The linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
Given, Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month.
we have to model the situation in a linear equation,
Let the number of months be, x
and the total amount in her emergency fund be, y
As, she starts with $2000 so the y-intercept will be 2000
also she save $320 every month so the slope be 320
So, the equation be,
y = 320x + 2000
Hence, the linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
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Your parents limit your
phone use to 18 hours every week. You need
to split that between hours spent on the phone
with your friends and hours spent using the
internet. Your parents count one hour on line
as 1/2 hour of phone time since some of your
time is spent doing homework. An algebraic
model is x + 1/2y
18 where x is hours spent
on the phone and y is the hours spent on line.
2
=
Step-by-step explanation:
x + 1/2y = 18
2x + y = 36
x = 36 - y
18 = 36 - y + 1/2y
18 = 36 - 1/2y
36 - 18 = 1/2y
18 = 1/2y
y = 36
x = 18 - 1/2(36)
x = 18 - 18
x = 0
Therefore, you can spend 0 hours on the phone and 36 hours on the internet.
consider a population that grows according to the recursive rule p n = p n − 1 + 80 p n = p n - 1 + 80 , with initial population p 0 = 60 p 0 = 60 .
The population grows according to the recursive rule is-
Pn = 60 + n×80P100 = 8060Explain the term recursive rule?A recursive rule provides the first term and terms of the a sequence and uses a recursive equation to show how each term relates to the term(s) before it. Sequences in mathematics and geometry, for instance, can be represented recursively.For the stated question-
initial population p0 = 60recursive rule pn = p(n − 1) + 80Then,
P1 = P0 + 80
P1 = 60 + 80 = 140
P2 = P1 + 80
P2 = 140 + 80 = 220
Thus, an explicit formula for the population
Pn = P0 + n×80 = 60 + n×80
P100 = 60 + 100×80 = 8060
Thus, explicit formula for the population growth is
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The complete question is-
Consider a population that grows according to the recursive rule pn = p
(n − 1) + 80 , with initial population p0 = 60
Find an explicit formula for the population. Your formula should involve n (use lowercase n)
Pn=
Use your explicit formula to find
P100 =
A student is taking a multiple-choice test in which each question has four possible answers. She knows the answers to 5 of the questions, can narrow the choices to 2 in 3 cases, and does not know anything about 2 of the questions. What is the probability that she will correctly answer A) 10, b) 9, c) 8 d) 7, e) 6, and f) 5 questions?
Do not need to answer every part if they are worked the EXACT same way.
given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 which of the following scatter diagrams accurately represents the data?
the regression equation:
y = 0.9x+ 7.5
given that:
Xi: 2; 6; 9; 13; 20
Yi: 7; 18; 9; 26; 23
from the given data we have:
∑x = 2+6+9+13+20 = 50
∑y = 7+18+9+26+23 = 83
Also, we need to calculate:
∑XY = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001
∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex]+[tex]9^{2}[/tex] + [tex]13^{2}[/tex]+ [tex]20^{2}[/tex] = 690
∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex]+ [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] +[tex]23^{2}[/tex] = 1659
the slope b is calculated:
b = ∑XY - ∑x × ∑y/n ÷ ∑ - (∑x)^2 /n
now we need to substitute the above values in the equation:
b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5
b= 0.9
the y-intercept (a) is :
a = y - bx
where
y = ∑y/n = 83/5 = 16.6
x = ∑x/n = 50/5 = 10
now substitute these values
a = 16.5 - 0.9 × 10
a = 7.5
the regression equation:
y = bx + a
now ,
y = 0.9x+ 7.5
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jason did a distance spatial join to find city-to-airport distances in illinois, and found that the distance values were all less than 3.0. what are the units?
Illinois city-to-airport distances can be discovered using a distance spatial join. The utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.
Explain the term GIS?A system called a geographic information system (GIS) is one that collects, organizes, processes, and maps all kinds of data.
GIS connects data to a map and combines all kinds of descriptive data with location data (where objects are) . This offers a basis for mapping and analysis, which are applied in science and practically every sector of the economy. GIS aids users in comprehending trends, connections, and geographic context. The advantages include better management and decision-making, as well as enhanced communication and efficiency. GIS is being used by hundreds of thousands more organizations worldwide to create maps that facilitate communication, analysis, information sharing, and the resolution of challenging issues.Illinois city-to-airport distances can be discovered using a distance spatial join.
Thus, the utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.
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the subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x, y}, {w, x, y}, and { } (the empty subset). how many subsets of the set {w, x, y, z} contain w ?
Answer:
4
Four subsets of {w, x, y} contain w.
Step-by-step explanation:
There are four subsets that have w in it:
{w} has w in it.
{w, x} has w in it.
{w, y} has w in it.
{w, x, y} has w in it.
