Kaya can ride her bike 3mi/h faster than Josh can ride his bike. If Kaya and Josh ride their bikes at the same time, Kaya will travel 60 miles and Josh will travel 12 miles less. How fast can Josh and Kaya ride their bikes?

The pizza is 6.5 feet tall in height

From the question, we have the following parameters that can be used in our computation:

Volume = 195 cubic feet

Length = 6 feet

Width = 5 feet

The height of the pizza can be calculate using

Height = Volume/(Length * Width)

Substitute the known values in the above equation, so, we have the following representation

Height = 195/(6 * 5)

Evaluate

Height = 6.5

Hence, the height is 6.5 feet

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Answer: The solution of this system of equations is the point of cut of these line.

Point of cut is when x is close to -1, and y is close to 0; therefore the best estimate of the solution would be:

A) (-1,0)

We can check it out our answer solving the system of equations:

-3x+y=2

-4x+7y=1

We solve this system by substitution method.

-3x+y=2   ⇒  y=2+3x

-4x+7(2+3x)=1

-4x+14+21x=1

-4x+21x=1-14

17x=-13

x=-13/17=-0.764....≈-1

y=2+3x

y=2+3(-0.764)

y=2-2.292

y=-0.292≈0

The approximate solution will be (-1,0)

The term used to denote the process that builds a regression equation by testing one variable at a time, starting with the one which is significantly corelated and keeping only the other significant coefficients is known as stepwise regression.

Iteratively building a regression model step by step, stepwise regression entails choosing independent variables to be included in the final model. It entails successively introducing or eliminating putative explanatory factors and assessing statistical significance after each iteration.

Stepwise regression can be accomplished in one of two ways: either by including all potential independent variables in the model and removing those that are not statistically significant, or by attempting each independent variable one at a time and including it in the regression model if it is statistically significant.

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discount= 27.5

S.P= 522.5

Step-by-step explanation:

Marked price of dress(m.p)= 550

Discount % = 5%

Discount amount = 5% of MP

=5÷100×550

=27.5

S.P of the dress = ?

we know,

S.P = MP- discount

= 550-27.5

=522.5

On factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3.

What is factorization by splitting middle term?

The method of Splitting the Middle Term by factorization is where you divide the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers.

Rule to factorize trinomial expression where coefficients are real numbers, is to split b (the coefficient of x) into two real numbers such that the algebraic sum of these two numbers is b and their product is c, then factorize by grouping method.

According to the given question:

Factorizing 2v² + 4v = 6 by Splitting the Middle Term method

2v² + 4v = 6

2v² + 4v - 6 = 0

2v² + 6v - 2v - 6 = 0

2v(v+3) - 2(v+3) = 0

(2v-2)(v+3) = 0

Therefore the solutions are

2v - 2 = 0                                      v +3 = 0

v = 1                                                   v = -3

Hence on factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3

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The value of the equation after the evaluation is 35

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

The distributive property is straightforward to recall. Numerous mathematical features allow us to make algebraic expressions as well as arithmetic calculations simpler.

Using the distributive property we can rewrite this expression as:

[tex]15(2\frac{1}{3} )= (15*2)+(15*\frac{1}{3} )[/tex]→[tex]30[/tex]→[tex]\frac{15}{3}[/tex]→[tex]30+5[/tex]→[tex]35[/tex]

Evaluating the equation:

[tex]15(2\frac{1}{3} )=15*(\frac{7}{3} )=35[/tex]

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The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Now calculate 30 percentage of a dollar.

1 dollar = 100 cents.

30% of 100 cents = (30/100) × 100 = 30 cents.

2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents

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This statement best describes the coefficient, 3,700 is "the amount of the initial deposit". which is the correct answer would be option (C).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function is given in the question as:

3700(1.05)^4t

This expression is for the amount that will be in the account, in dollars, after t years.

As per the question,

The coefficient, 3,700 represents the amount of the initial deposit in the given exponential function

Thus, the correct answer would be an option (C).

