The next two terms of the arithmetic sequence are 14 and 12.75, the value -18.5 is the 30th term in the sequence.
The Arithmetic sequence given to us is 17.75, 16.5, 15.25,.... An arithmetic sequence is the one in which the terms increase or decrease with the constant value.
We can find this common difference by finding the difference of any two constant terms, so, in this sequence the common difference in -1.25.
1. The next two terms of the sequence will be (15-1) and (14-1).
So, the next two terms are 14 and 12.75.
2. The nth terms of the sequence is given by the formula,
aₙ = a₁ + (n-1)d, d is the common difference, n is the nth term, a₁ is the first term and aₙ is the nth term.
Now, putting aₙ = 18,
-18.5 = 17.75 + (n-1)(-1.25)
n = 30
So, the 30th term is -18.5 in the sequence.
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Find an equation of the line with gradient 1/3 and passes through the point (5,-1)
Answer:
y = x/3 - 8/3 (OR) 3y = x - 8
Both of the above solutions are the same
Step-by-step explanation:
Using the form 'y=mx+c',
Since m = 1/3,
y = 1/3x + c
Substituting (5, -1) into the above equation:
-1 = 5/3 + c
c = -1 - 5/3
= -8/3
Hence,
y = x/3 - 8/3
(which is also the same as)
3y = x - 8
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Salim walked 1 1/3 miles to school and then 2 1/2
miles to work after school. How far did he walk in all?
In response to the query, we can state that Salim thereby covered a total fraction distance of about 3.83 miles.
what is fraction?To represent a whole, any number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. They can all be expressed as simple fractions as integers. In the numerator or denominator of a complex fraction is a fraction. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.
Salim therefore walked a total of:
4/3 Plus 5/2 miles
We must identify a common denominator in order to add these fractions:
Six is the least frequent multiple of 3 and 2.
We may therefore rephrase the following fractions with denominators of 6:
4/3 = (4/3) x (2/2) = 8/6
5/2 = (5/2) x (3/3) = 15/6
We can now combine the fractions:
8/6 + 15/6 = 23/6
Salim covered a distance of 23/6 miles in all.
This fraction can be simplified by dividing both the numerator and denominator by their largest common factor, which is 1:
3.83 miles, or 23/6 miles (rounded to two decimal places)
Salim thereby covered a total distance of about 3.83 miles.
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I need some help with it
The Answer is approximately equal to 942.48 or 300π
(π=pi)
Solve for a.
18= a/2
Use this tax table to find how much tax you need to pay on a taxable income of $25,000.
If taxable income is over-- But not over-- The tax is:
$0 $7,825 10 percent of the amount over $0
$7,825 $31,850 $782. 50 plus 15 percent of the amount over 7,825
$31,850 $77,100 $4,386. 25 plus 25 percent of the amount over 31,850
$77,100 $160,850 $15,698. 75 plus 28 percent of the amount over 77,100
$160,850 $349,700 $39,148. 75 plus 33 percent of the amount over 160,850
$349,700 no limit $101,469. 25 plus 35 percent of the amount over 349,700
On a taxable income of $25,000, you must pay $3,358.75 in taxes.
To find how much tax you need to pay on a taxable income of $25,000, you will need to use the tax table given.
Since $25,000 falls in the third row of the table, which is for taxable income over $7,825 but not over $31,850, we will need to use the formula for this row:
Tax = $782.50 + 15% of the amount over $7,825
To calculate the tax, we need to first find the amount over $7,825, which is:
25,000 - 7,825 = 17,175
Now we can substitute this into the formula to get:
Tax = 782.50 + 0.15 x 17,175
Tax = 782.50 + 2,576.25
Tax = 3,358.75
Therefore, the amount of tax you need to pay on a taxable income of $25,000 is $3,358.75.
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I Need help with this
During gym class, there were 7 teams in the four-square match. Each team was made of 5 third-graders.
Which shows how many students were in the four-square match in all?
