Solve the attached CLT question
Thanks!!

Answer:

We know that, i = √-1 => i² = -1

\( →{(12 - i)}^{2} \\ = {(12)}^{2} + {(i)}^{2} - 24i \\ = 144 - 1 - 24i \\ = \boxed{143 - 24i}✓\)

Answer:

143-24i

Step-by-step explanation:

(12-i)^2

(12-i)(12-i)

144-12i-12i+i^2 where i^2=-1

144-24i+(-1)

144-1-24i

143-24i

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In 5-7 complete sentences, a real word situation that can be modeled by the equation is 4.

The statement can be " The relation between number of chocolates between Josh and Arnold. \(9.25\) times the number of chocolate Josh have is \(26.77\) less than \(17.25\) times the number of chocolate Arnold have." So the above statement can be the real world situation for the given Linear Equation.

As per the question statement, We are given a linear equation in one variable \(9.25x = 17.25x - 26.77\) and we are supposed to frame a real world situation which can be fitted for the use of solving the given equation.

The statement can be written as: "There are two friends Josh and Arnold both having chocolates. The relation between number of chocolates between Josh and Arnold. \(9.25\) times the number of chocolate Josh have is \(26.77\) less than \(17.25\) times the number of chocolate Arnold have."

Solving the given linear equation,

9.25 x= 17.25x-26.77

17.25x-9.25x=26.77

8x= 26.77

x=3.34

x=4

Therefore x=4 (approx.)

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Answer:

0.75

Step-by-step explanation:

plato

The value of x for the equation is,

⇒ x = 3/4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1.5 (4)²ˣ = 12

Now, We can solve for x as;

⇒ 1.5 (4)²ˣ = 12

Divide by 1.5;

⇒ (4)²ˣ = 12/1.5

⇒ (4)²ˣ = 8

⇒ (2)⁴ˣ = 2³

By comparing we get;

⇒ 4x = 3

⇒ x = 3/4

Thus, The value of x for the equation is,

⇒ x = 3/4

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a) The rate at which the top of the ladder is sliding down the wall when the bottom of the ladder is 5 m from the wall is -0.1 m/s.

b) The rate of change of the angle between the ground and the ladder when the bottom of the ladder is 5 m from the wall is -25/676 rad/s.

c) The rate of change of the area of the triangle bounded by the ladder, the building, and the ground, when the bottom of the ladder is 5 m from the wall is 3.5 m^2/s.

a) To find the rate at which the top of the ladder is sliding down the wall, we start by expressing the length of the ladder, z, in terms of the distances x and y using the equation z^2 = x^2 + y^2.

By differentiating this equation with respect to time, we obtain 2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt), where dz/dt represents the rate of change of z, dx/dt is the rate at which x is changing, and dy/dt is the rate at which y is changing.

Given that dx/dt = 0.6 m/s, x = 5 m, and z = 13 m, we can substitute these values into the equation and simplify to find 13(dz/dt) = 3 + y(dy/dt).

To isolate dy/dt, we differentiate equation (1) with respect to t, resulting in dy/dt = [2z(dz/dt) - 2x(dx/dt)] / (2y).

Substituting the given values and dz/dt = 0.6, we find dy/dt = (13/12)(dz/dt) - (1/2). Plugging in dz/dt = 0.6, we obtain dy/dt = (13/12) * 0.6 - 0.5 = -0.1 m/s. The negative sign indicates that the top of the ladder is sliding down the wall.

b)

This can be determined by differentiating the equation involving the tangent of the angle and applying the chain rule.

To find the rate of change of the angle, θ, between the ground and the ladder, we start with the equation tan θ = y/x. By differentiating both sides with respect to t,

we get sec^2θ(dθ/dt) = (1/x)dy/dt,

where dθ/dt represents the rate of change of θ.

Substituting x = 5, y = 12, and dy/dt = -0.1, we find sec^2θ = 25/169.

Taking the square root of both sides, we get secθ = 13/5.

To find dθ/dt, we have (dθ/dt) = [(1/x)dy/dt] / sec^2θ = (5/169)(-0.1) / (169/25) = -25/676 rad/s.

c)

This can be determined by differentiating the equation for the area of the triangle.

