Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet,
2 answers:
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Answer:
Now we can calculate the p value with the following probability:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
estimated proportion of interest
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic
represent the p value
System of hypothesis
We want to verify if the true proportion is higher than 0.5:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
Now we can calculate the p value with the following probability:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Answer: OPTION D.
Step-by-step explanation:
<h3> The complete exercise is: "Which arrangement showsConvert from mixed numbers to decimal numbers.
The steps to do this, are the following:
1. You must divide the numerator of the fraction by the denominator.
2. Then you must add the quotient obtained to the whole number part.
Applying this procedure, you get that:
Now that you have all the numbers in decimal form, you can order from least to greatest:
Therefore, you can conclude that the correct arrangement is:
Answers:
x = angle MLN = 35 degrees
angle FLJ = 55 degrees
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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
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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.
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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.
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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
