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Mathematics

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3 parts
b

1110three1110_{\text{three}}

c

504,000 Shs.504,000 \text{ Shs.}

d

0 Shs.0 \text{ Shs.}

Step-by-step solution

9 steps

Huu hapa ni ufumbuzi wa Kifungu cha 1:

Part a· 2 steps

**Bainisha aina ya mazao ya kupanda kwenye ardhi.

  1. Kokotoa eneo halisi la ardhi.

    Eneo kwenye ramani ni 8.5 cm28.5 \text{ cm}^2.
    Kiwango cha ramani ni 1:15001:1500.
    Eneo halisi katika cm2\text{cm}^2:

    Eneo halisi=8.5 cm2×(1500)2\text{Eneo halisi} = 8.5 \text{ cm}^2 \times (1500)^2 =8.5×2,250,000 cm2= 8.5 \times 2,250,000 \text{ cm}^2 =19,125,000 cm2= 19,125,000 \text{ cm}^2

    Badilisha cm2\text{cm}^2 kuwa m2\text{m}^2 (1 m2=10,000 cm21 \text{ m}^2 = 10,000 \text{ cm}^2):

    Eneo halisi=19,125,00010,000 m2\text{Eneo halisi} = \frac{19,125,000}{10,000} \text{ m}^2 =1912.5 m2= 1912.5 \text{ m}^2
  2. Linganisha eneo halisi na masharti ya upandaji.

    Kwa kuwa 1912.5 m2<2000 m21912.5 \text{ m}^2 < 2000 \text{ m}^2, mjomba atapanda kahawa na kakao.

    Jibu la (a): Mjomba atapanda kahawa na kakao.

Part b

1110three1110_{\text{three}}

**Bainisha PIN halisi utakayotumia kutoa pesa.

  1. Badilisha kiasi kilichohifadhiwa kutoka base nne kwenda base kumi.

    Kiasi kilichohifadhiwa ni 213four213_{\text{four}}.

    213four=(2×42)+(1×41)+(3×40)213_{\text{four}} = (2 \times 4^2) + (1 \times 4^1) + (3 \times 4^0) =(2×16)+(1×4)+(3×1)= (2 \times 16) + (1 \times 4) + (3 \times 1) =32+4+3= 32 + 4 + 3 =39ten= 39_{\text{ten}}
  2. Badilisha namba ya base kumi kwenda base tatu ili kupata PIN.

    39÷3=13 baki 039 \div 3 = 13 \text{ baki } 0 13÷3=4 baki 113 \div 3 = 4 \text{ baki } 1 4÷3=1 baki 14 \div 3 = 1 \text{ baki } 1 1÷3=0 baki 11 \div 3 = 0 \text{ baki } 1

    Kwa kusoma mabaki kutoka chini kwenda juu, PIN ni 1110three1110_{\text{three}}.

    Jibu la (b): PIN halisi ni 1110three\boxed{1110_{\text{three}}}.

Part c

504,000 Shs.504,000 \text{ Shs.}

**Ni kiasi gani cha pesa kitatumika kununua nguzo za chuma?

  1. Kokotoa kiasi cha pesa kilichotolewa kwa usafiri na chakula cha mchana.

    Jumla ya pesa iliyotolewa ni Shs. 1,680,000.
    Pesa kwa usafiri na chakula cha mchana ni 14\frac{1}{4} ya jumla:

    Pesa kwa usafiri na chakula cha mchana=14×1,680,000\text{Pesa kwa usafiri na chakula cha mchana} = \frac{1}{4} \times 1,680,000 =420,000 Shs.= 420,000 \text{ Shs.}
  2. Kokotoa kiasi kilichobaki baada ya gharama za usafiri na chakula cha mchana.

    Kiasi kilichobaki=1,680,000−420,000\text{Kiasi kilichobaki} = 1,680,000 - 420,000 =1,260,000 Shs.= 1,260,000 \text{ Shs.}
  3. Kokotoa kiasi cha pesa kitakachotumika kununua nguzo za chuma.

    Pesa kwa nguzo za chuma ni 40%40\% ya kiasi kilichobaki:

    Pesa kwa nguzo za chuma=0.40×1,260,000\text{Pesa kwa nguzo za chuma} = 0.40 \times 1,260,000 =504,000 Shs.= 504,000 \text{ Shs.}

    Jibu la (c): Kiasi cha pesa kitakachotumika kununua nguzo za chuma ni 504,000 Shs.\boxed{504,000 \text{ Shs.}}.

Part d

0 Shs.0 \text{ Shs.}

**Ni kiasi gani kinachotarajiwa kutoka mahindi?

  1. Rejea uamuzi wa mazao kutoka sehemu (a).

    Kutoka sehemu (a), eneo la ardhi ni 1912.5 m21912.5 \text{ m}^2, ambayo ni chini ya 2000 m22000 \text{ m}^2. Hivyo, mjomba atapanda kahawa na kakao.

  2. Bainisha mapato yanayotarajiwa kutoka mahindi.

    Kwa kuwa mjomba atapanda kahawa na kakao, hatapata mapato yoyote kutoka mahindi.

    Jibu la (d): Kiasi kinachotarajiwa kutoka mahindi ni 0 Shs.\boxed{0 \text{ Shs.}}.

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