Question

Which of the following quantities are continuous?

I. the population of dogs in a village
II. the distance covered by a train
III. the number of books shelved in the fiction section of a library
IV. the number of bracelets sold

Answer 1

Only ll

Explanation:

Discrete quantities are countable and restricted to specific values.

A continuous quantity is not restricted to specific values and can occupy any value over a continuous range.

The population of dogs in a village can be any positive integer. Since the population is countable and can be represented by a set of specific values, the population of dogs in a village is a discrete quantity.

The distance covered by a train can be any real number. Since distance is a variable that can occupy any value over a continuous range, the distance covered by a train can be classified as a continuous quantity.

The number of books shelved in the fiction section of a library can be any positive integer. Since the number of books are countable and can be represented by a set of specific values, the number of books shelved in the fiction section of a library is a discrete quantity.

The number of bracelets sold can be any positive integer. Since the number of bracelets are countable and represented by a set of specific values, the number of bracelets sold is a discrete quantity.

Therefore, only II represents a continuous quantity

Answer 2

A. only II

Explanation:

Mathematics calculus differentiates things into discrete and continuous. Discrete things have indivisible units, the example will be how many dogs in a village. There is no half dog, it's either one, two, etc. But the distance covered by train can be written as half miles, it's divisible unit.

The number of books and bracelets also discrete, thus the answer is A.