Triangle MOP has been rotated to create triangle M'O'P'. MP = M'P' = 2 units, MO = M'O' = 2 units, and OP = O'P' = 2.82 units. W
2 answers:
Answer: SSS
Step-by-step explanation:
Given : Triangle MOP has been rotated to create triangle M'O'P'.
such that MP = M'P' = 2 units
MO = M'O' = 2 units
OP = O'P' = 2.82 units.
Then , by SSS postulate of congruence , we have
- The SSS postulate of congruence says that if three sides of a triangle are congruent to three sides of any other triangle then the triangles are congruent.
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Answer:
The standard deviation for the income of super shoppers is 76.12.
Step-by-step explanation:
The formula to compute the standard deviation for the grouped data probability distribution is:
Here,
<em>x</em> = midpoints
Consider the Excel table attached below.
The mean is:
Compute the standard deviation as follows:
Thus, the standard deviation for the income of super shoppers is 76.12.
The box-and-whisker plot is attached.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.