The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?


your answer should be a decimal rounded to the fourth decimal place

The number of boys more than girls altogether in the two programs is 6 boys

The number of boys and girls in the sport-studies program is :

= 30 x 60 %

= 18 girls

Boys in sport-studies program are:

= 30 - 18

= 12 boys

Boys in media tic program :

= 30 x 70 %

= 21 boys

Girls in media tic program:

= 30 - 21

= 9 girls

The difference is :

= ( 12 + 21 ) - ( 18 + 7 )

= 6 boys

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The measure of EFG in the triangle is 58

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

WE have been given that Angles in a triangle add up to equal 180

So, 65 + 57 + ? must equal 180

Solve for the x;

65 + 57 + x = 180

Combine like terms;

122 + x = 180

Subtract 122 from both sides

122 - 122 + x = 180 - 122

x = 58

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Answer:

if 49.4 moles of MnO4- are available, 4300 g (or 4.3 kg) of MnO2 will be produced.

Step-by-step explanation:

16H+ (aq) + 2MnO4- (aq) + 10Br- (aq) → 2MnO2 (s) + 5Br2 (aq) + 8H2O (l)

From the balanced equation, we can see that 2 moles of MnO4- reacts with 2 moles of MnO2. Therefore, the number of moles of MnO2 formed is equal to the number of moles of MnO4- used.

First, let's calculate the number of moles of MnO4- used:

m(H2O) = 445 g

M(H2O) = 18.015 g/mol

n(H2O) = m/M = 445 g / 18.015 g/mol = 24.7 mol

Since 1 mol of H2O reacts with 2 moles of MnO4-, the number of moles of MnO4- required to react with 24.7 mol of H2O is:

n(MnO4-) = 2 × n(H2O) = 49.4 mol

Therefore, if we have 49.4 moles of MnO4- available, all of the MnO4- will be consumed and form the same number of moles of MnO2. The molar mass of MnO2 is 86.94 g/mol. The mass of MnO2 produced can be calculated as:

m(MnO2) = n(MnO2) × M(MnO2) = 49.4 mol × 86.94 g/mol = 4300 g

Therefore, if 49.4 moles of MnO4- are available, 4300 g (or 4.3 kg) of MnO2 will be produced.

The width of the arch at floor level is 10 feet.

In mathematics, a function is a relationship between two sets of objects, where each object in the first set (called the domain) is paired with exactly one object in the second set (called the range). In other words, a function is a rule that assigns a unique output value to each input value.

Functions can be described in several ways, including algebraic expressions, tables of values, graphs, and verbal descriptions. They can be used to model real-world phenomena, solve equations, and make predictions based on data.

The input values of a function are typically denoted by the variable x, while the output values are denoted by the variable y. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input value.

Functions can be classified into different types based on their properties, such as linear, quadratic, exponential, trigonometric, and logarithmic functions. They can also be combined and manipulated using operations such as addition, subtraction, multiplication, division, composition, and inversion.

One of the key concepts in calculus is the derivative, which is the rate at which the output of a function changes with respect to its input. The derivative is used to calculate slopes, rates of change, and optimization problems in a wide range of applications.

Overall, functions are a fundamental concept in mathematics and have many important applications in science, engineering, economics, and other fields.

To find the width of the arch at floor level, we need to find the x-intercepts of the function y = -1/3(x-5)(x+5). At the x-intercepts, y is equal to zero, so we can set the equation equal to zero and solve for x:

0 = -1/3(x-5)(x+5)

There are two solutions to this equation: x = -5 and x = 5. These are the x-coordinates of the points where the arch intersects the x-axis.

The distance between these two points is the width of the arch at floor level. We can calculate this distance by subtracting the smaller x-value from the larger x-value:

Width = 5 - (-5) = 10 feet

Therefore, the width of the arch at floor level is 10 feet.

