[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]
Step-by-step explanation:
[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]
Let's multiply both parts of the equation by 9/5:
[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]
[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]
[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]
[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]
The function f(x)=80(1.5)x models a bacteria population after x hours. how does the average rate of change between hour 4 and hour 8 compare to the average rate of change between hour 0 and hour 4?
The average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given,
The function f(x)=80(1.5)x
where x is the time in hours
Then,
f(4)=80(1.5)4=480
f(8)=80(1.5)8=960
f(0)=80(1.5)0=0
Then the average rate of change between 4 and 8 hours =[tex]\frac{960-480}{4}[/tex]
=120 units per hour
The average rate of change between 0 and 4 hours=[tex]\frac{480-0}{4}[/tex]
=120 units per hour
Hence, the average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
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Sinita wants to make 35 picture frames.
She needs 4 nails for each frame.
Sinita has 3 boxes of nails.
There are 48 nails in each box.
Has Sinita got enough nails to make all 35 frames?
Show how you get your answer.
Answer:
Yes, 144>140
Step-by-step explanation:
Since Sinita has 3 boxes of 48 nails, Sinita has a total of 144 nails. (48x3=144)
Sinita needs enough for 35 frames, and each frame uses 4 nails, so she will need a total of 140 nails. (35x4=140)
what Sinita has: 144
what Sinita needs: 140
Sinita has more than what she needs, so yes Sinita has enough nails. (144>140)
Complete each part.
(a) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Does not go through the origin
c. At least 2 terms
(b) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Contains an radical
(c) Find
(f g x )( )
(3 points)
(d) Find
(g f )(6)
(3 points
Using composite functions, we have that:
a) f(x) = x² + 3.
b) [tex]g(x) = \sqrt{x}[/tex]
c) f(g(x)) = x + 3.
d) [tex](g \circ f)(6) = \sqrt{39}[/tex]
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by:
(f ∘ g)(x) = f(g(x)).
For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:
f(x) = x² + 3.
For item b, we also want a non-linear function with a radical, hence the function can be:
[tex]g(x) = \sqrt{x}[/tex].
For item c, the composite function is:
[tex]f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3[/tex]
For item d, the composite function is:
[tex]g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}[/tex]
At x = 6, we have that:
[tex](g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}[/tex]
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what equations are equivalent to 18 − 15 = − 2x/5 + 7x/15
The equation which is equivalent to the given expression 18 − 15 = − 2x/5 + 7x/15 is (-3 = 5x/5).
What is defined by the linear equation with one variable?The basic equation used to demonstrate and overcome for an unknown quantity is a linear equation for one variable.
It is always a straight line and can be conveniently represented graphically. A linear function is a simple way to represent a mathematical statement. Unknown quantities can be represented by any variable or symbol, but in most cases, a variable 'x' is employed to represent the arbitrary number in a linear equation with one variable. A linear equation can be solved using a variety of simple methods. To produce a desired value of the unknown quantity, the variables have been separated on one side of the equation as well as the constants are isolated on the other.The given equation is;
18 − 15 = − 2x/5 + 7x/15
Simplifying the constant and variable part.
- 3 = 5x/5
Multiplying both side by 5;
- 15 = x
or, x = -15.
Thus, the required equivalent equation is - 3 = 5x/5 and the value of variable x is -15.
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answer pls! NEED HELP
Answer:
The first one
Step-by-step explanation:
Because the max is 6, the left ones are only right. Also a point is must be negative so it is the top left one.
Convert 13000 milligrams into pounds. Round your answer to the nearest hundredth
Answer:
0.03 is the correct answer
Step-by-step explanation:
0.02866009 = 0.03
jayden's walkie-talkie has a range of 3 miles. jayden is traveling on a straight highway and is at mile marker 253. identify the absolute-value equation and solution to find the minimum and maximum mile marker from 253 that jayden's walkie-talkie will reach.
