Find the center of the ellipse defined by the equation... 100 points

Answer:  [tex]x=200[/tex]

Step-by-step explanation:

    [tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]

[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]

    [tex]\frac{1}{5}x-10=30[/tex]

            [tex]\frac{1}{5}x=40[/tex]

              [tex]x=\frac{40}{\frac{1}{5}}[/tex]

             [tex]x=40*\frac{5}{1}[/tex]

             [tex]x=200[/tex]

Answer:

A''(-1, 1), B''(-4, 2), C''(-2, 4)

Step-by-step explanation:

When rotated 180°, the symbol of the coordinames change

i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4

so the coordinates A(1, -1), B(4, -2), C(2, -4)

change to A''(-1, 1), B''(-4, 2), C''(-2, 4)

We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.

To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.

In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.

Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:

1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.

2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.

3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.

Alternatively:

4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.

5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.

6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.

By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.

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Answer:

PO = 12

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then

the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

OP × OQ = NO²

OP × 27 = 18² = 324 ( divide both sides by 27 )

OP = 12

El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.

En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.

El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.

Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.

La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.

El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.

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The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

To find the equations of the asymptotes of the hyperbola defined by the equation:

[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]

We can rewrite the equation in the standard form by isolating the x and y terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]

Rearranging the terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]

Next, let's complete the square for both the x and y terms:

[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]

Expanding and simplify

[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]

Dividing both sides by -4913:

[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]

Comparing this equation to the standard form of a hyperbola:

[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]

We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).

The equations of the asymptotes can be found using the formula:

y - k = ±(b/a)(x - h)

Substituting the values we found:

y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)

Simplifying:

y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)

y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)

Rationalizing the denominators and simplifying:

y + 7 = ±(5/9) ×(x - 2)

Finally, rearranging the equation to isolate y:

y = ±(5/9)x - 10/9 - 7

Simplifying further:

y = ±(5/9)x - 79/9

In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

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Answer:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Step-by-step explanation:

First, rewrite the given equation in the standard form of a hyperbola by completing the square.

Given equation:

[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]

Factor out the coefficient of the x² term and the coefficient of the y² term:

[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]

Factor the two perfect trinomials on the left side and simplify the right side:

[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]

      [tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]

        [tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]

As the y²-term is positive, the hyperbola is vertical (opening up and down).

The standard equation of a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

Therefore, comparing this with the rewritten equation:

The formula for the equations of the asymptotes of a vertical hyperbola is:

[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]

Substitute the values of h, k, a and b into the formula:

[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]

Therefore, the equations for the asymptotes are:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Based on the quadratic function, an 18 year old would spend 3 hours watching television.

Using the quadratic function given :

The age is represented as the variable , 'z'

substitute z = 18 into the equation

y = (0.004*18²) - 0.314(18) + 7.5

y = 3.144

y = 3 hours approximately

Hence, an 18 year old spend approximately 18 hours watching television.

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Answer:

102

Step-by-step explanation:

we substitute x by 7

7^2+9(7)-10

49+63-10

=102

Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

Answer:

arc VL = 91°

Step-by-step explanation:

the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is

[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF

[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction

143° + VL = 234° ( subtract 143° from both sides )

VL = 91°

Answer:

m

Step-by-step explanation:

The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.

Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.

Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)

Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.

When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.

According to the given formula,

H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.

As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.

Therefore, the angular frequency,b = 2π/2= π

Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Answer: H(t) = 7.5.cos(π.t) + 22.5.

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Answer:

x=4 explanation: I got it right

After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 3ft per year, where t is time in years. So, the tree will grow 5 feet in the first year.

We have to find the number of feet the tree will grow in the first year, given that 5(t + 1)³. The rate of growth of a tree is given as 3ft/year. Therefore, in the first year, the tree will grow 3 feet.

To find the number of feet the tree will grow in the first year, we substitute t = 0 in the given expression.

5(t + 1)³ = 5(0 + 1)³= 5(1)³= 5(1)= 5. Therefore, the tree will grow 5 feet in the first year.

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Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

Answer:

That Platonic solid is a dodecahedron.

B is the correct answer.

The probability of Lashonda winning a prize is 9/11.

To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.

Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.

In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.

The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.

To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.

In this case, the total number of outcomes is 9 + 2 = 11.

The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:

Probability = Favorable outcomes / Total outcomes

Probability = 9 / 11.

Therefore, the probability of Lashonda winning a prize is 9/11.

In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.

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Answer:The present worth of the project for Bronson Building Inc is $6,389,137.

In order to calculate the present worth, follow these steps:

1. The given information is:

Initial cost (first cost) = $18,000,000

Annual revenue = $5,000,000

Annual expenses = $2,000,000

Net annual cash flow = Annual revenue - Annual expenses = $5,000,000 - $2,000,000 = $3,000,000

MARR = 11%

Project duration = 18 years

Sale price at the end of the project = $8,000,000

2. To calculate the present worth, we first need to find the present value of the net annual cash flows using the MARR as the discount rate. Then, we will add the present value of the sale price and subtract the initial cost.

