What is the median of the set of data? {293, 154, 254, 259, 267, 276, 263, 389, 253, 224, 215} Enter your answer in the box.

The joint probability density function (pdf) of random variables X and Y is given as f(x, y) = 6y for 0 ≤ x ≤ 1/4 and 3/4 ≤ x ≤ 1, and 0 ≤ y ≤ 1. We are asked to find the conditional probability P(X = 3/4 | Y = 1/4).

To find this conditional probability, we first need to find the marginal pdf of X. The marginal pdf of X is obtained by integrating the joint pdf over the range of y.

Integrating the joint pdf f(x, y) = 6y over the range of y from 0 to 1 gives us the marginal pdf of X:

∫(0 to 1) 6y dy = 3.

Next, we can use Bayes' theorem to find the conditional probability. Bayes' theorem states that P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the conditional probability of A given B.

To find P(X = 3/4 | Y = 1/4), we need to calculate the joint probability P(X = 3/4 ∩ Y = 1/4) and the marginal probability P(Y = 1/4).

Integrating the joint pdf f(x, y) = 6y over the range of x from 3/4 to 1/4 gives us the joint probability:

P(X = 3/4 ∩ Y = 1/4) = ∫(3/4 to 1/4) 6y dx = 3/4.

Integrating the joint pdf f(x, y) = 6y over the range of y from 0 to 1 gives us the marginal probability:

P(Y = 1/4) = ∫(0 to 1) 6y dy = 3.

Finally, we can calculate the conditional probability:

P(X = 3/4 | Y = 1/4) = (P(X = 3/4 ∩ Y = 1/4)) / P(Y = 1/4) = (3/4) / 3 = 1/4 ≈ 0.25 (rounded off to the second decimal place).

Therefore, the conditional probability P(X = 3/4 | Y = 1/4) is approximately 0.25.

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The dimensions of the rectangle are 7 cm (width) and 13 cm (length).

Let's assume the width of the rectangle is x cm. According to the given information, the length of the rectangle would be x + 6 cm.

The area of a rectangle is calculated by multiplying its length and width. Therefore, we can set up the following equation:

Area = Length × Width

91 cm² = (x + 6 cm) × x cm

To solve this equation, we can expand it and rearrange it:

91 cm² = x² + 6x cm

Now, let's rearrange it to a quadratic equation form:

x² + 6x - 91 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In the given equation, a = 1, b = 6, and c = -91. Substituting these values into the quadratic formula, we get:

x = (-6 ± √(6² - 4(1)(-91))) / (2(1))

Simplifying further:

x = (-6 ± √(36 + 364)) / 2

x = (-6 ± √400) / 2

x = (-6 ± 20) / 2

Now, we have two possible solutions for x:

x = (-6 + 20) / 2 = 14 / 2 = 7

x = (-6 - 20) / 2 = -26 / 2 = -13

Since a negative value doesn't make sense for the width of a rectangle, we discard the second solution.

Therefore, the width of the rectangle is 7 cm.

Using this information, we can find the length:

Length = Width + 6 = 7 cm + 6 cm = 13 cm

So, the dimensions of the rectangle are 7 cm (width) and 13 cm (length).

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The volume of the solid generated by revolving the region bounded by the graphs of the equations y = x, y = 4, and x = 0 about the line y = 5 is (32π/3) cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by the given equations is a trapezoidal region with vertices (0, 4), (0, 0), (4, 4), and (4, 0). When revolved about the line y = 5, it forms a solid with a cylindrical shape.

The height of each cylindrical shell is given by the difference between the y-coordinate of the line y = 5 and the equation y = x, which is 5 - x. The radius of each cylindrical shell is the distance from the x-axis to the line x = 0, which is simply x.

Integrating the volume of each cylindrical shell from x = 0 to x = 4, and using the formula for the volume of a cylindrical shell, we obtain:

V = ∫[0 to 4] 2πx(5 - x) dx

Evaluating this integral gives V = (32π/3) cubic units.

Therefore, the volume of the solid generated by revolving the given region about the line y = 5 is (32π/3) cubic units.

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The Arrhenius equation is a mathematical formula that describes the temperature dependence of chemical reactions. It states that the rate constant (k) is proportional to the activation energy (Ea), temperature (T), and a constant factor (A) known as the pre-exponential factor or frequency factor. The equation is expressed as k = A * e^(-Ea/RT), where R is the gas constant.