Jayden's maximum and minimum walkie-talkie will reach mile marker is:
|x + 253| = 3
x = 253
The range of Jayden's walkie-talkie is three miles.
At mile 253, Jayden is moving straight along a highway.
Find the least and maximum milepost that Jayden's walkie-talkie will reach from 253 by solving the absolute-value equation.
range of 3 miles.
mile marker 253.
Find maximum and minimum of walkie talkie will reach
|x + 3| - 253 = 3x
= 253 or x
= 250
|x + 3| = 253
x = 250 or x
= -256|x - 253|
= 3
x = 256 or x
= 250
|x + 253| = 3
x = 253
Therefore, Jayden's minimum and maximum mile marker from 253 that walkie-talkie will reach is
|x + 253| = 3
x = 253
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What is the quotient of 7/8 divided by 2/5?
9/13
7/20
35/16
51/40
The quotient of 7/8 divided by 2/5 will be C. 35/16.
How to calculate the value?The quotient simply means that we have to divide.
Therefore, the quotient of 7/8 divided by 2/5 will be:
= 7/8 ÷ 2/5
= 7/8 × 5/2
= 35/16
In conclusion, the correct option is C
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Evan needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 4.5 hours and charged him $97 for parts. The
total was $479.50. What was the cost of labor, per hour?
if a circle passe though point (-4,2) and is tangent to the x-axis at (2,0), determine the coordinates of its center.
The coordinates of its center will be (2,10)
How can we express the equation of the circle?(x - h)²+ (y - k)² = r² is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.
A circle with a radius of r and a center is represented as
(x - a)² + (y - b)² = r² where (a, b) is the center of the circle.
Circle passes points (-4, 2) and (2, 0):
Both (-4 - a)² + (2 - b)² and (2 - a)² + (-b)² are equal to r²
Currently, the center's x coordinate (a) is 2 due to the tangent at (2, 0)
The equations then read:
6² + (2 - b)² = r²
b² = r²
⇒ 36 + (2 -b)² -b² = 0
⇒ 36 + 4 + b² - 4b - b² = 0
⇒ 4b = 40
⇒ b = 10.
So, the center is (2,10)
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Which shows a way to factor the
expression 24 - 32x8
A -8(-3+4x)
B-4-6-8x)
C 41-6+8
D 81-3-4)
Answer:
Pretty sure A would be the answer
Step-by-step explanation:
A ship sails 300 km west and then 500 km south. How far, to the nearest km, is the ship now from its starting position?
Step-by-step explanation:
this creates a right-angled triangle, with the pure coordinate changes being the legs, and the actual distance being the Hypotenuse (the side opposite of the 90° angle).
and so, we can use Pythagoras :
distance² = leg1² + leg2² = 300² + 500² =
= 90000 + 250000 = 340000
distance = sqrt(340000) = sqrt(10000×34) = 100×sqrt(34) =
= 583.0951895... km ≈ 583 km
consider randomly selecting a student at a large university, and let a be the event that the selected student has a visa card and b be the analogous event for mastercard. suppose that
It is not possible that the intersection case is P(A B)=0.5 .
What is intersection?The set of all objects that are members of both sets A and B is represented by the intersection of the two sets A and B, abbreviated as A∩B.
If there is any element x that is an element of both A and B, then we can also say that A intersects (meets) B at x. If A∩B is an inhabited set, which means that there must be some x such that x∈A∩B exists, then A intersects B equivalently.
If A does not intersect B, then A and B are said to be disjoint. They share no elements, to put it simply. If the intersection of A and B contains nothing—A∩B=Ф—then A and B are disjoint.
Explanation:
The likelihood of occurring of an event is called probability.
Consider two events A and B are occurred with probabilities P(A) and P(B) respectively.
