The effect of the transformation is a vertical srhink of scale factor 1/9.
What is the effect of the transformation to the graph of f(x)?For a function f(x), can define a vertical dilation of scale factor k as:
g(x) = k*f(x).
if k > 1, we have a stretch.if 0 < k < 1, we have a contraction.In this case the transformation is:
f(x) ---> (1/9)*f(x)
So we have a vertical dilation of scale factor k = 1/9, so we have a vertical contraction.
Then the effect that this will have in the graph is that it will contract/shrink it vertically.
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Write a recursive sequence that represents the sequence defined by the following explicit formula:
The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:
[tex]a_1 = -32[/tex][tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The first term and the common ratio for this problem is given as follows:
[tex]a_1 = -32, q = -\frac{1}{4}[/tex]
The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:
[tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]
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Which triangle could be drawn as it is described?
The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure 20° and 80°.
Triangle which can be drawn as per the measurements are,
An acute triangle with sides measuring 7, 4, 2.
In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.
According to the Pythagorean theorem.
7²< 4² + 2²
49 < 16 + 4
49 < 20
This is a contradiction, since 49 cannot be less than 20.
It is not possible to draw triangle.
An isosceles triangle with measures of angle 20° and 80°.
Sum of interior angles of a triangle is 180°
Here, third angle = 180° - ( 20° + 80° )
⇒Third angle = 80°
Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.
It forms a isosceles triangle.
An obtuse triangle with sides measuring 5, 10 and 15.
Side lengths 5, 10, and 15 do not form a triangle at all.
Since the sum of the two shorter sides is less than the longest side.
5 + 10 = 15
It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.
An scalene triangle with angle measuring 110° and 35°.
Sum of the interior angles is always 180°.
Measure of the third angle ,
180° - 110° - 35° = 35°
Three angles of the triangle measure 110°, 35°, and 35°.
It represents isosceles triangle.
Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.
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Maria wants to attend University of Bayou, a 4-year college. The
tuition is $15,300 per semester. Rounding the cost of each
semester to the nearest thousand, what can Maria estimate the
total tuition for all 4 years to be?
Maria can estimate the total tuition for all 4 years to be $122400
How to determine the tuition fee?
Tuition payments, usually known as tuition in American English and as tuition fees in Commonwealth English, are fees charged by education institutions for instruction or other services.
The given parameters are
Period of school = a 4-year college
Tuition fee per semester = The tuition is $15,300 per semester.
Number of semester = 2=4 = 8 semesters
Total cost = $15,300 per semester. * 8 = $122400
Therefore the cost of the tuition for 4 years is $122400
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The total amount Maria can estimate for the cost of a 4-year college program at the University of Bayou is $122,400
What is a college program?A college program consists of courses that are taken as part of an accredited course, which leads to the award of a degree.
The tuition per semester for the University of Bayou = $15,300
The number of semester in an academic year = Usually 2 semesters
The number of years Maria intends to spend in college = 4 years
The estimate of the total tuition, found using the basic arithmetic operations is therefore;
Tuition for a 4 year program = 15,300 × 2 × 4 = 122400
The total tuition Maria can estimate for 4 year of college is $122,400
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Find the polar coordinates of a point with Cartesian coordinates (x,y)=(−√2,−√2).
Answer: The correct answer is (2,5π/4).
Step-by-step explanation:
The correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((-√2)^2 + (-√2)^2)
= √(2 + 2)
= √4
= 2
θ = atan2(-√2, -√2)
= 5π/4 radians
So, the correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).
A certain virus infects one in every 300 people. A Test used to detect the virus in a person is positive 85% of the time if that prerson has the virus and 5% of the time if the person does not have the virus. This 5% result is called a false positive. Let "A" be the event the person is infected and "B" the event the person tests positive. Find the probability that a person has the virus given that they have tested positive find the P(A/B)= Round to nearest tenth of a % Don't include % sign.
The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045
We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:
P(A | B) = P(B | A) * P(A) / P(B)
where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.
To find P(B), we can use the law of total probability, which states that:
P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)
where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.
Substituting the values, we get:
P(B) = 0.85 * 1/300 + 0.05 * 299/300
= 0.059
Now we can plug in the values into Bayes' theorem:
P(A | B) = 0.85 * 1/300 / 0.059
= 0.0045 or 0.45%
Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).
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need help asap please
Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.
