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3 years ago

3)

Mathematics

1 answer:

jonny [76]3 years ago

3 0

Answer:

Mean: 10.3

Median: 12

Mode: 13

Range: 15

Step-by-step explanation:

First, let's define what all these terms mean.

Mean is the average of all the numbers in a set of data. Median is the number in the middle of a range whenever the numbers are put in ascending order. If there are two numbers in the middle instead of one, then take the average of those two numbers. Mode is the number that occurs the most in the set of data. Range is the difference between the largest and the smallest number in a set of data.

To make things a little easier overall, let's just go ahead and put all our numbers in ascending order, which will be as follows: 1, 6, 7, 7, 11, 13, 13, 13, 16, 16.

To find the mean, just add up all the numbers and divide by how many there are. So we'll add 1 + 6 + 7 + 7... and so on to get a total of 103. Next, we'll divide that number by 10 since there are 10 students. This gives us a mean of 10.3.

Next, we'll find the median. To find this, just figure out which number(s) is in the center of your data. Since we have an even number of terms (10), we'll have two numbers in the middle, being 11 and 13. To find our median from here, just add 11 and 13 and then divide by 2. 11 + 13 = 24 and then 24 / 2 = 12. This means that our median is 12.

Next, we'll find the mode. The mode is the number that is seen the most in a set of numbers. In our set, we see that there are three 13s. Since 13 is the most frequently used number in our set, this makes it the mode.

Finally, we'll find the range. The range is just the largest number in the set minus the smallest number in the set. In our set, 16 is our largest number and 1 is our smallest. Just do 16 - 1 = 15 and we'll see that 15 is the range of the set. Hope this helps!

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A = ???? 4 −2

irinina [24]

Answer:

1. The matrix A isn't the inverse of matrix B.

2. |B|=12, |A|=12

Step-by-step explanation:

1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.

We have:

$A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]$

and

$B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]$

A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.

Then if A is the inverse of B:

$B.A=I$

Where,

$I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

Observation:

If you have two matrices:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]\\\\\\A.B=\left[\begin{array}{cc}(a.e+b.g)&(a.f+b.h)\\(c.e+d.g)&(c.f+d.h)\end{array}\right]$

Now:

$B.A=\left[\begin{array}{cc}3&2\\1&4\end{array}\right].\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}4.3+(-2).1&4.2+(-2).4\\(-1).3+3.1&(-1).2+3.4\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}12-2&8-8\\-3+3&-2+12\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]$

$B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]\neq \left[\begin{array}{cc}1&0\\0&1\end{array}\right]=I\\\\\\B.A\neq I$

Then, the matrix A isn't the inverse of matrix B.

2. If you have a matrix A:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

The determinant of the matrix is:

$|A|=ad-bc$

Then the determinant of B is:

$B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]$

$a=3, b=2, c=1, d=4$

$|B|=3.4-2.1\\|B|=12-2=10$

The determinant of A is:

$A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]$

$a=4, b=-2, c=-1, d=3$

$|A|=4.3-(-2).(-1)\\|B|=12-2=10$

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