The probability that both the events occurs is,
P(A and B)=P(A∩B)
When both the events are independent,
P(A and B)=P(AB) = P(A)x P(B)
The probability that either A or B occurs is,
P(A or B)= P(AUB) = P(A)+P(B)-P(A∩B)
When both the events are mutually exclusive the probability that either A or B occurs is,
P(A or B)=P(AUB) = P(A)+P(B)
The compliment of the probability is,
P(A)=1-P(A)
The conditional probability of occurring of an event A when it is given that B had already occurred is,
P(A|B)=P(A∩B)/P(B)
Let A represent the situation where the chosen person has a Visa credit card and B represent the situation where they have a Master card. The probability of occurring event A is 0.6 and the probability of occurring event B is 0.4 that is, P(A)=0.6, P(B)=0.4 .
It is known that P(A B)∠P(A) and P(A B)∠P(B) . So, it is not possible that the intersection case, P(A B)=0.5 .
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The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied. How much would her new total be? Show all necessary work.
The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied. New total be 11x/10.
Let the original purchase price without discount be 'x';
Tip to installation specialist = 10% of original purchase price
= (10/100) × x
= x/10;
Her new total is x + x/10 = 11x/10;
We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the phrase used to describe a refund or an offer made to clients on the listed price of goods.
Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. Discounts are sometimes referred to as "off" or "reductions." It should be noted that the discount is always determined using the item's marked price (list price).
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Answer : $611.29
Step-by-step explanation:
.10 x 719.99 =71.99
539.30 (from previous answer) +71.99 =611.29
Emma is thinking of three numbers from 1 to 9 that have the sum of 20 find of the possible numbers
The possible numbers are
( 9 , 9 ,2 ) ;( 9 , 8 , 3 );( 9 , 7 , 4 );( 9 , 6 , 5 )
All 4 combinations have the sum of 20 .
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Multiply each side of the equation by a power of 10 to get the repeating digit(s) to the left of the decimal point. since you only need to move one place, multiply each side by 10.
To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.
when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.
Example :
5/200 = 0.025
To express this answer with the power of 10
0.025 = 2.5 * 10 ^-2
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PLEASE HELP!! Im not sure with my answers and solution. Correct answers and solutions will be marked as "BRAINLIEST".
Answer:
[tex]\textsf{(a)} \quad -4 < x\leq 1[/tex]
[tex]\textsf{(b)} \quad [3, 19)[/tex]
Step-by-step explanation:
Part (a)Given compound inequality:
[tex]\dfrac{9+x}{5} < 5+x\leq 6[/tex]
[tex]\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.[/tex]
[tex]\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}[/tex]
Solve the inequalities separately:
Inequality 1
[tex]\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}[/tex]
Inequality 2
[tex]\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}[/tex]
Combine the intervals:
[tex]-4 < x\leq 1[/tex]
Part (b)Given equation:
[tex]y=x^2+3[/tex]
As the domain is restricted to -4 < x ≤ 1, the range is also restricted.
The vertex (minimum point) of [tex]y = x^2 + 3[/tex] is when x = 0.
As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.
[tex]x=-4 \implies y=(-4)^2+3=19[/tex]
Therefore, the range is:
Solution: 3 ≤ y < 19.Interval notation: [3, 19)factor 36(2x-y)^2-25(u-2y)^2
Solution After Factoring:
[tex]144x^2-144xy+86y^2-25u[/tex]
Hope this helps! If not, comment below and I'll see what else I can do to help. If it does help though, lmk! Thanks and good luck!
Given the following information: P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.
Find P(DIE):
According to the given statement
P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.
P(DIE):0.75
What is Conditional Probability?The possibility of an event or outcome occurring conditional on the occurrence of a prior event or outcome is known as conditional probability. The conditional probability is calculated by multiplying the probability of the previous event by the present probability of the upcoming, or conditional, occurrence.
Contrast Unconditional probability with conditional probability. The possibility that an event will occur regardless of whether any previous occurrences have occurred or any other circumstances are present is known as Unconditional probability.
According to the given value;
P(DIE): 0.15/0.2
=0.75.
hence,P(DIE):0.75.
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The graph above shows the frequency distribution of
a list of randomly generated integers between O and
10. What is the mean of the list of numbers?
Solving the Question
The frequency tells us how many times the integer appears in the set of numbers.
