A school received Ksh 18 000 to support three clubs. The money was shared among the Science, Agriculture and Wildlife clubs in the ratio 3 : 4 : 5. The Agriculture Club spent Ksh 1 500 on materials. Determine: (a) The amount of money each club received.

$$2^n \times 2^1 = 2^{n+1}$$

Jibu ni $\boxed{2^{n+1}}$.

b) Kwa hivyo, andika jibu kama nambari ya kawaida.
Kwa kuwa thamani ya 'n' haijatolewa, haiwezekani kuandika $2^{n+1}$ kama nambari ya kawaida.

c) Rahisisha: $\frac{5^4 \times 5^4}{5^3}$

$$\frac{5^8}{5^3} = 5^{8-3} = 5^5$$

Jibu ni $\boxed{5^5}$.

Swali la 23:

a) Kiasi cha pesa kila klabu ilipokea.

• Klabu ya Sayansi: $3 \times \text{Ksh } 1500 = \text{Ksh } 4500$
• Klabu ya Kilimo: $4 \times \text{Ksh } 1500 = \text{Ksh } 6000$
• Klabu ya Wanyamapori: $5 \times \text{Ksh } 1500 = \text{Ksh } 7500$ Klabu ya Sayansi ilipokea $\boxed{\text{Ksh } 4500}$, Klabu ya Kilimo ilipokea $\boxed{\text{Ksh } 6000}$, na Klabu ya Wanyamapori ilipokea $\boxed{\text{Ksh } 7500}$.

b) Ni kiasi gani cha pesa Klabu ya Kilimo ilibakiwa nacho baada ya kununua vifaa.

$$\text{Pesa iliyobaki} = \text{Ksh } 6000 - \text{Ksh } 1500 = \text{Ksh } 4500$$

Klabu ya Kilimo ilibakiwa na $\boxed{\text{Ksh } 4500}$.

Swali la 24:
Tathmini kwa kutumia jedwali za hisabati: $0.6543^2 - \sqrt[3]{0.05654}$

Kutumia logariti:

$$\log(0.05654) = \bar{2}.7524$$ $$\frac{1}{3} \log(0.05654) = \frac{1}{3}(\bar{2}.7524) = \frac{1}{3}(-3 + 1.7524) = \bar{1}.5841$$

Antilog ya $\bar{1}.5841 \approx 0.3838$

$$0.4280 - 0.3838 = 0.0442$$

Jibu ni $\boxed{0.0442}$.