A picture needs a border of uniform width to surround it before it is framed. For the most pleasing effect the border needs to have the exact same area as the picture to be framed. If the original picture is 12 em by 17 cm, determine the required width of the border, rounded to twe decimal places.

$0.03 pretzels cost more than the cost of a bag of chips.

What is Unitary Method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use the Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.

The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

price of 16 snack-size bags of chips = 7.84

Cost of 1 bag of chip = 7.84 /16

                                 = $0.49

and, the price of 24 snack-size bags of pretzels = 12.48

Cost of 1 snack-size bag of pretzels = 12.48 / 24

                                                             = 0.52

Hence, by $0.03 pretzels cost more than the cost of a bag of chips.

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Complete question:

Brenda went to the store with her dad to buy snacks. They bought a box of 16 snack-size bags of chips for $7.84 and a box of 24 snack-size bags of pretzels for $12.48. How much more do pretzels cost per bag than chips?

Therefore, the volume of the jewelry box is 462 cubic inches.

Volume is the amount of space occupied by a three-dimensional object or substance. It is a physical quantity that describes how much space an object takes up. The unit of measurement for volume depends on the system of measurement being used, but some common units include cubic meters (m³), liters (L), and fluid ounces (Fl oz).

In simple terms, volume is the measure of how much a container can hold. For example, if you pour water into a cup, the volume of water that the cup can hold is equal to the volume of the cup. Similarly, if you have a box, the volume of the box is the amount of space it occupies, and you can calculate it by multiplying its length, width, and height.

To find the volume of the rectangular jewelry box, we need to multiply its length, width, and height. However, we need to first convert the mixed numbers to improper fractions to perform the multiplication accurately.

[tex]V = length x width x height[/tex]

[tex]Width = 7 1/2 inches = (7 x 2 + 1)/2 inches = 15/2 inches[/tex]

[tex]Height = 4 2/5 inches = (4 x 5 + 2)/5 inches = 22/5 inches[/tex]

Now, we can calculate the volume using the formula:

[tex]V = length x width x height[/tex]

[tex]V = (28/3) x (15/2) x (22/5) cubic inches[/tex]

[tex]V = 13860/30 cubic inches[/tex]

V = 462 cubic inches (rounded to the nearest whole number)

Therefore, the volume of the jewelry box is 462 cubic inches.

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Answer:

An=31n-49

Step-by-step explanation:

1550=A1(1-5^3) / 1-5 =31

1550=A1 × 31 / 31

A1= 50

Answer:

minutes took to finish the race = 54 minutes

Step-by-step explanation:

It's known that:

[tex]speed = \frac{distance}{time}[/tex]

then:

[tex]time = \frac{distance}{speed}[/tex]

IN THE 1ST 10 MILES:

time = [tex]\frac{10}{25} = \frac{2}{5} = 0.4 hours[/tex]

IN THE 2ST 10 MILES:

time = [tex]\frac{10}{20} = 0.5 hours[/tex]

Hence, Overall time took to finish the race = 0.4 + 0.5 = 0.9 hours

time in minutes = 0.9 × 60 = 54 minutes


Another Solution:

Overall speed = [tex]\frac{S_1 + S_2}{2}[/tex], Where: S1: 1st speed, S2: 2nd speed

then:

speed = [tex]\frac{25 + 20}{2}= 22.5 mph[/tex]

Hence, time took = [tex]\frac{20}{22.5} = 0.9 hours = 54 minutes[/tex]




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Starting points = 7,985

Doubling the points: 7,985 x 2 = 15,970

Subtracting 3,500 points: 15,970 - 3,500 = 12,470

Adding 4,972 points: 12,470 + 4,972 = 17,442

Therefore, Daniel has 17,442 points at the end of the game.

In summary, the domain of the given function f(x) =[tex]3x^2 - 6x - 13[/tex] is all real numbers.

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function f(x) is a quadratic function, which is given by [tex]f(x) = 3x^2 - 6x - 13.[/tex]

Quadratic functions are defined for all real numbers.

There are no restrictions on the input values of x for this function.

Therefore, the domain of f(x) is all real numbers.
To answer the student question, the correct option is "all real numbers."

The other options, "x ≥ 1," "x ≤ -6," and "x ≥ -13," do not apply in this case as there are no constraints on the values of x for a quadratic function.

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Answer: 1/2 chance of drawing a blue marble

Step-by-step explanation:

Add the total number of marbles.

