Segment AB is being dilated with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4). What is the s
cale factor of the dilation and the coordinates of point B"
The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 1.25 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 0.8 and the coordinates of point B"are (–5, –7.5).
The scale factor is 1.25 and the coordinates of point B" are (–5, –7.5).
The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 1.25 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 0.8 and the coordinates of point B"are (–5, –7.5).
The scale factor is 1.25 and the coordinates of point B" are (–5, –7.5).
2 answers:
Answer: The correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation: Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).
We are to find the scale factor of the dilation and the co-ordinates of the point B''.
From the given graph, we note that
the co-ordinates of point A are (4, 8).
Now, If S is the scale factor of dilation, then we must have
So, the scale factor is 0.8.
Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be
Thus, the correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
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Answer:
Yes, it would be unusual.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
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.
If or
, the outcome X is considered unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Would it be unusual for this sample mean to be less than 19 days?
We have to find Z when X = 19. So
By the Central Limit Theorem
, so yes, the sample mean being less than 19 days would be considered an unusual outcome.