an essay contest requires that essay entries consist of 500 words with an absolute deviation of at most 30 words. what are the possible numbers of words that the essay can have?

470 to 530

To find the possible numbers of words that the essay can have, we need to consider the absolute deviation of at most 30 words from the required 500 words.

Let's calculate the minimum and maximum numbers of words allowed:

Minimum number of words: 500 - 30 = 470 words.
Maximum number of words: 500 + 30 = 530 words.

Therefore, the possible numbers of words for the essay can range from 470 to 530 words inclusively.

To determine the possible numbers of words that the essay can have, we need to consider the given conditions: the essay must consist of 500 words with an absolute deviation of at most 30 words.

An absolute deviation is the difference between a number and a reference value, regardless of direction (positive or negative). In this case, the reference value is 500 words, and the absolute deviation is given as at most 30 words. This means the essay's word count can deviate by a maximum of 30 words in either direction from 500 words.

To find the range of possible word counts, we can calculate both the upper and lower bounds by applying the deviation to the reference value.

Upper bound: 500 + 30 = 530 words
Lower bound: 500 - 30 = 470 words

Therefore, the possible numbers of words that the essay can have range from 470 to 530 words, inclusive.