You are taking an international trip for summer break and you must not miss your flight. To be on time, you need to make it to the airport within the next 15 minutes. Your driving app has a nifty feature where, rather than simply selecting the shortest route, you can enable it to give you the route that gets you to your destination on time with the highest probability.



Suppose the possible routes are shown above, where you begin at point A and the airport is at
point C. Travel time (in minutes) along each path in the diagram above is given by the following normal
r.v.’s: X1 ∼ N(10,6), X2 ∼ N(2,0.5), and X3 ∼ N(10,1.5). Assume that X1, X2 and X3 are independent
of each other.
1. Which route will the navigation app choose if you enable ‘highest probability of being on time’ mode ?
2. Your best friend is also coming with you. They also start at point A and leave at exactly the same time as
you, but they are driving separately. Assume you take the route the app selected in part 1 and your
friend takes the other route. What is the probability that at least one of you does not make it on time?

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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In an inverse function, the x's can have multiple outputs because the original function might not be one-to-one, meaning that different x-values can result in the same y-value. However, the y's have a single output because an inverse function is defined as swapping the roles of x and y.


1. In a function, each input (x) corresponds to a unique output (y), which is why y's have a single output.
2. However, some functions are not one-to-one, meaning that different x-values can result in the same y-value.
3. In an inverse function, the roles of x and y are swapped, meaning that x's can have multiple outputs if the original function was not one-to-one.

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If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.

Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.

Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.

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Expression A is 4 times as great as expression B.

Sure hope this helps you and pls mark me brainiest

Here books can be arranged in: a) 39,916,800 ways b) 17,280 ways c) 86,400 ways d) 86,400 ways e) 30,240 ways

a) When the books can be arranged in any order, the total number of ways is given by 11!, which is the factorial of the number of books that is 39,916,800 ways. b) We have 2! ways to arrange the group and within the group, the math books can be arranged in 6! ways and the biology books can be arranged in 5! ways which is 17,280 ways.

c) The math books can be arranged in 6! ways, and the remaining books can be arranged in 5! ways that is 86,400 ways. d) If the math and biology books must alternate, we consider them as one group. Within this group, the math and biology books can be arranged in 6! ways that is 86,400 ways.

e) When none of the biology books can be next to each other, we consider the arrangements of the math books and the spaces between them. There are 7 spaces available for the biology books to be placed, and we use the permutation formula 7P5 to calculate the number of arrangements which can be 30,240 ways.

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Step-by-step explanation:

The sum of 2 and 2 can be derived using basic arithmetic operations.

Starting with 2, we can add 1 to get 3:

2 + 1 = 3

Then, we can add another 1 to get 4:

3 + 1 = 4

Therefore, the derivation of 2 + 2 is:

2 + 2 = (2 + 1) + 1 = 3 + 1 = 4

Hence, 2 + 2 is equal to 4.

Answer:

4

Step-by-step explanation:

There is no minimum value for the side length x, and thus it is not possible to determine the dimensions of the most economical shed.

To find the dimensions of the most economical shed, we need to consider the cost of each component (base, roof, and sides) based on the given cost per square foot. Let's denote the side length of the square base as x.

The volume of the shed is given as 729 cubic feet, and since the base is square, the height of the shed is also x.

The cost of the base would be the area of the base (x * x) multiplied by the cost per square foot, which is 5 * x².

The cost of the roof would be the area of the base (x * x) multiplied by the cost per square foot, which is 6 * x².

The cost of the sides would be the sum of the areas of all four sides (2 * x * x) multiplied by the cost per square foot, which is 4 * 5.5 * x².

To find the most economical shed, we need to minimize the total cost, which is the sum of the costs of the base, roof, and sides.

Total Cost = Cost of Base + Cost of Roof + Cost of Sides

= 5 * x² + 6 * x² + 4 * 5.5 * x²

= 11 * x² + 22 * x²

= 33 * x²

To minimize the total cost, we need to minimize x², which means finding the minimum value of x.

Taking the derivative of the total cost function with respect to x and setting it to zero, we can find the critical points:

d(Total Cost)/dx = 66 * x = 0

From this, we can see that x = 0 is not a valid solution. Therefore, we can divide both sides by 66 to find:

x = 0

Since the side length cannot be zero, we can conclude that the minimum value of x is not achievable.

Hence, there is no minimum value for the side length x, and thus we cannot determine the dimensions of the most economical shed based on the given volume and cost information.

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Answer:8%

Step-by-step explanation:Since the cards are put back after each pick, the two picks are independent events.

The probability of picking a 4 on the first pick is 1/5, as there is one card with a value of 4 out of five cards in total.

