Here are the solutions to the problems: 3. a) Change $1\frac{1}{5}$ as a percentage. Step 1: Convert the mixed number to an improper fraction. $$1\frac{1}{5} = \frac{(1 \times 5) + 1}{5} = \frac{6}{5}$$ Step 2: Convert the fraction to a decimal. $$\frac{6}{5} = 1.2$$ Step 3: Convert the decimal to a percentage. $$1.2 \times 100\% = 120\%$$ The percentage is $\boxed{120\%}$. b) Find the smallest number that can be divided by $48, 32$ and $40$. This requires finding the Least Common Multiple (LCM) of $48, 32,$ and $40$. Step 1: Find the prime factorization of each number. $$48 = 2^4 \times 3$$ $$32 = 2^5$$ $$40 = 2^3 \times 5$$ Step 2: Take the highest power of each prime factor present in any of the numbers. Highest power of $2$: $2^5$ Highest power of $3$: $3^1$ Highest power of $5$: $5^1$ Step 3: Multiply these highest powers together. $$\text{LCM}(48, 32, 40) = 2^5 \times 3^1 \times 5^1 = 32 \times 3 \times 5 = 480$$ The smallest number is $\boxed{480}$. c) Find the next number in the series below: $2, 3, 5, 7, 9, \_$ Step 1: Analyze the differences between consecutive terms. $3 - 2 = 1$ $5 - 3 = 2$ $7 - 5 = 2$ $9 - 7 = 2$ Step 2: Identify the pattern in the differences. The differences are $1, 2, 2, 2$. After the first term, each subsequent term is found by adding $2$ to the previous term. Step 3: Apply the pattern to find the next number. The next number is $9 + 2 = 11$. The next number is $\boxed{11}$. 4. a) Find the square of $3^2$. Step 1: Calculate $3^2$. $$3^2 = 3 \times 3 = 9$$ Step 2: Find the square of the result. $$\text{Square of } 9 = 9^2 = 9 \times 9 = 81$$ The square of $3^2$ is $\boxed{81}$. b) Calculate $\sqrt{441} - \sqrt{256}$. Step 1: Calculate $\sqrt{441}$. $$\sqrt{441} = 21$$ Step 2: Calculate $\sqrt{256}$. $$\sqrt{256} = 16$$ Step 3: Subtract the values. $$21 - 16 = 5$$ The result is $\boxed{5}$. c) Write $0.75$ as a simple fraction. Step 1: Write the decimal as a fraction. $$0.75 = \frac{75}{100}$$ Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is $25$. $$\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$$ The simple fraction is $\boxed{\frac{3}{4}}$. 5. a) The bus started the journey from Sumbawanga at $1220$hours and arrived in Tabora at $1855$hours. How long did the bus take to travel from Sumbawanga to Tabora? Step 1: Identify the start and end times. Start time: $12$ hours $20$ minutes End time: $18$ hours $55$ minutes Step 2: Subtract the start time from the end time. Subtract minutes: $55 \text{ minutes} - 20 \text{ minutes} = 35 \text{ minutes}$. Subtract hours: $18 \text{ hours} - 12 \text{ hours} = 6 \text{ hours}$. The bus took $\boxed{6 \text{ hours and } 35 \text{ minutes}}$. b) A chicken hatches a chick after incubating eggs for $21$ days. What is this duration in hours? Step 1: Convert days to hours. There are $24$ hours in $1$ day. Step 2: Multiply the number of days by $24$. $$21 \text{ days} \times 24 \frac{\text{hours}}{\text{day}} = 504 \text{ hours}$$ The duration in hours is $\boxed{504 \text{ hours}}$.