is the independent variable in case A

(a) Grades
(b) Services to help improve grades
(c) Teachers

(b) Services to help improve grades

To determine the independent variable in case A, let's start by understanding what an independent variable is. An independent variable, generally denoted as X, is the variable that is manipulated or changed by the researcher in an experiment or study. It is the variable that is hypothesized to have an effect on the dependent variable.

In case A, the options given are:
(a) Grades
(b) Services to help improve grades
(c) Teachers

Since the question asks for the independent variable, we need to identify which of the options is being manipulated or changed in the case.

(a) Grades: Grades are usually an outcome or dependent variable that is influenced by other factors. They are not typically manipulated directly by researchers.

(b) Services to help improve grades: Services to help improve grades are usually introduced or provided by researchers or educational institutions in order to observe their impact on the dependent variable. Therefore, services to help improve grades would be the independent variable in this case.

(c) Teachers: While teachers play a crucial role in influencing students' grades, they are not typically manipulated by researchers in an experiment. Instead, teachers would generally be considered as an external factor affecting the dependent variable.

So, in case A, the correct option for the independent variable is (b) Services to help improve grades.

To determine the independent variable in case A, we need more information about the context or experiment being referred to. Please provide additional details about the case A you are referring to.