A triangle has the coordinates (7, 6), (6, 3), and (8, 3) at its vertices. The transformed triangle has the coordinates (6, −7),
(3, −6), and (3, −8) at its vertices. Are the triangle and its transformation congruent? Why or why not?
A. Yes, the transformation is a 90° clockwise rotation.
B. No, the transformation is a 180° clockwise rotation.
C. Yes, the transformation is a 270° clockwise rotation.
D. No, the transformation is a 360° clockwise rotation.
A. Yes, the transformation is a 90° clockwise rotation.
B. No, the transformation is a 180° clockwise rotation.
C. Yes, the transformation is a 270° clockwise rotation.
D. No, the transformation is a 360° clockwise rotation.
2 answers:
Answer with explanation:
Vertices of Triangle are (7, 6), (6, 3), and (8, 3) .
When the triangle is transformed that is rotation has taken place and the coordinates of vertices of Image are (6, −7), (3, −6), and (3, −8).
When you will compare Pre image and Image
1.⇒ Rotation in clockwise direction has taken place to get the Image.
2.⇒Pre Image is in First Quadrant, and Image is in fourth Quadrant
Among the four transformation , Reflection, Rotation, Translation and Dilation , in first three that is, Reflection, Rotation,and Translation Preimage and Image are Congruent , while in Dilation the two, Preimage and Image are Similar.
So , Yes the two triangles are Congruent.
⇒Option A: Yes, the transformation is a 90° clockwise rotation.
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Answer:
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
A statistician calculates that 8% of Americans own a Rolls Royce.
This means that
Sample of 595:
This means that
Mean and standard deviation:
What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05. So
By the Central Limit Theorem
has a p-value of 0.0035
2*0.0035 = 0.0070
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%