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Prior to performing the clustering analysis, we select the value for k, the statement regarding k-means clustering is accurate and the minimum distance between the clusters should be used.

Data is divided into groups (clusters) using cluster analysis that is relevant, practical, or both. If creating meaningful groups is the goal, the clusters should reflect the data's inherent structure. However, cluster analysis can occasionally merely serve as a valuable starting point for other tasks, including data summarization. In a wide range of disciplines, including biology, statistics, pattern recognition, information retrieval, machine learning, and data mining, cluster analysis has long been crucial, whether for understanding or usefulness. Cluster analysis has been used to solve numerous practical issues.

Hartigan (1975, pp 90-91) provides the following general guideline when determining the number of clusters. When (sum(k$withinss)/sum(kplus1$withinss)-1)*(nrow(x)-k-1) is more than 10, it is justified to add the extra group if k is the result of k-means with k groups and kplus1 is the result with k+1 groups.

As a result, choice B is the appropriate response.

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Therefore the value of the z score comes out to be Z = 1.1261

Simply expressed, a z-score (sometimes called a standard score) gives you a sense of how distant from the mean a data point is. Technically, however, it's a calculation of how far a raw score deviates from or exceeds the population mean.

The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviation. The mean and population standard deviation must be known in order to use a z-score.

Here,

In a World Atlas study, 10% of people have blue eye color. Lane decided to observe 44 people and she concluded 7 people had blue eyes. Calculating the z-score

Given that :

Sample size (n) = 44

Number of people with blue eyes (x) = 7

Proportion (p) = 10% = 0.1

Using the relation :

Z = (p" - p) / [tex]\sqrt{\frac{pq}{n} }[/tex]

Since : q = 1 - p = 1 - 0.1 = 0.9

p" = x / n = 7/ 44

p"= 0.15909

pq = 0.1 * 0.9 = 0.09

Hence,

Z = (0.15909- 0.1) / [tex]\sqrt{\frac{0.09}{44} }[/tex]

Z = 0.0509 / 0.0452

Z = 1.1261

Therefore the value of the z score comes out to be

Z = 1.1261

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Answer:

6

Step-by-step explanation:

all are divisible by 6 or can be added by six to get the next number

The required value of the contant of proportionality is given as 1/4.

Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.

Here,

Let G be the number of games and T be the number of tickets,

G ∝ T

So,

G = kT

From the table,

4 = 16k

k = 4/16

k = 1/4

Thus, the required value of the contant of proportionality is given as 1/4.

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Therefore, the slope of the line of best fit is 1.4.

Average By adding a collection of numbers and then dividing by their count, the arithmetic mean—also known as the median—is determined. For instance, 30 divided by 6 equals 5, which is the https://brainly.com/question/24057012of 2, 3, 4, 5, 7, and 10.

To find the slope of the line of best fit, you will need to use the formula:

slope = (mean(x) * mean(y) - mean(x*y)) / (mean(x)^2 - mean(x^2))

where x represents the average daily temperature and y represents the total ice cream sales.

First, you will need to calculate the mean of x, the mean of y, the mean of x*y, and the mean of x^2.

The mean of x is (56.1 + 60.3 + 64.2 + 66.4 + 71.3 + 73.9 + 74.2 + 75.2 + 80.1 + 84.8) / 10 = 71.54

The mean of y is (107 + 116 + 120 + 122 + 125 + 130 + 132 + 135 + 141 + 152) / 10 = 128.6

The mean of xy is (56.1107 + 60.3116 + 64.2120 + 66.4122 + 71.3125 + 73.9130 + 74.2132 + 75.2135 + 80.1141 + 84.8*152) / 10 = 8707.7

The mean of x^2 is (56.1^2 + 60.3^2 + 64.2^2 + 66.4^2 + 71.3^2 + 73.9^2 + 74.2^2 + 75.2^2 + 80.1^2 + 84.8^2) / 10 = 6043.17

Plugging these values into the formula for the slope, we get:

slope = (71.54 * 128.6 - 8707.7) / (71.54^2 - 6043.17) = 1.4

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Answer:

Look below

Step-by-step explanation:

There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:

Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.

Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.

Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.

Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.

Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.

To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.

To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).

The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:

(f(x + h) - f(x))/h

where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.

The number of pieces of blue chalk is 6.

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

Let x be the number of blue chalk and y be the number of yellow chalk.

Given that, the ratio of yellow chalk and blue chalk is 1:2.

And there are 18 pieces of chalk.

That means the expression x + y = 18

And according to condition,

x/y = 1/2
Using cross multiplication,

2x = y

And we have the expression ,

x + y = 18

substituting 2x = y,

x + 2x = 18

3x = 18

x = 6

Therefore the number of pieces of blue chalk is 6.

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The percentage of respondents who said the magazine is useful is referred to as the population parameter of interest.

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x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.

What is perpendicular in triangle?

The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.

The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.

A(0, 0), B(0, 8), C(6, 0)

Circumcenter , P(x,y)

AP = BP = CP

AP² = BP²

(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²

x² + y² + 64 - 16y = x² + y²

 64 - 16y = 0

 16y = 64

     y = 4

BP = CP

BP² = CP²

(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²

x² + y² = x² 36 - 12x + y²

       36 - 12x = 0

         12x = 36

           x = 3

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To write its equation in the form y is a(xh)2+k and then determine the value of the coefficient a.

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The boat's distance and bearing from the port regions are as follows;

The boat is located around 157.15 kilometers from the harbor on a bearing of 150°.

In mathematics, a bearing is an angle measured clockwise from the north or y-axis direction.

The Coast Guard cutter travels at a speed of 30 kno

Angelica, a Coast Guard cutter, has a bearing of 95 degrees.

The coast guard goes for 2 hours in the first direction.

The shift in direction of the Coast Guard cutter = 185°

Travel time in the new direction = 2 hours

30 knots equals 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr = 111.12 km in 2 hours

Distance traveled in the other direction = 55.56 km/hr 2 hours = 111.12 km

According to the accompanying graphic, the figure produced by the Coast Guard cutter's course is an isosceles triangle.

The Pythagorean theorem gives the distance from the port to the position of the boat as l = √(111.122^2 + 111.122^2) ≈ 157.15.

The boat is roughly 157.15 kilometers away from the port.

An isosceles right triangle has 45° base angles.

As a result, the bearing is 95° + 45° = 150°.

The angle between the port and the boat is 150°.

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On solving the provided question, we got to know that - carpenter should make the diagonals 37 ft

A diagonal is a line connecting two vertices of a solid or polygon whose vertices do not share an edge in mathematics. The vertices of a shape are connected by oblique or sloping lines, which are known as diagonals. A horizontal shape with sides/edges, corners, and is called a diagonal.

We can answer this problem using Pythagoras' Theorem since the diagonal would turn the angle into a right angle.

[tex]12^2+35^2= d^2[/tex]

[tex]d^2 = 144 + 1225\\d^2 = 1369\\d = 37\\[/tex]

So, carpenter should make the diagonals 37 ft

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Answer:

Step-by-step explanation:

Hello...

y=x-8

2x+y=-5 -> y=-2x-5

subsitution

-2x-5=x-8

3x=3

x=1

y=x-8

y=1-8

y=-7

(1,-7)

The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .

What are arithmetic calculations?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,

Addition : (+)

The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.

Subtraction : (-)

Subtraction is the process in which we remove objects from the original group.

Multiplication : (×)

Multiplication is adding the same number to itself a certain number of times.

Division : (÷)

The division is breaking a large object or group into smaller parts or groups.

