Question

the table shows janisas scores in an archery tournament qualifying event.
janisas scores
10
10
8
8
3
?
janisa needs a mean score of 8 to qualify for the archery tournament. how many points does she need on her last arrow to qualify for the tournament?
janisa needs total points to have a mean score of 8.
janisa has points so far.
janisa needs to score points on her last arrow to qualify for the tournam
7
8
9
10

Explanation:

Step1: Calculate total points needed

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 6$ (6 arrows in total) and $\bar{x}=8$. So the total points needed $\sum_{i=1}^{6}x_{i}=n\times\bar{x}=6\times8 = 48$.

Step2: Calculate points scored so far

Sum the known scores: $10 + 10+8 + 8+3=39$.

Step3: Calculate score on last arrow

Let the score on the last arrow be $x$. We know that $39 + x=48$. Solving for $x$, we get $x=48 - 39=9$.

Answer:

Janisa needs $48$ total points to have a mean score of 8.
Janisa has $39$ points so far.
Janisa needs to score $9$ points on her last arrow to qualify for the tournament.