Here are the solutions to the questions: 1. Find the diameter of a circle whose radius is 3.4m. Step 1: The formula for the diameter ($d$) of a circle in terms of its radius ($r$) is $d = 2r$. Step 2: Substitute the given radius $r = 3.4$m into the formula. $$d = 2 \times 3.4\, \text{m}$$ Step 3: Calculate the diameter. $$d = 6.8\, \text{m}$$ The correct option is B. The final answer is $\boxed{\text{B. 6.8m}}$. 2. In the balance below, the mass of one shape is given in kilogram. Find $\square$ if $\bigcirc = 15$. Step 1: From the balance, two circles balance three squares. Let $M_{\bigcirc}$ be the mass of one circle and $M_{\square}$ be the mass of one square. $$2 M_{\bigcirc} = 3 M_{\square}$$ Step 2: Substitute the given mass of one circle, $M_{\bigcirc} = 15$ kg. $$2 \times 15\, \text{kg} = 3 M_{\square}$$ $$30\, \text{kg} = 3 M_{\square}$$ Step 3: Solve for $M_{\square}$. $$M_{\square} = \frac{30\, \text{kg}}{3}$$ $$M_{\square} = 10\, \text{kg}$$ The correct option is C. The final answer is $\boxed{\text{C. 10kg}}$. 3. In the figure below MK and RS are straight lines. Find the value of angle marked n. Step 1: The angles $127^\circ$ and the angle adjacent to it on the straight line MK (or RS) are supplementary, meaning they add up to $180^\circ$. Let the angle adjacent to $127^\circ$ be $x$. $$127^\circ + x = 180^\circ$$ Step 2: Solve for $x$. $$x = 180^\circ - 127^\circ$$ $$x = 53^\circ$$ Step 3: Angle $n$ and angle $x$ are vertically opposite angles. Vertically opposite angles are equal. $$n = x$$ $$n = 53^\circ$$ The correct option is B. The final answer is $\boxed{\text{B. 53°}}$. 4. A line that divides a circle into two segments is called... A chord is a line segment whose endpoints lie on the circle, dividing the circle into two segments. A diameter is a special type of chord that passes through the center. The correct option is B. The final answer is $\boxed{\text{B. Chord}}$. 5. Which of the following construction of angles represents 45°? A $45^\circ$ angle is half of a $90^\circ$ angle. To construct a $45^\circ$ angle, one typically constructs a $90^\circ$ angle first and then bisects it. Option A shows the construction of a $90^\circ$ angle being bisected, which results in a $45^\circ$ angle. The correct option is A. The final answer is $\boxed{\text{A}}$. 6. Simplify: $2^3 \times 3^2 \times 5$. Step 1: Calculate the powers. $$2^3 = 2 \times 2 \times 2 = 8$$ $$3^2 = 3 \times 3 = 9$$ Step 2: Substitute the calculated values back into the expression. $$8 \times 9 \times 5$$ Step 3: Perform the multiplication. $$8 \times 9 = 72$$ $$72 \times 5 = 360$$ The correct option is B. The final answer is $\boxed{\text{B. 360}}$. 7. Solve for n: $2n + 5 = 3n - 7$. Step 1: Subtract $2n$ from both sides of the equation to gather terms with $n$ on one side. $$5 = 3n - 2n - 7$$ $$5 = n - 7$$ Step 2: Add 7 to both sides of the equation to isolate $n$. $$5 + 7 = n$$ $$12 = n$$ The correct option is A. The final answer is $\boxed{\text{A. 12}}$.