In order to determine the Arrhenius parameters of the reaction, we need to know the activation energy and frequency factor. Unfortunately, we only have the rate constant given in the question, which is 3.80 × 10^-3 mol^-1. Therefore, we cannot directly calculate the Arrhenius parameters.

However, we can make some general observations based on the value of the rate constant. Since the rate constant is relatively low, it suggests that the activation energy is also low. This is because a high activation energy would result in a slower reaction and a lower rate constant. Additionally, we can infer that the frequency factor is relatively high, since a low frequency factor would also result in a slower reaction and a lower rate constant.

Overall, while we cannot calculate the Arrhenius parameters directly, we can use the rate constant to make some educated guesses about the activation energy and frequency factor of the reaction.

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The appropriate null hypothesis (H0) would be that the proportion of students who support sports passes being included in tuition is equal to or less than 50%. The alternative hypothesis (Ha) would be that the proportion is greater than 50%.

In hypothesis testing, the null hypothesis represents the default assumption, while the alternative hypothesis challenges this assumption. In this case, the null hypothesis (H0) would state that the proportion of students supporting sports passes being included in tuition is 50% or less (i.e., not more than half). The alternative hypothesis (Ha) would assert that the proportion is greater than 50%.

To express this formally, we can define the null and alternative hypotheses as follows:

H0: p ≤ 0.5

Ha: p > 0.5

Here, 'p' represents the true population proportion of students who support sports passes being included in tuition. The null hypothesis assumes that 'p' is 0.5 or less, while the alternative hypothesis suggests that 'p' is greater than 0.5.

By conducting hypothesis testing using the collected sample data, we can determine whether there is sufficient evidence to reject the null hypothesis and support the claim that more than half of the students support the inclusion of sports passes in tuition.

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The percentage of data with z-scores lying between -1.2 and 1.2 in the normal distribution N(35, 10) is approximately 68%.

To calculate this percentage, we can use a standard normal distribution table or a statistical software that provides the cumulative distribution function (CDF) for the standard normal distribution. By subtracting the cumulative probability corresponding to -1.2 from the cumulative probability corresponding to 1.2, we can find the proportion of data falling within this range. Multiplying this proportion by 100 gives us the percentage.

The standard normal distribution has a mean of 0 and a standard deviation of 1. By finding the cumulative probabilities associated with the z-scores of -1.2 and 1.2, we can determine the percentage of data within that range.

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The given value, which is the percentage of married 25-year-old women in a specific city, is a sample statistic.

A sample statistic is a numerical value calculated from a sample, which is a subset of a population. In this case, the researcher has determined the percentage of married 25-year-old women in her city, which is based on a specific sample of women within that age group.

On the other hand, a population parameter refers to a numerical value that describes a characteristic of an entire population. It would involve data collected from every individual within the population of interest. In this scenario, if the researcher had information on the percentage of married 25-year-old women in the entire population of women in the city, it would be considered a population parameter.

Since the information provided specifically pertains to a subset of the population (25-year-old women in the city), the value is a sample statistic.

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The standard form equation of a circle with a center at (0, -2) and a point on the circle (3, 5) is (x - 0)² + (y + 2)² = 58.

The standard form equation of a circle with a center at (0, -2) and a point on the circle (3, 5) is (x - h)² + (y - k)² = r², where (h, k) represents the center coordinates and r represents the radius.

Given that the center is at (0, -2), we substitute h = 0 and k = -2 into the equation. Additionally, the distance between the center (0, -2) and the point on the circle (3, 5) represents the radius.

Using the distance formula, we calculate the radius:

r = √[(x2 - x1)² + (y2 - y1)²] = √[(3 - 0)² + (5 - (-2))²] = √(9 + 49) = √58.

Thus, the equation becomes:

(x - 0)² + (y - (-2))² = (√58)²,

x² + (y + 2)² = 58.

Therefore, the correct standard form equation of the circle is x² + (y + 2)² = 58.

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The simplified fraction is 7/24.

7/24 of the people surveyed were born in France.

To find the fraction of people born in France, we need to calculate the ratio of the number of people born in France to the total number of people surveyed.

The total number of people surveyed is the sum of the values in the pie chart: 57 (UK) + 66 (Germany) + 105 (France) + 75 (Ireland) + 57 (Other) = 360.

The number of people born in France is given as 105.

Therefore, the fraction of people born in France is 105/360.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 15:

105/15 = 7/1

360/15 = 24/1

So, the simplified fraction is 7/24.

