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mariarad
1 month ago
5

The final score of a figure skating competition is determined by finding the average of six judges' scores. Write a formula for

the average A
of six scores x1, x2, x3, x4, x5, and x6. Then solve the formula for x4, the fourth judge's score.
A=


x4=


The table shows the scores given to a figure skater by the judges. The skater receives a final score of 5.7. Find the score given by the fourth judge.

Judge 1 2 3 4 5 6
Score 5.6 5.8 5.6 x4 5.9 5.4
Mathematics
2 answers:
PIT_PIT [12.4K]1 month ago
3 0

Answer:

a)  \text{Average of Scores} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}

x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)

b)x_4 = 5.9

Detailed explanation:

a) The judges provided a total of six scores: x_1, x_2, x_3, x_4, x_5, x_6

We need to calculate the average of these scores:

\text{\bold{Average of Scores}} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}

To determine the fourth judge's score, we can rearrange the formula to yield x_4

x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)

b) The computed average score = 5.7

Judge: 1       2       3       4       5       6

Score: 5.6    5.8    5.6    x      5.9     5.4

Substituting the values into the equation provides us with:

x = 6(5.7) - (5.6+5.8+5.6+5.9+5.4)

x = 5.9

This indicates the score recorded by the fourth judge is 5.9

x_4 = 5.9

AnnZ [12.3K]1 month ago
3 0

The average A is calculated by adding the scores given by each judge and dividing by the total number of judges.

Hence A =\frac{x1 + x2 + x3 + x4 + x5 + x6}{6}

To determine the score given by judge 4, we need the final average score (A) and the scores from the other five judges.

The overall score A comes to 5.7

The scores from judges 1, 2, 3, 5, and 6 are 5.6, 5.8, 5.6, 5.9, and 5.4 respectively.

With this information, we can compute x4:

x4=6A-x1-x2-x3-x5-x6

x4=6*5.7 -5.6-5.8-5.6-5.9-5.4

x4=5.9

Thus, the fourth judge's score was x4=5.9

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