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Answer:

The least whole number of bags of concrete mix that Roger needs in order to make the sidewalk is G, 44. To calculate this, we must first convert the cubic feet of the sidewalk into cubic inches, which would be 345,600 cubic inches. Then, we need to divide this by the amount of cubic inches in one bag (0.6 cubic feet = 630 cubic inches). This gives us 550 bags of concrete mix, but since Roger will be using a whole number, the closest he can get is 44 bags.

Answer:

Step-by-step explanation:

ITS GOING LEFT AND RIGHT HOPE THIS HELPS IF NOT TEXT ME PLSS .

the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.

How to solve it?

To solve this integral, we can use partial fraction decomposition. We first write:

(2x²2 + x - 1)/(x - 2) = A + B/(x - 2)

Multiplying both sides by (x - 2), we get:

2x²2 + x - 1 = A(x - 2) + B

Substituting x = 2, we get:

7A + B = 7

Substituting x = 1, we get:

-A + B = -2

Solving these equations simultaneously, we get:

A = -3 and B = 10

So we have:

(2x²2 + x - 1)/(x - 2) = -3 + 10/(x - 2)

Now we can integrate this expression:

∫[-3 + 10/(x - 2)] dx from 1 to 2

= [-3x + 10 ln|x - 2|] from 1 to 2

= [-3(2) + 10 ln|2 - 2|] - [-3(1) + 10 ln|1 - 2|]

Since ln|0| is undefined, we know that the natural logarithm term evaluates to zero. Therefore, we get:

= -6 + 3 + 0

= -3

So the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.

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Answer:

Yes, it is possible to determine which man has the different weight by using the seesaw three times. Here is one possible method

Divide the 12 men into three groups of four: A, B, and C.

Weigh group A against group B on the seesaw. (First use)

If the seesaw balances, then the odd man is in group C. Otherwise, he is in the heavier or lighter group (A or B).

Take two men from group C and weigh them against two men from group A or B that were balanced. (Second use)

If the seesaw balances again, then the odd man is one of the remaining two men from group C. Otherwise, he is one of the two men from group C that were weighed.

Weigh one of the suspected men against any other man. (Third use)

If the seesaw balances, then the odd man is the other one. Otherwise, he is the one that was weighed.

This method works because it eliminates half of the possible candidates at each step and identifies whether the odd man is heavier or lighter by comparing him with known balanced men.

Step-by-step explanation:

The cubic root of z = -27 is -3

A real cube and tree roots may be the first images that come to mind when we hear the terms "cube" and "root." Is it not? Well, the concept is the same. Root refers to the main source or starting point. So, all we need to do is consider "which number's cube should be taken to get the given number." The cube root definition in mathematics is expressed as The cube root is the quantity that must be three times multiplied to yield the initial quantity. Let's look at the cube root equation: ∛x = y, where y is the cube root of x. Every number with a little 3 inscribed on it can be represented by the radical sign as the cube root symbol.

In this problem, the cubic root of z = -27 can be calculated as;

z = -∛-27

z = -3

This is because 27 is a perfect cube

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The formula of 15% of 60kg is down below and it equals 9:

Given:

⇒ Formula = 15% of 60kg

⇒ Formula = 15 x 60

⇒ Formula = 100

⇒ Formula = 9

Check:

So, we used 15% of 60kg to find are answer:

We are going to use 100 and divide by 900:

Hence, the formula of 15% of 60kg it equals 9.

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A function f(x) is said to have a jump discontinuity at x = a if:

3. The left and the right limits are not equal.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

Since the lateral limits have to be equal, one of the conditions is that the limit must exist.

A jump discontinuity is when the limits do not exist, that is, if the lateral limits are different.

Hence option 3 is the correct option for this problem.

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Therefore, x³ must be even. Therefore, if -z is irrational, then z must also be irrational.