The answer is 4.
Determine the equation of the circle with center (-1,-2)(−1,−2) containing the point (0,6)
The equation of the circle with center (−1,−2) containing the point (0,6).
(x + 1)^2 + (y + 2)^2 = 65
How to determine the equation of the circle?
Remember that the equation of a circle with radius R and center (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Here we know that the center of the circle is (-1, -2), then our equation is something like:
(x + 1)^2 + (y + 2)^2 = R^2
We know that our circle contains the point (0, 6), replacing these values in the equation above we get:
(0 + 1)^2 + (6 + 2)^2 = R^2
1 + 8^2 = R^2
65 = R^2
Then the circle equation is:
(x + 1)^2 + (y + 2)^2 = 65
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emilio drive 450 miles on 18 gallons of gas. how far can he travel on one gallon
Answer:
25
Step-by-step explanation:
450 divided by 18 is 25
Answer: 25 miles
Step-by-step explanation:
450/18 = 25
25 miles with 1 gallon of gas
o build a robust distributed system, you must know what kinds of failures can occur. a. list three possible types of failure in a distributed system. b. specify which of the entries in your list also are applicable to a centralized system
Three common failures in a distributed system include
network link failure host failurestorage medium failureHost failure and storage medium failure are failures that could also occur in a centralized system, whereas a network link failure can occur only in a networked-distributed system.
CENTRALIZED SYSTEMS
Centralized systems are systems that use client/server architecture where one or more client nodes are directly connected to a central server. This is the most commonly used type of system in many organizations where a client sends a request to a company server and receives the response.
DECENTRALIZED SYSTEMS
These are other types of systems that have been gaining a lot of popularity, primarily because of the massive hype of Bitcoin.
In decentralized systems, every node makes its own decision. The final behavior of the system is the aggregate of the decisions of the individual nodes.
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please help!
What is/are the vertical asymptote(s) of the function?
y=3x+6x2+2x-35
Answer:
I don't think there would be any asymptotes because there are no denominators.
Step-by-step explanation:
if you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head?
The scenario assumed to be the number of flips until you land on a head is P(x) = 1 + (1 - p)/p.
Given info,
If you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head,
To solve the above condition, have a formula;
P(x) = 1 + ( 1 - p )/p
Hence, P(x) = 1 + ( 1 - p )/p is the case expected to number of flips before you end up with a head.
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an economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. these functions are r(x) = -x^2 + 10x and c(x) = 4x+5, respectively
The average profit is positive if the number of snowboards is less than 67418 .
Given:
An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = (Px)/x, where P(x) is the profit function.
The profit is P ( x ) = R ( x ) - C ( x )
= -x^2 + 10x - ( 4x + 5 )
= -x^2 + 10x - 4x + 5
= -x^2 + 6x + 5
Then AP( x ) = ( P( x )) / x
= -x^2 + 6x + 5 / x > 0
As x > 0 then the sign of AP(x) depends on numerator only.
-x^2 + 6x + 5 > 0
D = 36 + 20
= 56
x = 6.7417
Therefore AP(x) > 0 if 0 < x < 6.7417
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Full question:
An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x)/x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.
a kite 75ft above the ground moves horizontally at a speed of 8ft/s. at what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?
When 200ft of string has been let out, the angle is decreasing at a rate of 0.015 radians per second.
In this question, we have been given the height of the kite from the ground is y = 75 ft.
The kite moves horizontally at a speed of 8 ft/s
So, dx/dt = 8 ft/s
The length of the string is 200 ft
so, L = 200 ft
Consider the following figure for this situation.
Now consider the sine of angle theta.
sin(θ) = 75/200
sin(θ) = 3/8
Now consider the tangent of angle theta.
tan(θ) = 75/x
1 / tanθ = x/75
cot(θ) = x/75
Differentiating the above equation with respect to t.
-csc²(θ) * dθ/dt = 1/75 * dx/dt
- csc²(θ) * dθ/dt = 1/75 * 8
- csc²(θ) * dθ/dt = 8/75
We know that, csc(θ) = 1/sin(θ)
csc(θ) = 8/3
So above equation becomes,
-(8/3)² × dθ/dt = 8/75
dθ/dt = - (8/75 * 9/64)
dθ/dt = 0.015
Therefore, the angle is decreasing at a rate of 0.015 radians per second.
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x varies directly with Y, when X equals 30, Y equals 20 find Y when X is 3
Answer:
f X varies directly with Y, then the relationship between them can be expressed as Y = kX, where k is a constant. Therefore, we can calculate the value of Y when X is 3 by substituting the values into the equation: Y = (20/30) * 3 = 2
Step-by-step explanation:
The manager of a store buys weather radios in lots of 48. Suppose that, on the average, 4 out of each group of 48 are defective. The manager randomly selects 4 radios out of the group to test. (Round your answers to 4 decimal places.) (a) What is the probability that he will find 2 defective radios? (b) What is the probability that he will find no defective radios?
