When Mr. Serrano preheated his oven, the oven's temperature rose 3 degrees in
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The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.
Which vertex will be in the top position of the regular decagon?
A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.
Now, the smallest angle of rotation will be the angle between the two sides of the decagon.
In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction, point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)
Learn more about decagon here:
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Answer:
μ=23.710740....
σ=3.592592....
Step-by-step explanation:
At first, we are told that it´s a normal distribution and the following:
P(x≤15.34)=0.1
P(x≤16.31)=0.2
We start looking for those values (0.1 and 0.2) and the probabilities that gives us those values in a normal standard distribution. There´s some tools that´ll help us out but i´ll be using a chart with the values of some probabilities in a normal standard distribution (That it´s attached).
The probability of P(z≤ a.b) where "a" is the whole part of a number and "b" the decimal part is in the coordinates (a,b). For example for our problem:
P(z≤-2.33)=0.099≈0.1
P(z≤-2.06)=0.197≈0.2
To find a probability of a normal (not standard) distribution we use a method called Normalize that proceeds:
P(x≤a)=P( (x-μ)/σ ≤ (a-μ)/σ )
Where μ is the Mean of the data and σ is the Standard deviation. P( (x-μ)/σ ≤ (a-μ)/σ ) is now part of a normal standard distribution and we are able to look for it in the chart.
We will use it to find the Mean and the STD for our distribution.
P(x≤15.34)=P(z≤-2.33)≈0.1
P(x≤16.31)=P(z≤-2.06)≈0.2
so we have the equations:
(15.34 - μ)/σ= -2.33 and (16.31 - μ)/σ= -2.06
And we solve them for μ and σ:
(15.34 - μ)/-2.33= σ and (16.31 - μ)/-2.06= σ
(15.34 - μ)/-2.33 = (16.31 - μ)/-2.06
2.06*(15.34 - μ) = 2.33(16.31 - μ)
2.33μ - 2.06μ = 2.33(16.31) - 2.06(15.34)
μ= 6.4019 / 0.27
μ= 23.710740...
With this value we find σ in one equation:
(15.34 - (23.710740...)/σ = -2.33
(15.34 - (23.710740...)/-2.33 = σ
σ=3.592592...
We finally have our answers:
μ=23.710740....
σ=3.592592....