30+50+20=100

then put the number of marbles you are trying to find over the total number of marbles.

blue/total = 50/100 =.5

Answer:

P(blue) = 1/2

Step-by-step explanation:

P(blue) = number of blue marbles / total number of marbles

blue marbles = 50

Total marbles = 30+50+20 = 100

P(blue) = 50/100 = 1/2

The Classify each of the given sets of measurements is given below:

a) 52, 63, 65°: These measurements form a unique triangle. This is a right-angled triangle, also known as a Pythagorean triple.

b) 31°, 102°, 46°: These measurements do not form a triangle. The sum of the angles in a triangle is always 180°, but in this case, the sum is 179°, which is less than 180°.

c) 70.6°, 47.4°, 62°: These measurements do not form a unique triangle. There are multiple possible triangles that can be formed with these measurements.

d) 3 cm, 4 cm, 5 cm: These measurements form a unique triangle. This is another example of a Pythagorean triple.

e) 7.9 cm, 2.4 cm, 2.9 cm: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

f) 12% in, 6% in, 5% in: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

g) 124 mm, 432 mm, 385 mm: These measurements form a unique triangle.

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Step-by-step explanation:

7 x 5 =35   cubes in each layer

then multiply this by 4  layers   ( the final dimension)

= 140 cubes

The syntax function_name(const vector<int>& scores) best defines the function's integer vector parameter scores, if scores has a large amount of elements, and the function will not change scores.

To define a function's integer vector parameter scores if scores has a large amount of elements and the function will not change scores, we can use the following syntax in most programming languages:

function_name(const vector<int>& scores)

This defines a function called function_name that takes an integer vector parameter called scores, which is passed by reference using the '&' operator and is not modified by the function. The 'const' keyword indicates that the function will not modify the contents of the vector.

By using this syntax, we ensure that the function can accept any size of the integer vector scores and that it does not modify the contents of the vector. This is important because it allows us to write functions that can be used with different data sets without changing the original data.

It also ensures that the function is efficient and does not require unnecessary copying or allocation of memory.

Passing the vector by reference also means that the function can access the vector's elements without making a copy of the entire vector, which can be beneficial for performance when dealing with large data sets.

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Answer:

x = 6.5

Step-by-step explanation:

-3 × ( 4x - 5 ) = 2 × ( 1 - 5x )     ------------->      (By multiplying each bracket times its coefficient)

= -12x + 15 = 2 - 10x      ------------->     (By subtracting "2" from each side)

= -12x + 13 = -10x       -------------> (By moving the "-10x" to the other side and the "13" to the right side different signs "-10x becomes +10x and 13 becomes -13")

= -12x + 10x = -13

= -2x = -13             ------------->   (Dividing by "-2")

then, x = 6.5

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The equation of the linear function that fits the given data is y = 10x - 2.

To find the equation of a linear function in slope-intercept form, we need to determine the slope (m) and y-intercept (b).

m = (y2 - y1) / (x2 - x1)

(x1, y1) = (0, -2)

(x2, y2) = (4, 38)

m = (38 - (-2)) / (4 - 0)

= 40 / 4

= 10

y = mx + b

To find the y-intercept, we can use any point on the line. Let's use (0, -2):

-2 = 10(0) + b

b = -2

So,

y = 10x - 2

We can check that this equation satisfies all the given data points:

When x = 0, y = 10(0) - 2 = -2

When x = 1, y = 10(1) - 2 = 8

When x = 2, y = 10(2) - 2 = 18

When x = 3, y = 10(3) - 2 = 28

When x = 4, y = 10(4) - 2 = 38

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The solution to the equation -2 = -4m + 10 is m = 3.

Here are the solutions to the given equations:

1. -10 = 5+y

To solve for y, we need to isolate y on one side of the equation.

We can do this by adding 10 to both sides of the equation.

-10 + 10 = 5 + y + 10

Simplifying,

-0 = 5 + y

We can further simplify the equation by subtracting 5 from both sides of the equation.

-5 = y

Therefore, the solution to the equation -10 = 5+y is y = -5.2.

10x = 40

To solve for x, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 10.10x/10 = 40/10

Simplifying,

x = 4

Therefore, the solution to the equation 10x = 40 is x = 4.3.

-2 = -4m + 10To solve for m, we need to isolate m on one side of the equation.

We can do this by subtracting 10 from both sides of the equation.-2 - 10 = -4m.

Simplifying,

-12 = -4mWe can further simplify the equation by dividing both sides of the equation by -4.-12/-4 = m3 = m.

