Based on student records, 30% of the students at a large high school have a GPA of 3.5 or better, 19% of the students are currently enrolled in at least one AP class, and 16% of the students have a GPA of 3.5 or better and are enrolled in at least one AP class. If we select one student at random, what is the probability that the student has a GPA higher than 3.5 and is not taking any AP classes?

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: