Answer:
Step-by-step explanation:
A circle is inscribed in an equilateral triangle PQR with centre O. If angle OQR = 30°, what is the perimeter of the triangle?
This is a circle inscribed in an equilateral triangle with side s.
If you are asking for the perimeter of PQR, it is 3s.
If you are asking for the perimeter of OQR, it is (3+23–√3)s
Since OR and SR are the hypotenuses of right triangles with adjacent side equal to ½ s, their length is ½s / cos 30° = (√3) /3.
(3/3)s + ((√3) /3)s + ((√3) /3)s = ((3 + 2√3)/3)s ≈ 2.1547s
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Answer:
![S_6 = -63](https://tex.z-dn.net/?f=%20S_6%20%3D%20-63%20)
Step-by-step explanation:
The sequence above is a geometric sequence.
The common ratio (r) = ![\frac{-6}{3} = \frac{12}{-6} = -2](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6%7D%7B3%7D%20%3D%20%5Cfrac%7B12%7D%7B-6%7D%20%3D%20-2%20)
The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: ![S_n = \frac{a_1(1 - r^n)}{1 - r}](https://tex.z-dn.net/?f=%20S_n%20%3D%20%5Cfrac%7Ba_1%281%20-%20r%5En%29%7D%7B1%20-%20r%7D%20)
a1 = 3
r = -2
n = 6
Plug in the values into the formula
![S_6 = \frac{3(1 - (-2^6)}{1 - (-2)}](https://tex.z-dn.net/?f=%20S_6%20%3D%20%5Cfrac%7B3%281%20-%20%28-2%5E6%29%7D%7B1%20-%20%28-2%29%7D%20)
![S_6 = \frac{3(1 - (64)}{1 + 2}](https://tex.z-dn.net/?f=%20S_6%20%3D%20%5Cfrac%7B3%281%20-%20%2864%29%7D%7B1%20%2B%202%7D%20)
![S_6 = \frac{3(-63)}{3}](https://tex.z-dn.net/?f=%20S_6%20%3D%20%5Cfrac%7B3%28-63%29%7D%7B3%7D%20)
![S_6 = -63](https://tex.z-dn.net/?f=%20S_6%20%3D%20-63%20)
Answer:
Knowing others is intelligence; knowing yourself is true wisdom. mastering others is strength; mastering yourself is true power. if you realize that you have enough, you are truly rich, "And the cause of not following your heart, is in spending the rest of your life wishing you had."
Using the mean concept, it is found that the mean difference between the call times and the company's average call time is given by:
<h3>What is the mean?</h3>
- The <em>mean </em>of a data-set is given by the <u>sum of all observations in the data-set divided by the number of observations</u>.
In this problem:
- The four observations are the differences between the time of each phone call and the average time.
- They are: {-2.32, -1.55, 4.79, 0.68}
Hence, the mean difference is:
![M = \frac{-2.32 - 1.55 + 4.79 + 0.68}{4} = 0.4](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B-2.32%20-%201.55%20%2B%204.79%20%2B%200.68%7D%7B4%7D%20%3D%200.4)
Hence, option C is correct.
To learn more about the mean concept, you can take a look at brainly.com/question/13451786