A recent article1 claims that "Green Spaces Make Kids Smarter." The study described in the article involved 2623 schoolchildren in Barcelona. The researchers measured the amount of greenery around the children's schools, and then measured the children's working memories and attention spans. The children who had more vegetation around their schools did better on the memory and attention tests.

(a) What are the cases in this study?

(b) What is the explanatory variable?

(c) What is the response variable?

(d) Does the headline imply causation?

(e) Is the study an experiment or an observational study?

(f) Is it appropriate to conclude causation in this case?

Cases : 2623 school children , Explanatory Variable : Greenery or Vegetation around school , Response Variable : Children's Memory & attention spans , Yes  causation, Observational study

Step-by-step explanation:

a) Cases refers to the people or units of population studied in the research. In this case, it is sample of 2623 school children in Barcelona

b) Explanatory variable is variable which leads to, or causes the change in other variable. In this case, it is greenery or vegetation around researched students' schools

c) Response variable is the variable which is affected due to change in independent explanatory variable. In this case, it is children's working  memory & attention spans

d) Yes, the headline implies causation. As it implies cause effect relationship of greenery around children's school on their working memory & attention spans.

e) It is an observational study, as it observes the variables relationship as it is, without any specific experimental intervention.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.