Mathematics High School

[6.01] Systems of equations with different slopes and different y-intercepts have more than one solution.

Always

Sometimes

Never

Answers

Answer 1
Sometimes systems of equations with different slopes and different y-intercepts have more than one solution. This is, for the most part true but should be answered sometimes.

Related Questions

Given f(x)=2x-8, find f(3)

Answers

f(3)=2*3-8=-2. 
Hope that helps. 

Tickets for a school play cost $7 and $10 for the adults. The equation 7x+10y=80 represents the number of students(x) and the number of adults(y) who can attend the play for $80. If no students attend, how many adults can see the play for $80?

Answers

There could only be 8 because 10 *8 is 80 and that is your maximum number you can have 
Final answer:

If no students attend the play, then 8 adults can see the play for $80.

Explanation:

The subject of this question is Mathematics, specifically linear equations. The scenario presented involves ticket sales for a school play with different ticket prices for students and adults. $7 is the price for a student ticket and $10 is for an adult ticket. The given equation 7x+10y=80 represents the total sum of $80 that needs to be reached with a combination of student tickets (x) and adult tickets (y).

If no students attend, x in the equation is 0, so we have 10y = 80. To find the number of adults (y) that can attend the play for $80, we need to solve this equation for y. So, y = 80 / 10. Therefore, y = 8, meaning 8 adults can attend the play for $80 when no students attend.

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You have a part time job. You work for 3 hours on Friday and 6 hours on Saturday. You also receive an allowance of $20 per week. You earn $92 per week. How much do you earn per hour at your part time job?

Answers

$92 - $20 = $72, because we shouldn't take allowance into account
3 + 6 = 9, because that is the total number of hours this person works per week
We should just do this:
72 / 9 = 8
This means that this person earns $8 per hour at his part time job. 

Lane is 10 times Mel's age. If the difference in their age is 27, how old is Mel? A. 26 B. 4 C. 3 D. 30

Answers

L = 10M
27 = L - M

27 = 10M - M

27 = 9M

M = 3

L = 10M = 10(3) = 30

Lane is 30 years old
Mel is 3 years old
The answer id C. 3 

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There are 4 different French books and 4 different Spanish books. How many ways are there to arrange them on a shelf if

(a) Books of the same language must be grouped together, French on the left, Spanish on the right?

(b) French and Spanish books must alternate in the grouping, beginning with a French book? ...?

Answers

(a) Books of the same language must be grouped together, French on the left, Spanish on the right
a.) Number of ways the French books will be arranged in the left = 4! = 4 x 3 x 2 x 1 = 24
b.) Number of ways the Spanish books will be arranged = 4! = 24
Number of ways of arranging the books such that the same language must be grouped together French on the left and Spanish on the right are 24 x 24 = 576 ways.

b.) Number of ways af arranging the books such that the books alternate beginning with a French book = 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 24 x 24 = 576 ways.

Which of the following at the three cs of credit

Answers

the 3 c's of credit are : Character, Capital, and Capacity
Final answer:

The three Cs of credit are character, capacity, and capital, which represent the creditworthiness of an individual or business as assessed by lenders based on reputation, ability to repay, and assets for collateral respectively.

Explanation:

The three Cs of credit refer to character, capacity, and capital. These are the main criteria that lenders consider when assessing the creditworthiness of an individual or business. Character refers to the borrower's reputation and track record for repaying debts. Capacity is the borrower's ability to repay the loan, determined by their income and existing debt levels. And capital relates to the wealth or assets the borrower can offer as collateral. When banks conduct credit checks or require a co-signer, they are evaluating these aspects to decide on lending money.

mulitply (x + 5)(2x - 6)

Answers

the answer is 2x²+4x-30

Answer

2x^2+4x-30

Step-by-step explanation:

Foil

First

Outside

Inside

Last

find the x-intercept of the parabola with vertex (4,-1) and y- intercept (0,15). write answer in (x1,y1) (x2,y2) form :D ...?