Therefore, approximately 7/24 of the people surveyed were born in France.

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Answer:

7

Step-by-step explanation:

Because the parts of the circle are congruent, the segments are as well, we can use that to make an equation then solve it like normal

9x-34=4x+1

-1 on both sides

9x-35=4x

-9x on both sides

-35=-5x

x=7

To calculate the overall speedup of a system that spends 55% of its time on I/O with a disk upgrade that provides for 50% greater throughput, we need to determine the impact of the upgrade on the overall system time.

If the system spends 55% of its time on I/O, then the remaining 45% of the time is spent on other tasks. With a disk upgrade that provides for 50% greater throughput, the I/O time can be reduced by 50% of its original value.

To calculate the overall speedup, we need to consider the weighted impact of the improvement. Since the I/O time contributes 55% to the overall system time, the speedup of that portion will have a 55% weight in the overall speedup calculation.

The overall speedup can be calculated as follows:

Overall Speedup = 100% - (55% * 50%) = 100% - 27.5% = 72.5%

Therefore, the overall speedup of the system with the disk upgrade is 72.5, expressed as an integer value without the percentage sign.

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A) The radius of the circle is 4 units. The position at time t = 0 is (x, y) = (0, 4). The motion is counterclockwise. It takes π units of time to complete one revolution around the circle.

B) New parametric equations: x(t) = 8sin(2t), y(t) = 8cos(2t).

C)  Therefore, the rectangular-coordinate equation for the same curve is:[tex](x/4)^2 + (y/4)^2 = 1[/tex]

D)  The Polar equation for the same curve is:r = 4, θ = π/2 - 2t.

(a) In the given parametric equations x = 4sin(2t) and y = 4cos(2t), we can observe that the position of the object in circular motion is defined on a circle.

The radius of the circle is determined by the coefficient of the sine and cosine functions, which is 4 in this case. Therefore, the radius of the circle is 4 units.

At time t = 0, the position of the object can be found by substituting t = 0 into the parametric equations:

x(0) = 4sin(2(0)) = 0

y(0) = 4cos(2(0)) = 4

So, at t = 0, the position of the object is (x, y) = (0, 4).

The orientation of motion can be determined by observing the coefficients inside the sine and cosine functions. Since sin(2t) has a positive coefficient, the motion is counterclockwise. the time it takes to complete one revolution around the circle, we know that one complete revolution corresponds to a full cycle of the sine or cosine function. The period of a sine or cosine function is given by T = 2π/ω, where ω is the coefficient inside the trigonometric function. In this case, ω = 2.

Therefore, the time taken to complete one revolution is T = 2π/2 = π units of time.

- The radius of the circle is 4 units.

- The position at time t = 0 is (x, y) = (0, 4).

- The motion is counterclockwise.

- It takes π units of time to complete one revolution around the circle.

(b) If the speed of the object is doubled, we can modify the parametric equations by multiplying the coefficients inside the sine and cosine functions by 2:

New parametric equations: x(t) = 8sin(2t), y(t) = 8cos(2t).

(c) To eliminate the parameter and express the curve in rectangular coordinates, we can use the trigonometric identity [tex]sin^2(t) + cos^2(t) = 1:[/tex]

Divide both sides of the equation x = 4sin(2t) by 4 and square it:

[tex](x/4)^2 = sin^2(2t)[/tex]

Divide both sides of the equation y = 4cos(2t) by 4 and square it:

[tex](y/4)^2 = cos^2(2t)[/tex]

Adding the two equations together, we get:

[tex](x/4)^2 + (y/4)^2 = sin^2(2t) + cos^2(2t) = 1[/tex]

Therefore, the rectangular-coordinate equation for the same curve is:

[tex](x/4)^2 + (y/4)^2 = 1[/tex]

(d) To find the polar equation, we can use the relationships between polar and rectangular coordinates:

x = rcos(θ), y = rsin(θ)

Substituting these expressions into the given parametric equations:

rcos(θ) = 4sin(2t)

rsin(θ) = 4cos(2t)

Dividing the second equation by the first equation gives us:

tan(θ) = (4cos(2t))/(4sin(2t)) = cot(2t)

Taking the inverse tangent of both sides, we have:

θ = arctan(cot(2t)) = π/2 - 2t

Therefore, the polar equation for the same curve is:

r = 4, θ = π/2 - 2t.

