The angle of elevation of the femur is 71°.
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the femur.
Data given:
length of femur = 18 inches
elevated = 6.2 inches
Formula to calculate the angle of elevation:
Tangent of the angle of elevation = height of the object/distance from the object
tan Ф = 18/ 6.2
tan Ф = 2.903
Ф = [tex]tan^{-1}[/tex]( 2.903)
= 71°
Therefore the angle of elevation is 71°.
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X 2.3.PS-17
Question He
Peter says, "If you subtract 16 from my number and multiply the difference by -6, the result is -66." What is Peter's
number?
Peter's number is?
Peter's number is 27
Step-by-step explanation:
You would need to multiply -6 with 11 to get -66. 11+16=27 this 27-16=11 so 11×(-6)=-66.
Each of the 6 people in Mandy's family orders 2 tacos. Each taco costs $3. What
is the total cost of the tacos?
Answer:
$36
Step-by-step explanation:
Each of the 6 people in Mandy's family orders 2 tacos. Each taco costs $3. What is the total cost of the tacos?
$3 * 2 * 6 = $36
A rectangle yas area 3 square feet and with 1/2 foot. what is the length of the rectangle
Answer:
6ft
Step-by-step explanation:
3 divided by 1/2 = 6
How many time in one day will the number on a digital clock (only minute and hour), if added together, equal ix? Explain your anwer
The traditional division of a day into 24 hours of 60 minutes each, with each minute made up of 60 seconds.
What is a clock?A tool used to measure and indicate time is a clock, often known as a timepiece.
One of the earliest human creations, the clock satisfies the requirement to measure time intervals less than those found in natural units like the day, lunar month, and year.
Over the centuries, various physical mechanisms have been utilized to power devices.
A few clocks that predate the contemporary model and are based on natural movement include:
A sundial displays the location of a shadow on a flat surface to indicate the time. There are various duration timers; the hourglass is one well-known type. The two time-telling devices that may be the oldest are water clocks and sundials.
The development of led to a significant advancement.
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The cost of a movie ticket is \$ 8. 00$8. 00 for each adult and \$ 6. 00$6. 00 for each child. Assume you have \$ 40. 00$40. 00 to spend on tickets. Write an equation in standard form to represent the number of adult tickets, xx, and the number of children's tickets, yy, you can buy with your \$ 40. 00$40. 0.
Since an adult movie ticket costs $8 and a kid movie ticket costs $6, the equation for the given condition is 8x+6y=40.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
The cost of movie ticket for adult= $8
The cost of movie ticket for adult= $6
Total amount to spend= $40
Let x be the number of adult and y be the number of children,
8x+6y=40
The equation for the given condition is 8x+6y=40 as the cost of movie ticket for adult is $8 and for children, it is $6.
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Match each item with the correct unit price.
1. 78 cents each 20 for $1.56
2. 40 cents each 2 for one dollar
3. $1.05 each 5 at $3.90
4. 7.8 cents each $3.78 for 6
5. 63 cents each 1 for $1.58
1. 20 for $1.56 = A. 7.8 cents each
2. $3.78 for 6 =B. 63 cents each
3. For one dollar =C. 40 cents each
4. 5 at $3.90 = D. 78 cents each
5. for $1.58 = E. $1.05 each
1. 20 for $1.56
Since cost of 20 items = $1.56
So, cost of 1 item = 1.56/20
=$0.078
1 dollar = 100 cents
So, $0.078= 0.078 × 100
=7.8 cents.
2. $3.78 for 6
Since cost of 6 items = $3.78
So, cost of 1 item = 3.78/ 6
=$0.63
1 dollar = 100 cents
So, $0.63 = 0.63 × 100 =63 cents.
3. 2 1/2 for one dollar
Cost of 2 1/2 = 5/2 = $1
So, cost of 1 item = 1/5/2
= 2/5
1 dollar = 100 cents
So, $2/5 =2/5 × 100
=40 cents.
4. 5 at $3.90
Since cost of 5 items = $3.90
So, cost of 1 item = 3.90/5
=$0.78
1 dollar = 100 cents
So, $0.78 = 0.78 × 100
=78 cents.
5. 1 1/2 for $1.58
Cost of 1 1/2 = $1.58
So, cost of 1 item = 1.58/3/2
= 1.05
Thus,
1. 20 for $1.56 =A. 7.8 cents each
2. $3.78 for 6=B. 63 cents each
3. or one dollar =C. 40 cents each
4. 5 at $3.90 = D. 78 cents each
5. for $1.58 = E. $1.05 each
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calculate 1001 base two +1011 base two
question 7 a restaurant gathers data about a new dish by providing free samples to parties of six or more diners. what does this scenario describe? 1 point sampling bias geographically limited sampling unbiased sampling random sampling
The scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.
