two horizontal lines are cut by a transversal. what is the least number of angle measures you need to know in order to find the
measure of every angle? explain your reasoning
1 answer:
Answer: The answer is only one angle. Explained.
Step-by-step explanation: As given in the question and shown in the attached figure, the lines horizontal lines 'p' and 'q' are cut by the transversal 'r'. We need to determine the least number of angles among the eight angles mentioned in the figure to find the measure of all the angles.
Suppose, the measure of ∠1 is given as x°.
So, ∠2 = 180° - x (linear pair of angles),
∠3 = x (=∠1, vertically opposite angles),
∠4 = 180° - x (=∠2, verticaly opposite angles),
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8. These are pairs of correspomding angles.
Thus, we need the measure of only one angle to find the measure of all the angles.
Hence explained.
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Answer:
a) Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.
b) Rachel, because her time had the lowest z-score.
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
The lower the time, the better the runner is. So whoever's time has a lower z-score is a better runner. So initially, we find the z-score of each student's time.
An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes.
This means that for Rachel's time, we have that . So
A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.
This means that for Kenji's time, we have that . So
A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.
This means that for Nedda's time, we have that . So
(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.
(b) Who is the fastest runner with respect to his or her class? Explain why
Rachel, because her time had the lowest z-score.