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Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

To set up an integral that represents the length of a curve over the interval 5 ≤ t ≤ 9, we need the parametric equations of the curve.

Let's assume the curve is described by the equations x = f(t) and y = g(t), where f(t) and g(t) represent the x-coordinate and y-coordinate of the curve, respectively.

The length of the curve can be approximated by breaking it into small line segments and summing their lengths. As the line segments become infinitely small, the approximation approaches the exact length of the curve.

The length of a small line segment between two points (x₁, y₁) and (x₂, y₂) can be calculated using the distance formula:

[tex]d = √[(x₂ - x₁)² + (y₂ - y₁)²][/tex]

We can apply this formula to each successive pair of points on the curve to calculate the length of each line segment. The integral that represents the length of the curve is then obtained by summing these lengths over the interval of interest.

Mathematically, the length of the curve over the interval 5 ≤ t ≤ 9 can be represented by the integral:

L = ∫[5 to 9] √[(dx/dt)² + (dy/dt)²] dt

Where dx/dt and dy/dt represent the derivatives of x and y with respect to t, respectively.

It's important to note that the specific form of the parametric equations f(t) and g(t) would be required to evaluate this integral.

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The point which is √2 distance away from the point (-1, 5) is (-1, 5 - √2).

In order to find a point that is √2 away from (-1, 5), we need to find a point that is at a distance of √2 from (-1, 5). Let the point we need to find be (x, y),

Using the distance formula, we can set up the following equation:

√[(x - (-1))² + (y - 5)²] = √2,

Simplifying this equation,

We get,

(x + 1)² + (y - 5)² = 2,

This equation represents a circle with center (-1, 5) and radius √2.

So, one point that satisfies this equation is (-1, 5 - √2), which is √2 away from (-1, 5).

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The linear equation representing the instructor's total pay based on the number of students in the class is y = 100x + 2000.


To express the information in a linear equation, let x represent the number of students in the class, and y represent the instructor's total pay.


1. The per-class fee is $2,000, which is a fixed amount, so it's the constant term.
2. The instructor also gets paid $100 for each student, so the variable term is 100x, where x is the number of students.
3. Combining the constant and variable terms, we get the linear equation:

y = 100x + 2000


The linear equation representing the instructor's total pay based on the number of students in the class is y = 100x + 2000.

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Therefore, the solution to the initial value problem dy/dt = 2ty - 4, y(1) = 3 is: y = ((2/e)e^t + 4)/(2t).

The given equation dy/dt = 2ty - 4 is separable because it can be written as dy/(2ty - 4) = dt.

To solve the initial value problem, we can integrate both sides of the equation:

∫ dy/(2ty - 4) = ∫ dt

Using substitution, let u = 2ty - 4, then du = 2t dt.

The integral becomes:

(1/2) ∫ du/u = ∫ dt

ln|u| = t + C1

Substituting back u = 2ty - 4:

ln|2ty - 4| = t + C1

To solve for y, we can exponentiate both sides:

e^(ln|2ty - 4|) = e^(t + C1)

|2ty - 4| = e^t * e^(C1)

Since e^(C1) is a positive constant, we can rewrite the equation as:

2ty - 4 = Ce^t

Simplifying, we get:

y = (Ce^t + 4)/(2t)

To find the value of the constant C, we use the initial condition y(1) = 3:

3 = (Ce^1 + 4)/(2*1)

3 = (Ce + 4)/2

6 = Ce + 4

Ce = 2

C = 2/e

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The area under the graph of f(x) between x = 0 and x = b is equal to 120. By solving the definite integral, the value of b is approximately equal to 7.746.

To find the value of b, we can use the fundamental theorem of calculus, which states that if F(x) is an antiderivative of a function f(x) on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a). In this case, we have f(x) = x².

We want to find the value of b such that the definite integral of f(x) from 0 to b is equal to 120. Using the fundamental theorem, we can set up the equation:

∫[0, b] x² dx = 120

To solve this equation, we need to find the antiderivative of x². The antiderivative of x²is (1/3)x³. Applying the fundamental theorem, we have:

(1/3)b³ - (1/3)(0)³ = 120

Simplifying the equation, we get:

(1/3)b³ = 120

Multiplying both sides by 3 and taking the cube root, we find:

b³= 360

Taking the cube root of both sides, we get:

b ≈ 7.746 (rounded to three decimal places)

Therefore, the value of b that satisfies the condition is approximately 7.746.

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False. Three hexadecimal digits can represent 12 binary bits.