The probability of picking a number greater than 4 on the second pick is 2/5, as there are two cards with values greater than 4 (5 and 6) out of five cards in total.

The probability of both events occurring (picking a 4 and then a number greater than 4) is the product of the probabilities of each event:

1/5 x 2/5 = 2/25

So the probability of picking a 4 and then picking a number greater than 4 is 2/25.

To express this as a percentage, we can multiply by 100:

2/25 x 100 = 8%

Therefore, the probability of picking a 4 and then picking a number greater than 4 is 8%.

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer: 30

Step-by-step explanation:

Tony should buy the paint from Ready-Steady-Paint because it would be cheaper, costing him £28.05 compared to £30 from Paint-O-mine.

To determine which shop Tony should buy the paint from, let's compare the total cost of 12 tins of paint from both shops.

Paint-O-mine:

The cost of 3 tins of paint from Paint-O-mine is £7.50.

Cost of 1 tin = £7.50 / 3 = £2.50 per tin.

Since Tony needs 12 tins, the total cost from Paint-O-mine would be: £2.50 × 12 = £30.

Ready-Steady-Paint:

The normal price of a box of 4 tins from Ready-Steady-Paint is £11. However, there is a 15% discount on the normal price.

To calculate the discounted price, we multiply the normal price by (100% - 15%):

Discounted price = £11 × (100% - 15%) = £11 × 85% = £9.35.

So, the cost per tin from Ready-Steady-Paint is

= £9.35 ÷ 4

= £2.3375

Since Tony needs 12 tins, the total cost from Ready-Steady-Paint would be: £2.3375 × 12 = £28.05.

Comparing the total costs:

The total cost from Paint-O-mine is £30.

The total cost from Ready-Steady-Paint is £28.05.

Therefore, Tony should buy the paint from Ready-Steady-Paint because it would be cheaper, costing him £28.05 compared to £30 from Paint-O-mine.

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a. False. The statement is incorrect. If Ax = λx for some scalar λ, then x is an eigenvector of A. The equation Ax - λx = 0 is used to determine eigenvectors.

b. True. The statement is correct. If Ax - 2x = 0 for some scalar λ, then x is an eigenvector of A. The only solution to this equation is the trivial solution, which means x must be an eigenvector.

c. False. The statement is incorrect. The condition Ax - x = 0 for some scalar λ is sufficient to determine if x is an eigenvector of A. If this equation holds, x is an eigenvector associated with the eigenvalue λ.

d. True. The statement is correct. The vector x must be nonzero to be considered an eigenvector. An eigenvector is defined as a nonzero vector that satisfies the equation Ax = λx.

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Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{50}{360}\)

   = π × 7.13² × \(\frac{5}{36}\)

    = 50.8369π × \(\frac{5}{36}\)

    ≈ 22.2 ft² ( to the nearest tenth )

Answer:

x^2 - x^3 - 3x^2y - 3xy^2

Step-by-step explanation:

x^3 +y^3 - (x + y)^3​

Expand the expression

x^2 + y^3 - (x^3 + 3x^2y + 3xy^2 +y3)

Remove the parentheses

x^2 +y^3 -x^3 -3x^2y -3xy^2 - y^3

Remove the opposites

Answer:

x^2 - x^3 - 3x^2y - 3xy^2

Hope this Helps!

The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The two rays are called the sides of an angle, and the common endpoint is called the vertex.

The angle that lies in the plane does not have to be in the Euclidean space.

An angle is formed when two non-collinear rays join at a common endpoint.

This endpoint is called the vertex of the angle.

The two rays are referred to as the arms of the angle.

Angles can be classified according to their degree measurement.

An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle

measures between 90 and 180 degrees.

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Answer:

jhj

Step-by-step explanation:

The angle θ between the vectors in radians and in degrees. u=⟨1,1⟩,v=⟨2,−2⟩ (a) radians θ= (b) degrees θ= This implies that the angle θ is 90 degrees or π/2 radians.

To find the angle θ between two vectors u and v, we can use the dot product formula:

u · v = |u| |v| cos(θ),

where u · v is the dot product of u and v, |u| and |v| are the magnitudes of u and v respectively, and θ is the angle between the two vectors.

Given vectors u = ⟨1, 1⟩ and v = ⟨2, -2⟩, we can calculate the dot product:

u · v = (1)(2) + (1)(-2) = 2 - 2 = 0.

The magnitudes of u and v can be calculated as follows:

|u| = √(1^2 + 1^2) = √2,

|v| = √(2^2 + (-2)^2) = √8 = 2√2.