The integer tells us the numbers that appear in the set of numbers.
To find the mean, we add up all the numbers in the set and divide the sum by the number of integers.
Let's write the information on the graph as a list of numbers:
0, 1, 2, 3, 3, 3, 4, 4, 6, 7, 8, 10
Find the sum:
51
Divide the sum by the number of integers (which is 12):
51/12
= 4.25
AnswerThe mean is 4.25.
A =
૫ {q) n)
2
solve for a
Answer:
5 x = Solve: 2. 8 x = . x has 2 multiplied to it, so we divide 2 from both sides. 2.
Step-by-step explanation:
A sample of n = 5 scores has m = 20 and s2 = 4. what is the sample standard deviation?
The sample standard deviation is 0.89
In the given statement is:
A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and [tex]s^{2}[/tex] = 4 is the variance of these samples.
Let us know the :
What is meant by Sample Standard deviation?
The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.
Standard deviation is the square root of the variance.
Therefore, [tex]s^{2}[/tex] =4 => s = 2
(Where, s denotes sample standard deviation ,σ)
Also, Standard error of the sample S(E) = Sample standard variance / [tex]\sqrt{number of samples}[/tex]
= σ /[tex]\sqrt{n}[/tex] = 2/[tex]\sqrt{5}[/tex]
and, root 5 = 2.24
put the value of root 5
=2 / 2.24
= 0.89
Hence, The sample standard deviation is 0.89
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in a petri dish, a certain type of bacterium doubles in number every 40 minutes.
There were originally 64 or 2 to the 6th power, bacteria in the dish. After 120 minutes, the number of bacteria has doubled 3 times, multiplying by 2 to the 3rd power
Now the population of bacteria is is 2 to the 6th power times 2 to the 3rd power. Expressed as a power, how many bacteria are in the petri dish after 120 minutes?
Applying exponent properties, it is found that there are 2^9 = 512 bacteria after 120 minutes.
What happens when we multiply two terms with the same base and different exponents?We keep the base and add the exponents.
This is what happens in this problem, when we multiply 2^6 by 2^3, as follows:
[tex]2^6 \times 2^3 = 2^{6 + 3} = 2^9 = 512[/tex]
Hence, there are 512 bacteria after 120 minutes.
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A (-5, -2) and B (7, 4)
The length of line AB with coordinates A (-5, -2) and B (7, 4) is; 6√5 units
What is the distance between the coordinates?
The formula for distance of a line between two coordinates is;
D = √[(x2 - x1)² + (y2 - y1)²]
From the coordinates given as A (-5, -2) and B (7, 4), we can say that;
x1 = -5
x2 = 7
y1 = -2
y2 = 4
Thus;
D = √[(7 - (-5))² + (4 - (-2))²]
D = √(12² + 6²)
D = √180
D = 6√5 units
Thus, we conclude that the length of line AB with coordinates A (-5, -2) and B (7, 4) is; 6√5 units
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Complete question is;
Find the distance of the line AB with coordinates A (-5, -2) and B (7, 4).
24 - (2x7) expression
Step-by-step explanation:
24-(14)
10
use bidmas...
you would like to investigate whether smokers are more likely than nonsmokers to get lung cancer. you take the students in your class, select half at random and tell them to smoke a pack of cigarettes each day, and you tell the other half not to ever smoke. fifty years from now, you will analyze whether more smokers than nonsmokers got lung cancer. is this an experiment or an observational study? experiment observational study summarize at least three practical difficulties with this planned study.
According to the question, to investigate through an experiment by telling people to smoke a pack of cigarettes each day by putting their health at risk. This causes serious health issues. And the other half are told not to smoke but might smoke at their own discretion. In the end, it is very difficult to keep track of 50 years of both types of people. That means people who are smoking and others who are not smoking. And, after 50 years, checking their consistency has become extremely difficult, if not impossible. Therefore, this experiment is not possible in both ways, that is, experimental or observational.
