Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,

(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.

------------------- grams


(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.

-------------------- years

The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc TV = 2(m∠TUV)

54x - 2 = 2(80)

54x - 2 = 160

54x = 160 + 2 {collect like terms}

54x = 162

x = 162/54 {divide through by 3}

x = 3

Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.

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[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]

Answer:

D=2, 3, 5, 6, 7, 8, 9,

Step-by-step explanation:

btw can i js get 1  brainly?

{2,3,5,6,7,8,9}

The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.

Note that in  Circle Q, m∠1  = 66° (Option A)

Note that inthe circle above, the angle which creates the arc 114° lies ont he same line with ∠1. Since sum of angles on a Straight line sum up to 180°.

∠1 = 180 -114 = 66°

A circle is defined as a form made up of points in a two-dimensional plane that are equidistant from a particular location. A circle is defined as a closed curve with no corners or vertices. Circles define several circular forms in our everyday lives.

Circular shapes include:

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The expected value of the investment is $600,000.

The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.

If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:

(0.3 x $2,000,000) + (0.7 x $0) = $600,000

This means that the expected value of the investment is $600,000.

Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.

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Answer:

2a+15b+11

Step-by-step explanation:

2*a + 2*4b + 5 + 7b + 6

2a + 8b + 5 + 7b + 6

2a + 8b + 7b + 5 + 6

2a + 15b + 11

The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.

Recall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.

In this case

∠1 ≅ ∠2 - Given

hence they is bisected by AX

Also ∠5 ≅ ∠6. This means that they are bisected by CX

Since AX and CX form AC, and

AC = CA (Reflexive Property)
Also

BD = DB  (Reflexive Property)

Then it means that AC ⊥ BC (QED)

Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.

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The rate of change of the number of oil changes with respect to the number of hours will be 3.

The table is given below.

Number of hours              Number of oil changes

            1.5                                          4.5

             3                                             9

           5.5                                         16.5

             8                                            24

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The rate of change is calculated as,

Average rate = (24 - 9) / (8 - 3)

Average rate = 15 / 5

Average rate = 3

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Answer:

? ≈ 9.09

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a, b , c are the sides opposite angles A , B , C

we require the third angle in the triangle

third angle = 180° - (51 + 109)° = 180° - 160° = 20°

then with

a = 4 , ∠ A = 20°

b = ? , ∠ B = 51°

[tex]\frac{4}{sin20}[/tex] = [tex]\frac{?}{sin51}[/tex] ( cross- multiply )

? × sin20° = 4 × sin51° ( divide both sides by sin20° )

? = [tex]\frac{4sin51}{sin20}[/tex] ≈ 9.09 ( to the nearest hundredth )

Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.  

For Design 1:

Dimensions: 3 m x 3 m x 30 cm

We find the total area:

Two faces measures 3 m x 3 m = 9 m² each for the bottom and top

Two faces measures 3 m x 30 cm = 0.9 m² each for back and front

Two faces measures 3 m x 30 cm = 0.9 m² each

Therefore the total area of materials needed for Design 1 is found as

= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²

Design 2:

Dimensions: 3.25 m x 3.25 m x 25 cm

In the same way, we find  the area of materials needed for Design 2:

Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²

Design 1 volume is :

Volume = Length x Width x Height

Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³

Design 2 volume is :

Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³

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There are 10 possible results when Dan spins the wheel of destiny with the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 20.

Every possible result is represented by a different number, and Dan has an equal probability of choosing any of them.

The wheel serves as a tool for randomization, adding a degree of ambiguity and unpredictability to the experiment. There are 20 possible outcomes total, with increments of 2 between the lowest and highest numbers.

Thus, these results stand in for various values that Dan might get from spinning the wheel. We may analyse the likelihood and probable range of results for this particular experiment by taking into account all the conceivable possibilities.