(a) The probability that two radios are being defective= 0.035
(b) The probability that all radios are not defective = (11/12)^4
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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suppose x is a normal random variable with and find p(x > 105.0). a) 0.9993 b) 0.9994 c) 0.9995 d) 0.0007 e) 0.0006 f) none of the above.
The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
Explain the term normal random variable?A randomly distributed variable with a mean of 0 and a standard deviation of 1 is referred to as a standard random variable. The letter Z will always stand in for it. regularly distributed random variable, also known as a with standard deviation, is a continuous random variable which probabilities are defined by the normal distribution of mean and standard deviation.For the stated question -
The formula for the z score -
z = (x - μ)/σ
In which,
μ = 140 and σ = 20
Put the values-
z = (150 - 140)/20
z = 0.5
p(x > 105.0) = p(z > 0.5)
p(x > 105.0) = 0.6915
Thus, the value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
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The complete question is-
suppose x is a normal random variable with μ = 140 and σ = 20 and find p(x > 105.0).
The ratio of h minus 4 to 3 is 5.
Answer:
19
Step-by-step explanation:
therefore the answer is 19
From 2006-2018 Jeff Bezo's net worth increased by 127 billion dollars. During that time Mr. Bezos paid 1.4 million in federal taxes. What percentage of that increase in worth was paid to the federal government in form of taxes? ALL WORK MUST BE SHOWN IN SCIENTIFIC NOTATION.
He paid 0.0012% of his total wealth increase as federal tax.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have Mr. Bezos, who paid 1.4 million in federal taxes between 2006 -2018. His net worth increased by 127 billion dollars during this time span.
Assume that he paid [x]% of money to federal taxes. Then, we can write -
1.4 x 1,000,000 = (x/100) x 127 x 1000,000,000
1.4 = (x/100) x 127000
x = (1.4 x 100)/(127000)
x = 1.4/1270
x = 14/12700
x = 0.0012%
Therefore, he paid 0.0012% of his total wealth increase as federal tax.
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Ellie runs 2700 meters in 12 minutes. How many meters can Ellie run in one minute?
Answer: 225
Step-by-step explanation:
f(x) = 3x² + 17
Find f(-5)
there are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, how many have sprinkles or filling?
There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling
What is Venn Diagram ?Circles that overlap or do not overlap each other are used in a Venn diagram to illustrate similarities and distinctions between objects or groups of objects.Objects that share characteristics are represented as overlapping circles, whereas objects that are unique stand alone.Venn diagrams are currently utilized in many academic and business settings as demonstrations.Let S represent the set for donut with Sprinklers.
Let F represent the set for donut with Filling.
To find :- How many have sprinkles or filling?
i.e. n ( S ∪ F )
Formula,
n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )
Given,
n ( S ) = 6
n ( F ) = 7
n ( S ∩ F ) = 3
Putting in formula
n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )
= 6 + 7 - 3
= 10
Donuts with Sprinklers or Filling = 10
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There are 28
students in a class. 12
of them are girls and
the rest are boys.
What percent are
boys? Round to a
tenth of a percent
Answer:
The percentage of boys is 57.1%.
Step-by-step explanation:
I don't have to explain.
Hope this just helps!
Have a great day/night!
a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700. if the firm produced 800 units per day, its total cost would be $450, and if it produced 500 units per day, its total cost would be $425.
if it produced 500 units per day, its total cost would be $425. then average total cost is $0.61
The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:
1. 1,000 units per day at a total cost of $700.
ATC = Total cost/output
ATC = $700/1000
ATC = $0.58
2. If the firm produced 1,000 units per day, its total cost would be $450.
ATC = Total cost/output
ATC = $450/1000
ATC = $0.45
3. If it produced 700 units per day, its total cost would be $425.
ATC = Total cost/output
ATC = $425/700
ATC = $0.61
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10c - cd + d^3 (if c = -6 and d= 2)
Answer:
-40
Step-by-step explanation:
Given that,
c = -6
d = 2
To find the value of the given expression, replace c & d with 6 & 2 respectively.
Let us solve it now.
10c - cd + d³
( 10 × -6 ) - ( -6 × 2 ) + 2³
- 60 - ( -12 ) + 8
- 60 + 12 + 8
- 40
The breaking strength of a rivet has a mean value of 10,100 psi and a standard deviation of 499 psi. (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300? (Round your answer to four decimal places.) (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning O Yes, the probability in part (a) can still be calculated from the given information O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. O No, n should be greater than 50 in order to apply the Central Limit Theorem. You may need to use the appropriate table in the Appendix of Tables to answer this question.
the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300 P(10000 ≤ x ≤ 10300) = 0.54
We would assume a normal distribution for the breaking strength of a rivet. We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
n = number of samples
x = Breaking strengths of rivet.
