Answer:
6 socks
Step-by-step explanation:
What we must do is calculate the probability of this happening, that he takes out two black socks in the first two taken out.
There are 12 black socks and in total they are 24, therefore the probability of drawing 1 is:
12/24
and now the probability of getting another one is 11 (there is one less outside) and in total they are 23:
11/23
the final probability is the multiplication of these events:
(12/24) * (11/23)
P = 0.24
Now, to know how many you should get, we multiply the probability by the total number of socks, that is:
0.24 * 24 = 5.76
So you must take out at least 6 socks for the above to happen.
We want to find the values of a, b, c, and d such that the given matrix product is equal to a 2x2 identity matrix. We will solve a system of equations to find:
<h3>
Presenting the equation:</h3>
Basically, we want to solve:
![\left[\begin{array}{cc}-1&2\\a&1\end{array}\right]*\left[\begin{array}{cc}b&c\\1&d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5Ca%261%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db%26c%5C%5C1%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix product will be:
![\left[\begin{array}{cc}-b + 2&-c + 2d\\a*b + 1&a*c + d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-b%20%2B%202%26-c%20%2B%202d%5C%5Ca%2Ab%20%2B%201%26a%2Ac%20%2B%20d%5Cend%7Barray%7D%5Cright%5D)
Then we must have:
-b + 2 = 1
This means that:
b = 2 - 1 = 1
We also need to have:
a*b + 1 = 0
we know the value of b, so we just have:
a*1 + b = 0
Now the two remaining equations are:
-c + 2d = 0
a*c + d = 1
Replacing the value of a we get:
-c + 2d = 0
-c + d = 1
Isolating c in the first equation we get:
c = 2d
Replacing that in the other equation we get:
-(2d) + d = 1
-d = 1
Then:
c = 2d = 2*(-1) = -2
So the values are:
If you want to learn more about systems of equations, you can read:
brainly.com/question/13729904
1.20 - .90 = .30
.30 / 5 = .06 (Same as 30 / 5)
The price of a pound of oranges went up by 6 cents per year.
Answer:
7z^3+6z^2-27z+22
Step-by-step explanation:
The given question is of subtraction:
So,
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
=7z^3+42z^2-15z+1-36z^2-12z+21
Combining alike terms to simplify
=7z^3+42z^2-36z^2-15z-12z+1+21
=7z^3+6z^2-27z+22
So the answer in simplified form is:
7z^3+6z^2-27z+22 ..
Answer:
$14.75 per person
Step-by-step explanation:
because there are 4 people in total including Mrs Cats you would add up 33 + 17 + 3 + 6 to get 59 then you would divide that by the amount of people there are in this case 4 to get 14.75.
