Answer:
The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.
Step-by-step explanation:
Let x points be the score that 4th judge gave to the dancer.
The first three judges gave the dancer 8.9 points, 7.1 points and 8.3 points.
In total, the dancer got
[tex]8.9+7.1+8.3+x=24.3+x[/tex] points
The average score is
[tex]\dfrac{24.3+x}{4}[/tex]
This average score must be at least of 8 points, so
[tex]\dfrac{24.3+x}{4}\ge 8\\ \\24.3+x\ge 32\\ \\x\ge 32-24.3\\ \\x\ge 7.7[/tex]
The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.