How to explain the strategies usedMary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.
Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.
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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.
15x^2 + x - 2 = (? -1) (? + 2)
3x, 5x
x, 15x
5x, 3x
15x, x
The correct terms in the expression are,
⇒ 3x and 5x
We have to given that;
The quadratic equation is,
⇒ 15x² + x - 2 = (? - 1) (? + 2)
Now, We can simplify as;
⇒ 15x² + x - 2
⇒ 15x² + 6x - 5x - 2
⇒ 3x (5x + 2) - 1 (5x + 2)
⇒ (3x - 1) (5x + 2)
Thus, The correct terms in the expression are,
⇒ 3x and 5x
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You are going on a long trip and want to calculate your fuel efficiency. When you start your trip your odometer read 106069 miles. At the end of your trip your odometer reads 106485 miles.
You started your trip with a full tank of gas. After the trip, you refill the tank with 13 gallons of gas.
What was your fuel efficiency for this trip, in miles per gallon?
Answer:32mi/gal
Step-by-step explanation:
106485 - 106069 = 416mi (the distance that you traveled)
416/13 = 32
32mi/gal
Arrange the steps in order to simplify the expression
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
QUICK I NEED HELP! ILL MARK BRAINLIEST IF CORRECT
Suppose you deposit $1000 in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 4 years?
b. How much will be in the account after 16 years?
c. How many years will it take for the account to contain $1,500?
d. How many years will it take for the account to contain $2,00?
Answer:
a. $1,240
b. $1,960
c. 9 years
d. 17 years
Step-by-step explanation:
For interest you multiply the percent with 1,000 and add the number you get for your answer. So 1,000 times 6% is 60. Each year the account earns $60 worth of interest. You multiply 60 by 4 and your result is 240. You add 240 to 1,000 and get your answer for a $1,240.
You repeat the same process for b. 16 times 60 is 960. You add 960 and 1,000 and your answer is $1,960.
So we know the account already has $1,000 so all that has to be done is to divide 500 by 60 and your result is 8.3. However you it is anual interest so you cannot but in a decimal so you round up to 9. Making it 9 years
Same process dividing 1,000 by 60 which gives you 16.6 rounding up to 17. Making it 17 years.
Ben has some goldfish in a fish tank. The ratio of orange goldfish to yellow goldfish is 3:5.
He has 6f orange goldfish. Write the number of yellow goldfish he has in terms of f.
Answer:
Step-by-step explanation:
If the ratio of orange goldfish to yellow goldfish is 3:5, then we can write:orange goldfish : yellow goldfish = 3 : 5We know that Ben has 6f orange goldfish. We can use this information to set up a proportion and solve for the number of yellow goldfish in terms of f:3/5 = 6f/yellow goldfishTo solve for yellow goldfish, we can cross-multiply:3 * yellow goldfish = 5 * 6fSimplifying:yellow goldfish = 30f/3 = 10fTherefore, Ben has 10f yellow goldfish in terms of f, given that he has 6f orange goldfish and the ratio of orange to yellow goldfish is 3:5.
Given: a || b
Find the missing angle measures in the diagram. Explain how you find each angle measure. (explain please)
The missing angles measures in the diagram above when calculated is given below:
<1 = 42°
<2 = 76°
<3 = 62°
<4 = 76°
How to calculate the missing angle measures?For <1:
The total angle on a straight line = 180°
That is: angles <1+62°+<4 = 180
<1 = 180-62+76
= 180-138
= 42°
For <4: 180= 62+42+<4
<4 = 180-104
= 76°
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An automobile purchased for use by the manager of a firm at a price of $32,500 is to be depreciated by using the straight-line method over 5 years. What will be the book value of the automobile at the end of 3 years? (Assume that the scrap value is $0.) $
The book value of the automobile at the end of 3 years is $13,000.
What is the book value?The straight-line method is method of depreciation that allocates the same depreciation expense each year.
Straight line depreciation expense = (Cost of asset - Salvage value) / useful life
($32,500 - 0) / 5 = $6,500
Total depreciation in 3 years = $6,500 x 3 = $19,500
Book value = cost of the automobile - total depreciation
$32,500 - $19,500 = $13,000
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Complete the equation that represents the relationship between p and a.
The equation that represents the relationship between p and a is a = p - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 0)/(7 - 6)
Slope (m) = 1/1
Slope (m) = 1.
