Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Answers
Shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
What is difference between fraction and mixed number?
Single fraction is represented as [tex]\frac{p}{q}[/tex] form where p is numerator and q is denominator and value of q can't be zero. Example [tex]\frac{5}{9}[/tex] .
Mixed number contains two part one is an integer and other is fractional part. It is represented as N [tex]\frac{p}{q}[/tex]. Example 5[tex]\frac{1}{2}[/tex] .
According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.
There are three shaded circle and a circle with 7 sector shaded.
So, Total shaded area in single fraction = 1 + 1 + 1+ [tex]\frac{7}{10}[/tex] = [tex]\frac{37}{10}[/tex]
and total shaded area in mixed number = 1 + 1 + 1 + [tex]\frac{7}{10}[/tex] = 3 + [tex]\frac{7}{10}[/tex] = 3[tex]\frac{7}{10}[/tex] .
Hence, shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
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Related Questions
What is the value of X in the equation 1/5x - 2/3y = 30, when y = 15?
Answers
Answer:
x = 200
Step-by-step explanation:
a) Simplify both sides of the equation.
1/5x - 2/3(15) = 30
1/5x + -10 = 30
1/5x - 10 = 30
b) Add 10 to both sides.
1/5x - 10 + 10 = 30 + 10
1/5x = 40
c) Multiply both sides by 5.
5 * (1/5x) = (5) * (40)
x = 200
1. Plug 15 in for y
1/5x - 2/3y = 30
→ 1/5x - 2/3(15) = 30
→ 1/5x - 10 = 30
2. Add 10 to both sides
1/5x - 10 = 30
→ 1/5x = 40
3. Divide both sides by 1/5
1/5x = 40
→ x = 200
4. Plug in 200 for x to see if it’s correct
1/5(200) - 2/3(15) = 30
→ 40 - 10 = 30
Because this equation is true, we have found our answer.
Answer Recap: When y = 15 in this problem, x = 200.
problem 2 select all of the equations that represent a proportional relationship. (select all that apply.) the remaining length, , of a -inch rope after inches have been cut off: . the total cost, , after an sales tax is added to an item's price, : . the number of marbles each sister gets, , when marbles are shared equally among four sisters: . the volume, , of a rectangular prism whose height is cm and base is a square with side lengths cm: .
Answers
An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.
Equation: y = mx and m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
t/p=1.08
C. Equation: x=m/4
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
m/x=4
D. Equation: V= 12s^2
This equation is NOT proportional because side length is squared, so it is not constant linearly.
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2.) The amount of sleep that elementary school children get per night follows a Normal distribution with a
mean of 9.5 hours and a standard deviation of 0.55 hours.
a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep per
night. Sketch the Normal curve and shade the area under the curve that is the answer to the
question.
Answers
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
The amount of sleep that elementary school children get per night be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.
the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to
P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)
P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)
P(9≤ X ≤ 10) = 0.6367
P(X > 12) = P(Z>(12 - 9.50)/0.55)
P(X > 12) = P(Z>4.5455
P(X> 12) = 0.000
THere is zero possibility of student to get more than 12 houtrs of sleep
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
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What’s 12:28 reduced
Answers
Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.
Step-by-step explanation: I hope this helps!
Here are Ryan's scores in nine French tests.
4
6
4
7
8
a
6
7
7
The mean of Ryan's nine scores is 6
Work out the value of a.