Answers

Vertex form of the equation:
y = a ( x - h )² + k;
15 = a ( 0 - 4 )² - 1
15 = 16 a - 1
16 a = 16
a = 16 : 16
a = 1
After that we have to transform the equation to the standard form:
y = ( x - 4 )² - 1
y = x² - 8 x + 16 - 1
y = x² - 8 x + 15
Finally we have to find the zeroes:
x² - 8 x + 15 = 0
x² - 5 x - 3 x + 15 = 0
x ( x - 5 ) - 3 ( x - 5 ) = 0
( x - 5 ) ( x - 3 ) = 0
x = 3, x = 5
Answer:
( x 1, y 1 ) ; ( x 2 , y 2 ) = ( 3, 0 ) ; ( 5 , 0 )
 

Answer:

(3,0),(5,0)

Step-by-step explanation:

Add the comma in the middle or Plato will mark it wrong

Explain why the vertical line test is used to determine if a graph represents a function.
PLEASE HELP ANYTHING WILL HELP!!!!!!!!!!!!

Answers

Hi there Mary Dominguez, So what a vertical line test down is to find out if a particular graph is a function or not. What you do is take a vertical strait line and move it right to left or left to right, depending on your preference, along the X axis. The reason this works is a function can not have an x that has 2 different y values. If we use the vertical line test on a graph with say a graph that has (2,3) and (2,4) we can use the vertical line test and see that the line hits 2 points at once which means its not a function :)

When a vertical line passes through the graph of a function, it will intersect the graph at only one point. More than one point on any given vertical line means that the same x is being paired with 2 different y's and that make the graph not a function.


Please rate and thank : )

And btw copying and pasting is plagiarism

A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 31 meters and its width from left to right is 13 meters.

What is the vertical clearance 2 m from the edge of the tunnel?

Answers

Answer:

previous is correct

Step-by-step explanation:

Which best describes the meaning of the term theorem? A.A statement that is easily deduced from a proven theorem B.A conclusion proved by deductive reasoning C.A conjecture based on inductive reasoning D.A statement explaining the meaning of a geometric term

Answers

The option which best describes the meaning of the term theorem is B. A conclusion proved by deductive reasoning.
A refers to hypothesis, C to an axiom, and D to a definition. 

(4n^2 3n) (2n^3-4) (3n^2-2n) ?

Answers

(4n² 3n ) = 12n³

(12n³) (2n³-4) (3n²-2n) = (24n^6 - 48n³) (3n²-2n)
= 72n^8 - 48n^7 - 144n^5 + 96n^4

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 17 feet and the height from the ground to the front doors is 7 feet, how long is the ramp? (Round to the nearest tenth.)

Answers

One suggestion is to start by drawing a diagram.  I find it easier to work with what I can visualize.  

Now, you might be familiar with the term hypotenuse, and probably Pythagorean theorem, which can be used to find any side of a right triangle if given the two other sides.

In this case we are given the length of two sides of a right triangle.  The height of the ramp, 7 feet, and the distance of the base of the ramp, 17 feet.

Pythagorean theorem is generally written as a² + b² = c², where c = hypotenuse.  To find hypotenuse we must get it by itself.  It is being squared in this form.  So to get c by itself(or to isolate c) we must use the opposite operator of c(²) (squaring) which is square rooting (√).  What we do to one side we must do to both so now our equation looks like √(a² + b²) = c .
a and b are the base and height.  It doesn't matter which you plug in for a or b due to commutative property.

I would suggest using a calculator.  If you are not comfortable with using parenthesis with your calculator either plug it in just like the way I typed it or do the squaring and addition first then square root the sum of the two sides after they have been squared. 

