The octal system only uses digits 0-7, so 8 is not a valid numeral.

In base 3, only digits 0, 1, and 2 are valid. '230' contains '3', which is invalid.

'22' cannot represent 10 in any base since it would require base 3 or higher.

Higher costs for schools is not mentioned as a benefit; rather, the passage focuses on positive aspects of technology.

The passage does not mention wider accessibility as a benefit, focusing instead on the other three aspects.

Higher costs are not mentioned as a benefit; instead, the passage focuses on positive aspects like efficiency and accessibility.

Wider acceptance is not mentioned as a benefit of the new approach in the passage.

Job creation is not mentioned as a benefit of the new technology in the passage.

The passage does not mention increased funding as a benefit, focusing instead on health outcomes and understanding.

The passage does not mention enhanced data security as a benefit of digital sum.

The passage does not mention limited funding as a challenge, focusing instead on other obstacles faced by the researchers.

The passage does not mention lack of public interest as a challenge, focusing instead on funding, technology, and ethics.

The passage does not mention technological limitations as a challenge, making option 3 the correct answer.

The passage does not mention focusing too much on mock tests as a common mistake.

The passage discusses various negative consequences of climate change, but it does not mention any improvement in air quality.

Cultural beliefs are not mentioned as a factor influencing scientific research in the passage.

While the passage discusses job displacement, efficiency, and environmental issues, it does not mention enhanced communication as a consequence.

The passage does not mention data compression techniques as an application of digital sum.

The base of the natural logarithm is e, approximately equal to 2.718.

A factor is defined as a number that divides another number without leaving a remainder.

The binary representation of the decimal number 8 is 1000.

The decimal number 10 is represented as 1010 in binary.

The quadratic x^2 - 5x + 6 factors to (x - 2)(x - 3).

The expression factors to (x - 2)(x - 3) since -2 and -3 are the roots.

log_5(1) = 0 because any number raised to the power of 0 equals 1.

The correct order is to first solve the parentheses (4 - 1), then multiply by 3, and finally add 2.

Binary is the simplest (base-2), followed by Decimal (base-10), and then Hexadecimal (base-16), making the correct order Binary, Decimal, Hexadecimal.

All the listed properties are correct and fundamental to logarithmic functions.

15 divided by 4 gives a remainder of 3, hence 15 mod 4 = 3.

To convert 10 to base-3, divide by 3: 10 ÷ 3 = 3 remainder 1, 3 ÷ 3 = 1 remainder 0, 1 ÷ 3 = 0 remainder 1. Reading the remainders from bottom to top gives 110.