Answer:
<em>Q'</em> = (-4, -2)
<em>R' </em>= (4, -2)
<em>S'</em> = (4, 2)
<em>T'</em> = (-4, 2)
Step-by-step explanation:
First, we can create a matrix to scale this rectangle by putting all the x coordinates in the top row and all the y coordinates in the bottom row and multiply it by 4.
Our initial matrix to multiply:
![4\left[\begin{array}{cccc}-1&1&1&-1\\-2&-2&-1&-1\end{array}\right]](https://tex.z-dn.net/?f=4%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%261%261%26-1%5C%5C-2%26-2%26-1%26-1%5Cend%7Barray%7D%5Cright%5D)
Moved to the origin:
![4\left[\begin{array}{cccc}-1&1&1&-1\\-0.5&-0.5&0.5&0.5\end{array}\right]](https://tex.z-dn.net/?f=4%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%261%261%26-1%5C%5C-0.5%26-0.5%260.5%260.5%5Cend%7Barray%7D%5Cright%5D)
Multiplied by four:
![\left[\begin{array}{cccc}-4&4&4&-4\\-2&-2&2&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-4%264%264%26-4%5C%5C-2%26-2%262%262%5Cend%7Barray%7D%5Cright%5D)
This gives us the points of
<em>Q'</em> = (-4, -2)
<em>R' </em>= (4, -2)
<em>S'</em> = (4, 2)
<em>T'</em> = (-4, 2)
which are our answers.
Answer:
the second bottle
Step-by-step explanation:
To get the amount it costs per ounce, divide the amount of money by the number of ounces.
A water bottle that costs $1.25 for 12 ounces costs roughly 10 cents per ounce. A water bottle that costs about 9 cents per ounce.
therefore, the 16 ounce bottle is cheaper per ounce
We have to define an interval about the mean that contains 75% of the values. This means half of the values will lie above the mean and half of the values lie below the mean.
So, 37.5% of the values will lie above the mean and 37.5% of the values lie below the mean.
In a Z-table, mean is located at the center of the data. So the position of the mean is at 50% of the data. So the position of point 37.5% above the mean will be located at 50 + 37.5 = 87.5% of the overall data
Similarly position of the point 37.5% below the mean will be located at
50 - 37.5% = 12.5% of the overall data
From the z table, we can find the z value for both these points. 12.5% converted to z score is -1.15 and 87.5% converted to z score is 1.15.
Using these z scores, we can find the values which contain 75% of the values about the mean.
z score of -1.15 means 1.15 standard deviations below the mean. So this value comes out to be:
150 - 1.15(25) = 121.25
z score of 1.15 means 1.15 standard deviations above the mean. So this value comes out to be:
150 + 1.15(25) = 178.75
So, the interval from 121.25 to 178.75 contains the 75% of the data values.