Answer:

18.4 ft

Step-by-step explanation:

Use Pythagorean Theorem: a^2+b^2=c^2

17^2+7^2=c^2

sqrt 338=sqrt c^2

(sqrt and power 2 cancel)

sqrt 338=c

sqrt 338= 18.4 ft

f(x)=128(0.5)^x

(0, 1)


(1, 64)


(3, 16)


(8, 0.5)

Answers

The correct answers are:
_____________________________
Answer choices:
________________
[B]: (1, 64)
[C]: (3, 16)
[D]: (8, 0.5)
___________________________________________
Explanation:
___________________________________________
For clarity, let us rewrite the problem as:
___________________________________________
F(x)=128* (0.5)ˣ   
___________________________________________
Examine our answer choices;
_________________________
  [all of which are given as ordered pairs:  "(x, y)".].
________________________________
Start with the first "Answer Choice: [A]": (0, 1).
    Is this correct?
   (In other words, when "x" = 0; does "y" = 1 ?
____________________________________
Looking at the problem:
____________________
F(x)=128* (0.5)ˣ ;   If  x = 0, then y = 128.  

(0.5)⁰ = 1 ;  Then 128 * 1 = 128.  
____________________________
So, answer choice: [A]:  (0, 1): is incorrect).
____________________________________ 
Now let us examine answer choice: [B]:  (1, 64)
__________________________________________
Given our problem: 
___________________________________________________
F(x)=128* (0.5)ˣ ;  When we substitute "1" for "x", do we get "64"?
___________________________________________________
128 * (0.5)¹ =? 64? ;  Note:  (0.5)¹ = 0.5; so: 
___________________________________________________
128 * (0.5)¹ = 128 * (0.5) = 64 . Yes! 
So this answer choice, "Answer choice: [B]: (1, 64)", is correct.
___________________________________________________
Technically, there could be multiple correct answer choices, so let us examine the rest of the answer choices given:
_______________________________________________
Let us examine answer choice: [C]: (3, 16) .
____________________________________________________________
Given: F(x)=128* (0.5)ˣ ; when we substitute "3" for "x", do we get "16"?
________________________________________________
Let us substitute "3" for "x"; and write as: 
________________________________________________
F(x)=128 * (0.5)³  ;  Note: (0.5)³ = 0.125 = 1/8 ; so:
__________________________________________________
128 * (0.5)³ = 128 * 0.125 = 128 * (1/8) = 16.  Yes.
__________________________________________________
So this answer choice, "Answer choice: [C]: (3, 16)" is correct.
__________________________________________________
Let us examine answer choice: [D]: (8, 0.5) .
__________________________________________________
Given: F(x)=128* (0.5)ˣ ; when we substitute "8" for "x", do we get "0.5"?
__________________________________________________
Let us substitute "8" for "x"; and write as: 
________________________________________________
F(x)=128 * (0.5)⁸   ;  Note: (0.5)⁸  = 0.00390625 = 1/256 ; so:
__________________________________________________
128 * (0.5)⁸  = 128 * 0.00390625 = 128 * (1/256) = 0.5.  Yes.
________________________________________________
So this answer, "Answer choice: [D]: (8, 0.5)" is correct.

a bowling ball is dropped from a height of 24 feet. write a function that gives the height h (in feet) of the bowling ball after t seconds

Answers

gravity pulls at 32 feet per second so it would take .75sec to hit the ground now make an equation that can make this applicable so after .75 second T it would be at 0 feet H

Answer:

[tex]h=16t^2[/tex]

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 32 ft/s²

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow h=ut+\frac{1}{2}32\times t^2\\\Rightarrow h=ut+16t^2[/tex]

Here, u = 0 so,

[tex]h=0t+16t^2\\\Rightarrow h=16t^2[/tex]

The equation is [tex]h=16t^2[/tex]

[tex]24=16t^2\\\Rightarrow t=\sqrt{\frac{24}{16}}\\\Rightarrow t=1.22\ s[/tex]

Time taken by the ball to hit the ground is 1.22 seconds

Which of the following is a polynomial with roots 4,6, and -7?