In mathematics, an integer is a whole number that can be either positive, negative, or zero. It can be written without a fractional or decimal component. Some examples of integers are -3, -2, -1, 0, 1, 2, 3. Integers are used in many different areas of mathematics, including number theory, algebra, and geometry. They are a fundamental concept in mathematics and have many important properties, such as the ability to add, subtract, and multiply them.

Here,

Proof of "x³ is even if and only if x is even":

First, assume that x is even. Then x can be written as x = 2k for some integer k. Substituting this into x³, we get:

x³ = (2k)³ = 8k³ = 2(4k³)

Since 4k³ is an integer, this shows that x³ is even.

Now, assume that x³ is even. This means that x³ is divisible by 2. We can write x³ as x³ = 2m for some integer m. Taking the cube root of both sides, we get:

x = (2m)*(1/3)

If x is an integer, then (2m)*(1/3) must also be an integer. However, the only way for the cube root of an even number to be an integer is if the original number is even. Therefore, x must be even.

Proof of "z is irrational if and only if -z is irrational":

First, assume that z is irrational. By definition, this means that z cannot be expressed as the ratio of two integers. Now suppose that -z is rational. This means that -z can be expressed as the ratio of two integers, say -z = p/q, where p and q are integers and q is not equal to 0. Multiplying both sides of the equation by -1, we get:

z = -p/q

This shows that z can be expressed as the ratio of two integers, which contradicts our assumption that z is irrational. Therefore, if z is irrational, then -z must also be irrational.

Now, assume that -z is irrational. By definition, this means that -z cannot be expressed as the ratio of two integers. We can rewrite this as z = (-1)(-z), which means that z is the product of -1 and a number that is not the ratio of two integers. Multiplying a number by -1 does not change its irrationality, so z must also be irrational. Therefore, if -z is irrational, then z must also be irrational.

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The value of 1+1 is 2.

Addition is a fundamental operation in mathematics that involves combining two or more numbers or quantities to find a total or sum. The process of addition involves adding together individual digits, numbers, or quantities to find their sum or total.

In the simplest form of addition, two numbers are added together to find their sum. For example, 2 + 3 = 5, where 2 and 3 are the addends, and 5 is the sum. The order in which the addends are added does not affect the sum, so 3 + 2 = 5 as well.

Addition can be extended to more than two numbers by adding each pair of numbers in turn. For example, to find the sum of 2, 3, and 4, we can add 2 + 3 first, which equals 5, and then add 5 + 4 to get the final sum of 9.

Addition can be represented visually using symbols such as the plus sign (+) and the equals sign (=). The plus sign is used to indicate that two numbers are being added together, while the equals sign indicates that the sum has been found.

Addition is used in many different applications, from simple arithmetic to complex mathematical models. It is a fundamental skill that is taught early on in mathematics education and is essential for understanding more advanced concepts in algebra, calculus, and other branches of mathematics.

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The solution is, the average cost of nuts is $15.02.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

from the given information we get,

cost of 9 pound b.nuts = $11.99 *9

cost of 13 pound m.nuts = $17.99 *13

cost of 11 pound p.nuts = $13.99 *11

so, total cost = 107.91 + 233.87 + 153.89

                     =495.67

i.e. average cost = 495.67 / 33

                            =15.02

Hence, The solution is, the average cost of nuts is $15.02.

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The term B. One Optimal Solution best describes the system of inequalities 2x + y < 15, 3x + y < 12, f(x, y) = 2x + 2y.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two inequalities 2x + y < 15 and 3x + y < 12.

has one optimal solution as if we subtract these two inequalities, 'y' will get canceled and we can have the value of 'x' from that we can determine 'y' also.

Q. Which term best describes the solution of the situation represented by the system of inequalities? 2x + y < 15, 3x + y < 12, f(x,y) = 2x+2y

A. alternate optimal solutions

B. One Optimal Solution

C. Unbounded

D. Infeasible

The terminal point of p(x,y) on the unit circle is (-2, -1).