1. 5 times 5
2. 5 minus 7
3. 7 times 5
4. 7 plus 5
7 times 5 shows the number of students in the four-square match. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
It is stated that the four fundamental operations, often known as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.
We are given that there were 7 teams in the four-square match and each team was made of 5 third-graders.
Now, in order to find the total students, we will use the multiplication operation.
From this, we get 7 times 5 which represents the total students.
Hence, 7 times 5 shows the number of students in the four-square match.
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i dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:
13 matches
Step-by-step explanation:
Notice 1st have 4 matches
then 2nd have 7 matches (since one is shared), this is 8-1
then 3rd have 10 matches (since two are shared) this is 12-2
Notice the pattern 4 matches per square minus one per aditional square from the first.
This give an equation
4n-1(n-1)= 3n+1
lets check
For n=1 matches= 3(1)+1=4
For n=2 matches= 3(2)+1=7
For n=3 matches= 3(3)+1=10
It works.
so
For n=4 matches= 3(4)+1=13
Consider drawing four cards without replacement from a standard deck of cards. What is the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts?
Group of answer choices:
13/52 or 1/4
10/49
10/52 or 5/26
13/49
The conditional probability of drawing a heart on the fourth draw given that the first three cards are not hearts is 13/49.. The correct answer is D.
After drawing three cards without replacement, there are 52 - 3 = 49 cards remaining in the deck, of which 13 are hearts and 36 are not hearts.
If the first three cards are not hearts, then there are 36 cards remaining in the deck for the fourth draw, of which 13 are hearts and 23 are not hearts.
The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes' theorem:
P(heart on 4th draw | first 3 not hearts) = P(heart on 4th draw and first 3 not hearts) / P(first 3 not hearts)
The probability of drawing a heart on the fourth draw and the first three not being hearts is:
P(heart on 4th draw and first 3 not hearts) = (36/52) * (35/51) * (34/50) * (13/49) = 0.0334
The probability of the first three cards not being hearts is:
P(first 3 not hearts) = (36/52) * (35/51) * (34/50) = 0.5764
Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:
P(heart on 4th draw | first 3 not hearts) = 0.0334 / 0.5764 ≈ 0.058 or approximately 5.8%.
Therefore, the answer is 13/49. The correct answer is D.
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What is the equation for part a?
The rectangle shown has a perimeter of 52 inches.
a. Write an equation describing the possible values of x and y.
Using the perimeter formula of a rectangle we can write an equation describing the values of x and y is as follows:
2y + 2x = 52 inches
Define perimeter?The perimeter of a rectangle is the total length of its edges. It is expressed in linear units like centimetres, inches, and the like and can be taken to mean the total measurement of the rectangle's length and width. For instance, you may rapidly calculate how much ribbon you'd need if you needed to decorate the edge of your rectangular notebook. Similar to how calculating the perimeter will help you determine how much wire you'll need to erect a fence around your garden.
The formula P = 2(l + w), where l is the length and w is the width, determines the perimeter of a rectangle. Since we are aware that this rectangle's perimeter is 52 inches, we can write the following equation: 2l + 2w = 52 inches.
We can express the equation in terms of x and y to discover the potential values for x and y. We may substitute the width (x) and the length (y) into the equation to get 52 inches: 2y + 2x.
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suppose we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample. approximately how many of those intervals will contain the population mean?
There are approximately 2425 of those intervals that will contain the population means.
What is a confidence interval?A confidence interval is a range of values that includes a parameter estimate with a certain degree of certainty. A confidence interval is a measure of uncertainty about an estimation procedure, rather than a statement about a parameter. A confidence interval is a specific value or a range of values in statistics that is used to estimate population characteristics.
This is because a 97% confidence interval means that if we were to repeat the sampling process many times, about 97% of the resulting intervals would contain the population mean. In other words, we would expect 97% of the intervals to be "correct" in the long run, while about 3% of them would not contain the population mean.
