To answer this question we need to solve both equations simultaneously. So, multiply the first equation with -2 and add the two equations together:

Now, substitute this value of x into any one of the equations to obtain the value y=-53/30. Hence the correct answer is B.

When we calculate the values we obtain:

Thus, the maximum value is 82

We multiply first equation by 2 obtain the cofficient of the

to have different signs. Hence the linear equations become

Now we add the equations to eliminate the term

 then one has 

into the equation

we obtain 

The solution is the ordered pair

Correct answer is C.

As we can see below, the brown circles are the vertices that has degree three, which gives the answer as 4.

The correct answer is E.

Consider the pair (4,6). The first component 4 is the greatest among the first components in the 2nd column. The second component 6 is also the greatest among the second components in the 3rd row. Therefore (3rd row, 2nd column)is an equilibrium pair.

When we evaluate the values of given corner points under the goal function f:

Hence the minimum value of given constraint set is -15

The Gini index is calculated using the formula

where L(x) is the Lorenz curve. Inserting L(x) given in the question we find;

Therefore the correct answer is the C option.

The coefficient matrix of the given system of linear equations is

We find the determinant of the coefficient matrix using Sarrus’ rule:

and we find  

Minimum

Minimum

Minimum

Minimum

The   maximum of the numbers -5,6,-1,1  is 6 .The corresponding row is the 2 nd row.

Correct answer is D

Let G be a connected planar graph with n vertices and m edges, and let f be the number of regions in any plane diagram of G. Then f + n = m + 2 holds. This is called Euler’s theorem on planar graphs. Now for n=3 and m=6 we have f=6-3+2=5, which is the number of regions. Thus the correct answer is C.

The price may be found as S(10) = 2 + 2 = 4. Using the integral formula for the producer surplus, we obtain:

which is the required answer. E is the correct answer.

From the linearity of the integral, we find

Therefore the correct answer is the E option.

Since

we obtain

Hence

x - 2y = 8          -2x + 4y = -8

2x - 2y = 10       2x - 2y = 10             

y = 1,   x – 2(1) =8,  x = 10,  (10, 8)

Since

one has

6=k.(-1)-1.8

k= -14

Since the curve intersects the

required area  is evaluated with the definite integral

and the limits of integration are changed from 0 to 4. Therefore, we have

The right answer is E.

We need to solve the equations two at a time. Observe that

For the point (0, 4) if we insert this point into first inequality we see that

is not true. Also for the point (6, 0) if we insert this point into the third inequality we see that

is not true. Therefore the points (0, 4) and (6, 0) do not belong the constraint set. The corner points for the constraint set are (0, 3), (-4, 0), (0, 0) and (-2/3, 10/3). Hence the correct answer is B.

Since there are 8 teams in this league, the corresponding graph must have 8 vertices.