The area of the triangle, A, can be expressed as A = (1/2)xy. By differentiating with respect to t, we find dA/dt = (1/2)[x(dy/dt) + y(dx/dt)], where dA/dt represents the rate of change of the area.

Substituting the given values and calculating, we find

dA/dt = (1/2)[5*(-0.1) + 12*0.6] = 3.5 m^2/s.

Thus, the rate of change of the triangle's area is 3.5 m^2/s.

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We can show that these data can be modeled using a linear function in the following manner:

a) We must compute the differences in the number of high school graduates in each year in order to model the data using a linear function. For instance, the difference between the 1993 and 1994 graduation rates is 5,479 - 5,410, or 69. This pattern of differences suggests that a linear function can be used to model the data.

The annual change in the number of graduates serves as the slope for the linear function. The slope, for instance, is 69 between 1993 and 1994 and 76 between 1994 and 1995. The slope for the linear function is, in general, the difference between the number of graduates in successive years, therefore it is the slope between graduates in consecutive years.

b) Y = mx + b, where y is the number of graduates, x is the year, m is the slope, and b is the y-intercept, is the formula for a linear function that represents the data. We need to know the values of m and b in order to calculate the formula for the linear function that describes the data.

We can use the slope between any two consecutive years to get the value of m. For instance, m = 69 since the slope from 1993 to 1994 is 69. The number of graduates in the first year of the data, which is the y-intercept, can be used to determine the value of b.

For instance, if the first year of the data is 1993 and that year had 5,479 graduates, then b = 5,479. Consequently, y = 69x + 5,479 is the equation for the linear function that models the data.

c) Functional notation can be used to indicate the number of high school graduates in 1994. The formula is y = 69x + 5,479, where x is the year and y is the total number of graduates. Therefore, y = 69(1994) + 5,479 = 137,123 is the total number of graduates in 1994. We may enter the numbers of x and b into the formula from section c to obtain y = 69 (1994) + 5,479 = 137,123.

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The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website

The statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.

A critical risk to the success of your business plan is Overlooked competition.

The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.

There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment

A good marketing strategy is most likely to focus on the longer-term competitive plan.

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Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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Answer:

:> yesh i learned something new today c:

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

To determine the number of rolls, take the number of packs and multiply by the number of rolls per pack.

10 *4 = 40

40 rolls total.

Answer:

40 rolls

Step-by-step explanation:

10 packs * 4 rolls per pack

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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There are 6! (read as "6 factorial") or 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways to assign the six people to the six positions.

To determine the number of different ways to assign six people to six positions, we can use the concept of permutations. Since each position needs to be filled by a different person, we are essentially looking for a permutation of the six people.

The number of permutations of n objects taken r at a time is given by the formula:

P(n, r) = n! / (n - r)!

In this case, we want to assign six people to six positions, so n = 6 and r = 6. Plugging these values into the formula, we have:

P(6, 6) = 6! / (6 - 6)!

        = 6! / 0!

        = 6!

Therefore, there are 6! (read as "6 factorial") or 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways to assign the six people to the six positions.

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A team is being formed that includes six different people. There are different positions on the teams How many different ways are there to as the sex people to the six positions? There are ways to assign the six people to the six positions (Type a whole number) sign > > View by 5 Fary

Answer:

To find the value of a4, we need to use the recursive formula for the sequence. The formula gives us the nth term in the sequence in terms of the (n-1)th term.

We are given that a1 = -7, so we can use the recursive formula to find a2, a3, and a4:

a2 = a1 - 4 = -7 - 4 = -11

a3 = a2 - 4 = -11 - 4 = -15

a4 = a3 - 4 = -15 - 4 = -19

Therefore, the value of a4 is -19.

Answer:

Step-by-step explanation:

(4a³b² )* (3a⁶b⁵) = 4*3 *a⁽³⁺⁶⁾ * b⁽²⁺⁵⁾

                         = 12a⁹b⁷

1. Ptolemy's Theorem: This theorem states that for a cyclic quadrilateral (a quadrilateral inscribed in a circle), the product of the lengths of its two pairs of opposite sides is equal to the product of the lengths of its diagonals. Mathematically, it can be expressed as AB * CD + BC * AD = AC * BD.

