Final answer:
The symbols used for "not equal to" in mathematics are d. ≠. This symbol is key in expressing that two values do not have the same quantity or value. It is commonly used in statistical hypothesis testing to denote the alternative hypothesis, which does not include an equality. The correct answer is option d. ≠
Step-by-step explanation:
The symbols used for "not equal to" are d. ≠. In mathematics, the not equal to symbol communicates that two values are not the same. For example, if we say 3 ≠ 4, we mean that the number 3 is not equal to the number 4.
When formulating hypotheses in statistics, the alternative hypothesis (H₁) is often expressed using symbols that indicate a relationship other than equality. These can include less than (<), greater than (>), or not equal to (≠). The null hypothesis (H₀) typically includes an equal sign, but it's important to note that some researchers might use the equals symbol even when referring to H₁ in contexts that assume variability.
To demonstrate how such symbols can be used in various contexts, consider the following usage: two vectors are described as not equal because they have different magnitudes and directions.