In the diagram below of triangle ABC, the medians meet at point G. If CF = 39, what is the length of CG?
1 answer:
Applying the centroid theorem of a triangle, the length of CG is: 26.
<em><u>Recall:</u></em>
- Medians join the vertices to the midpoint of the opposite sides of a triangle.
- The center that all the three medians intersect at is called the centroid.
- Based on the centroid theorem, the distant from the centroid to the vertex = 2/3 of the median length.
Triangle ABC is shown in the image attached below. G is the centroid.
CF = 39 (median)
CG = 2/3(CF) ---> Centroid Theorem.
- Substitute
CG = 2/3(39)
CG = 26
Therefore, applying the centroid theorem of a triangle, the length of CG is: 26.
Learn more about centroid theorem on:
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Answer:
- 56.25 feet
Step-by-step explanation:
As per diagram, the two triangles are similar, as all angles are congruent (one is vertical, one is right, one is the
Let the distance across the river be x.
<u>The ratio of corresponding sides is same. Find x using ratios:</u>
- x/45 = 75/60
- x = 45*75/60
- x = 56.25 feet
Answer:
H0: μ ≤ 34
H1: μ > 34
The z-test statistic is ≈ 1.8
The critical z-score is 1.28
we fail to reject the null hypothesis H0: μ ≤ 34
Step-by-step explanation:
H0: μ ≤ 34
H1: μ > 34
The z-test statistic is calculated using the formula:
z= where
- X is the average class size found in the sample (35.6)
- M is the mean according to the null hypothesis (34)
- s is the standard deviation for class size (9)
then z= ≈ 0.18
The critical z-score is 1.28 for α=0.10 (one tailed)
Because the test statistic is less than the critical value, do not reject the null hypothesis.