Please help with #10 and #13!!

The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.

To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.

Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.

This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.

In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.

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The size of angle DAB in the quadrilateral is 49°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

∠A + ∠B + ∠C + ∠D = 360°

∠A + 34° + ∠C + 228° = 360°

∠A  + ∠C + 262° = 360°

∠A  + ∠C = 360 - 262

∠A  + ∠C = 98

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

∠A  + ∠A = 98

2∠A  = 98

∠A = 98/2

∠A  = 49°

Therefore, the size of angle DAB is 49°.

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Complete Question

Check the attached image

In the figure of circle provided. the value of x is

In a circle, equal chords subtends equal arc length.

In the problem it was given that:

chord SU is equal to chord ST hence we have that

x + x + 38 = 360 (angle in a circle)

collecting like terms

2x + 38 = 360

2x = 360 - 38

2x = 322

Isolating x by dividing both sides by 2

2x / 2 = 322 / 2

x = 161

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

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Answer:  ^4√11^5 = 11^(5/4)

Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.

So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:

^4√11^5 = (11^5)^(1/4) = 11^(5/4)

Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.

Hope this helps, and have a great day!

The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation:

2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

y = -5x² + 5 is the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)

We know that the vertex of the parabola is (0, 5), which means that the equation for the parabola has the form:

y = a(x - 0)² + 5

where 'a' is a constant that determines the shape of the parabola. Since the parabola passes through the point (1, 0), we can substitute these values into the equation and solve for 'a':

0 = a(1 - 0)² + 5

0 = a + 5

a = -5

Therefore, the equation of the parabola is: y = -5x² + 5

This equation represents a parabola that opens downwards (since the coefficient of x² is negative), has a vertex at (0, 5), and passes through the point (1, 0).

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The given equation 3x + 7y = 11 is equal to (1,-2).

The given equation is 3x + 7y = 11.

To find the solution of the equation, we need to consider the given options:

(6,-1)(1,-2)(0,4)

Now substitute each value of x and y in the given equation, we get,

If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11

If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11

If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11

Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).

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Check the picture below.

[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]

The value of x is 4.5 rounded to the nearest tenth.

Tangent of a circle is defined as the line which passes through exactly one point on the circle.

Secant of a circle is the line which passes through two points on the circle.

Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.

Using the theorem, we can say here that,

(8 + 2) 2 = x²

x² = 10 × 2

x² = 20

x = √20

x = 4.472 ≈ 4.5

Hence the value of x is 4.5.

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A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

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Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

Rounding off the value of X to the nearest whole number, we get that approximately 35 people would be expected to have consumed alcoholic beverages among 50 randomly selected 18-20 year-olds.

In exercise 3.25, it was learned that about 69.7% of 18-20 year-olds consumed alcoholic beverages in 2008.

Now, consider a random sample of fifty 18-20 year-olds.

It is required to calculate the number of people who would be expected to have consumed alcoholic beverages.

Let X be the number of people who have consumed alcoholic beverages out of 50 randomly selected 18-20 year-olds.

Let p be the proportion of 18-20 year-olds who consumed alcoholic beverages in 2008.

Therefore, the sample proportion is given as \hat{p}

Hence, p=0.69 \hat{p}=X/50

Now, by the properties of the sample proportion, E(\hat{p})=p

Therefore,

E(\hat{p})=E(X/50)

Thus, p=E(X/50) Or, X=50p

Substituting the value of p, we have

X=50(0.697)=34.85

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The answer of the given question based on the  linear regression  is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.

Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.

Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.

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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.

The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.

The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is

y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:

y = 34.38x - 91.75

y = 34.38(10) - 91.75

y = 343.8 - 91.75

y = 252.05

The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.

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The complete question is,

The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.

Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.

(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:

*****|**********|***|****

The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:

C(27, 3) = 27! / (3! * 24!) = 2925

(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:

C(16, 3) = 560 for the Tootsie rolls

C(10, 3) = 120 for the Twizzlers

To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:

560 * 120 = 67200

Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.

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Complete question:

After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.

(A) How many different ways can she do this?

(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?

We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

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Area of the solid composite shape with triangle and rectangle is =832cm².

The area of a composite shape can be determined by adding or subtracting its component pieces.

Hence, we can use two formulas:

Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)

Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)

In the figure,

Dimensions of the triangle are height, h = 16cm and base, b = 12cm.

Area = 1/2 ×b ×h

= 1/2 × 16× 12

=96cm²

There are two triangles, so the total area = 96+ 96 = 192cm².

Now area of the rectangle = length × width

= 20 × 32

= 640cm².

Total area of the solid= 192 + 640 = 832cm².

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b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

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The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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Answer:

  13/32

Step-by-step explanation:

You want the area of the shaded portion of the unit square shown.

Points B, C, E are shown as equidistant from point F, so will lie on a circle centered at F. The center of that circle is at the point of coincidence of the perpendicular bisectors of BE, BC, and CE.

Without loss of generality, we can let line EF lie on the x-axis such that E is at the origin. Chord EB of the circle has a rise of 1/2 for a run of 1, so a slope of 1/2. Its midpoint is (1, 1/2)/2 = (1/2, 1/4). The perpendicular line through this point will have slope -2, so its equation can be written ...

  y -1/4 = -2(x -1/2)

  y = -2x +5/4

Then the x-intercept (point F) will have coordinates (0, 5/8):

  0 = -2x +5/4 . . . . . y=0 on the x-axis

  2x = 5/4

  x = 5/8

Trapezoid EFCD will have upper base 5/8, lower base 1, and height 1/2. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5/8 +1)(1/2) = (1/4)(13/8) = 13/32

The shaded area is 13/32.

__

Additional comment

The point-slope equation of a line through (h, k) with slope m is ...

  y -k = m(x -h)

The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation: