Amathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must shown. if an examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen?

450 ways

Step-by-step explanation:

Given that a mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must shown.

An examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems

8 multiple choice questions can be selected from 10 in 10C2 ways and 3 open ended problems in 5/c3 ways

In 450 ways  the questions and problems can be chosen

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

i dont know

step-by-step explanation: