Olga is a park ranger in a large national park. The
park is in a rural area that has no cellular phone
service. Olga has a walkie-talkie that allows her
to her to transmit weather updates to other
rangers in the park. Her walkie-talkie has a range
of 10 miles in all directions. The other park
rangers have receivers in their cars that can pick
up her weather updates when they are in range
of her walkie-talkie. On a particular day, Olga is at
the ranger station in the center of the park. Her
coworker Neil is doing a survey of the land by
driving along a straight road through the park.
The road that Neil is on starts 15 miles west and
15 miles south of the ranger station and ends 20
miles north and 10 miles east of the ranger
station.
For approximately how many miles of road will
Neil be able to receive Olga's weather updates?

Quadratic Equation _____?

The expected number of patients who will report symptomatic relief is 20.9. and the probability of exactly 20 patients reporting relief being 0.1977, and the probability of at least 20 patients reporting relief being 0.3832.

(a) The expected number of patients who will report symptomatic relief is 20.9.

The probability of a patient reporting symptomatic relief is 0.95, so the probability of a patient not reporting relief is 0.05. Using the binomial distribution formula, the expected value of the number of patients who will report relief is:

E(X) = n * p = 22 * 0.95 = 20.9

(b) The probability that exactly 20 patients will report symptomatic relief is 0.1977.

Using the binomial distribution formula, we can calculate the probability of exactly 20 patients reporting relief:

P(X = 20) = (22 choose 20) * 0.95^20 * 0.05^2 = 0.1977

(c) The probability that at least 20 patients will report symptomatic relief is 0.3832.

Using the binomial distribution formula, we can calculate the probability of 20 or more patients reporting relief:

P(X >= 20) = P(X = 20) + P(X = 21) + ... + P(X = 22)

P(X >= 20) = 1 - P(X < 20)

P(X >= 20) = 1 - (P(X = 0) + P(X = 1) + ... + P(X = 19))

P(X >= 20) = 1 - 0.6168

P(X >= 20) = 0.3832

Therefore, the probability that at least 20 patients will report symptomatic relief is 0.3832.

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Answer:

See below, please.

Step-by-step explanation:

To estimate the size of the town, we can use a proportion.

Number of middle school students / Total town population = Number of interviewed middle schoolers / Total number of interviewed townspeople

Let x be the total town population. Then we have:

800 / x = 40 / 125

Simplifying this proportion, we get:

40x = 800×125

40x = 100000

x = 100000 / 40

x = 2500

Answer: 1/3

Step-by-step explanation:

4 + 8 = 12 so there's 12 marble in the bag and only 4 purple ones. so the probability is 4/12 which we can simplify to 1/3

it might be 12

this is because there are6 pairs and 2 pairs

2×6=12

Answer:24

Step-by-step explanation: 6 times 2 = 12 times 2= 24

Answer:

To create a line plot for this data, we can first convert all the fractions to a common denominator, such as eighths:

Monday: 6/8 of an hour

Wednesday: 4/8 of an hour

Friday: 2/8 of an hour

Sunday: 4/8 of an hour

Then, we can draw a number line with tick marks representing each day of the week and plot a dot for each amount of time spent working out:

0         1         2         3         4

|---------|---------|---------|---------|   <- Number line

         .     .

       .             .

   .                     .

.                             .

To find out how much time June should work out each day to spend an even amount of time working out, we can first find the total amount of time she spent working out:

6/8 + 4/8 + 2/8 + 4/8 = 16/8 = 2 hours

Since there are four days she worked out, to find out how much time she should work out each day, we can divide the total time by four:

2 hours ÷ 4 = 0.5 hours

Therefore, June should work out for 0.5 hours, or 30 minutes, each day to spend an even amount of time working out.

The probability of having exactly 10 pedestrians crossing from left to right during a 2-minute period is extremely low, at approximately 0.00118%.

We can approach this problem by using the Poisson distribution, which describes the probability of a certain number of events occurring within a given time period, given a known rate of occurrence.

Let X be the number of pedestrians crossing from left to right during a 2-minute period. Since the arrival processes from the left and right sides are independent Poisson processes with rates λL and λR, respectively, we can model X as a Poisson random variable with rate λ = λL + λR = 6.

