A line segment is dilated by a factor of 4 and the center of the dilation is a point on the line segment. Which of the following
is the result of this dilation?
a. A line segment that is 4 times longer and in the some position as the original line segment
b. a line segment that is 4 times longer and perpendicular to the original line segment, crossing the original line segment at the center of the dilation point
c. a congruent line segment that is parallel to the original line segment
d. a line segment that is 4 times longer and parallel to the original line segment
a. A line segment that is 4 times longer and in the some position as the original line segment
b. a line segment that is 4 times longer and perpendicular to the original line segment, crossing the original line segment at the center of the dilation point
c. a congruent line segment that is parallel to the original line segment
d. a line segment that is 4 times longer and parallel to the original line segment
1 answer:
Answer:
a. A line segment that is 4 times longer and in the same position as the original line segment.
Step-by-step explanation:
In dilation, when the center of dilation lies on the line segment, the dilated line segment remains at the same position.
Also, the dilated line segment has length 4 times that of original line segment if the factor of dilation is 4.
As shown is the figure attached:
PQ is the line segment. Center of dilation is 0.
0P' is four times that of OP and OQ' is four times that of OQ.
The dilated line segment is at the same position.
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Answer:
The 95% confidence interval is
A 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval
Step-by-step explanation:
From the question we are told that
The sample size is
The mean is
The standard deviation is
Given that the confidence level is 95% then the level of significance is mathematically represented as
=>
=>
Next we obtain the critical value of from the normal distribution table , the value is
Generally the margin of error is mathematically represented as
substituting values
The 95% level of confidence interval is mathematically represented as
substituting values
The 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval
Answer:
2.28% probability that a person selected at random will have an IQ of 110 or greater
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 have that:
What is the probability that a person selected at random will have an IQ of 110 or greater?
This is 1 subtracted by the pvalue of Z when X = 110. So
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
2.28% probability that a person selected at random will have an IQ of 110 or greater