When a shape is rotated, it must be rotated through a point.
- <em>90 degrees counterclockwise rotation negates the y-coordinates, and then swap the x and y-coordinates</em>
- <em>Chanel is incorrect</em>
The rule of 90 degrees counterclockwise is:
This means that:
- <em>The y-coordinate is negated</em>
- <em>Then the y and x coordinates are swapped</em>
<em />
However, Charlies transformation is incorrect.
- This is so because, the shape was not rotated, but instead it was reflected across the x-axis.
- Then, the shape was dilated
Using points L and Q
When L is reflected across the x-axis.
The rule is:
So, we have:
Next, it is dilated by 2.
The rule of this is:
So, we have:
From the diagram, the coordinate of Q is:
Same as the calculated point
Hence, Chanel is incorrect
Read more about transformation at:
brainly.com/question/11709244
Using the normal distribution, we have that:
- For a single value, P(X < 79.1) = 0.5517.
- For the sample of n = 155, P(X < 79.1) = 0.9463.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The mean and the standard deviation are given, respectively, by:
.
The probability is the <u>p-value of Z when X = 79.1</u>, hence:
Z = (79.1 - 76.2)/22.4
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
Hence: P(X < 79.1) = 0.5517.
For the sample of 155, applying the Central Limit Theorem, the standard error is:
s = 22.4/sqrt(155) = 1.8
Hence:
Z = (79.1 - 76.2)/1.8
Z = 1.61
Z = 1.61 has a p-value of 0.9463.
P(X < 79.1) = 0.9463.
More can be learned about the normal distribution at brainly.com/question/15181104
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Answer:
r = 18 cm
Step-by-step explanation:
The formula for the circumference of a circle is 2πr.
Hence,
2πr = 36π
r = 18 cm
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