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Answer:

B

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° ( n - 2) ← n is the number of sides

given sum = 10080 , then

180° (n - 2) = 10080 ( divide both sides by 180 )

n - 2 = 56 ( add 2 to both sides )

n = 58

that is the polygon has 58 sides

For the given information of standard deviation, the correct answer is option B) Between 65.5 inches and 75.5 inches.

What is standard deviation?

Standard deviation is a statistical measure that measures the amount of variation or dispersion of a set of data values from the mean. It tells how much the data deviates from the average of the data set.

We can use the z-score formula to solve this problem. If we assume a normal distribution, we can find the z-score associated with the 95th percentile (or 0.95 probability) using a standard normal distribution table or calculator. The z-score is approximately 1.96.

Then we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Solving for x:

1.96 = (x - 70.5) / 2.5

Multiplying both sides by 2.5:

4.9 = x - 70.5

Adding 70.5 to both sides:

x = 75.4

So 95% of the men fall between 65.5 inches and 75.5 inches (option B).

Therefore, the correct answer is option B) Between 65.5 inches and 75.5 inches.

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Answer:

11 quarters and 35 dimes

Step-by-step explanation:

We can create a system of equations to find the number of both dimes and quarters that are in the parking meter.

1st equation:  We know that the value of a dime ($0.10) * the number of dimes (D) + the value of a quarter ($0.25) * the number of quarters (Q) = $6.25

2nd equation: If we allow D to represent dimes and Q to represent quarters, the number of dimes = 3 times the number of quarters is 3Q and 2 more than this is 3Q + 2

Thus, our two equations are:

0.10D + 0.25Q = 6.25

D = 3Q + 2

The equations are already set up in a way where we can use substitution to solve and substitute the formula for D in the second equation for D in the first equation:

[tex]0.10(3Q+2)+0.25Q=6.25\\0.30Q+0.20+0.25Q=6.25\\0.20+0.55Q=6.25\\0.55Q=6.05\\Q=11[/tex]

Now that we've found the number of quarters, we can use either equation to find the number of dimes:

[tex]D=3(11)+2\\D=33+2\\D=35[/tex]

It's always helpful to check the solutions (time-permitting) in both equations to make sure our math was accurate

1st equation:

0.10(35)+0.25(11)=6.25

3.50 + 2.75 = 6.25

6.25 = 6.25

2nd equation:

35 = 3(11) + 2

35 = 33 + 2

35 = 35

Triangle ABC's vertices are A (-5,5), B (-2,3), and C (-4,3). The coordinates of the vertex C'are if ABC is reflected across the line y=1 to generate the image A'B'C' (-4, -1).

To reflect a point across the line y=1, we need to flip the y-coordinate over the line y=1.

The y-coordinate of point C is already 3, which is less than the line y=1. The distance between point C and the line y=1 is (1-3)= -2, which is negative, so we need to add twice this distance to the y-coordinate to get its reflection.

y-coordinate of C' = 3 + 2*(-2) = -1

Therefore, the coordinates of C' are (-4, -1).

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Hence, one teacher must be 21 years old, while the other must be 3 years old.

The difference between a dataset's highest and lowest values is known as the range. For instance, suppose we have the dataset shown below:

1, 3, 5, 7, 9

This dataset's range is 9 - 1 = 8.

Let's first estimate the age ranges of the school's ten mathematics instructors. The range of a dataset is the difference between its highest and lowest values. It is therefore 21 since 22 - 43 = 21.

Let's now include the ages of two additional Maths teachers in this list. Let's use x and y as their ages.

When their ages are included in this list, the range is increased by five. We thus have:

43 - 22 = 21 (the original range) (the original range)

max(x,y) = 5 - min(x,y) (the new range)

We can find the solutions to x and y from these two equations:

maximum(x,y) = 21 + 5 = 26 minutes

(x,y) = maximum (x,y) - 5 = 21

Let's now determine the average age of the school's twelve maths teachers. Addition is used to calculate the mean.

Adding together all the values in a dataset and dividing by the total number of values yields the mean. Here are the facts:

(31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36 + x + y) / 12

If we are aware that x and y together raise the mean by 1, we may write:

(31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36 + x + y) / 12 = (31 + 43 + 25 + 37 + 28 + 22 + 25 + 32 + 31 + 36) /10 +1

When we simplify this equation, we get:

x+y=24

Let's now determine the median age of the school's twelve mathematics instructors. When a dataset is ordered from lowest to highest, the median is the midway value (or highest to lowest). Here are the facts:

22,25,25,28,31,31,32,36,37,43,x,y

The median is equal to (31.5 (31 + 32) / 2)

Let's finally figure out the average age of the school's twelve math teachers. The value that appears most frequently in a dataset is the mode. In this instance, "25" and "31" both appear twice, giving us two modes.