µ = mean breaking strength
σ = standard deviation
From the information given,
µ = 10,100 psi
σ = 499 psi
n = 40
The probability that the sample mean breaking strength for a random sample of 40 rivets is between 10000 and 10,300 is expressed as
P(10000 ≤ x ≤ 10300)
For x = 10000,
z = (10000 - 10100)/499/√40 = - 0.13
Looking at the normal distribution table, the probability corresponding to the z score is 0.45
For x = 10300,
z = (10300 - 10100)/499/√40 = 2.54
Looking at the normal distribution table, the probability corresponding to the z score is 0.99
Therefore,
P(10000 ≤ x ≤ 10300) = 0.99 - 0.45 = 0.54
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If ΔSTU ≅ ΔHIJ, then what corresponding parts are congruent?
∠I and ∠U
segment TU and segment HI
∠I and ∠S
segment US and segment JH
Segment US and segment JH are congruent is correct.
What is congruent triangles?
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Given:
ΔSTU ≅ ΔHIJ
⇒ All three sides of ΔSTU are equal to all three sides of ΔHIJ.
⇒ ST ≅ HI, TU ≅ IJ and US ≅ JH.
Also all three angles of ΔSTU are same as the angles of ΔHIJ
⇒ ∠S ≅ ∠H, ∠T ≅ ∠I, and ∠U ≅ ∠J
So, from the given options segment US and segment JH are congruent is correct.
Hence, segment US and segment JH are congruent is correct.
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an online gardening magazine wants to understand why its subscriber numbers have been increasing. what kind of reports can a data analyst provide to help answer that questio
The analyst should provide a report addressing the following
Analyzing customer buying behaviorsAnalyzing consumer preferences using artificial intelligenceAnalyzing the number of customers by calculating daily foot trafficAnalyzing social media engagementA sale’s affect on subscription purchases is an example of customer buying behavior analysis.
Data analysis is the process of modifying, processing, and cleaning raw data in order to obtain useful, pertinent information that supports commercial decision-making. The process offers helpful insights and statistics, frequently presented in charts, graphics, tables, and graphs, which lessen the risks associated with decision-making.
Every time we make a decision in our daily lives, we can see a basic example of data analysis by assessing what has happened in the past or what will happen if we take that action. In its simplest form, this process involves looking at the past or future and making a choice based on that analysis.
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use differentials to estimate the amount of paint needed to apply a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m. (round your answer to two decimal places.)
The amount of paint needed to apply a coat of paint is 1.00 m³.
Given:
a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m.
we are asked to estimate the amount of paint needed to apply a coat of paint.
The amounts
Volume of a hemisphere, V = (2/3)πr³
r = 40/2
= 20 m
dr = 0.04 cm = 0.0004 m
dV≈2πr²dr
= 2π(20)²(0.0004) m³
= 1.0048 m³
rounding it of to two decimal places.
= 1.00 m³
Hence the amount of paint needed is 1.00 m³
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What is the sequence of transformations that maps △ABC to △A′B′C′?
Select from the drop-down menus to correctly identify each step.
The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, △ ABC is transformed in to △ A′B′C′
Firstly, △ ABC is being rotated 90° counterclockwise about the origin, and then it translated 3 units up.
Hence, The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
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PLEASE HELP!! The graph g(x) is a transformation of the graph f(x)=3^x. Enter the equation of g(x) in the box.
The equation of g(x) = y=[tex]3^{x+1}[/tex]+1 is if the function f(x)=3ˣ
What is a graph?A graph is a visual depiction or diagram that organizes facts or values. The points on the graph frequently reflect the relationship between two or more objects.
A function graph is a subset of a relation. In the current foundations of mathematics, and most notably in set theory, a function is truly equivalent to its graph. However, it is frequently beneficial to consider functions as mappings, which include not only the relationship between input and output, but also which set is the domain and which set is the codomain. For example, while determining whether a function is onto (surjective) or not, the codomain must be considered. The graph of a function does not determine the codomain on its own.
The graph is as follows: f(x) =[tex]3^{x}[/tex]
The graph g(x) represents a transformation of the graph f(x).
The g(x) curve travels through (-2,2) and (-1,4).
Let (a, b) represent any point on f(x).
After translation, a new curve g(x) is obtained that is parallel to the line, y=1 or asymptode is, y=1 or the graph becomes parallel to the x axis when y reaches 1.
g(x)= y-1=[tex]3^{x+1}[/tex]
g(x) = y=[tex]3^{x+1}[/tex]+1
The graph of the translated curve is +1.
The two graphs are shown below.
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