Therefore, out of the 2500 intervals we compute, we would expect approximately 0.97 x 2500 = 2425 intervals to contain the population mean, and about 0.03 x 2500 = 75 intervals not to contain the population mean. However, it's important to note that the actual number of intervals that contain the population means may vary from this expected value due to random sampling variability.
Where, [tex]\[\bar{x}\][/tex] is the sample mean
[tex]\[\frac{s}{\sqrt{n}}\][/tex] is the standard error of the mean
zα/2 is the z-score that covers α/2 in the tails of a normal distribution.
As we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample, the proportion of the sample will contain the population means.
Therefore, the number of intervals that will contain the population mean is approximately 2425.
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A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses 676 ft 676 ft 338 ft 338 ft 52 ft 52 ft 26 ft
The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.
To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:
63,679 = πr²(30)
Dividing both sides by 30π gives:
r² = 676
Taking the square root of both sides gives:
r ≈ 26
Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.
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Complete Question:
A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses
a) 676 ft
b) 676 ft
c)338 ft
d) 338 ft
e) 52 ft
f) 26 ft.
Surface area of the prism
Answer: 450
Step-by-step explanation:
9x10x5
unit 7 right triangle and trigonometry quiz 7-2
Yes, trigonometry only works on the right angled triangles.
Explain about the Right triangle and trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry.
A triangle with one right angle is referred to as a right triangle as well as right-angled triangle. Trigonometry's foundation is the relationship between a right triangle's sides and angles.The area of mathematics called trigonometry deals with calculating triangles' unknowable sides and angles.There are numerous uses for trigonometry in both engineering and science. We will just provide a couple of instances from surveying as well as navigation in this section.Thus, the right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.
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The complete question is-
Right triangle and trigonometry:
Does trigonometry work on right triangles?
Pls help help Algebra1
Answer:
(x-1)(x+6)
Step-by-step explanation:
5.8 Khomo and Peter bought a house for R575 000 as an investment. Khomo payed R245 000 and Peter payed the rest. They sold the house 5 years later and made a profit of R234 500.if they share the profit in the same ratio as their respective investments,how much profit will peter recieve
Answer:
133,380
Step-by-step explanation:
Cost of house 575,000
Khomo paid 245,000
Peter paid 575,000 - 245,000 = 330,000
Ratio of Khomo to Peter = 245,000 : 330,000 = 49:66
Profit made = 234,500
Khomos share is 49/ 115 x 234,00 = 0.43 x 234,000 = 100,620
Peters share is 66/115 x 234,000 = =0.57 x 234,000 = 133,380
Write the first 5 terms of a sequence whose general term, An, is given as an =-9n-9
The first 5 terms of the sequence, whose general term is an = -9n - 9, would be the following: -18, -27, -36, -45, -54.
How to Calculate the Terms of a Sequence?In mathematics, a sequence is an ordered list of numbers, called terms, that follow a particular pattern or rule. Each term in a sequence is identified by its position in the sequence, which is usually represented by an integer index or subscript.
To find the first 5 terms of the sequence with the general term an = -9n - 9, we can simply substitute the values of n from 1 to 5 into the formula and simplify:
a1 = -9(1) - 9 = -18
a2 = -9(2) - 9 = -27
a3 = -9(3) - 9 = -36
a4 = -9(4) - 9 = -45
a5 = -9(5) - 9 = -54
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A car dealership uses the linear model y= -1100x + 25,000 to predict the depreciation of car values as time progresses. If x is how old the vehicle is in years and y is the current value of the vehicle,
what will the value of the vehicle be 5 years after purchase?
The value of the vehicle 5 years after purchase will be $12,500. After we predict the depreciation of car values as time progresses.
Due to use, wear, and tear, or becoming obsolete, an asset loses value over time. Depreciation is the measurement of this decrease.
