You need to note first two things.
1. The function f(x) need to be a continuous function on [-3,-1] (indeed f(x) is a polynomial function, is continuous on every real number x)
2. Take the closed interval [-3,-1]
Now, evaluate f(-3) and f(-1).
So, we have f(-3) < 0 and f(-1). So, , then by the Intermediate Value Theorem, there exist
such that
.
7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.
Step-by-step explanation:
The given is,
Year Students
7 80
8 110
9 160
Total 350
Mr.Ford wants to survey 50 of these students stratified by year group.
Step:1
Formula to find the ratio of number of grouped students to total students,
=
= 0.1428
Step:2
Formula for Number of students surveyed from year wise,
For year 7 students,
= (Ratio) × (Students from year 7)
= 0.1428 × 80
= 11.424
≅ 11 (∵ For students we convert into whole number)
For year 8 students,
= (Ratio) × (Students from year 8 )
= 0.1428 × 110
= 15.708
≅ 16 (∵ For students we convert into whole number)
For year 8 students,
= (Ratio) × (Students from year 9 )
= 0.1428 × 160
= 22.8
≅ 23 (∵ For students we convert into whole number)
Step:3
To find How many more year 9 students than year 8 students should be in the survey
= ( Students from year 8 for group) -
( Students from year 8 for group)
= 23 - 16
= 7 students
Result:
7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.
