1 answer:
Claim: The measures of and
are equal
Answer: True
Explanation: Dilations preserve the shape of an image, so this means the angles are kept the same whether you shrink or enlarge the preimage.
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Claim: The coordinates of A and A' are the same
Answer: True
Explanation: The phrasing "dilating about point A" means that point A is the center of the universe, so to speak, in terms of this dilation operation. Point A is the fixed point that does not move while every other point does move. Because the scale factor is 2/3, which is less than 1, this means every other point comes closer to point A. So something like segment AB will get shorter.
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Answer:
(a)
(b) 0.7910
(c) 0.0401
(d) 0.6464
Step-by-step explanation:
Let <em>X</em> = amount of time that people spend at Grover Hot Springs.
The random variable <em>X</em> is normally distributed with a mean of 73 minutes and a standard deviation of 16 minutes.
(a)
The distribution of the random variable <em>X</em> is:
(b)
Compute the probability that a randomly selected person at the hot springs stays longer than 60 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays longer than an hour is 0.7910.
(c)
Compute the probability that a randomly selected person at the hot springs stays less than 45 minutes as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly selected person at the hot springs stays less than 45 minutes is 0.0401.
(d)
Compute the probability that a randomly person spends between 60 and 90 minutes at the hot springs as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that a randomly person spends between 60 and 90 minutes at the hot springs is 0.6464