Substituting these values into the dot product formula, we have:

0 = (√2)(2√2) cos(θ).

Simplifying, we get:

0 = 4 cos(θ).

To find θ, we solve for cos(θ):

cos(θ) = 0.

This implies that the angle θ is 90 degrees or π/2 radians.

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The maximum value of f(x, y) subject to the constraint x^2 + y^2 = 2 is -e^(2sqrt(2))/(4sqrt(e^2 - 1)).

We will use the method of Lagrange multipliers to find the maximum value of f(x, y) subject to the constraint x^2 + y^2 = 2.

Let g(x, y) = x^2 + y^2 - 2, then the Lagrangian function is given by:

L(x, y, λ) = xe^y + λ(x^2 + y^2 - 2)

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we get:

∂L/∂x = e^y + 2λx = 0

∂L/∂y = xe^y + 2λy = 0

∂L/∂λ = x^2 + y^2 - 2 = 0

Solving the first two equations for x and y, we get:

x = -e^y/(2λ)

y = -xe^y/(2λ)

Substituting these expressions into the third equation and simplifying, we get:

λ = ±sqrt(e^2 - 1)

We take the positive value of λ since we want to maximize f(x, y). Substituting λ = sqrt(e^2 - 1) into the expressions for x and y, we get:

x = -e^y/(2sqrt(e^2 - 1))

y = -xe^y/(2sqrt(e^2 - 1))

Substituting these expressions for x and y into f(x, y) = xe^y, we get:

f(x, y) = -e^(2y)/(4sqrt(e^2 - 1))

To maximize f(x, y), we need to maximize e^(2y). Since y satisfies the constraint x^2 + y^2 = 2, we have:

y^2 = 2 - x^2 ≤ 2

Therefore, the maximum value of e^(2y) occurs when y = sqrt(2) and is equal to e^(2sqrt(2)).

Substituting this value of y into the expression for f(x, y), we get:

f(x, y) = -e^(2sqrt(2))/(4sqrt(e^2 - 1))

Therefore, the maximum value of f(x, y) subject to the constraint x^2 + y^2 = 2 is -e^(2sqrt(2))/(4sqrt(e^2 - 1)).

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The maximum value of f(x, y) = xe^y subject to the constraint x^2 + y^2 = 2 is e, and it occurs at the point (1, 1).

To find the maximum value of the function f(x, y) = xe^y subject to the constraint x^2 + y^2 = 2, we can use the method of Lagrange multipliers.

First, we define the Lagrangian function L(x, y, λ) as follows:

L(x, y, λ) = xe^y + λ(x^2 + y^2 - 2)

We need to find the critical points of L, which satisfy the following system of equations:

∂L/∂x = e^y + 2λx = 0

∂L/∂y = xe^y + 2λy = 0

∂L/∂λ = x^2 + y^2 - 2 = 0

From the first equation, we have e^y = -2λx. Substituting this into the second equation, we get -2λx^2 + 2λy = 0, which simplifies to y = x^2.

Substituting y = x^2 into the third equation, we have x^2 + x^4 - 2 = 0. Solving this equation, we find that x = ±1.

For x = 1, we have y = 1^2 = 1. For x = -1, we have y = (-1)^2 = 1. So, the critical points are (1, 1) and (-1, 1).

To determine the maximum value of f(x, y), we evaluate f(x, y) at these critical points:

f(1, 1) = 1 * e^1 = e

f(-1, 1) = -1 * e^1 = -e

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The simplified expression using  the commutative property is : \(\frac{6}{3}\) + \(\frac{3}{4}\)

commutative property can be defined as a mathematics attribute that is possessed by a mathematical equation, that enables the objects undergoing addition or multiplication to change position.

In conclusion, The simplified expression using  the commutative property is : \(\frac{6}{3}\) + \(\frac{3}{4}\)

4/3 + 3/4 + 2/3 =  ( \(\frac{4}{3}\) +  \(\frac{2}{3}\) ) +  \(\frac{3}{4}\)  =   \(\frac{6}{3}\) + \(\frac{3}{4}\)

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Answer:

y = 4x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = E(4, 4) and (x₂, y₂ ) = F(2, - 4)

m = \(\frac{-4-4}{2-4}\) = \(\frac{-8}{-2}\) = 4 , then

y = 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 4), then

4 = 16 + c ⇒ c = 4 - 16 = - 12

y = 4x - 12 ← equation of line

Answer:

y = -4x + 17

Step-by-step explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Answer:

∠BCE is 115°

Step-by-step explanation:

The given parameters are;

