In a math class with 28 students, a test was given the same day that an assignment
was due. There were 18 students who passed the test and 23 students who completed
the assignment. There were 16 students who passed the test and also completed the
assignment. What is the probability that a student who passed the test did not
complete the homework?

Probability that a student who passed the test did not  complete the homework = 0.07

Step-by-step explanation:

Given:

Total number of students = 28

Number of students who passed the test = 18

Number of students who completed  the assignment = 23

Number of students who passed the test and also completed the  assignment = 16

To find: probability that a student who passed the test did not  complete the homework

Solution:

Probability refers to chances of occurrence of some event.

Probability = number of favorable outcomes/total number of outcomes

Let A denotes the event that students passed the test and B denotes the event that students completed  the assignment

P(A only) =

Here,

So,

Therefore,

probability that a student who passed the test did not  complete the homework = 0.07

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2