The unit circle is a circle with a radius of 1, centered at the origin (0, 0) on a Cartesian coordinate system. It is used to illustrate relationships between angles and their corresponding trigonometric functions. The unit circle is also used to explain concepts in trigonometry such as the sine and cosine functions, the Pythagorean theorem, and the definitions of the six trigonometric functions. It is especially useful in solving problems involving angles, such as finding the values of trigonometric functions given the angle in radians.

Step 1: Find the angle t in its standard form.

t = -4π/3 + 2π = -2π/3

Step 2: Calculate the coordinates using the unit circle formula.

x = cos(-2π/3)

x = -1/2

y = sin(-2π/3)

y = -√3/2

Step 3: The terminal point of p(x,y) on the unit circle is (-2, -1).

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The value of x is given as follows:

The angle measures are given as follows:

First we obtain the value of x, considering that the sum of the measures of the internal angles of a triangle is of 180º, hence:

4x - 16 + 9x - 26 + 2x + 12 = 180

15x = 210

x = 210/15

x = 14.

Hence the angle measures are given as follows:

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Answer:

Point Q

Step-by-step explanation:

Point Q corresponds to Point V, because if you turn the green triangle around, it matches almost exactly the same.

There is no true equation among the given equations.

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Mathematical expressions are constants, numbers, values, or variables written with algebraic operands, including addition, subtraction, division, and multiplication.

A. 34 − 12 = 14.  This equation is not true because (34 - 12 = 22).

B. 916 − 48 = 58. This equation is not true since (916 - 48 = 868).

C. 78 − 34 = 18. This equation is not true since (78 - 34 = 44).

D. 715 − 13 = 615. This equation is not true because (715 - 13 = 702).

E. 12 − 20 = 10. This equation is untrue since (12 - 20 = -8).

Thus, since the solutions to the equations are not the same values given, we can conclude that none of the equations is true.

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A. 34 − 12 = 14

B. 916 − 48 = 58

C. 78 − 34 = 18

D. 715 − 13 = 615

E. 12 − 20 = 10

Answer:

x= −1088

Step-by-step explanation:

Answer:

-1088

Step-by-step explanation:

-17      =    x/64

*64           *64

-1088 = x

a) The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = 0.1406

b) The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

The number of possible answers = 4

Let the probability that the answer is correct P ( C ) = 1/4

Let the probability that the answer is wrong P ( W ) = 3/4

Now , probability that the first two guesses are wrong and the third is correct is P ( WWC ) = P ( W ) x P ( W ) x P ( C )

On simplifying , we get

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 3/4 ) x ( 3/4 ) x ( 1/4 )

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 9/64 ) = 0.1406

And ,

The probability that exactly one correct answer when 3 guesses are made is = P ( WWC ) + P ( WCW ) + P ( CWW )

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 3 x 0.140625

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

Hence , the probabilities are solved

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The height of the triangle is h = 2A/6.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).


To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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The return on total assets (ROTA) can be calculated using the formula:

ROTA = Net Income / Average Total Assets

Using the given information, we have:

ROTA = $386,760 / $5,230,000 = 0.0739 or 7.39%

Therefore, the return on total assets for the company is 7.39%. Note that this answer is rounded to two decimal places.

Answer:

Step-by-step explanation:

Because the interior angle, which cannot be greater than 180, is apparently 184 degrees.

The area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1] is approximately 15.43 square units.

What is integration ?

Integration is a fundamental concept in calculus that involves finding the integral of a function, which is the area under the curve of the function between two given limits. It is the reverse process of differentiation and is used to find the antiderivative of a function. In other words, integration involves finding a function whose derivative is a given function. Integration is a powerful tool that is used in many fields, including physics, engineering, economics, and statistics, to name a few.

Given by the question:

To find the area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1], we can use the formula:

[tex]A =2\pi \int\limits^a_b {y} \, ds[/tex]

where a and b are the limits of integration, ds is the arc length element, and y is the height of the curve at each point.