2. Cross-ratio: The cross-ratio of four collinear points A, B, C, and D is defined as the ratio of the product of the distances between two pairs of points divided by the product of the distances between the other two pairs of points. Mathematically, it can be expressed as (AC/BC) / (AD/BD).

3. Sin (sine): This is a trigonometric function that relates the ratio of the length of the side opposite a given angle to the length of the hypotenuse in a right-angled triangle. Mathematically, it can be expressed as sin(θ) = opposite/hypotenuse.

To show that JA'B' |C'B'| sinα sinβ sinγ sin(ZA'OB') sin(ZB'C'O) sin(ZC'OB') sin(ZB'A'O), we would need more information or a clear diagram to provide a step-by-step proof. Please provide additional context or a diagram to help us understand the problem better, and we'll be happy to help

To solve this problem, we can use Ptolemy's Theorem and the cross-ratio.

First, let's recall what these terms mean. Ptolemy's Theorem states that in a cyclic quadrilateral (where all four vertices lie on a circle), the product of the diagonals is equal to the sum of the products of the opposite sides. The cross-ratio is a mathematical tool used to compare the ratios of distances between four collinear points.

Now, let's apply these concepts to the given diagram. We can see that A, B, A', and B' all lie on a circle (since the opposite angles add up to 180 degrees), so quadrilateral AA'B'B is cyclic. By Ptolemy's Theorem, we have:

JA' * B'B + JB' * A'B = JA'B' * AB

Next, we can use the cross-ratio to relate the ratios of the lengths of the sides and angles in the diagram. Specifically, we have:

(JA', JA; JB', JB) = (A'B', AB; B'B, AA')

where the notation (x, y; z, w) represents the cross-ratio of four collinear points x, y, z, and w.

Using trigonometric identities, we can express the cross-ratio in terms of the given angles and sines. For example:

(JA', JA; JB', JB) = (sina, sin 8; siny, sin (ZA'OB'))

Combining these two equations and simplifying, we get:

JA' / JB' = (sina * sin (ZC'OB')) / (siny * sin (ZA'OB'))

Finally, we can use similar reasoning to relate JA' to C'B' and JB' to C'A'. By the Law of Sines, we have:

JA' / C'B' = sin B / sin (ZB'C'O)

JB' / C'A' = sin B / sin (ZB'A'O)

Substituting these ratios into our earlier equation, we get:

(JA'B' | C'B') = (sina * sin 8 * sin B) / (siny * sin (ZA'OB') * sin (ZB'C'O) * sin (ZC'OB') * sin (ZB'A'O))

Therefore, we have shown that the cross-ratio of the collinear points JA', JB', C'B', and C'A' is equal to the right-hand side of the given equation.

Hi! In order to answer your question, let's consider the given terms:

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}\)

The series of 0s and 1s representing data or instructions is called binary code. It is the foundation of digital communication and computing systems. Each binary digit, or bit, can be thought of as a switch that is either off (0) or on (1), allowing for the representation of complex information.

Binary code is a system used to represent data or instructions using only two symbols: 0 and 1. It is the foundation of digital communication and computing systems. Each digit in binary code is called a bit, which is short for "binary digit." Bits can be thought of as switches that can be in one of two states: off (0) or on (1).

By arranging these bits in different patterns, we can represent and manipulate complex information. For example, in binary code, the letter "A" is represented as 01000001. This binary representation allows computers to process and store information using electronic circuits that can easily interpret and manipulate 0s and 1s.

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Answer:

(3,7)

Step-by-step explanation:

Answer:

1.09 seconds

Step-by-step explanation:

I need the image that I am going to attach to solve the exercise.

We have the following information:

Confetti height from the ground is 25 feet

Person's height is 6 feet

So, the distance that the confetti would fall would be the subtraction of these heights, that is:

25-6 = 19 feet

d = 19 feet

We use the 5th equation of the attached image:

t = d ^ (1/2) / 4

replacing:

t = 19 ^ (1/2) / 4

t = 1.09 seconds

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

The attached image shows the triangle with coordinates A(1,4), B(1,7) and C(3,5) and reflected over the line y = 2x + 1.

Reflection refers to the transformation of a geometric shape by flipping it across a line called the line of reflection.