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Answer: Thats a Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

Answer: 15/38 or 0.39473684210526315789473684210526

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

Answer:

[tex]\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

[tex]\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}[/tex]

[tex]x=\cos \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]x=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The base of one of the right triangles can be found by using the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

[tex]\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}[/tex]

[tex]y=\sin \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]y=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

[tex]\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}[/tex]

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}[/tex]

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

[tex]\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Using the equation y=−x+9.6, we can calculate the predicted values for y as follows:

When x = 1: y = -(1) + 9.6 = 8.6

When x = 2: y = -(2) + 9.6 = 7.6

When x = 3: y = -(3) + 9.6 = 6.6

When x = 4: y = -(4) + 9.6 = 5.6

When x = 5: y = -(5) + 9.6 = 4.6

When x = 6: y = -(6) + 9.6 = 3.6

We can then calculate the residuals by subtracting the predicted values from the actual values of y:

When x = 1: residual = 5.8 - 8.6 = -2.8

When x = 2: residual = 8.7 - 7.6 = 1.1

When x = 3: residual = 2.9 - 6.6 = -3.7

When x = 4: residual = 0.8 - 5.6 = -4.8

When x = 5: residual = 5.1 - 4.6 = 0.5

When x = 6: residual = 1.7 - 3.6 = -1.9

There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Therefore, we can say that the equation y=−x+9.6 is not a good fit for this data.

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Answer:

Step-by-step explanation:

I don't quite understand the problem but:

2 2/4 -1 =1 1/2, and 3/4 can't be simplified more.

14 inches taller by the tallest player than the shortest player on the basketball team. The correct option is A .

To determine how much taller the tallest player is than the shortest player on the basketball team, we need to examine the given line plot and calculate the difference between their heights.

To find the height difference, we need to identify the tallest and shortest players on the team. The line plot should display the heights of each player, allowing us to determine these values.

Once we have these heights, we can subtract the height of the shortest player from the height of the tallest player to calculate the difference.

Based on the options provided, we can consider each possibility:

A. If the height difference is 14 inches, then the tallest player is 14 inches taller than the shortest player. B. If the height difference is 10 inches, then the tallest player is 10 inches taller than the shortest player.

C. If the height difference is 13 inches, then the tallest player is 13 inches taller than the shortest player. D. If the height difference is 12.5 inches, then the tallest player is 12.5 inches taller than the shortest player.

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The number of jerseys they can purchase for $430 is 53 jerseys.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Based on the information provided about the cost of the jerseys, we have the following quadratic function;

C = 0.1x² + 2.4x + 25

430 = 0.1x² + 2.4x + 25

0.1x² + 2.4x + 25 - 430 = 0

0.1x² + 2.4x - 405 = 0

By solving the quadratic function using the quadratic formula, we have:

[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]

x = 52.76 ≈ 53 jerseys.

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After considering the given data we conclude that the value generated after performing divison of the given expression is 18x, under the condition that we follow the principles of divison.

Let us proceed by evaluating the given expression by applying division
4x(3+6) divided by 2
= 4x9/2
= 36x/2
= 18x
Division is considered one of the four basic mathematical operations, then the other three are addition, subtraction, and multiplication.
In short , division is referring to the breaking down of a given bigger number or expression into simpler yet smaller forms to meet the criteria of performing a function.
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The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.

The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,

f(4) = 2(4)² - 9

Evaluating 2(4)²,

f(4) = 2(16) - 9

Simplifying 2(16) - 9:,

f(4) = 23

Therefore, f(4) = 23. So, the correct answer is Option A.

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Complete question - Determine f(4) for A piecewise function

f(x) = x³ ____ x<-3

f(x) = 2x²-9 ____ -3 ≤ x≤ 4

f(x) = 5x+ ____ when x>4

A. 23

B. 24

C. 41

D. 64

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Step-by-step explanation:

Fred has two possible outcomes on his first test: he either scores less than 60 or he scores 60 or higher.

If he scores less than 60, there is a 55% chance he will pass the course, and a 45% chance he will fail. We know there is a 70% chance he will score less than 60, so the probability that he scores less than 60 and fails the course is 0.7 * 0.45 = 0.315.

If he scores 60 or higher, there is a 70% chance he will pass the course, and a 30% chance he will fail. We don't know the exact probability that he scores 60 or higher, but we know that it is 1 - 0.7 = 0.3 (since there is a 70% chance he scores less than 60). So the probability that he scores 60 or higher and fails the course is 0.3 * 0.3 = 0.09.