Therefore, the probability of having exactly k pedestrians crossing from left to right during a 2-minute period is given by the Poisson distribution:

P(X = k) = (e^(-λ) * λ^k) / k!

Now we want to find the probability that in a particular crossing, there are a total of 10 pedestrians crossing from left to right. Let Y be the total number of pedestrians crossing in both directions during a 2-minute period.

Since the arrival processes from the left and right sides are independent, we can model Y as a Poisson random variable with rate 2λ = 12.

Since we know that there are 10 pedestrians crossing from left to right, there must be a total of 10 pedestrians crossing in both directions. Therefore, we want to find the probability that out of the 10 pedestrians, exactly 10 of them are crossing from left to right.

We can use the binomial distribution to calculate this probability. Let Z be the number of pedestrians crossing from left to right out of the 10 pedestrians. Since each pedestrian has an independent probability of crossing from left to right of 1/2, we have:

P(Z = 10) = (10 choose 10) * (1/2)^10

= 1/1024

Therefore, the probability that in a particular crossing, there are a total of 10 pedestrians and they are all crossing from left to right is:

P(X = 10, Y = 10) = P(X = 10) * P(Z = 10)

= (e^(-6) * 6^10 / 10!) * (1/1024)

≈ 0.0000118

Writing this probability in percentage gives = 0.0000118 x 100% = 0.00118%

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Complete question is:

Pedestrians approach a crossing from the left and right sides following independent Poisson processes with average arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or from right to left). Assume that the left and right arrival processes are independent, that the light flashes every T = 2 minutes, and that crossing takes zero time – it is instantaneous.

1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?

Answer:

-407/42

Step-by-step explanation:

-8 6/7 - 5/6

-8 6/7 = -62/7

-62/7 - 5/6

= -372/42 - 35/42

= -407/42

The numerical value of x in the expression (x+5) and 2(x-4) is 61.

The sum of angles on a straight line equals 180 degrees.

From the figure in the image:

We know that the sum of angles on a straight line equals 180 degrees.

Since angle GDC and its supplement are on a straight line.

Hence;

Angle GDC + Supplemetary angle to GDC = 180

Plug in the given values and solve for x.

( x + 5 ) + 2( x - 4 ) = 180

Apply distributive property.

x + 5 + 2x - 8 = 180

Collect like terms

x + 2x - 8 + 5 = 180

3x - 3 = 180

3x = 180 + 3

3x = 183

x = 183/3

x = 61

Therefore, the value of x is 61.

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Answer:

18. x = 80°

19. y = 85°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

18.

x + x + 20 = 180

2x = 160

x = 80

Answer: x = 80°

y + y + 10 = 180

2y = 170

y = 85

Answer: y = 85°

Answer: x = 80°  and  y = 85°

Step-by-step explanation: In a cyclic quadrilateral, opposite angles add up to 180°.

x + (x + 20) = 180  and

y + (y + 10) = 180.

Solving for x

x + (x + 20) = 180

x + x + 20 = 180

2x = 180 - 20

2x = 160

2x/2 = 160/2

x = 80°

Solving for y

y + (y + 10) = 180

y + y + 10 = 180

2y = 180 - 10

2y = 170

2y/2 = 170/2

y = 85°

The domain and range of the function is (-∞, ∞),  (-∞, 18]

A function is a rule that gives each element from the domain set to a single element from the range set. The range is the set of values that the function can take, whereas the domain is the set of values for which the function is defined.

Consider the function f(x) = x^2, for instance. As the function may be defined for any value of x, the domain of this function includes all real numbers. Nevertheless, as the function may only accept values larger than or equal to zero, the range is limited to non-negative real numbers.

a. The domain and range of the function f(x) = -2x² + 8x + 10 are;

domain = (-∞, ∞)

range = (-∞, 18]

b. The domain and range of the function is;

domain = [0, 12]

range = [0, 18]

c. The domain and range of the function are;

domain = (-∞, ∞)

range = [-7, ∞)

d. The domain and range of the function are;

domain = (-∞, ∞)

range = [1, ∞)

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As per the geometric sequence, the common ratio is -7.