Answers

the polynomial would be:
P(x)=(x-4)(x-6)(x+7)
P(x)=(x²-6x-4x+24)(x+7)
P(x)=(x²-10x+24)(x+7)
P(x)=x³+7x²-10x²-70x+24x+168
P(x)=x³-3x²-46x+168

Answer: P(x)=x³-3x²-46x+168

Answer:

P(x)=  x³ - 3 x² - 46 x +168

Step-by-step explanation:

given roots of the polynomial are given as    (4,6, -7)

hence the polynomial will be equal to

P(x) = (x-4) (x-6) (x+7)

P(x) = (x-4) (x²+7 x -6 x -42)

P(x) = (x-4) (x²+x -42)

P(x) = x³ + x²-42 x -4 x² -4 x +168

P(x) =  x³ - 3 x² - 46 x +168

hence, the required polynomial is P(x) =  x³ - 3 x² - 46 x +168

What is 1 third of 48?

Answers

1/3 times 48/1
48/3 = 16
1/3 of 48 is 16
1 third of 48 is 16!

How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?

Answers

The correct answer is:
4.

Explanation:
To find this answer, we divide the number of windows, 50, by the length (in windows covered) of each covering, 15:
[tex] \frac{50}{15} = 3 \frac{1}{3} [/tex].
This means that 3 coverings won't quite be long enough, so we will need 4. 
Final answer:

To find out how many 15-window coverings are needed for 50 windows, divide 50 by 15, which gives approximately 3.33. Rounding up because we can't have partial window coverings, we will need 4 coverings.

Explanation:

The question asks: How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?

To answer this question, we can do a simple division. We divide the total number of windows (50) by the length of each window covering (15).

So, we have 50 ÷ 15 which equals approximately 3.33. However, since we cannot have a fraction of a window covering, we need to round this number up. Therefore, we would need 4 window coverings to span 50 windows.

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HELPPP!!

Find the dimensions of a box with a square base with
(a) volume 12 and the minimal surface area
(b) surface area 20 and minimal volume ...?

Answers

Final answer:

The dimensions of the box for minimal surface area when volume is 12 are both the cube root of 3. When surface area is 20 for minimal volume, the dimensions are sqrt(5) for the base and (15 / (4*sqrt(5))) for the height.

Explanation:

The concept in this problem is about minimizing surface area and volume with relation to the dimensions of a box.

Let's consider a box with a square base of side 'x' and height 'h'. For part (a), the volume V of a box is given by V = x^2 * h which implies h = V / (x^2).

Substituting V = 12, we get h = 12/x^2. The surface area S of a box is given by S = x^2 + 4xh.

Substituting the value of h in the surface area equation, we have S = x^2 + 48/x.

To find the minimum surface area, we differentiate the above with respect to 'x' and set it equal to 0, which gives the dimensions of the box to be x = h = cube root of 3.

For part (b), the surface area S is given to be 20. So, S = x^2 + 4xh implies 4xh = 20 - x^2. The volume of the box is V = x^2 * h = (20 - x^2) / 4.

To minimize the volume, we differentiate V with respect to 'x' and set it to 0. That gives us the value of 'x' to be sqrt(5), and 'h' to be (20 - 5) / (4*sqrt(5))

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90 in fraction form show your work

Answers

it would be 90/100 
which could then be simplified to 9/10

hope this helps you

Solve for b2 in A = 1/2 h(b1+b2), if A = 16, h = 4, and b1 = 3. 16= 1/2* 4(3+b2) =6+2b2 or, b2= [16-6]/2= 5

Answers

Assuming you are referring to the area of a "trapezoid"; in which one calculates the Area, "A", as follows:
________________________
 A = 1/2* h(b1+b2) ;