We are aware that this dataset's mode is unaffected by the addition of x and y.

We thus have:

x+y=24

max(x,y)=26

min(x,y)=21

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Answer:

The equation of the line joining Q(-1/2, 3.5) and midpoint AP [A(4, 1) P(3, 7)] is y = (-5/19)x + (117/38)

The equation of the line joining Q(-1/2, 3.5) and the midpoint of AP (4, 1) and P(3, 7) is y = 0.125x + 3.5625. This is found using the two-point form of the equation of a line and the midpoint formula.

First, find the midpoint, M, of AP using the formula M = [(x1+x2)/2, (y1+y2)/2]. Plugging in the coordinates given for A(4,1) and P(3,7), M = [(4+3)/2, (1+7)/2] = [7/2, 8/2] = [3.5, 4]. Now, use the two-point form of the equation of a line to find the equation of the line QM: (y - y1) = m(x - x1), where m is the slope of the line. The slope is found by the formula (y2-y1)/(x2-x1). Substituting Q(-1/2, 3.5) and M(3.5, 4), you get m = (4 - 3.5)/(3.5 - (-1/2)) = 0.5/4 = 0.125. Now substitute Q(-1/2, 3.5) and m = 0.125 into the formula to get the equation of the line: (y - 3.5) = 0.125(x +1/2). This can be simplified as: y = 0.125x + 3.5625. So the

equation of the line

joining Q(-1/2, 3.5) and the midpoint of AP is y = 0.125x + 3.5625.

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part a.

Carter needs 116 yards of fencing to enclose the flat area of his backyard.

part b.

Carter needs 720 square yards of sod to cover the flat area of his backyard.

estimating the coordinates of the vertices of the figure and using  the distance formula to calculate the length of each side:

AB: √((16-(-16))^2 + (4-4)^2) = 32 yards n

BC: √((16-4)^2 + (4-12)^2) = 14 yards

CD: √((4-8)^2 + (12-16)^2) = 5 yards

DE: √((8-(-12))^2 + (16-(-8))^2) = 37 yards

EA: √((16-(-16))^2 + (4-(-8))^2) = 28 yards

The total perimeter is: 32 + 14 + 5 + 37 + 28 = 116 yards

b.

Rectangle ABED: 32 yards × 16 yards = 512 square yards

Triangle BCD: (1/2) × 4 yards × 8 yards = 16 square yards

Triangle DEA: (1/2) × 24 yards × 12 yards = 144 square yards

Triangle EFA: (1/2) × 8 yards × 12 yards = 48 square yards

The total area is: 512 + 16 + 144 + 48 = 720 square yards

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The sample of the songs in the musical is likely to be representative.

As per the given details, Nicholas listened to 2 songs from each act of a musical.

Each act has an equal number of songs.

In order to determine whether the sample of the songs in the musical likely to be representative, we need to determine the number of acts of the musical.

Let the number of songs in each act be x.

Since Nicholas listened to 2 songs from each act, the total number of songs Nicholas listened to will be equal to 2x. Thus, we can represent the number of acts in the musical as a function of the total number of songs listened to as follows:

Number of acts = total number of songs listened to / x = 2x / x = 2.

Since there are 2 acts in the musical, Nicholas listened to all the songs in the musical.

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To find how many miles Roger travels in one hour, we need to divide the total distance he traveled by the time he took:

miles per hour = total miles ÷ total time

In this case, Roger traveled 440 miles in 8 hours, so:

miles per hour = 440 miles ÷ 8 hours

miles per hour = 55 miles per hour

Therefore, Roger travels 55 miles in one hour.

Answer:

To find how many miles Roger travels in one hour, we can divide the total distance he traveled by the total time he took to travel that distance.

We are given that Roger traveled 440 miles in 8 hours, so:

miles per hour = total distance / total time

miles per hour = 440 miles / 8 hours

miles per hour = 55 miles per hour

Therefore, Roger travels 55 miles in one hour.

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The drug company tested a new cold medication for children with a sample size of 500 children, out of which 250 children shortened their cold symptoms. The margin of error over a 99% confidence interval is 0.657. The 99% confidence interval is 0.5 ± 0.657, or (0.157, 0.843).