Firstly, let's start with a brief introduction to what a sequence is. A sequence is simply a list of numbers that follow a certain pattern or rule. For example, the sequence 1, 3, 5, 7, 9 is a sequence of odd numbers.

Now, let's talk about a geometric sequence specifically.

Now, let's apply this to the sequence you were given: -3, 21, -192. To find the common ratio, we need to look at the ratio of any term to the previous term. For example, we can look at the ratio of the second term (21) to the first term (-3):

r = 21 / (-3) = -7

This means that the common ratio of the sequence is -7, since each term is found by multiplying the previous term by -7.

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Confidence intervals provide more information than hypothesis tests as they give an estimate of the parameter value as well as a range of plausible values, whereas hypothesis tests only give a decision about the null hypothesis.

To solve problems 3 and 4 in homework 2 by constructing confidence intervals about the parameters to be tested, rather than performing hypothesis testing, we need to take the following steps:

Step 1: Calculate the sample mean and sample standard deviation from the given data.

Step 2: Calculate the standard error (SE) using the formula: SE = σ / √n`,

where `σ` is the population standard deviation (if known), or the sample standard deviation (if population standard deviation is unknown)

and `n` is the sample size.

Step 3: Calculate the margin of error (ME) using the formula: `ME = z * SE`,

where `z` is the z-score corresponding to the desired level of confidence.

Step 4: Calculate the confidence interval (CI) using the formula: `CI = sample mean ± ME.

Step 5: Interpret the confidence interval in the context of the problem.

Statement: Do you get the same results as before.

No, we do not get the same results as before.

When we construct a confidence interval, we obtain a range of plausible values for the parameter with a certain level of confidence, whereas in hypothesis testing, we either reject or fail to reject the null hypothesis based on the sample data at a certain level of significance.

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Step-by-step explanation:

Without seeing the graph, it's difficult to determine the exact solution to the system of equations. However, the point of intersection between the two lines represents a solution that satisfies both equations. To find the x-coordinate of this point, you can use algebraic methods, such as substitution or elimination, to solve for the value of x.

The bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time

The bball3 dataset appears to take the form of panel data. Panel data is a type of longitudinal data where observations are made on the same individuals over time. This means that the dataset likely consists of multiple observations of a set of individuals, with the observations collected at different points in time. In a panel data set, each individual can be referred to as a ‘panel unit’.

Cross-sectional data, on the other hand, consists of observations that are collected only once, at a single point in time. This means that each observation consists of a snapshot of the population at a given moment, which is different from panel data where each observation may represent different points in time for the same individuals.

Time series data is a type of data that is collected over a period of time. It captures how a certain variable changes over time, and is often used for forecasting purposes. This is different from panel data, which captures information about the same individuals at different points in time.

In conclusion, the bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time. It is not cross-sectional or time series data.

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answer for number 14 is 1115

you mutliply 27 into 1 ×45 into 100

it is 100 because we are dealing with percentage

so you say (write in fraction form)

27÷1×45÷100

=1215÷100

you get the answer of 1115

so there were 1115 female butterflies

we can subtract the answer from the original number to get the number of male butterflies

1215-1115 =100 male butterflies

There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.

In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

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Total cost of racquet at Bob's Tennis Racquet Emporium is $192.60 with a 7% sales tax on the original price of $180.00. The price tag on a similar racquet at Tennis Pro, which offers a 10% discount, is $162.00 before tax.

To calculate the total cost of the tennis racquet at Bob's Tennis Racquet Emporium, we need to add the sales tax to the original price.

Sales tax = 7% of $180.00 = 0.07 x $180.00 = $12.60

Total cost = $180.00 + $12.60 = $192.60

Therefore, the total cost of the tennis racquet at Bob's Tennis Racquet Emporium is $192.60.

If Tennis Pro offers a before-tax price that is 10% less than Bob's store for a similar racquet, we can calculate the price tag as follows:

Price at Bob's store = $180.00

Discounted price at Tennis Pro = 10% less than $180.00 = 0.10 x $180.00 = $18.00 discount

Price at Tennis Pro = $180.00 - $18.00 = $162.00

Therefore, the price tag on the similar racquet at Tennis Pro is $162.00 before tax. The sales tax amount will depend on the applicable tax rate in the area where the store is located.

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The other diagonal of the rhombus is 4 cm.

