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Graph the image of this triangle after a dilation with a scale factor of 1/2 centered at (-5,1)
1 answer:
Answer:
Red triangle on the diagram
Step-by-step explanation:
The center of dilation is point D(-5,1). The scale factor is 1/2. This means that all distances need to be halved.
If triangle ABC has vertices A(-1,7), B(7,9) and C(3,1), then the image triangle has vertices at points E(-3,4), G(1,5) and F(-1,1).
Points E, G and F are midpoints of the segments DA, DB and DC (see attached diagram for details).
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Answer:
a) 26.76% probability that a student in the psychology department has a score less than 480.
b) 69.73% probability that a student in the psychology department has a score between 480 and 730.
Step-by-step explanation:
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.
In this problem, we haev that:
a. Find the probability that a student in the psychology department has a score less than 480.
This is the pvalue of Z when X = 480. So
has a pvalue of 0.2676.
26.76% probability that a student in the psychology department has a score less than 480.
b. Find the probability that a student in the psychology department has a score between 480 and 730.
This probability is the pvalue of Z when X = 730 subtracted by the pvalue of Z when X = 480.
X = 730
has a pvalue of 0.9649.
X = 480
has a pvalue of 0.2676.
0.9649 - 0.2676 = 0.6973
69.73% probability that a student in the psychology department has a score between 480 and 730.