What type of ratio compares the amount of rice to tomato paste when making jollof rice? What does a rate compare? What does a horizontal line on a distance-time graph represent? What does the gradient

Here are the solutions to the questions you sent:

1. The question asks what type of ratio compares the amount of rice to tomato paste when making jollof rice. This is a comparison of two different parts of a whole recipe.
The correct option is C.

• Part-to-part ratio compares two distinct quantities within a whole.

2. The question asks what a rate compares. A rate compares two quantities with different units.
The correct option is B.

• Different units are essential for a comparison to be considered a rate, such as speed (distance/time) or density (mass/volume).

3. The question asks what a horizontal line on a distance-time graph represents.
A horizontal line on a distance-time graph means that the distance is not changing over time. This indicates that the object is stationary.
The correct option is B.

• Object at rest means its position is constant over time.

4. The question asks what the gradient of the line in a distance-time graph represents.
The gradient of a distance-time graph is calculated as $\frac{\text{change in distance}}{\text{change in time}}$, which is the definition of speed.
The correct option is C.

• Speed is the rate of change of distance with respect to time.

5. The question asks what a sequence where the difference between consecutive terms is constant is called.
This is the definition of an arithmetic progression.
The correct option is C.

• An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant.

6. The general term of an arithmetic progression is given by $U_n = a + (n-1)d$, where $a$ is the first term, $n$ is the term number, and $d$ is the common difference.
The correct option is B.

• $U_n = a + (n-1)d$ is the standard formula for the $n$-th term of an arithmetic progression.

7. The general term of a geometric progression is given by $U_n = ar^{n-1}$, where $a$ is the first term, $n$ is the term number, and $r$ is the common ratio.
The correct option is C.

• $U_n = ar^{n-1}$ is the standard formula for the $n$-th term of a geometric progression.

8. The sum of the first $n$ terms of an arithmetic progression is given by $S_n = \frac{n}{2}[2a + (n-1)d]$.
The correct option is A.

• $S_n = \frac{n}{2}[2a + (n-1)d]$ is the standard formula for the sum of the first $n$ terms of an arithmetic progression.

9. The surface area of a cuboid with length $l$, width $w$, and height $h$ is given by the sum of the areas of its six faces: $2(lw + lh + wh)$.
The correct option is B.

• The formula $2(lw + lh + wh)$ accounts for the area of all six rectangular faces of the cuboid.

10. The volume of a cylinder with radius $r$ and height $h$ is given by the formula $\pi r^2 h$.
The correct option is A.

• The formula $\pi r^2 h$ is derived from the area of the circular base ($\pi r^2$) multiplied by the height ($h$).

11. The question asks how many feet are in 1 meter.

$$1 \text{ meter} \approx 3.281 \text{ feet}$$

The correct option is B.

• This is a standard conversion factor.

12. The question asks how many square centimeters are in 1 square meter.
We know that $1 \text{ meter} = 100 \text{ centimeters}$.
Therefore, $1 \text{ square meter} = (1 \text{ meter}) \times (1 \text{ meter}) = (100 \text{ cm}) \times (100 \text{ cm}) = 10,000 \text{ cm}^2$.
The correct option is C.

• $1 \text{ m}^2 = (100 \text{ cm})^2 = 100^2 \text{ cm}^2 = 10,000 \text{ cm}^2$.