At data point (6, 0) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 1(x - 6)
y = x - 6 ≡ a = p - 6
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question in the picture
1.) The average monthly income for Brianna would be = $1,850
2.) The average monthly expenses for Brianna would be =$3,145
3.) The total monthly cash flow = =$ −1,295
How to calculate the monthly income for Brianna?The monthly pay check after tax = $1600
The annual scholarship stipend = $3000
That is 3000/12 = $250
Therefore, the average monthly income = 1600+250 = $1,850.
The average monthly expenses = 700+120+75+140+25+110+100+300+250+(12000+1000+1500+800+600/12)
= 1820 + 15900/12
= 1820 + 1325
= $3,145
The monthly cash flow = 1850-3145 =$ −1,295
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Please help! Show your work.
The value of the variable x in the equation 6 / -4.5 = 8 / 4x is - 3 / 2.
How to solve equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's solve the equation.
The variable in the equation is x . A variable is a number represented with letter in an equation.
Therefore,
6 / -4.5 = 8 / 4x
cross multiply
6(4x) = -4.5(8)
24x = - 36
divide both sides of the equation by 24
Therefore,
x = -36 / 24
x = - 3 / 2
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Which pair shows equivalent expressions? A. 3(x+2)=3x+6 B. 3x+2x=x squared(3+2) C. 3x+2=3(x+2) D. -3(2+x)=-6x-3
Answer: A.
Step-by-step explanation: we just need to distribute and see that the only plausible answer is a because when distributed it equals 3x=6
Which number line shows the solutions to x+8 > 15? O A. B. O C. O D. -8-6-4-2 -8 -6 -4 -2 -8 -6 -4 2 4 6 8 4 -8 -6 -4 -2 0 2 4 8
Answer:
The correct number line that shows the solutions to x+8 > 15 is option B.
Step-by-step explanation:
The correct number line that shows the solutions to x+8 > 15 is option B.
On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.
Karissa wants to use the data to determine which brand is most absorbent. Based on the data collected at the beginning of the contest, enter the approximate number of paper towels needed to clean each square foot of the spill. Enter the number of Brand A paper towels needed per square foot in the first box. Enter the number of Brand B paper towels needed per square foot in the second box. Enter the number of Brand C paper towels needed per square foot in the third box.
Therefore, we need 17 towels of brand C to clean a single sq ft
How to solveBrand A:
we add up all the sq ft cleaned by brand a
0.75+1.50+2.25=4.5
and we add up all paper towels used in total
6+13+20=39
now
to clean 4.5 square ft, we need 39 towels. how many we need to clean a single square foot?
4.5 sq ft ___________39 towels
1 sq ft_____________A
and A= 1 sq ft * 39 towels / 4.5 sq ft
and that gives us 8.6 towels, so we need 9 towels to clan a square foot with the brand A
now we repeat this with bran b and c
brand B:
0.75+1.75+2=4.5 sq ft
9+22+25= 56 towels
4.5 sq ft________56 towels
1 sq ft__________B
B= 1 sq ft * 56 towels / 4.5 sq ft = 12.4
so we need 13 towels of brand B
at last
brand C:
1+1.75+2.5=5.25 sq ft
17+29+41= 87 towels
5.25 sq ft________87 towels
1 sq ft__________C
C= 1 sq ft * 87 towels / 5.25 sq ft = 16.57 towels
Therefore, we need 17 towels of brand C to clean a single sq ft
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Find the multiplicative inverse of
[tex] \frac{ - 4}{9} + ( \frac{2}{5} + \frac{3}{8} )[/tex]
Multiplicative inverse of given expression is 9/5.
The given expression,
-4/9 + (2/5 + 3/5)
Simplify it,
⇒ -4/9 + (2+3)/5
⇒ -4/9 + 5/5
⇒ -4/9 + 1
⇒ (-4 + 9)/9
⇒ 5/9
So its multiplicative inverse = 1/(5/9) = 9/5
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7(x-2) - 2(x-3)
expand and simplify
7(x-2) - 2(x-3)
= 7x - 14 - 2x + 6 // Distribute the coefficients
= 5x - 8 // Combine like terms and simplify
Therefore, 7(x-2) - 2(x-3) simplifies to 5x - 8.
Answer:
7(x-2) - 2(x-3) simplifies to 5x - 8.