The shape Tanya cut from the striped piece = Isosceles triangles

The measure of the vertex angle of the isosceles triangle = 50°

The segment \(\overline {BC}\) is parallel to the base \(\overline {FG}\)

Therefore, we have;

∠GAF + ∠AGF + ∠AFG = 180°; Sum of the interior angles of a triangle

∴ ∠AGF + ∠AFG =  180° - ∠GAF =  180° - 50° = 130°

∠AGF = ∠AFG;  Base angles of an isosceles triangle

∴ ∠AGF + ∠AFG = ∠AGF + ∠AGF = 2 × ∠AGF = 130°

∠AGF = 130°/2 = 65°

∠AGF = 65°

∠AGF ≅ ∠ACB, corresponding angles of two parallel lines, \(\overline {BC}\) and \(\overline {FG}\) cut by a transversal \(\overline {AG}\)

∠AGF = ∠ACB = 65°, definition of congruency

∠ACB + ∠BCE = 180° Sum of angles on a (straight) line

∠BCE = 180° - ∠ACB =  180° - 65° = 115°

∠BCE = 115°

The proof to show that △STU≅△QUT.

Congruency is a property which implies that two given shapes are equal in respect of their length of corresponding sides, and measure of their corresponding internal angles.

Thus, the proof to show that △STU≅△QUT are explained below;

<QRU ≅ <SRT                           (vertically opposite angle property)

QT = QR + RT          

SU = SR + RU

So that;

QT ≅ SU                                   (Reflexive property of congruent triangles)

TU ≅ UT                                   (common side of congruent triangles)

QU ≅ ST                                    

<SUT ≅ <QTU                         (Reflexive property of congruent triangles)

Therefore, it can be concluded that;

△STU≅△QUT

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The average rate of change of an exponential function can be calculated by finding the difference in function values at the endpoints of the given interval and dividing it by the difference in the corresponding x-values.

In this case, since the table represents values of an exponential function, we'll use the formula for average rate of change to determine the value. Let's assume the table contains the following values: |  x  |  y  |
| --- | --- |
|  2  |  8  |
|  4  |  32 |

To calculate the average rate of change for the interval from x=2 to x=4, we first find the difference in y-values: 32 - 8 = 24. Next, we calculate the difference in x-values: 4 - 2 = 2. Finally, we divide the difference in y-values by the difference in x-values: 24 / 2 = 12. Therefore, the average rate of change for the given exponential function over the interval from x=2 to x=4 is 12. This means that, on average, the function is increasing by 12 units for every unit increase in x within the specified interval.

The average rate of change is a measure of how the output of a function changes on average over a given interval. For an exponential function, it can be determined by calculating the difference in function values at the endpoints of the interval and dividing it by the difference in the corresponding x-values . In this case, the average rate of change for the function represented by the given table is found to be 12, indicating an average increase of 12 units in the function's output for every unit increase in the input from x=2 to x=4.

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this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

One possible example is:

A = [[1, 2], [2, 4]]

b = [3, 6]

The solution set of Ax = b is the set of all vectors of the form x = [x1, x2] such that:

x1 + 2x2 = 3

2x1 + 4x2 = 6

Solving this system of equations, we get:

x1 = 3 - 2x2

x2 = x2

So the solution set is the set of all vectors of the form x = [3 - 2x2, x2]. This is a line in R² with slope -2 and y-intercept (3, 0)

Note that this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

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Answer:

kinda sus =456ijdhdiieoq

Answer:

D (12)

Step-by-step explanation:

10%= 6 tickets

Therefore 20%= 12 tickets

Your welcome :)

Answer:

2100 - 987 = 1113

1113/2100= 0.53

0.53 X 100 = 53%

Answer:

It will be D. 9/10

Step-by-step explanation:

Sorry if i get it wrong

Answer: A which is 6/7

Step-by-step explanation:

The answer is A, 6/7 is cuz I got it right on my test anddd It was a wild guess some how I got it right!! A is the right answer

Answer:

21

Step-by-step explanation:

\(\left[\begin{array}{cc}5&9\\-6&9\end{array}\right] +6\left[\begin{array}{cc}-5&2\\7&8\end{array}\right]\)

Multiply the second matrix by 6.

\(\left[\begin{array}{cc}5&9\\-6&9\end{array}\right] +\left[\begin{array}{cc}-30&12\\42&48\end{array}\right]\)

Add the corresponding cells in each matrix.

\(\left[\begin{array}{cc}5-30&9+12\\-6+42&9+48\end{array}\right]\)

\(\left[\begin{array}{cc}-25&21\\36&57\end{array}\right]\)