数字がちょうど3つだけ連続し ている確率を求めよ。 (4) 操作Bの終了後, 並んでいるカードに書かれたどの2つの数字も連続していな い確率を求めよ. (カードが1枚も残っていない場合も, 連続していない場合と見 なす。) (5) 操作 Aの終了後には3つ以上の連続した数字が並んでいるとき, 操作Bの終了 後にはどの2つの数字も連続していない条件付き確率を求めよ。

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