What is sampling bias?
Sampling bias occurs when some members of a population are systematically more likely than others to be chosen for a sample. In the medical world, this is known as ascertainment bias. Because it threatens external validity, specifically population validity, sampling bias reduces the generalizability of findings.
Sampling bias occurs when some people in a community being surveyed are purposefully placed to be chosen or not chosen over others. If a sample process consistently favors some results over others, it is said to be biased. Ascertainment bias particularly in biological areas)/ and systematic bias are other terms for sampling bias. Bias can be intentional, but it is frequently unintentional.
Hence, the scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.
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A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are
C(x) = 75,000 + 60x and p(x) = 300 - x/30, 0 ≤ x ≤ 9000.
A) Find the maximum revenue.
B) Find the maximum profit, the productionlevel that will realize the maximum profit, and the price the company should charge for each television set.
C) If the government decides to tax the company $5 for each set it produces, how many sets should the company manufacture each month to maximize its profit What is the maximum profit What should the company charge for each set?
A) The maximum revenue is $__________ .
B) The maximum profit is $____________ when __________ sets are manufactured and sold for $________ each.
C) When each set is taxed ate $5 , the maximum profit is $________ when ______ sets are manufactured and sold for $__________ each.
A) The maximum revenue is 450000$
B) The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
C) When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
A)p(x)=300−(x/20),
revenue R(x)=p*x
revenue R(x)=300x -(x2/20)
for maximum revenue dR/dx =0 ,
=>300-(2x/20)=0
=>x/10=300
=>x=3000
maximum revenue = R(3000)=300*3000 -(30002/20)
maximum revenue = R(3000)=450000$
B) profit =revenue -cost
profit P(x)=300x -(x2/20)-72000-60x
profit P(x)=240x -(x2/20)-72000
for maximum cost dP/dx =0
240 -(2x/20)=0
x=240*10
x=2400
p(2400)=300−(2400/20)=180
profit P(2400)=240*2400 -(24002/20)-72000 =216000
The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each
c)
profit =revenue -cost -tax
profit P(x)=300x -(x2/20)-72000-60x-55x
profit P(x)=185x -(x2/20)-72000
for maximum cost dP/dx =0
185-(2x/20)=0
x=185*10
x=1850
p(1850)=300−(1850/20)=207.5
profit P(1850)=185*1850 -(18502/20)-72000
profit P(1850)=99125$
When each set is taxed at $55, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.
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identify the most appropriate test to use for the following situation: a national computer retailer believes that the average sales are greater for salespersons with a college degree. a random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year, while 17 salespersons without a college degree averaged $3301 in weekly sales. the standard deviations were $468 and $642 respectively. is there evidence to support the retailer's belief?
99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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what is 11 feet 7 inches plus 10 feet plus 14 feet and 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches
After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.
Given that,
We have to find what is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.
We know that,
1 feet is equal to 12 inches.
So,
We can write as
11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.
11f 7in+ 14f 6in +35.5in+ 30in + 6f 10in
11(12)+7in+14(12)+6+35.5+30+6(12)+10
132+7+168+6+35.5+30+72+10
460.5
Therefore, After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.
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A movie theater has a seating capacity of 159. The theater charges $5.00 for children, $7.00 for students,
and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was S
1140, How many children, students, and adults attended?
Answer:12
Step-by-step explanation:
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let x represent the number
of slushies sold.
a. Write a linear function for cost.
C(x) =
Write a linear function for revenue.
R(x)=
c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——-
• Write a sentence that explains the meaning of the point in the context of the problem.
D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ———
Write a sentence that explains the meaning of the point in the context of the problem?
e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.
If the students sell 50 slushies, do they make——- a profit? Because——-
F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.
G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.
The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
What is a function?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable
solution:
The linear function:
C(x) = 1.25x + 500
For revenue function:
R(x) = 3.50x
R(50) = 3.50(50)
= $175
Using the C(x) and revenue function we can find the number of slushies and profit.
Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
Hence the linear and revenue functions are C(x) = 1.25x + 500 and R(x) = 3.50x
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You and a friend start running from the same location. Your distance d (in miles) after t minutes is d(t) = ⅕t. Your friend starts running 10 minutes after you. Your friend's distance f is given by the function f(t) = d(t - 10). Describe the transformation from the graph of d to the graph of f.
Answer: 23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
Enter the numerator and denominator of a fraction in simplest form that is equivalent to 0. 941941.
Answer:
The answer is 941/1000.
Step-by-step explanation:
The simplified decimal is 0.941 and the 1 is in the thousandth place.
Hope this helped!
if i don't get this right i fail
The value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A circle:
Applying intersecting secants theorem:
4(4 + x) = 3(3 + 5)
16 + 4x = 24
4x = 8
x = 2
In the second circle:
9(4x) = 8(4x+2)
After solving we get:
x = 4
Thus, the value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.
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explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet. find the mean and variance of the areas produced by these explosive devices.
The mean and the variance of the areas produced by these explosive devices is 314
Variance:
In statistics, variance refers a measure of dispersion that takes into account the spread of all data points in a data set.
Given,
Here explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet.
Now, we need to find the mean and variance of the areas produced by these explosive devices.
In order to find the means and variance we have to use the formula ,
A = πr²
Here the value of r is 10,
Then the value of A is calculated as,
=> A = π(10)²
=> A = π x 100
We know that the value of π = 3.14, then the value of A is,
=> A = 3.14 x 100
=> A = 314.
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An airplane that travels 550miles an hour is still Air encounters a 50 mph headwind . How long will it take the plane to travel 850 miles into the wind ?
Answer:
It will take the plane 11 mph to travel 850 miles
suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise. is the student's conclusion appropriate?
The student's conclusion is not appropriate or no, because there were not enough measurements to use standard deviation.
Given:
suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise.
standard deviation:
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
To find standard deviation :
σ = x - μ / z
But here sample mean and proportion , z score not given so there are not enough measurements to use standard deviation.
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Xavier downloaded 40 songs last week including 14 jazz songs . what percent of Xavier's downloads were jazz songs
Answer:
35%
Step-by-step explanation:
Xavier downloaded 40 songs last week,
14 of them were jazz songs.
Therefore, [tex]\frac{14}{40}[/tex] of Xavier's downloads were jazz songs.
In order to convert it into a percentage, we need to multiply 100 to the fraction.
We get [tex]\frac{1400}{40}[/tex], which is equal to 35%.
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what is exact value of sin ø
Answer:
Step-by-step explanation:
Answer:
(d) -(√2)/2
Step-by-step explanation:
You want the exact value of the sine of an angle when its terminal side intersects the unit circle at (√2/2, -√2/2).
SineThe coordinates of the point where the terminal side of angle θ intersects the unit circle are ...
(cos(θ), sin(θ))
Comparing this to the given point, we find that ...
sin(θ) = -√2/2
a study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86. 1. state the decision rule for 0.05 significance level: h0: rho ≤ 0; h1: rho > 0 (round your answer to 3 decimal places.) 2. compute the value of the test statistic. (round your answer to 2 decimal places.) 3. can we conclude that the correlation in the population is greater than zero? use the 0.05 significance level.
The decision rule is reject H(0) if t>1.714, test statistic t is 7.157 and Yes, we can conclude that the correlation in the population is greater than zero.
In the given question,
A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86.
n=20, r = 0.86
The decision rule for α=0.05 significance level:
H(0): P ≤ 0
H(1): P > 0
Degree of freedom(df) = n-2
Degree of freedom(df) = 20-2
Degree of freedom(df) = 18
This is the right tailed test using the t table.
Critical Value: [tex]t_{\alpha /2}[/tex], df = [tex]t_{\alpha /2}[/tex] = 1.714
(a) The decision rule is reject H(0) if t>1.714.
(b) Test statistic is t
t= r√(n−2)/√(1–r^2)
t= 0.86*√(20 -2)/√(1-(0.86)^2)
t= 0.86*√18/√(1-0.7396)
t= 0.86*4.243/√0.2604
t= 3.65/0.51
t= 7.157
Test statistic = 7.157
(c) We have to conclude that the correlation in the population is greater than zero.
Yes, we can conclude that the correlation in the population is greater than zero.
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what is the rate of change for y=2x+100
Answer: rate of change = 2
Step-by-step explanation:
let m be the number of five-element subsets that can be chosen from the set of the first 14 natural numbers so that at least two of the five numbers are consecutive. find the remainder when m is divided by 1000.
There are 123 different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.
Probability: The branch of mathematics known as probability deals with numerical expressions of the probability that an event will occur, or the probability that a statement will be true.
The probability of an event is a number between 0 and 1, with approximately 0 meaning improbability and 1 meaning certainty.