Step-by-step explanation:
To expand and simplify 7(x-2) - 2(x-3), we can use the distributive property and simplify the resulting expression.
7(x-2) - 2(x-3) = 7x - 14 - 2x + 6
Combining like terms, we get:
= (7x - 2x) + (-14 + 6)
= 5x - 8
Therefore, 7(x-2) - 2(x-3) simplifies to 5x - 8.
the area of a circle is 2464 cm². Calculate the diameters to 2 significant figure
Answer:
56 cm
Step-by-step explanation:
have a good day God bless :)
which of the following representations show y as a function of x
The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.
What is a Function?A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.
The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.
In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.
The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.
The answer is: B.
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A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have red marks on the bottom.
Answer:
We can use the information provided to estimate the number of ducks that have red marks on the bottom.
If only 3 out of 50 people have won a small prize, then we can estimate that the probability of winning a small prize is 3/50 or 0.06. Since the person wins a small prize if there’s a red mark on the bottom of the duck, we can estimate that the proportion of ducks with red marks is also 0.06.
So, we can estimate the number of ducks with red marks as follows:
Number of ducks with red marks = 0.06 x 160
Number of ducks with red marks = 9.6
We can estimate that there are about 9 or 10 ducks with red marks on the bottom.
Which numbers are equivalent to 10 ÷ 5? Choose ALL the correct answers.
10
5
5
10
2
1
2
5
HELPPPP
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is feet more than the length of the shortest side. Find the dimensions if the perimeter is feet.
I got you, buddy!
Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.
The perimeter of the triangle is the sum of the three sides, so we have:
x + 2x + (x + y) = 60
Simplifying this equation, we get:
4x + y = 60
We also know that the area of a triangle is given by:
A = (1/2)bh
where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:
A = (1/2)xy
Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:
y = 60 - 4x
Substituting this into the equation for the area, we have:
A = (1/2)x(60 - 4x)
Simplifying and expanding, we get:
A = 30x - 2x^2
To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:
dA/dx = 30 - 4x = 0
Solving for x, we get:
x = 7.5
Substituting this back into the equation for y, we get:
y = 60 - 4x = 45
Therefore, the dimensions of the flower bed are:
shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet
What’s the equation and solution?
The equation for the rectangle is adding the interior angles:
x + x - 5 + 71 + y + 21 = 360°
Solving that for y, we will get:
2x + y + 87 = 360
How to find the equation?Remember that the sum of the interior angles of any figure with 4 sides must be 360°.
Then we can write an equation:
x + x - 5 + 71 + y + 21 = 360°
2x + y + 87 = 360
Solving it for y:
y = 273 - 2x
Now there is a clear problem in the diagram because the angle in the bottom left is clearly larger than 90°, but it says that the angle measures 71°, so there we have a problem.
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Given f(x)
, find g(x)
and h(x)
such that f(x)=g(h(x))
and neither g(x)
nor h(x)
is solely x.
f(x)=−square root of x+4 minus 3
The functions g(x) = -√x - 3 and h(x) = x + 4 meet the requirements, and f(x) = g(h(x)) is true for f(x) = -√(x+4) - 3.
We are given f(x) and we need to find functions g(x) and h(x) such that f(x) = g(h(x)). The given function is f(x) = -√(x+4) - 3.
To find g(x) and h(x), we can split the given function into two simpler functions. Let's first look at the inner function, which deals with the input of the square root. We can define h(x) as the function inside the square root, which is:
h(x) = x + 4
Now we need to find g(x) such that when h(x) is plugged into it, we get the original function f(x). Since we have the square root and a subtraction, we can define g(x) as:
g(x) = -√x - 3
Now let's verify if f(x) = g(h(x)):
g(h(x)) = g(x + 4) = -√(x + 4) - 3
As you can see, g(h(x)) = f(x), which confirms that the functions g(x) and h(x) we found satisfy the condition.
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What is a square of a binomial?
A square of a binomial is a polynomial expression that results from multiplying a binomial by itself. The result is a trinomial expression with three terms.
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of three fifths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(5.8, −3), B′(1.6, −1.5), C′(−1.6, 3), D′(2.5, 3)
A′(−12, 18), B′(−6, 6), C′(12, −6), D′(12, 12)
A′(2.4, −3.6), B′(1.2, −1.2), C′(−2.4, 1.26), D′(−2.4, −2.4)
A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4)
If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:
Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).
Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).
Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).
Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).
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