The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.

We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:

20 = (10 × d₂)/2

Simplifying, we get:

20 = 5 d₂

Dividing both sides by 5, we get:

d₂ = 4

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According to the question, the exact value of side x in the Trina are  34.641016151377546in.

Value is an intangible concept that refers to the worth of something, whether it is tangible or intangible. It is based on the perceived benefits and costs associated with the thing in question. Value can be subjective, as different people may place different worth on the same item. Value can also be objective, as there may be a set market price for a certain item.

The exact value of side x in the triangle can be determined by using the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of a triangle.

Therefore, we can set up the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

x = 20in×(√(3)/1)

x = 20in×√(3)

x = 34.641016151377546in

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The exact value of side x in the Trina, according to the question, is 34.641016151377546in.

Where you cannot predict the value, you must be specific. An exact number is a value that can be determined with absolute precision. Counted quantities of objects or sure unit conversions are examples of exact numbers.

The term "approximate number" refers to a number that is close to the precise number, and there is always a difference among exact and approximate numbers. For instance, are exact integers because no approximation is required.

As a result, we can construct the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

Simplify the above equation,

x = 20in×(√(3)/1)

x = 20in×√(3)

The value of x is,

x = 34.641016151377546in

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The complete question is,

What is the exact value of side x in the Trina for below? 20in 30 degree and X? Determine the exact value of side x.

Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

What is division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Division is denoted by the symbol "÷" or "/", and it is usually expressed as a fraction or a quotient.

To solve this problem, we need to determine the amount of money represented by the shaded region. Here are the steps:

Assuming that each small square represents $0.01 and there are 143 shaded cells, the total amount of money represented by the shaded region is:

143 cells x $0.01/cell = $1.43

Now, we need to divide $1.43 evenly among Karla's three brothers to find the maximum number of pieces of candy each brother can buy.

$1.43 ÷ 3 = $0.476666...

Since we cannot buy fractional pieces of candy, we need to round down to the nearest whole number. Therefore, each of Karla's three brothers can buy a maximum of:

$0.47 ÷ $0.10/piece = 4 pieces of candy

So each of Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

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Answer: I believe the answer is 7

Step-by-step explanation:

To solve this I just divided 56 by 8, the answer then is 7. Hope this helps!!!

The number of feet of fabric will the individual need to make 11 blankets is 79.2 feet

To find out how many feet of fabric the individual will need to make 11 blankets, we can use the unitary method.

We know that the individual used 7.2 feet of fabric to make one blanket. So, to find out how much fabric is needed to make 11 blankets, we can set up a proportion

7.2 feet of fabric is needed for 1 blanket

x feet of fabric is needed for 11 blankets

We can solve for x by cross-multiplying and then dividing

7.2 × 11 = x

x = 79.2 feet

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The slope of the line of best fit in the scatterplot below can be determined using the formula for the slope of a line:
Slope = (y2-y1)/(x2-x1)

In this case, x1 = 3, y1 = 12, x2 = 6, y2 = 19. So, the slope of the line of best fit is (19 - 12) / (6 - 3), which equals 7/3 or 2.33.
The line of best fit is the line that best represents the data on a scatterplot. It is the line that is closest to all the data points in the graph. The slope of the line of best fit helps to indicate whether the data points are moving in a positive or negative direction. If the slope is positive, the data points are increasing, and if the slope is negative, the data points are decreasing.
A positive slope, like the one in this example, means that as x increases, y also increases. This means that in this case, as the x-values (3 and 6) increase, the y-values (12 and 19) also increase.

The slope of the line of best fit can also be used to make predictions about values of y, given values of x. For example, if x = 8, then y = 26, because the slope of the line of best fit is 2.33, and 8*2.33 = 19.8, which is approximately equal to 26.
Overall, the slope of the line of best fit on this scatterplot is 2.33, which is a positive number. This indicates that as the x-values increase, the y-values also increase, and it can also be used to make predictions about y-values, given x-values.

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Answer:

The Factor Theorem and Synthetic Division are not the same. The Factor Theorem states that if a polynomial f(x) has a root c, then x - c is a factor of f(x). Synthetic Division is a way of dividing a polynomial by a binomial.