To calculate the margin of error, we need to determine the critical value for a 99% confidence interval. For a sample size of 500 and a confidence level of 99%, the critical value is 2.58.

The margin of error can be calculated as follows:

Margin of error = critical value * standard error

where the standard error is the standard deviation of the sample divided by the square root of the sample size.

In this case, the standard error is 5.7/sqrt(500) = 0.255.

Therefore, the margin of error is 2.58 * 0.255 = 0.657.

We can construct a 99% confidence interval for the proportion of children whose cold symptoms are shortened by the new drug as follows:

p ± margin of error

where p is the proportion of children in the sample who shortened their cold symptoms when taking the new drug.

In this case, the point estimate of the proportion is 250/500 = 0.5.

The 99% confidence interval is 0.5 ± 0.657, or (0.157, 0.843). This means that we can be 99% confident that the true proportion of children whose cold symptoms are shortened by the new drug falls within this interval.

Since the confidence interval does not include the value of 0.5 (which represents no effect), we can conclude that the new cold medication is reliable and has a statistically significant effect on shortening the duration of cold symptoms in children.

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The annual installments for the sinking fund account can be calculated using the sinking fund formula, which takes into account the replacement cost, interest rate, and the number of years until the replacement is needed. In this case, the annual investment needed to provide for the replacement of the asset in 4 years is approximately GH¢1573.50.

To draw up the sinking fund schedule to show the growth fund, we can calculate the future value of the sinking fund account at the end of each year using the same formula. Assuming the first payments will be made now and 12 months thereafter, the annual payments will also be GH¢1573.50.

To illustrate this, we can create a sinking fund schedule that shows the annual investments, the interest earned, and the total fund balance at the end of each year. Using the sinking fund formula, the sinking fund schedule for Cross Ltd would look like this:

Annual Investment   Interest Earned           Total Fund Balance  year

GH¢1573.50             GH¢188.82                     GH¢1762.32               1

GH¢1573.50            GH¢221.48                      GH¢3557.30             2

GH¢1573.50             GH¢259.20                       GH¢5339.00            3

GH¢1573.50            GH¢302.68                        GH¢7115.18               4

This sinking fund schedule shows that by investing GH¢1573.50 at the end of each year at an interest rate of 12% per annum, Cross Ltd will have a total fund balance of GH¢7115.18 at the end of 4 years, which is sufficient to cover the replacement cost of the asset.

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Question:-Cross Ltd has bought an asset with a life span of 4 years. At the end of the 4 years, replacement of the asset will cost GH¢12,000. In this direction, the company has decided to provide for future commitment by setting up a sinking fund account into which equal annual investment will be made at the end of each year. The interest rate on the investment will be 12% per annum.

Required:

i. Calculate the annual installments

ii. Draw up the sinking fund schedule to show the growth fund

iii. Assuming the first payments will be made now and 12 months thereafter, what are the annual

payments? You are required to draw up the sinking fund schedule.

The required difference between the amount of cereal poured into a large and small bowl representing the difference of standard deviation is equal to 0.5 ounces.

Let X be the amount of cereal poured into a small bowl.

And Y be the amount of cereal poured into a large bowl.

Then, the standard deviation of the difference Y - X.

Mean of X is given as 1.5 ounces

Standard deviation of X is 0.3 ounces

Mean of Y is given as 2.5 ounces

Standard deviation of Y is 0.4 ounces

The difference between Y and X can be written as Y - X.

Mean of Y - X is given by the difference of the means,

= 2.5 - 1.5

= 1 ounce.

As we assume that X and Y are independent.

Variance of Y - X can be calculated as the sum of the variances of Y and X.

Thus, we have,

Var(Y - X) = Var(Y) + Var(X)

⇒Var(Y - X) = (0.4)^2 + (0.3)^2

⇒Var(Y - X) = 0.16 + 0.09

⇒Var(Y - X) = 0.25

The standard deviation of Y - X is the square root of the variance, so we have,

SD(Y - X) = √(Var(Y - X))

⇒SD(Y - X) = √(0.25)

⇒SD(Y - X) = 0.5

Therefore, the standard deviation of the difference between the amount of cereal poured into a large and small bowl is 0.5 ounces.

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Answer:

a = 2b - x

Step-by-step explanation:

2(x + a) = 4b  Divide both sides of the equation by 2

x + a = 2b   Subtract x from both sides

a = 2b - x

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