Adding these two probabilities together gives us the total probability that Fred gets more than 60 on the first test but fails the course: 0.315 + 0.09 = 0.405. However, we are looking for the probability that he gets more than 60 but fails, so we need to subtract the probability that he scores less than 60 and fails: 0.405 - 0.315 = 0.09. Therefore, the answer is B. 0.09.

i think so...

Answer:

The correct answer is option C. (-4,2) lies in the Quadrant II .

Based on the image attached, The the shape of the distribution is option c) data skewed right.

The term Right skewed is one where the mean  is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean  is one that has little of the common values in a rightly skewed dissemination.

So, therefore, if  most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.

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See text below



Gabriela recorded the ages of her shirts.

·

0 1 2 3 4 5 6 7 8 9 10

Age (years)

Which of these best describes the shape of the distribution?

Choose 1 answer:

Roughly symmetric

Skewed left

Skewed right

Good Question (141)

It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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The Triangle is Equilateral and Equiangular.

We will use theses property of Equilateral Triangle as

We have a Triangle.

The Triangle all three angles measured 60 degree each.

and, We know the equilateral Triangle all angles measures 60 degree.

Now, from the figure all the three sides of triangle are equal.

and, we know Equilateral triangle have the three sides equal

Thus, the Triangle is Equilateral and Equiangular.

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Given that a randomly selected applicant has more than 10 years of experience, the likelihood that they have a graduate degree is roughly 0.4016.

To find the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience, we need to use conditional probability. We can use the formula:

P(grad degree | over 10 years of experience) = P(grad degree and over 10 years of experience) / P(over 10 years of experience)

From the given information, we know that:

P(grad degree and over 10 years of experience) = 51 (number of applicants with over 10 years of experience and a graduate degree)

P(over 10 years of experience) = 127 (number of applicants with over 10 years of experience)

So, plugging in these values:

P(grad degree | over 10 years of experience) = 51 / 127

Using a calculator, we get:

P(grad degree | over 10 years of experience) ≈ 0.4016

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience, is approximately 0.4016.

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Answer:

Step-by-step explanation:

Given:

a₁ = 3

an+1 = (an)² + 1To find:

a₃Solution:

We can use the recursive formula given to find the value of a₃.a₂ = a₁ + 1² = 3 + 1 = 4

a₃ = a₂² + 1 = 4² + 1 = 17Therefore, the value of a₃ is 17.Answer: a₃ = 17

Scale drawings are valuable tools in various fields such as architecture, engineering, and design, allowing professionals to visualize and communicate ideas accurately. By employing scale factors and maintaining proportions, these drawings provide a reliable representation of real-world objects and spaces.

A scale drawing is a representation of an object or space that is proportional to the actual size or dimensions of the original. It involves using a scale factor, which is a ratio that compares the measurements on the drawing to the measurements of the real object or space. The scale factor determines how much the drawing is enlarged or reduced in relation to the actual size.

When creating a scale drawing, it is important to maintain the same proportion as the original object. Proportion refers to the relationship between the different parts of an object or space, ensuring that the relative sizes are accurate. This ensures that the scaled drawing provides an accurate representation of the original, even if it is smaller or larger in size.

The scale factor is typically expressed as a ratio or a fraction, such as 1:100 or 1/4. This ratio indicates how many times larger or smaller the drawing is compared to the actual object. For example, if the scale factor is 1:10, every unit on the drawing would represent ten units in reality. This allows for accurate measurements of length, as well as area.

Length is an essential aspect of scale drawings. By using the scale factor, the length of lines or dimensions on the drawing can be determined to reflect the corresponding measurements in the real object. For instance, if a line on the scale drawing represents 5 centimeters, and the scale factor is 1:10, the actual length of the line would be 50 centimeters.

In addition to length, scale drawings can also accurately represent areas. The scale factor can be used to determine the relationship between the areas on the drawing and the actual areas of the object or space. By applying the scale factor to the dimensions, the areas can be scaled up or down accordingly, maintaining the proportionality of the original.

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Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.

To find the direction angle of a vector, we can use the formula:

θ = arctan(y/x)

In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.

Plugging the values into the formula, we get:

θ = arctan(8/0)

However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.

When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.

In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.

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