Step-by-step explanation:

To use Synthetic Division, you first need to find the coefficients of the polynomial. Then, you set up the synthetic division table with the binomial on top and the coefficients of the polynomial on the bottom. Starting with the first coefficient, you multiply it by the first term of the binomial and write the product below the coefficient. Then, you add the two numbers below the product and write the sum below that. Continue until you reach the end of the binomial. The remainder at the bottom of the table is the remainder when f(x) is divided by x - c.

If the remainder is 0, then x - c is a factor of f(x).

Answer: 12

Step-by-step explanation: Just multiplied them

The sum of the deviations of the individual data elements from their mean is always equal to zero. Correct option is A.

This is because the deviation is defined as the difference between each data point and the mean of all the data points.

Since the mean is calculated as the sum of all the data points divided by the total number of data points, the positive deviations from the mean must be balanced out by the negative deviations from the mean. In other words, for every data point that is above the mean, there is a corresponding data point that is below the mean.

When we add up all the deviations from the mean, the positive deviations will cancel out the negative deviations, resulting in a sum of zero. This property of the sum of deviations from the mean is fundamental to many statistical concepts, such as variance and standard deviation.

Therefore, the correct answer to the question is (a) equal to zero, since the sum of the deviations from the mean is always zero.

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To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

A value or combination of values that satisfy an equation or system of equations are referred to as solutions in mathematics. For instance, if we substitute x = 2 into the equation, we get 2(2) + 3 = 7, which is a true statement, hence the answer to the equation 2x + 3 = 7 is x = 2. Similar to this, an equation system may have one or more solutions that simultaneously fulfil every equation in the system. Finding answers to equations or systems of equations is a key component of many branches of mathematics and has significant applications.

given

Find out how much pure alcohol is now contained in the 8% solution to start.

An 8% alcohol solution in 10 cm3 contains:

There are 0.8 cm3 of pure alcohol in 0.08 x 10 cm3.

Let's now calculate the amount of pure alcohol that has to be added to achieve an 80% solution using the alligation method.

We must add pure alcohol to the solution to raise the concentration from 8% to 100%. In order to connect 100% to 8% in the left column, we place 100% in the right column. There is a 92% discrepancy between these two percentages.

We put 80% in the middle column because we aim to arrive at an 80% solution. Between 80% and 100%, there is a 20% difference.

Now, we may construct the subsequent equation:

20/92 = x/10

After finding x, we obtain:

[tex]x = 2.17 cm^3[/tex]

To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

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Answer:

Step-by-step explanation:

E

The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.

A mathematical assertion that two expressions are equal is known as an equation. A typical equation has one or more variables, which are often denoted by letters and have a range of possible values. Equations are frequently used in a variety of fields to describe relationships between distinct numbers or to address issues. For instance, the equation x + 2 = 5 only has one variable, x. It denotes that the product of x and 2 equals 5.

given

We can represent 556 as a rectangle with length 556 and width 1, and 16 as a rectangle with length 16 and width 1 to calculate the quotient of 556 and 16 using an area model.

This is how it goes:

To start, we deduct 16 from 556 to obtain:

556 - 16 = 540

540 = 16 x 33 + 4

Finally, by multiplying the numerator and denominator of the fraction 33 4/16 by 4, we may express the quotient of 556 and 16 as a mixed number in the simplest form, which results in:

556 ÷ 16 = 33 4/16 = 33 1/4

The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.

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we need to buy at least 694 tickets to have a probability of winning at least 50%.

We can use the binomial distribution formula to solve this problem. Let X be the number of tickets we need to buy to have a probability of winning at least 50%. Then:

P(X ≥ 1) ≥ 0.5

This means that the probability of winning with at least one ticket is at least 50%. We can find this probability using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

The probability of not winning with any ticket is:

P(X = 0) = (999/1000)^n

where n is the number of tickets we buy. Therefore:

1 - (999/1000)^n ≥ 0.5

Simplifying this inequality, we get:

(999/1000)^n ≤ 0.5

Taking the logarithm of both sides, we get:

n log(999/1000) ≤ log(0.5)

n ≥ log(0.5) / log(999/1000)

n ≥ 693.15

Therefore, we need to buy at least 694 tickets to have a probability of winning at least 50%.

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