Answer:
1/12
Step-by-step explanation:
subtract the four soloists who can't be chosen from the total musicians
16-4=12
Itzhak is one person out of 12 who could be chosen to speak
Also the question is annoying because nobody calls an orchestra with 16 people a "16 piece orchestra"
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;
Answer:
3/4 cups of sugar
Step-by-step explanation:
So we know that 1/8 cup of sugar is for 1/3 OF a recipe.
So if we want the full recipe we jsut have to multiply 1/8 by 3 since its only worth 1/3 of the recipe.
You’ll get 3/8 cups of sugar for a whole recipe. The question asks for 2 full recipes and since we already know it takes 3/8 cups for one we can multiply that by 2 to find the amount of sugar needed for 2 full recipes.
You’d get 6/8 cups of sugar.
Simplified: 3/4
Answer:
k=-2
Step-by-step explanation:
11k - 16 - 2k = 17k
11k- 2k -17k=16
-8k=16
k=16/-8
k=-2
hope it helps u