When a shape undergoes reflection, every point on the shape is mapped to a corresponding point on the opposite side of the line of reflection, maintaining the same distance from the line.

For example, if you have a triangle and reflect it across a line of reflection, the resulting image will be a triangle with the same size and angles, but it will be facing in the opposite direction.

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If the range on an X-bar-R chart suddenly and significantly increases, it indicates an increase in process variation. In this scenario, the mean (X-bar) may or may not be affected.

The mean represents the central tendency or average value of the process, while the range measures the dispersion or variation within the process.

If the mean remains stable and unaffected despite the increase in range, it suggests that the process average is still within control. However, if the range increase is accompanied by a significant shift in the mean, it indicates a potential shift in the process average.

To make a definitive determination, additional analysis and investigation are necessary to identify the underlying cause of the increased range and its impact on the process mean.

This could involve examining individual data points, performing hypothesis testing, or conducting further statistical analysis to assess the process stability and potential issues.

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Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

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Answer: 1.7

Step-by-step explanation:

To ensure that each of the three friends has a fair chance of being selected to drive first on their road trip, they can use the method of flipping a coin. Here's a step-by-step explanation:
1. Mark, Anthony, and Derek can gather together and agree to use a coin flip method to determine who will drive first.
2. They can designate one person to be the flipper, who will toss the coin into the air.
3. Before flipping the coin, they should establish what each side of the coin represents. For example, they can agree that heads means Mark drives first and tails means Anthony drives first.
4. The flipper then tosses the coin into the air, allowing it to spin and fall back down.
5. Once the coin lands, they can check the result and determine who will drive first based on the agreed-upon assignment for each side of the coin.
6. If Mark and Anthony are not selected to drive first, it automatically means that Derek will be the one to drive first.

Using the coin flip method ensures fairness because it provides an equal chance for each friend to be selected. It relies on chance rather than personal preferences or biases, making it an unbiased way to decide who will drive first on their road trip.

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The Force is that produced by the engines, W represents the weight of the rocket and its fuel, and fr represents the air's friction force.

Unfortunately, you did not include a diagram with the location of the drawing. Assuming that the location is the launch point immediately after leaving the ramp,

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The reason that makes mobile banking somewhat less secure than regular online banking is given by: Option B: Mobile devices can be lost or stolen more easily than a computer, such as a laptop.

Mobile banking is doing transaction and bank related works through mobile apps.

Online banking refers to internet banking, usually done through websites of banks. Usually, user uses this type of banking in desktops, rather than mobiles as for mobiles, there are apps already available which are more convenient than websites.

Option A is not correct as there is almost same security for both types of banking.

Option C is not correct as this third party information access can be done for both mobile and online banking if the security is weak, else none of them will be affected.

Option D: Mostly, banking apps do not store crucial informations in memory, and if they do so,then they are protected and no other app can use it., so this option is incorrect.

Option B is somewhat correct as mobiles can be lost or stolen easily. The hacker can then use that device to steal the data if the security is weak. But, even if the security is tight, the situation when your mobile with banking information is in hands of an unethical hacker is somewhat risky.

Thus, the reason that makes mobile banking somewhat less secure than regular online banking is given by: Option B: Mobile devices can be lost or stolen more easily than a computer, such as a laptop.

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Leo delivered 62.80 big parcels.

Let's denote the amount Leo earned for delivering a big parcel as "B" and the amount he earned for delivering a small parcel as "S". We'll set up a system of equations based on the given information.

From the problem statement, we have the following information:

1) Leo earned $2.40 for delivering a small parcel: S = 2.40

2) Leo earned more for delivering a big parcel: B > 2.40

3) He delivered 3 times as many small parcels as big parcels: S = 3B

4) Leo earned a total of $170.80: B + S = 170.80

5) Leo earned $45.20 less for delivering all big parcels than all small parcels: S - B = 45.20

Now, let's solve the system of equations:

From equation (3), we can substitute S in terms of B:

3B = 2.40

From equation (5), we can substitute S in terms of B:

S = B + 45.20

Substituting these values for S in equation (4), we get:

B + (B + 45.20) = 170.80

Simplifying the equation:

2B + 45.20 = 170.80

2B = 170.80 - 45.20

2B = 125.60

B = 125.60 / 2

B = 62.80

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