Well, the answer will depend on whether the order will count or not (based on Permutations and Combinations). <em>If the order counts</em>, then we would use the formula for Permutations, which is:

Where n is the number of items you have, and r is the number of times you choose from the items.

Which simplifies to

Which simplifies to 15*14*13 (because all the numbers 1-12 in the factorial canceled out), which gets us the answer
2730.
Now, if you wanted to find the number of ways to order the toys without replacement (<em>order doesn't count</em>), you would use the formula:

The variables are still the same, but you are now multiplying by r!.

Simplifies to

Which simplifies to (using the same cancellation method above)

Dividing 2730 by 3! will get us an answer of
455.
Really, it depends on whether they are ordered or not. In this case (since you didn't specify whether the order mattered), the answer would be
455 or
2730.
:)
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
Answer:
I will just choosé the second one
Because it is possible to compare sizes In one triangle rather than comparing with another one which we don't reàlly know of its sizes.
Answer:
360 combinations
Step-by-step explanation:
To calculate the number of different combinations of 2 different flavors, 1 topping, and 1 cone, we are going to use the rule of multiplication as:
<u> 6 </u>* <u> 5 </u> * <u> 4 </u>* <u> 3 </u>= 360
1st flavor 2nd flavor topping cone
Because first, we have 6 possible options for the flavor, then we only have 5 possible options for the 2nd flavor. Then, we have 4 options for the topping and finally, we have 3 options for the cone.
It means that there are 360 different combinations of two different flavors, one topping, and one cone are possible