Using the given linear model y = -1100x + 25,000, we can substitute x = 5 (since we want to find the value after 5 years of purchase) and solve for y:
y = -1100(5) + 25,000
y = -5500 + 25,000
y = 19,500
Therefore, the value of the vehicle 5 years after purchase will be $19,500.
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Jessica earns 52 dollars per week working part- time at a book store she makes one dollar more for each book sells the amount,A(in dollars), that Jessica earns in a week if she sells b books is given by the following
The amount that Jessica will earns if she sells 34 books is 86 dollars.
How much will Jessica earns?An earning refers to the income that a person get from wages and salaries, security and other government benefits, dividends and interest, business ownership, other sources etc.
Our Equation to solve for earnings is:
A = 52 + (1)B
A = 52 + B
A(34) = 52 +34
A(34) = $86
Therefore, the total earned in one week if she sold 34 books is $86.
Missing words' Write an equation relating A to B. Then use this equation to find the amount of money Lena earns if she sells 34 books. Equation: Amount Jessica earns is she sells 34 books: ____ dollars".
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Find the sum and product of the complex numbers \( 2-3 i \) and \( -2+6 i \). The sum is (Type your answer in the form \( a+b i \).) The product is (Type your answer in the form \( \mathrm{a}+\mathrm{
The given complex numbers are 2 - 3i and -2 + 6i. We need to find the sum and product of the given complex numbers.
Sum of the complex numbers = (2 - 3i) + (-2 + 6i)
= 2 - 2 + (-3i + 6i)
= 4i
Therefore, the sum of the given complex numbers is 4i.
Now, let's find the product of the given complex numbers.
Product of the complex numbers = (2 - 3i) (-2 + 6i)
= -4 + 12i + 6i - 18i^2
= -4 + 18i + 18 (as i^2 = -1)
= 14 + 18i
Therefore, the product of the given complex numbers is 14 + 18i.
Hence, the sum of the given complex numbers is 4i and the product of the given complex numbers is 14 + 18i.
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Deandre wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 33 ft from the tree, and Deandre is standing 10.2 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
House Loan
Cost: $450,000
Length of Loan: 30 Years
Simple Interest Rate: 6.00%
Yearly Taxes: $2,000
Yearly Insurance: $1,500
What are your Monthly Payments with taxes & insurance:
Step-by-step explanation:
Your monthly payments with taxes and insurance included would be $2,903.71. This is calculated by taking the loan amount of $450,000 and multiplying it by the simple interest rate of 6.00%. The result is $27,000, which is then divided by the length of the loan, 30 years. This gives you
the principal and interest portion of your monthly payment, which is $2,033.33. To that, you add your yearly taxes of $2,000 and insurance of $1,500, divided by 12 months, to get an additional $416.67 and $125, respectively. Adding these two numbers together gives you your total monthly payment of $2,903.71.
A couple has $5,000 to invest and has to choose between three investment options.
• Option A: 2.25% interest applied each quarter
• Option B: 3% interest applied every 4 months
• Option C: 4.5% interest applied twice each year
If they plan on no deposits and no withdrawals for 5 years, which option will give them the largest
balance after 5 years? Use a mathematical model for each option to explain your choice. Share the
value of each investment.
Make sure you use the formula from the lesson for each option then compare. As an investment, you
want the option with the most money!
nt
A = P(1 +r )"nt
—
n
Is 14x + 2 equivalent to 16x?
Answer:
No
Step-by-step explanation:
14x + 2 ≠ 16x
Because 2 doesn't have an x variable, it can't be added with 14x!
13. (6 pts) Jasmine has a cube with an edge length of 4 inches. How would the volume of the cube change if the edge length were doubled?
A) The volume is multiplied by 2
B) The volume is multiplied by 6.
C) The volume is multiplied by 4.
D) The volume is multiplied by 8.
Answer: The volume of a cube is calculated by multiplying the edge length by itself three times, or V = l^3.
If the edge length of Jasmine's cube is doubled, the new edge length will be 4 inches x 2 = 8 inches.