Here ,

given equation: ax + b = 37

To calculate value of x :

ax  = 37 - b

As, it is given that a is non-zero constant then,

x = (37 - b)/a

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Answer:

(-41, 30)

Step-by-step explanation:

The midpoint of a segment lies on the segment.

x: (-88 + 6)/2 = -41

y: (61 + (-1)) = 30

Answer: (-41, 30)

If the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue with rational numbers.

In mathematics, a rational number is a number that can be written as the quotient or fraction p/q of two numbers, an integrand p and a non-zero denominator q.

For instance, −3/7 is a rational number, and so is every integer.

So, in that case, any even number would be 12 * 0.5 = 6.

The solution is reasonable because 12 began as rational (6).

Any odd number also is rational:

23 * 0.5 = 11.5

23 and 11.5: Both rational

1.818181818 is reasonable hence when multiplied by 0.5 the result will be rational 3.636363636.

Therefore, if we begin with an irrational number like π:

π*0.5: Not rational

Therefore, if the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue rational.

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Correct question:
Which number produces a rational number when multiplied by 0.5?

From the quadrilateral proof seen below we can prove that;

∠C + ∠D = 2∠AOB

The bisection of an angle simply means to divide an angle into two equal parts.

The sum of the interior angles of a quadrilateral is 360 degrees. Thus;

∠A + ∠B + ∠C + ∠D = 360°     ------(1)

In △AOB,

∠AOB + ∠A/2 + ∠B/2 = 180°

Multiply through by 2 to get;

2∠AOB + ∠A + ∠B = 360°

Thus;

∠A + ∠B = 360° - 2∠AOB

Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;

360° - 2∠AOB + ∠C + ∠D = 360°

This simplifies to;

∠C + ∠D = 2∠AOB

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Complete question is;

Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D

c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time required to finish building the transmission if Jose and Luis works together be = A

Now , the equation will be

The time required by Jose to build a transmission = 10 hours

The time required by Luis to build a transmission = 8 hours

If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker

So ,

If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour

If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour

And ,

Together they build the transmission in

1/A = 1/10 + 1/8

where A is the total time required to finish building the transmission if Jose and Luis works together

So , the equation is

1/A = 1/10 + 1/8

1/A = 18/80

Taking reciprocals on both sides of the equation , we get

A = 80/18

A = 40/9

On simplifying the equation , we get

A = 4.44 hours

Therefore , the value of A is 4.44 hours

Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

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The probability of having two hearts in a randomly drawn hand of 5 cards is 0.2637

Number of cards are drawn from a standard deck = 5

The favorable outcomes = 2 hearts

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Total number of cards = 52

Number of heart cards = 13

Number of remaining cards = 52 - 13

= 39

Then the probability of two hearts in five card hand = (5/2) × (13/52)^2 × (39/52)^3

= (5/2) × 1/16 × 27/64

= 0.2637

Therefore, the probability is 0.2637

I have solved the question in general, as the given question is incomplete

The complete question is:

What is the probability of having two hearts in a randomly drawn hand of 5 cards?

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Answer:

62.625

Step-by-step explanation:

First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35

8.35*7=58.45+(8.35*(1/2))= 62.625

Therefore, your answer is 62.625

I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.

please give brainliest! Thanks! Hope this helped.

Answer:

62.625 lb

Step-by-step explanation:

Define the variable:

Set up a ratio of weight to number of gallons:

[tex]\implies x:7.5=33.4 :4[/tex]

Solve for x:

[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]

Cross multiply:

[tex]\implies 4x=33.4 \cdot 7.5[/tex]

[tex]\implies 4x=250.5[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]

[tex]\implies x=62.625[/tex]

Therefore, the weight of 7.5 gallons of water is 62.625 lb.

The formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]  for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

Let us find the formula for entries of [tex]M^{n}[/tex], where n is a positive integer.

Let M be a 2 x 2 matrix  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]

we get the eigenvalues and their associated eigenvectors as follows-

Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]

Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]

now, we have

[tex]{\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }[/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}[/tex] [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

              = [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

hence, [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

So,

[tex]{\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]

Thus, the formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex] for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

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