Sarah is researching the connection between the time students spend watching television and their performance in school. her studies indicate that there is an inverse relationship between tv time and gpa, and that a student who watched 15 hours of tv per week can be expected to have a gpa of 3.5. what gpa would an inverse relation predict for a student who watches 24 hours of tv a week

a) 2.19
b) 2.47
c) 2.60
d) 2.88
e) 3.12

option A)

2.19

Step-by-step explanation:

Given that,

there is an inverse relationship between TV time and GPA as researched by Sarah.

where k is constant

Find k

A student who watched 15 hours of TV per week can be expected to have a GPA of 3.5

15 = k / 3.5

k = 52.5

GPA for student who watches 24 hours of tv a week

24 = 52.5 / GPA

GPA = 52.5 / 24

        = 2.187

        ≈ 2.19

i think the correct option is the second option.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is