in which: A = Area = 16 (given); 
               h = height = 4 (given);
               b1 = length of one of the two bases = 3 (given);
               b2 = length of the other of the two bases = ? (what we want to solve                                                                                            for) ;
______________________________________________________
Using the formula: A = 1/2 h(b1+b2) ;
________________________________
Let us plug in our known values:
___________________________
 →  16 = (1/2) * 4*(3 + b2) ;  → Solve for "b2".
________________________________
 →Note: On the "right-hand side" on this equation: "(1/2)*(4) = 2 ." 
________________________________
 So, we can rewrite the equation as:
________________________________
 → 16 =   2*(3 + b2) ;  → Solve for "b2".
________________________________
We can divide EACH side of the equation by "2"; to cancel the "2" on the "right-hand side" of the equation:
________________________________
 → 16 / 2 =   [2*(3 + b2)] / 2  ;  → to get:
___________________________
8 = (3 + b2) ;
_________________
 → Rewrite as: 8 = 3 + b2;
_______________________
Subtract "3" from EACH side of the equation; to isolate "b2" on one side of the equation; and to solve for "b2" :
______________________________
 → 8 - 3 = 3 + b2 - 3 ;  → to get:
_____________________
b2 = 5;  From the 2 (TWO) answer choices given, this value,
"b2 = 5", corresponds with the following answer choice:
____________________
b2= [16-6]/2= 5 ; as this is the only answer choice that has: "b2 = 5".
_________________________________________

As far getting "b2 = 5"  from: "b2= [16-6]/2= 5"; (as mentioned in the answer choice), we need simply to approach the problem in a slightly different manner.  Let us do so, as follows:
_____________________________________
Start from: A = 1/2 h(b1+b2); and substitute our known (given) values):
________________________
→ 16 = (1/2) *4 (3 + b2) ; → Solve for "b2".
_____________________________
Note that: (½)*4 = 2;  so we can substitute "2" for: "(1/2) *4" ; 
and rewrite the equation as follows:
_________________________
→ 16 = 2 (3 + b2) ;
____________________
Note: The distributive property of multiplication:
_________________________
a*(b+c) = ab + ac ;
_________
As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2). 
_________________
So we can substitute: "(6 + 2b2)" in lieu of "[2*(3 + b2)]"; and can rewrite the equation:
______________________
→ 16 = 6 + 2(b2) ; Now, we can subtract "6" from EACH side of the equation; to attempt to isolate "b2" on one side of the equation:
________________________________________________
 → 16 - 6 =  6 + 2(b2) - 6 ;
      → Since "6-6 = 0"; the "6 - 6" on the "right-hand side" of the equation cancel.
→ We now have: 16 - 6 = 2*b2 ; 
___________
Now divide EACH SIDE of the equation by "2"; to isolate "b2" on one side of the equation; and to solve for "b2":
____________________
   → (16 - 6) / 2 = (2*b2) / 2 ; 
     → (16 - 6) / 2 = b2 ;
       → (10) / 2 = b2 = 5.
______________
NOTE: The other answer choice given: 
_____________
"16= 1/2* 4(3+b2)= 6+2b2" is incorrect; since it does not solve for "b2".

The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken

Answers

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

The ratio is hot dogs to chicken the chicken isten tho to find the hot dogs first you do

10+6=16

So it says 20 members so then you needa see how much would equal the amont 20 obviously 4 so the hot dogs equal to 4 so the ratio is 4:10

Answer:

2/5

Step-by-step explanation:

just did it and it is correct

What is the expression for "the difference of five times a number and twice that number"?

5(2 - N)
5N - 2N
2N - 5N
5(N - 2)

Answers

"The difference of" means subtraction
"of 5 times a number" means 5N
"and twice that number" means 2N
So the statement is the subtraction of 5N and 2N

5N - 2N
The second option is correct.

prove tan3A= (cos(2A)-cos(4A))/ (sin(4A)- Sin(2A)) ...?

Answers

The solution to the problem is as follows:

cos2A - cos4A = -2 sin(6A/2).sin(-2A/2) = +2 sin(3A).sinA
 
and
 
sin4A - sin2A = 2 cos(6A/2).sin(2A/2) = 2 cos(3A).sinA

Hence RHS = (cos(2A)-cos(4A))/ (sin(4A)- Sin(2A)) = sin 3A / cos 3A = tan 3A = LHS


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Anna has put her money into various investments. Which of the three Cs of credit do these investments fall into?
A. Capital
B. Character
C. Capacity

Answers

The correct answer is:

A) Capital.

Explanation:

Capital is any valuable assets that you have such as real estate, personal property, or savings and investments that you could possibly use to repay credit debts if necessary.

