Break apart 213 into hundreds tens and ones
2 answers:
You might be interested in
Answer:
The answer to the question is;
The probability that the resulting sample mean of nicotine content will be less than 0.89 is 0.1587 or 15.87 %.
Step-by-step explanation:
The mean of the distribution = 0.9 mg
The standard deviation of the sample = 0.1 mg
The size of the sample = 100
The mean of he sample = 0.89
The z score for sample mean is given by
where
X = Mean of the sample
μ = Mean of the population
σ = Standard deviation of the population
Therefore Z = = -1
From the standard probabilities table we have the probability for a z value of -1.0 = 0.1587
Therefore the probability that the resulting sample mean will be less than 0.89 = 0.1587 That is the probability that the mean is will be less than 0.89 is 15.87 % probability.
Answers:
x = angle MLN = 35 degrees
angle FLJ = 55 degrees
=================================================
Explanation:
This problem is fairly tricky if you're not sure what to look for. A slight clue is that they've marked a red point that strangely doesn't have a label on it. It's a fairly small point but it's definitely there if you look closely. While this point's location isn't exactly what we want, we're fairly close. Start at point L and draw a ray through the center point P. Ray LP will intersect the circle at point A, as shown in the diagram below.
From here, draw segments FA and MA. Now notice that inscribed angle LMF = 55 and inscribed angle FAL both subtend the same arc. The term "subtend" basically means "cut off". This arc that the inscribed angles subtend is minor arc FL. A minor arc is where you travel the shorter path around the circle, which indicates its measure is less than 180 degrees.
Since inscribed angles LMF and FAL subtend the same minor arc, this makes the inscribed angles to be congruent.
In short: angle FAL is 55 degrees
----------------------
Segment LA goes through the center P. Through Thales theorem, we know that inscribed angle LFA is 90 degrees. Consequently, we can determine that inscribed angle FLA is 90-55 = 35 degrees.
Segment JL is tangent to the circle, meaning that angle ALJ is 90 degrees. So angle FLJ is 90-35 = 55 degrees.
It's not a coincidence that angle FLJ, angle FAL, and angle LMF are the same measure.
----------------------
We found that angle FAL was 55 degrees. Applying Thales theorem again shows that angle MAF is 90 degrees. Therefore, angle LAM is 90-55 = 35 degrees.
Focus now on triangle LMA. This is also a right triangle (Thales Theorem). The upper acute angle we found was angle LAM = 35, so the lower acute angle is ALM = 55.
Then we can find angle MLN = (angle ALN) - (angle ALM) = 90 - 55 = 35
In short, angle MLN = 35 degrees
Similar to the previous section, it is not a coincidence that angles LFM, LAM and MLN are the same measure.
------------------------
As an alternative, since we know angle FLJ = 55, and angle FLM is 90 degrees, this means...
(angle FLJ)+(angle FLM) + (angle MLN) = 180
55 + 90 + angle MLN = 180
145 + angle MLN = 180
angle MLN = 180 - 145
angle MLN = 35 degrees