Thus, the new volume of the cube would be V = 8^3 = 512 cubic inches.
Comparing this new volume to the original volume of the cube, V = 4^3 = 64 cubic inches, we can see that the new volume is multiplied by 8.
Therefore, the correct answer is D) The volume is multiplied by 8.
Step-by-step explanation:
A plane can fly 340 mph in still air. If it can fly 200 miles downwind in the same amount of time it can fly 140 miles upwind, find the velocity of the wind.
By using the speed fοrmula, the velοcity οf the wind is apprοximately 66.23 mph.
What is speed?Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn. Mathematically, speed is calculated as fοllοws:
speed = distance/time
where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.
Let's assume that the speed οf the wind is represented by the variable "v" (in mph). When the plane flies dοwnwind, the speed οf the plane relative tο the grοund is the sum οf its airspeed and the wind speed, οr (340 + v) mph. Similarly, when the plane flies upwind, the speed οf the plane relative tο the grοund is the difference between its airspeed and the wind speed, οr (340 - v) mph.
Nοw, lets use the fοrmula:
time = distance / speed
tο set up twο equatiοns and sοlve fοr the wind speed "v".
First, fοr the dοwnwind flight:
time = distance / speed
200 / (340 + v) = t
Secοnd, fοr the upwind flight:
time = distance / speed
140 / (340 - v) = t
Since the time taken fοr bοth flights is the same, we can equate the twο equatiοns:
200 / (340 + v) = 140 / (340 - v)
Nοw, we can sοlve fοr "v":
200(340 - v) = 140(340 + v)
68,000 - 200v = 47,600 + 140v
308v = 20,400
v ≈ 66.23
Therefοre, the velοcity οf the wind is apprοximately 66.23 mph.
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In the figure below, quadrilateral UVWX is a parallelogram.
Part a) What are the values of p, UV, and VW?
Part b) What property of a parallelogram did you use to solve?
For the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
What is parallelogram and its properties?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
The opposing sides are equal and parallel. Angles on either side are equal. The subsequent or neighbouring angles are additional. All of the angles will be at right angles if any one of them is a right angle.
We know that the opposite sides of a parallelogram are parallel and equal thus,
8p + 6 = 9p – 2
6 + 2 = 9p – 8p
8 = p
Now, the value of side is:
UV = 8(8) + 6 = 70
The value of side VW is:
VW = 5(8) – 6 = 34
Hence, for the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
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Geometry: Find the unknown lengths of these isosceles right triangles (ASAP!!)
22=4 square root 2
Step-by-step explanation:
Using Pythagorean Theory
the area of rectangular surface of a triangular prism having base sides 9 CM 10 cm and 17 cm is 864 CM square calculate the height of the prism
Answer:
The formula for the volume of a triangular prism is given by:
V = (1/2)bhL
where b is the base length of the triangle, h is the height of the triangle, and L is the length of the prism (i.e., the distance between the two triangular faces).
We are given the area of the rectangular surface of the prism, which is the product of the lengths of two adjacent sides of the rectangle, and we know that this area is equal to 864 cm^2. Therefore, we can use the Pythagorean theorem to find the length of the third side of the rectangle, which is also the base length of the triangular face:
17^2 = 9^2 + 10^2
289 = 81 + 100
289 = 181
So, the base length of the triangular face is 8 cm. Now we can plug in the known values into the formula for the volume of the prism:
864 = (1/2)(8 cm)(h)(L)
We are not given the length of the prism, L, but we know that it is equal to the base length of the triangle, which is 8 cm. Therefore, we can simplify the equation to:
864 = 32h
Solving for h, we get:
h = 864/32
h = 27
So the height of the prism is 27 cm.
→Be sure to use three to six complete sentences in your response.
Answer:
1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.
2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.
3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.
If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.
4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.
(6 sentences to use):
1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.
2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.
3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.
4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.
5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.
6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.
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