Anna has put her money into various investments. These are Anna's capital.

A capital amount is the money that is needed to start any business venture or investment. Capital is also an asset of any person. Apart from personal money, capital also include funds in ones deposit accounts, tangible things like machinery used for production purposes etc.

HELPPPPPP
A person can order a new car with a choice of 10 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?

Answers

Number of ways a new car can be ordered with regard to the options is 10 x 2! x 2! x 2! x 2! = 10 x 16 = 160 ways.

Final answer:

To find the number of different ways a new car can be ordered with various options, multiply the number of choices for each option.

Explanation:

To find the number of different ways a new car can be ordered with regard to the given options, we need to multiply the number of choices for each option. There are 10 possible colors, 2 choices for air conditioning (with or without), 2 choices for automatic transmission, 2 choices for power windows (with or without), and 2 choices for a CD player (with or without).

Therefore, the total number of different ways a new car can be ordered is:

10 colors × 2 choices for air conditioning × 2 choices for automatic transmission × 2 choices for power windows × 2 choices for a CD player = 10 × 2 × 2 × 2 × 2 = 160

The angle of depression from the top of a 150 m high cliff to a boat at sea is 7 degrees. How much closer to the cliff must the boat move for the angle of depression to become 19 degrees ...?

Answers

The first thing we need to do is use tan to find x. If the original angle of depression is 7 degrees, then the angle from the cliff to the bow of the boat is 90-7=83 degrees. Thus,tan83 = d / 150or we can express it like this:d =150 tan 83 ≈ 855.2where d is the total distance from the boat to the cliff when the angle of depression is 7 degrees. Hope this helps a lot

Numbers 1 - 10 are written on cards and placed in a bag. Find the probability of choosing a number greater than 5 or choosing an odd number. ...?

Answers

Final answer:

The probability of selecting a card greater than 5 or an odd number from a bag of cards numbered 1 to 10 is 0.8 or 80%.

Explanation:

The question asks for the probability of choosing a number greater than 5 or an odd number from a bag containing numbered cards from 1 to 10. To solve this, we should consider that numbers greater than 5 are 6, 7, 8, 9, and 10. There are 5 odd numbers in the set: 1, 3, 5, 7, and 9. The number 7 and 9 are both greater than 5 and odd, so they are counted only once when combining the two groups.

First, let's count the total unique outcomes that either meet the criterion of being greater than 5 or being odd: 6, 7, 8, 9, 10, 1, 3, 5 (7 and 9 are already counted). There are 8 such numbers.

The total number of possible outcomes is 10, as there are 10 cards. The probability is the number of favorable outcomes divided by the total number of possible outcomes: P = favorable outcomes / total outcomes = 8/10 = 0.8 or 80%.

Which statement is true for the set of natural numbers?

A. The set is closed under addition and closed under subtraction
B. The set is closed under addition and not closed under subtraction
C. The set is not closed under addition and closed under subtraction
D. The set is not closed under addition and not closed under subtraction

Answers

It's closed under addition. You can take any two natural numbers you want, add them up and you'll get some other natural number (eg: 3 and 5 ---> 3+5 = 8)

it's not closed under subtraction. Sure 5-3 = 2 is a natural number but 3-5 = -2 is not a natural number

so that leads us to the answer being choice B
Final answer:

The set of natural numbers is closed under addition but not under subtraction.

Explanation:

The statement that is true for the set of natural numbers is B. The set is closed under addition and not closed under subtraction.

In mathematics, a set is considered closed under an operation if applying that operation to any two elements in the set always produces an element that is also in the set.

For the set of natural numbers, adding two natural numbers will always result in another natural number, so it is closed under addition. However, subtracting two natural numbers may result in a negative number, which is not a natural number, so it is not closed under subtraction.

39/4 as a mixed number

Answers

39 ÷ 4 is 9, with a remainder of 3. Then, you put 3 as the numerator, so your answer is 9 3/4. Hope this helps!

Answer is provided in the image attached.

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