Present value of net annual cash flows (PV_ACF) = Net annual cash flow * [(1 - (1 + MARR)^(-duration)) / MARR]

PV_ACF = $3,000,000 * [(1 - (1 + 0.11)^(-18)) / 0.11] = $3,000,000 * 7.696 = $23,088,000

3. Find the present value of the sale price at the end of the project.

Present value of sale price (PV_SP) = Sale price / (1 + MARR)^duration

PV_SP = $8,000,000 / (1 + 0.11)^18 = $8,000,000 / 6.146 = $1,301,137

4. Calculate the present worth of the project.

Present worth = PV_ACF + PV_SP - Initial cost

Present worth = $23,088,000 + $1,301,137 - $18,000,000 = $6,389,137

Step-by-step explanation:

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

a + c= 131

9.60a + 5.20c= 1020

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable c from the first equation:

c= 131 -a

Substituting the expression in the second equation:

9.60a + 5.20×(131 -a)= 1020

Solving:

9.60a + 5.20×131 -5.20a= 1020

9.60a + 681.2 -5.20a= 1020

9.60a -5.20a= 1020 - 681.2

4.4a= 338.8

a= 338.8÷ 4.4

a= 77

In summary, 77 adult tickets were sold that day.

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Answer:

37.98

Step-by-step explanation:

Answer:

Reflection Property.

All-zero Property.

Proportionality.

Switching property.

Factor property.

Scalar multiple properties.

Sum property.

Triangle property.

1a. Compute NPV by calculating the present value of net cash flows and subtracting the investment amount.

1b. Compute PVI by dividing NPV by the investment amount.

2. Determine IRR by finding the discount rate corresponding to an NPV of zero.

3. Compare NPV, PVI, and IRR to identify the better financial opportunity.

1a. To compute the net present value (NPV) for each project, we need to calculate the present value of the annual net cash flows and subtract the amount to be invested. Using the present value of an annuity of $1 from the table, we can fill in the following values:

Wind Turbines:

Present value of annual net cash flows: $420,000 * 1.736 + $420,000 * 2.487 + $420,000 * 3.170 + $420,000 * 3.791

Less amount to be invested: $1,199,100

Net present value: NPV_Wind_Turbines = Present value of annual net cash flows - Amount to be invested

Biofuel Equipment:

Present value of annual net cash flows: $880,000 * 1.736 + $880,000 * 2.487 + $880,000 * 3.170 + $880,000 * 3.791

Less amount to be invested: $2,278,320

Net present value: NPV_Biofuel_Equipment = Present value of annual net cash flows - Amount to be invested

1b. The present value index (PVI) can be calculated by dividing the NPV by the amount to be invested:

Present Value Index = NPV / Amount to be invested

2. To determine the internal rate of return (IRR) for each project, we need to find the discount rate at which the NPV becomes zero. We can use the present value of an annuity of $1 from the table to calculate the present value factor for an annuity of $1. Then, we can find the discount rate that corresponds to an NPV of zero.

Wind Turbines:

Present value factor for an annuity of $1: Fill in the values from the table

Internal rate of return: IRR_Wind_Turbines = Discount rate corresponding to NPV = 0

Biofuel Equipment:

Present value factor for an annuity of $1: Fill in the values from the table

Internal rate of return: IRR_Biofuel_Equipment = Discount rate corresponding to NPV = 0

3. Based on the calculations of NPV, PVI, and IRR, we can compare the two projects. The project with the higher NPV, PVI, and IRR is considered the better financial opportunity. Both investments meet the minimum return criterion of 10%, but the project with the higher financial indicators is preferred.

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Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]

Answer:x=-28

Step-by-step explanation:

Distribute the 4 on the left side of the equation:

32 - 8x = 256

Move the constant term to the right side of the equation:

-8x = 256 - 32

-8x = 224

Divide both sides of the equation by -8 to isolate x:

x = 224 / -8

x = -28

Answer:

He needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.

Step-by-step explanation:

To determine how many more minutes Mason needs to study before taking a break, we can calculate the remaining study time.

Mason plans to study for 1 and 1-half hours, which is equivalent to 90 minutes.

He will take a break once he has studied for 1-third of the planned time, which is 1/3 * 90 minutes = 30 minutes.

Mason has already studied for 12 minutes.

Therefore, he needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.

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Answer:

(90°/360°)π(3^2) = (1/4)(9π) = 9π/4 m²

The customer would need to use more than 12.5 megabytes for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).

To determine when Plan B would be a better deal than Plan A, we need to compare the charges for both plans based on the number of megabytes used.

Plan A is represented by the linear function y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.

Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.

To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.

In other words, we need to find the x-value that satisfies the inequality:

4x + 75 < 10x

To solve this inequality, we subtract 4x from both sides:

75 < 6x

Then, we divide both sides by 6:

12.5 < x

Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.

This means that option 1) "more than 12.5 megabytes" is the correct answer.

For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.

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The product of the given fractions is 224/61.

To calculate the product of the given fractions, let's simplify and cancel out any common factors.

We have:

(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)

Starting from the numerator and denominator of the first fraction, we observe the following cancellations:

5 in the numerator and denominator cancel out.

7 in the numerator and denominator cancel out.

9 in the numerator and denominator cancel out.

11 in the numerator and denominator cancel out.

13 in the numerator and denominator cancel out.

15 in the numerator and denominator cancel out.

17 in the numerator and denominator cancel out.

19 in the numerator and denominator cancel out.

21 in the numerator and denominator cancel out.

23 in the numerator and denominator cancel out.

25 in the numerator and denominator cancel out.

27 in the numerator and denominator cancel out.

Now, let's multiply the remaining fractions:

(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)

This simplifies to:

(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)

Simplifying further:

(4 x 29 x 31) / (28 x 35)

We can calculate this to get the final result:

(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.

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