This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya, tutasuluhisha maswali haya. 8. Given the venn diagram below, describe the shaded region. Step 1: Chunguza mchoro wa Venn. Eneo lililotiwa kivuli linajumuisha kila kitu kilicho nje ya duara B, lakini ndani ya mstatili (seti ya ulimwengu). Step 2: Eneo hili linaweza kuelezewa kama kikamilisho cha seti B. Maelezo ya mwisho ni: Kikamilisho cha B (au B^c au B') 9. At a certain school, assembly was conducted on Monday at 8:00am. A teacher on duty was 5th from one side and 9th from the other side. How many teachers attended assembly that day? Step 1: Ikiwa mwalimu yuko wa 5 kutoka upande mmoja, inamaanisha kuna walimu 4 kabla yake. Step 2: Ikiwa mwalimu huyo huyo yuko wa 9 kutoka upande mwingine, inamaanisha kuna walimu 8 baada yake. Step 3: Jumla ya walimu ni idadi ya walimu kabla yake, pamoja na mwalimu mwenyewe, pamoja na idadi ya walimu baada yake. Jumla ya walimu = 4 + 1 + 8 = 13 Jibu la mwisho ni: 13 walimu 10. James deposited 20 notes of five thousand shillings. If the first note was serial number DV432370 after consecutive numbering. Find the serial number of the last note. Step 1: Tambua nambari ya mfululizo ya noti ya kwanza. Nambari ya kwanza ni 370. Step 2: Tambua idadi ya noti zilizowekwa. Kuna noti 20. Step 3: Kwa kuwa nambari zinafuatana, nambari ya mwisho itakuwa nambari ya kwanza pamoja na (idadi ya noti - 1). Nambari ya mwisho = 370 + (20 - 1) Nambari ya mwisho = 370 + 19 Nambari ya mwisho = 389 Step 4: Unganisha nambari hii na kiambishi awali cha nambari ya mfululizo. Jibu la mwisho ni: DV432389 11. Find the value of a in the diagram below. Step 1: Chora mstari msaidizi unaopita kwenye kipeo cha pembe 'a' na sambamba na mistari miwili iliyopewa. Hii itagawanya pembe 'a' katika sehemu mbili, a_1 (juu) na a_2 (chini). Step 2: Kwa sehemu ya juu (a_1): Pembe iliyo karibu na 150^ kwenye mstari ulionyooka ni 180^ - 150^ = 30^. Pembe hii ya 30^ ni alternate interior angle na a_1. Hivyo, a_1 = 30^. Step 3: Kwa sehemu ya chini (a_2): Pembe ya 75^ iliyopewa ni alternate interior angle na a_2. Hivyo, a_2 = 75^. Step 4: Jumla ya pembe 'a' ni jumla ya a_1 na a_2. a = a_1 + a_2 a = 30^ + 75^ a = 105^ Jibu la mwisho ni: 105^ 3 done, 2 left today. You're making progress.