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The ratio of the measures of the angles of a quadrilateral is 2: 4: 6: 3 . Find the measures of the angles of the quadrilateral.
Answer:
48º, 96º, 144º and 72º respectively
Step-by-step explanation:
PLEAS HELP ITS DUE TODAY
The slope for plane A is 375, this means its rate of speed is 375 ml/h.
The slope for plane B is 445, this means the rate of speed for Plane B is 445 ml/h.
What is the Slope of a Linear Equation?The slope of a linear equation = change in y / change in x.
A linear equation that is given as, y = mx + b or y = mx, has a slope that is represented as m.
Slope of Plane A:
Given the equation for Plane A as, y = 375x, the slope is, 375.
This means its rate of speed is: 375 ml/h.
Slope of Plane B:
Using two points, (1, 445) and (2, 890)
Slope for plane B = (890 - 445)/(2 - 1)
Slope for plane B = 445
This means the rate of speed for Plane B is: 445 ml/h.
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A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 7) and (3, 3), what is the equation for a parallel street that passes through (−2, 4)?
y = 4x + 12
y = 4x − 14
y equals negative one-fourth times x minus 1
y equals negative one-fourth times x plus 7 halves
Answer:
Step-by-step explanation:
The Answer is A
The equation for a parallel street that passes through the given point is y = 4x + 12
Equation of a line
From the question, we are to determine the equation of the street that is parallel to the first street
NOTE: Two lines are parallel if they have equal slopes.
Thus,
We will determine the slope of the first street.
From the given information,
The street passes through the points (4, 7) and (3, 3)
Using the formula,
Slope = (y₂ - y₁)/(x₂ - x₁)
x₁ = 4
y₁ = 7
x₂ = 3
y₂ = 3
∴ Slope = (3 -7)/(3 -4)
Slope = -4/-1
Slope = 4
Now,
For the equation of the parallel street
The street passes through the point (-2, 4)
Since, the street is parallel to the first street,
Slope = 4
Using the point-slope form
y - y₁ = m(x - x₁)
y - 4 = 4(x - -2)
y - 4 = 4(x + 2)
y - 4 = 4x + 8
y = 4x + 8 + 4
y = 4x + 12
Hence, the equation for a parallel street that passes through the given point is y = 4x + 12
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Suppose the equation for line A is y = 6/5 x - 10 Line A is parallel to line B, which is perpendicular to line C. If line D is perpendicular to line C and perpendicular to line E, what is the slope of line E? Justify your conclusion.
If slopes of the given lines are solved and observed, we get the slope of line E is [tex]m_{E}[/tex] = [tex]\frac{-5}{6}[/tex]
As per question statement, the equation for line A is [tex]y = \frac{6x}{5} - 10[/tex] Line A is parallel to line B, which is perpendicular to line C. The line D is perpendicular to line C and perpendicular to line E.
Before solving this question, we need to know about some basic formulas and concepts of equation for a line.
If Lines are parallel, their slopes are equal and if lines are perpendicular, the product of their slopes is -1.
i.e., if [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are slopes of two lines then if,
[tex]m_{1} = m_{2}[/tex] then lines are parallel
Now slope of line A can be found out by formula [tex]y=mx+c[/tex] hence slope of line A [tex]m_{A}[/tex]= [tex]\frac{6}{5}[/tex]
Line B is parallel to A so, [tex]m_{B}[/tex] = [tex]\frac{6}{5}[/tex]
Line C is perpendicular to B so [tex]m_{C} * m_{B} = -1\\m_{C} = \frac{-5}{6}[/tex]
Line D is perpendicular to C so [tex]m_{D} *m_{C} = -1\\m_{D} = \frac{6}{5}[/tex]
Line E is perpendicular to D hence [tex]m_{E} * m_{D} = -1\\m_{E} = \frac{-5}{6}[/tex]
Therefore the slope of line E is [tex]\frac{-5}{6}[/tex]
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