The probability of an event occurring increases with its probability. A simple example is tossing a fair (fair) coin.
Both outcomes (heads and tails) have equal probability, the coin is fair, heads are more likely than tails, there are no other possible outcomes, and either outcome has half the probability.
According to our question:
Let n be the maximum number of subsets of 5 elements that can be chosen from the first 14 natural numbers,
where at least 2 of the 5 digits are consecutive.
We created a block of two consecutive numbers ((1,2), (2,3), (13,14), etc.).
Now you can select this block in 13 different ways. You have to choose 3 numbers from the remaining 12 numbers.
So, from the multiplication principle, we know that we have 13 × (123).
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two cars leave towns kilometers apart at the same time and travel toward each other. one car's rate is kilometers per hour less than the other's. if they meet in hours, what is the rate of the slower car?
The rate of the slower car is 152 km/hr.
Given:
two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours.
Let x be the rate of slower car.
We have two cars heading towards each other. They start 340 km apart and meet up 2 hours later. This means that they are traveling:
340 / 2 = 170 km/hr towards each other.
If the two cars were traveling the same speed, they'd both be going:
170 / 2 = 85 km/hr
We know that one car is traveling 18 km/hr faster than the other car. One way we can account for this is to ± 9 km/hr to the average speed:
85 ± 9 = 94 , 76 km/hr
rate of slower car x = 84 - 9 * 2
x = 76 * 2 km/hr
= 152 km/hr
Therefore The rate of the slower car is 152 km/hr.
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Full question:
two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours, what is the rate of the slower car?
Which system of equations is equivalent to this system?5x=10=3(x+y) and x+7=3x+y
The system of equations is equivalent to this system is 2x = 3y - 10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the equation as;
5x + 10 = 3(x+y)
x+7=3x+y
Solving the equation as;
5x + 10 = 3(x+y)
5x + 10 = 3x+ 3y
combine the like terms;
2x = 3y - 10
The system of equations is equivalent to this system is 2x = 3y - 10
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Regan is making a square garden in her back yard with an area of 25ft² What factors could be the length and width of her garden
The required length and width of the square garden is 5ft.
Given that,
Regan is making a square garden in her backyard with an area of 25ft² length and width of the garden is to be determined.
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
According to the question, l = w
Area of the garden = 25
l × w = 25
l × l = 25
l = 5
Thus, the required length and width of the square garden is 5ft.
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m/4 = 77°, m/8 = 4x + 57
Given that (-2,3) is on the graph of y=f(x), find a point that must be on the graph of y=f(2x+1)+3. Express your answer as an ordered pair (a,b) where a and b are real numbers.
Answer for 100 points.
The ordered pair that is on the function y=f(2x+1)+3 is (-3/2, 6)
Which ordered pair is on the function y=f(2x+1)+3?
Here we know that for the function:
y = f(x)
And we know that the point (-2, 3) belongs to the function, this means that:
f(-2)= 3
Now we want to find a point on the function:
f(2x + 1) + 3
If we find x such that:
2x + 1 = -2
2x = -3
x = -3/2
Now we can evaluate the function in that value of x to get:
y = f(2*-3/2 + 1) + 3
y = f(-2) + 3
y = 3 + 3
y = 6
Then we have the point (-3/2, 6) on the function.
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use the appropriate normal distribution to approximate the resulting binomial distributions. a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. a random sample of 35 customers is made. if the store owner's claim is correct, what is the probability that fewer than 22 customers in the sample buy coffee during their visit on that certain day of the week? a) 0.7764 b) 0.7967 c) 0.7224 d) 0.8413 e) 0.8238 f) none of the above.
The probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.
What is a normal approximation to the binomial?
When we utilize a continuous distribution (the normal distribution) to approximate a discrete distribution, we use the normal approximation to the binomial (the binomial distribution). The Central Limit Theorem states that if the sample size is high enough, the sampling distribution of the sample means approximates normality.
In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Given, 55% of the customers buy coffee, p = 0.55
Sample of 35 customers, n = 35
mean [tex]\mu[/tex] = np = 35*0.55 = 19.25
standard deviation, [tex]\sigma = \sqrt{np(1-p)}[/tex] = [tex]\sqrt{35*0.55*0.45}[/tex] = 2.94
So, the probability that fewer than 23 customers in the sample buy coffee is
P(X < 22 - 0.5) = P(X < 21.5)
= [tex]P(\frac{X-\mu}{\sigma} < \frac{21.5-19.25}{2.94})[/tex]
= P(Z<0.765) = 0.7764
Hence, the probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.
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