In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?
2 answers:
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Answer:
The shadow of the building = 192 ft.
Step-by-step explanation:
∵ There is a proportional relation between the heights of the tree and the building and their shadows
∴ Height tree/height building = shadow tree/shadow building
x = = 192 ft ⇒ x is the length of the shadow of the building
Answer:
Step-by-step explanation:
You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:
You know that:
Then KE is:
Now you can substitute the value of KE and the value of KH into and solve for JK. Then the result is:
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is <u>one subtracted by the p-value of Z when X = 4</u>, hence:
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
More can be learned about the normal distribution at brainly.com/question/24663213
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