Hexadecimal is a base-16 numbering system, meaning it uses 16 distinct digits to represent numbers, namely 0-9 and A-F. Each hexadecimal digit corresponds to four binary bits. Since there are 16 possible values for each digit, it takes four bits to represent them. Therefore, three hexadecimal digits would correspond to a total of 12 binary bits (3 digits * 4 bits/digit = 12 bits).

In summary, three hexadecimal digits can be used to represent 12 binary bits, not more or less.

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The area of the shaded region is 22 inches².

Given a parallelogram and whose inside contains a rectangle.

We have to find the area of the shaded region which is inside the parallelogram but outside the rectangle.

Area of the shaded region = Area of parallelogram - Area of rectangle.

Area of parallelogram = Base × height

                                     = 5 × 5

                                     = 25 inches²

Area of rectangle = Length × width

                              = 3 × 1

                              = 3 inches²

Area of shaded region = 25 - 3 = 22 inches²

Hence the area is 22 inches².

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The total cost of renting the electronic skateboard for 94 minutes is $23.53.

We are given that;

Rate for 47 minute= $1.74

Electronic skateboard= 20.05$

Now,

We can write an equation for the rent and the tax as follows:

r = 20.05 + 1.74 * (t / 47)

where r is the total cost of renting the electronic skateboard, t is the time in minutes, and x is the tax.

For example, if Aous wants to rent the electronic skateboard for 94 minutes, we can substitute t = 94 into the equation:

r = 20.05 + 1.74 * (94 / 47) = $23.53

Therefore, by the equation the answer will be $23.53.

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The power series representation for the function f(x) = ln(9 + x²) is:

ln(9 + x²) = ln(9) + (∑ from n=1 to ∞) (-1)ⁿ * (x² - 9)ⁿ / (n * 9ⁿ)

How can we express the function f(x) = ln(9 + x²) as a power series?

To derive the power series representation for the function f(x) = ln(9 + x²), we start with the Taylor series expansion for ln(1 + t), where t = x² - 9:

ln(1 + t) = ∑ from n=1 to ∞ (-1)ⁿ * (tⁿ / n).

We substitute t = x² - 9 into the above equation:

ln(9 + x²) = ∑ from n=1 to ∞ (-1)ⁿ * ((x² - 9)ⁿ / n).

This gives us the power series representation for f(x) = ln(9 + x²). However, it's worth noting that this power series converges only within a certain interval of x values.

The radius of convergence can be determined using techniques such as the ratio test or the interval of convergence of the original function.

Therefore, the answer is ln(9 + x²) = ln(9) + (∑ from n=1 to ∞) (-1)ⁿ * (x² - 9)ⁿ / (n * 9ⁿ), but the convergence of the power series needs to be considered based on the interval of convergence.

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The limit - A. lim 3x = 21, x → 7. The correct choice is A.

The limit of 3x as x approaches 7 can be evaluated by substituting the value 7 into the expression 3x:

lim 3x = 3(7) = 21.

x → 7

Therefore, the correct choice is:

A. lim 3x = 21.

x → 7

To elaborate further, when we evaluate the limit of 3x as x approaches 7, we substitute the value of 7 into the expression 3x. This gives us:

lim (3x) = 3(7) = 21

This means that as x gets arbitrarily close to 7 (but not equal to 7), the value of 3x approaches 21. In other words, as we consider x values approaching 7 from both the left and the right sides, the corresponding values of 3x approach 21.

Therefore, the limit exists and we can determine its value (which is 21), we can conclude that the limit of 3x as x approaches 7 is indeed 21 (Choice A).

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There is not enough information to compare the two probabilities.

To compare P(10th Grade u Type A) with P(10th Grade | Type A), let's break down what each probability represents.

P(10th Grade u Type A) refers to the probability of a student being in the 10th grade and also being Type A.

This probability can be calculated by dividing the number of students who are both in the 10th grade and Type A by the total number of students.

P(10th Grade | Type A) refers to the probability of a student being in the 10th grade given that they are Type A.

This probability can be calculated by dividing the number of Type A students who are in the 10th grade by the total number of Type A students.

Based on the given table, we have the following information:

Type A: 55 students

Type B: 48 students

10th Grade: 75 students

11th Grade: 22 students

To calculate the probabilities, we need additional information about how the Type A and Type B students are distributed across the 10th and 11th grades.

