Answer:
6 dozens
Step-by-step explanation:
Vanilla, v = x
Chocolate, c = 3x
Strawberry, s = 3 dozens = 36
Total cupcakes = 132
Hence,
x + 3x + 36 = 132
4x = 96
x = 96 / 4
x = 24
Chocolate = 3 * 24 = 72
Dozens of chocolate = 72 /12 = 6 dozens
Answer:
a. or 
Step-by-step explanation:
Slope is equal to y1-y2 over x1-x2.
So the equation would be:

2-(-1)=2+1=3
-3-(-1)=-3+1=-2
So the answer is:

Answer:
$2.25
Step-by-step explanation:
Divide the cost ($18) by the amount of flowers (8.)
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then
.
C) Consider
. This set is orthogonal because
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in
. Then the columns of A form an orthonormal set. We have that
. To see this, note than the component
of the product
is the dot product of the i-th row of
and the jth row of
. But the i-th row of
is equal to the i-th column of
. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set
and suppose that there are coefficients a_i such that
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then
then
.
There are 12 squares in each 4 x 3 grid.
25% of 12 = 3
This means that there should be 3 shaded squares in the grid.
Your answer is B. because it has 3 shaded squares.