In this case, we can rewrite the curve as x = y/7 and use the formula for arc length:

[tex]ds = \sqrt[]{(1 + (dx/dy)^2) dy}[/tex]

We have dx/dy = 1/7, so [tex]ds =\sqrt{(1 + (1/49)) dy}[/tex].

Substituting this into the surface area formula, we get:

[tex]A = 2\pi \int\limits^1_0 {y \sqrt{(1 + (1/49)) } } \, dy[/tex]

Integrating, we get:

[tex]A = 2\pi (49/72) [y\sqrt{(1 + (1/49)) } + (1/3) *(1 + (1/98)^{3/2} ][/tex] from 0 to 1

[tex]A = 2\pi (49/72) [(1/7) \sqrt{(50/49)} + (1/3)*(99/98)^{3/2} ][/tex]

[tex]A = 2\pi (49/72) [(5/7)\sqrt{2} + (1/3)* (99/98)^{3/2} ][/tex]

A ≈ 15.43

Therefore, the area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1] is approximately 15.43 square units.

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The transformation from to f(x) = -√(x - 4) involves reflecting the function across the x-axis and shifting it 4 units to the right.

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

f(x) = -√(x - 4)

The parent function is

f(x) = -√x

The transformation is represented as

f'(x) = (x - 4, -y)

This represents a reflection across the x-axis and a translation 4 units right

The transformed function is added as an attachment

From the graph, we have

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The probability that at least one of the students will select a president who did not serve in the military is 1.00.

The probability that a student selects a president who did serve in the military is:

P(selects military president) = 31/43

Therefore, the probability that a student selects a president who did not serve in the military is:

P(selects non-military president) = 1 - 31/43 = 12/43

The probability that none of the 888 students select a non-military president is:

P(none select non-military president) = (31/43)^{888}

Therefore, the probability that at least one of the students will select a president who did not serve in the military is:

P(\text{at least one not in military}) = 1 - P(none select non-military president) = 1 - (31/43)^{888} ≈ 0.9996

Rounded to the nearest hundredth, the probability is 1.00.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a fair coin and it landing on heads is 0.5 or 50%, while the probability of rolling a 7 on a standard six-sided die is 6/36 or 1/6, since there are six ways to roll a 7 out of 36 possible outcomes. Probability theory is used in many fields, including statistics, mathematics, science, finance, and engineering, to model and analyze random events and to make predictions based on data.

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Using Monotone Convergence Theorem,  {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent

To show that the sequence {aₙ} defined by a₁ = 1 and aₙ₊₁ = 3 - (1/aₙ) is increasing, we need to prove that aₙ < aₙ₊₁ for all n.

Let's first prove that aₙ < 3 for all n by induction:

Base case: For n = 1, a₁ = 1 < 3.

Inductive step: Assume aₙ < 3 for some arbitrary n. Then we have:

aₙ₊₁ = 3 - (1/aₙ) < 3 - (1/3) = 8/3

Since aₙ₊₁ is positive (because aₙ < 3), we can also write:

aₙ₊₁ = 3 - (1/aₙ) > 3 - 1 = 2

Therefore, we have:

2 < aₙ < 3 < aₙ₊₁

This shows that {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent by the Monotone Convergence Theorem.

To find the limit of {aₙ}, we can take the limit of both sides of the recursive definition:

limₙ→∞ aₙ₊₁ = limₙ→∞ (3 - (1/aₙ))

Since {aₙ} is convergent, we can replace limₙ→∞ aₙ with a to get:

a = 3 - (1/a)

Multiplying both sides by a, we get:

a² = 3a - 1

This is a quadratic equation that can be solved using the quadratic formula:

a = (3 ± √(3² + 4))/2

a = (3 ± √13)/2

Since aₙ < 3 for all n, we have:

a = (3 - √13)/2

Therefore, the limit of {aₙ} is (3 - √13)/2.

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