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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Swali la 17: Kurahisisha usemi: (10 - 18 ÷ 9)/(5) × (1)/(2)1(1)/(2) × (4)/(7) - 2 + 2(1)/(7) Step 1: Rahisisha nambari (numerator). Kwanza, fanya mgawanyiko na kuzidisha katika nambari. 18 ÷ (9)/(5) = 18 × (5)/(9) = (18 × 5)/(9) = 2 × 5 = 10 Kisha, zidisha matokeo kwa (1)/(2): 10 × (1)/(2) = 5 Sasa, toa kutoka 10: 10 - 5 = 5 Hivyo, nambari ni 5. Step 2: Rahisisha denominata (denominator). Badilisha nambari mchanganyiko kuwa sehemu zisizofaa: 1(1)/(2) = (3)/(2) 2(1)/(7) = (16)/(7) Fanya kuzidisha kwanza: (3)/(2) × (4)/(7) = (3 × 4)/(2 × 7) = (12)/(14) = (6)/(7) Sasa, fanya kutoa na kujumlisha: (6)/(7) - 2 + (16)/(7) = (6)/(7) - (14)/(7) + (16)/(7) = (6 - 14 + 16)/(7) = (-8 + 16)/(7) = (8)/(7) Hivyo, denominata ni (8)/(7). Step 3: Gawanya nambari kwa denominata. (5)/(8)7 = 5 × (7)/(8) = (35)/(8) (35)/(8) = 4(3)/(8) Jibu la mwisho ni: (35)/(8) au 4(3)/(8) Swali la 18: Mkulima anazalisha lita 40 za maziwa asubuhi na lita 35 jioni. Anauza (2)/(5) ya jumla ya maziwa yaliyozalishwa. a) Pata jumla ya maziwa yaliyozalishwa kwa siku. Step 1: Jumlisha maziwa yaliyozalishwa asubuhi na jioni. Jumla ya maziwa = 40 lita + 35 lita = 75 lita Jumla ya maziwa yaliyozalishwa kwa siku ni: 75 lita b) Bainisha kiasi kilichouzwa. Step 1: Tumia sehemu ya maziwa yaliyozalishwa ili kupata kiasi kilichouzwa. Kiasi kilichouzwa = (2)/(5) × Jumla ya maziwa Step 2: Fanya hesabu. Kiasi kilichouzwa = (2)/(5) × 75 lita = 2 × (75)/(5) lita = 2 × 15 lita = 30 lita Kiasi kilichouzwa ni: 30 lita c) Kokotoa kiasi kilichobaki. Step 1: Toa kiasi kilichouzwa kutoka jumla ya maziwa. Kiasi kilichobaki = Jumla ya maziwa - Kiasi kilichouzwa Kiasi kilichobaki = 75 lita - 30 lita = 45 lita Kiasi kilichobaki ni: 45 lita d) Ikiwa maziwa yanauzwa kwa Ksh 60 kwa lita na gharama ya kila siku ni Ksh 1800, kokotoa asilimia ya faida. Step 1: Kokotoa mapato kutokana na mauzo. Mapato = Kiasi kilichouzwa × Bei kwa lita Mapato = 30 lita × Ksh 60/lita = Ksh 1800 Step 2: Kokotoa faida. Faida = Mapato - Gharama Faida = Ksh 1800 - Ksh 1800 = Ksh 0 Step 3: Kokotoa asilimia ya faida. Asilimia ya Faida = FaidaGharama × 100\% Asilimia ya Faida = Ksh 0Ksh 1800 × 100\% = 0\% Asilimia ya faida ni: 0\% Tuma swali linalofuata 📸