In this survey, 77 people prefer basketball. In a survey done a couple months later, only 70
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Answer:
Step-by-step explanation:
We have been given a data set that represents the number of rings each person in a room is wearing as: 0, 2, 4, 0, 2, 3, 2, 8, 6. We are asked to find the interquartile range of the data.
Let us arrange our data points from least to greatest order.
0, 0, 2, 2, 2, 3, 4, 6, 8.
Let us find median of our data set. Since our data set has 9 data points, therefore, median of our given data set will be value of 5th term, that is 2.
Now let us find lower quartile, which is also known as the median of the data points to the left of median.
We have 4 data points to the left of our median, so our lower quartile will be average of 2nd and 3rd data point.
Now let us find upper quartile of our given data set, which is the median of the data points to the right of median.
We have 4 data points to the right of the median, so our upper quartile will be the average of 7th and 8th data point.
Since we know that interquartile range is the difference between upper and lower quartile.
Therefore, IQR of our given data set is 4.
If the product of 2 matrices are I this means that B is inverse matrix of A.
the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
![\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] ](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%0A)
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values
D = -1x8 - (4x-3)
= -8 + 12 = 4
to find the inverse we need to exchange a and d and then multiply both b and c by -1
![\left[\begin{array}{ccc}8&-4\\3&-1\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-4%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)
and then have to divide all the terms in matrix by determinant (4)
![\left[\begin{array}{ccc} \frac{8}{4} & \frac{-4}{4} \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cfrac%7B8%7D%7B4%7D%20%26%20%5Cfrac%7B-4%7D%7B4%7D%20%5C%5C%20%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the simplified inverse matrix B is;
![\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%202%20%26%20-1%20%5C%5C%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values
D = -1x8 - (4x-3)
= -8 + 12 = 4
to find the inverse we need to exchange a and d and then multiply both b and c by -1
and then have to divide all the terms in matrix by determinant (4)
the simplified inverse matrix B is;