Final answer:
After simplifying each of the provided ratios, we find that none of them simplified to an equivalent fraction, indicating that none of the ratios represent quantities that are proportional to each other.
Step-by-step explanation:
To determine which two ratios represent quantities that are proportional, we need to see which ratios, when simplified, would have the same fundamental relationship between their components. A proportion is essentially an equation that states that two ratios are equivalent. In the context of ratios, the equivalent fractions or decimals would indicate proportional relationships.
Let's examine each pair of numbers:
- (a) 10:14 can be simplified to 5:7.
- (b) 17:15 does not simplify to an integer ratio.
- (c) 19:24 does not simplify to an integer ratio.
- (d) 11:48 also cannot simplify to an integer ratio that matches (a).
None of the ratios b), c), and d) simplifies to 5:7 or an equivalent fraction, indicating that none of these are proportional to (a) 10:14.
Therefore, none of the presented ratios represents quantities that are proportional to one another.