Without this information, we cannot determine the values of P(10th Grade u Type A) or P(10th Grade | Type A).

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To find the indicated partial derivative, we differentiate the function u with respect to the given variable. In this case, we are finding the partial derivative with respect to x, ay, and az.

Let's calculate each of the partial derivatives:

∂u/∂x:

To find ∂u/∂x, we treat all other variables (ay, bz, and c) as constants and differentiate the function u with respect to x. The partial derivative of x^ay * bz * c^a6 with respect to x is simply ay * x^(ay - 1).

∂u/∂x = ay * x^(ay - 1) * bz * c^a6

∂u/∂(ay):

To find ∂u/∂(ay), we treat all other variables (x, bz, and c) as constants and differentiate the function u with respect to ay. The partial derivative of x^ay * bz * c^a6 with respect to ay involves the use of logarithmic differentiation.

Using logarithmic differentiation, we can rewrite x^ay as e^(ay * ln(x)). Then, we differentiate e^(ay * ln(x)) with respect to ay, treating ln(x), bz, and c^a6 as constants. The derivative of e^(ay * ln(x)) with respect to ay is ln(x) * e^(ay * ln(x)).

∂u/∂(ay) = ln(x) * e^(ay * ln(x)) * bz * c^a6

∂u/∂(az):

To find ∂u/∂(az), we treat all other variables (x, ay, and c) as constants and differentiate the function u with respect to az. The partial derivative of x^ay * bz * c^a6 with respect to az is simply a6 * bz * x^ay.

∂u/∂(az) = a6 * bz * x^ay

These are the expressions for the indicated partial derivatives of the given function u.

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The lower limit of the 95% confidence interval for the difference in scores is approximately -1.9.

To calculate the lower limit of the 95% confidence interval, we need to determine the mean difference and the standard error.

The mean difference is calculated by subtracting the before lesson scores from the after lesson scores and finding the average. In this case, the mean difference is (11+3+4+1+7+3+1+2+3+3)/10 = 3.8.

The standard error is calculated by dividing the standard deviation of the differences by the square root of the sample size. In this case, the standard deviation of the differences is approximately 4.14, and the square root of the sample size (10) is approximately 3.16. Therefore, the standard error is 4.14/3.16 = 1.31.

To calculate the lower limit of the 95% confidence interval, we subtract 1.96 times the standard error from the mean difference. In this case, the lower limit is 3.8 - (1.96 × 1.31) = -1.9

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Answer: 5 with 7 on the top corner

Step-by-step explanation: 5 x 5 x 5 x 5 x 5 x 5 x 5 is basically 5 but is repeated 7 times.

(sorry if you can't understand this)

Answer:

[tex]\displaystyle{X = \left[\begin{array}{ccc}1&1\\1&1\end{array}\right] }[/tex]

Step-by-step explanation:

Solve the matrices like normal equation, you can add 2X both sides so we have:

[tex]\displaystyle{\left[\begin{array}{ccc}2&3\\3&2\end{array}\right] = \left[\begin{array}{ccc}0&1\\1&0\end{array}\right] + 2X}[/tex]

Now, subtract the matrices:

[tex]\displaystyle{\left[\begin{array}{ccc}2&3\\3&2\end{array}\right] -\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] = 2X}[/tex]

Follow the matrices subtraction laws:

[tex]\displaystyle{\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] -\left[\begin{array}{ccc}e&f\\g&h\end{array}\right] = \left[\begin{array}{ccc}a-e&b-f\\c-g&d-h\end{array}\right] }[/tex]

Therefore:

[tex]\displaystyle{\left[\begin{array}{ccc}2-0&3-1\\3-1&2-0\end{array}\right] = 2X}\\\\\displaystyle{\left[\begin{array}{ccc}2&2\\2&2\end{array}\right] = 2X}[/tex]

Divide both sides by 2, leaves us with:

[tex]\displaystyle{\dfrac{1}{2}\left[\begin{array}{ccc}2&2\\2&2\end{array}\right] = X}[/tex]

Expand 1/2 inside the matrix, multiplying whole elements. Therefore:

[tex]\displaystyle{\left[\begin{array}{ccc}1&1\\1&1\end{array}\right] = X}[/tex]

Hence,

[tex]\displaystyle{X = \left[\begin{array}{ccc}1&1\\1&1\end{array}\right] }[/tex]

Answer: y=(x-1)(x+3)+6

Step-by-step explanation: you do opposite x-values and then you add the y-intercept.