Answer:
<u>The correct answer is 3.77 strokes as the average score for the ninth hole of the Cottonwood Golf Course.</u>
Step-by-step explanation:
1. To find the average score, we need to know how many strokes the 75 golfers needed to play this ninth hole. For doing that, we will do the following addition, using the frequency data given:
1 x 1 = 1
1 x 2 = 2
32 x 3 = 96
27 x 4 = 108
8 x 5 = 40
6 x 6 = 36
1 + 2 + 96 + 108 + 40 + 36
<u>283</u>
<u>This means that all the 75 golfers scored 283 strokes for playing the ninth hole</u>
2. Now that we know that the total number of strokes was 283, we will do a division for find the average score, using also the number of golfers. For doing it, we will do the following division:
Total number of strokes/ total number of players
<u>283/75 = 3.77</u>
<u>The average score is 3.77. It means that the 75 golfers in average hit 3.77 strokes to play the ninth hole.</u>
These are the steps, with their explanations and conclusions:
1) Draw two triangles: ΔRSP and ΔQSP.
2) Since PS is perpendicular to the segment RQ, ∠ RSP and ∠ QSP are equal to 90° (congruent).
3) Since S is the midpoint of the segment RQ, the two segments RS and SQ are congruent.
4) The segment SP is common to both ΔRSP and Δ QSP.
5) You have shown that the two triangles have two pair of equal sides and their angles included also equal, which is the postulate SAS: triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.
Then, now you conclude that, since the two triangles are congruent, every pair of corresponding sides are congruent, and so the segments RP and PQ are congruent, which means that the distance from P to R is the same distance from P to Q, i.e. P is equidistant from points R and Q