Answers
Answer:
a = 5
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{4+6+4+7+8+a+6+7+7}{9}[/tex] = 6 ( multiply both sides by 9 to clear fraction )
49 + a = 54 ( subtract 49 from both sides )
a = 5
please help with this homework
Answers
Answer:
a.) x = 5
b.) x = 35/2 = 17.5
Step-by-step explanation:
In both problems, we are trying to solve for x, which means we need to isolate it on one side of the equation.
a.) 5/2 x + 1 = 11
5/2 x = 10
Now to divide by a fraction is the same as multiplying by the reciprocal.
x = 10 * 2/5 = 4
b.) 2/7 x - 3 = 2
2/7 x = 5
To divide by a fraction is the same as multiplying by the reciprocal.
x = 5 * 7/2 = 35/2 = 17.5
a bag contains 8 green marbles and 12 blue marbles. You draw a marble, return it to the bag and draw another. What is the possibility of drawing two green marbles
Answers
Answer:
2/5
Step-by-step explanation:
8+12=20
8/20 12/20
8 ÷ 4= 2
20÷4= 5
2/5
4. In the graph below, what is the line of reflection for triangle XYZ and triangle X'Y'Z"? (1 point)
the x-axis
Othe y-axis
Ox=2
Oy=2
Answers
In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.
Given, the coordinates of the triangle XYZ are:
X = (4,5)
Y = (6,3)
Z = (3,2)
and the coordinates of the triangle X'Y'Z' are:
X' = (0,5)
Y' = (-2,3)
Z' = (1,2)
for image of the triangle XYZ to get reflected and become X'Y'Z',
reflection of axis takes place.
But the images are not identical and symmetrical, so the reflection is not about y axis.
we check for x=2
hence reflection of axis when x=a is :
P(x,y) →x'(2a-x , y)
therefore use the above formula and check the coordinates of the reflected image.
X(4,5) when x=2X(4,5) → X'(2(2)-4 , 5)
x(4,5) → X'(0,5)
Y(6,3) when x=2Y(6,3) → Y'(2(2)-6 , 3)
Y(6,3) → Y'(-2,3)
Z(3,2) when x=2Z(3,2) → Z'(2(2)-3 , 2)
Z(3,2) → Z'(1,2)
hence x=2 is the reflection of triangle XYZ and X'Y'Z'.
Therefore we get the requires answer.
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Select all input values for which f(x) =3.
Answers
Answer:
B. x = -3
Step-by-step explanation:
f(x) = y
or however the vertical axis is called.
that is just something you always have to consider.
so, for what value of x does the functional curve ever reach the result (y) value of 3 ?
imagine a horizontal line you put through y = 3.
at what points is the functional graph touching or intersecting this line ?
at exactly 1 point. and that is at x = -3.
In the diagram AB = CD and CD = BC find BC
Answers
Answer:
BC = 10
Step-by-step explanation:
given CD ≅ BC , then
BC = CD , that is
3x + 1 = 13 - x ( add x to both sides )
4x + 1 = 13 ( subtract 1 from both sides )
4x = 12 ( divide both sides by 4 )
x = 3
Then
BC = 3x + 1 = 3(3) + 1 = 9 + 1 = 10
Please help! Really struggling on this subject! ASAP
Given the function below, determine the following.
f(x)= 10x +8
Find f(5).
Find f(-7).
Find a if f(x) = 88.
Answers
Answer:
Solutions Below.
Step-by-step explanation:
These questions test on the concept of Functions Substitution.
Function SubstitutionFunction Substitution is about giving an input (domain) to a function to produce an output (range)
Example: f(x) = 9x , f(9) = 9(9) = 81
ApplicationWe are given the following function:
f(x) = 10x + 8, where we can express it as
y = 10x + 8
Now we can find the value of f(5) by substituting x = 5 into the function. (Meaning: Find the value of y when x = 5.)
f(5) = y = 10(5) + 8 = 50 + 8 = 58
Next, applying the same concept, we can find the value of f(-7) by substituting x = - 7 into the function. (Meaning: Find the value of y when x = -7.)
f(-7) = y = 10(-7) + 8 = -70 + 8 = - 62
This last question requires us to work in reverse, where we find the value of x when f(x) = y = 88.
f(x) = y = 10x + 8
10x + 8 = 88
10x = 88 - 8
10x = 80
x = 80 ÷ 10 = 8
We an equivalent agression for 40+8(n-3)
Answers
Answer:
8n+16
Explanation:
Given the expressions:
[tex]40+8\left(n-3\right)[/tex]First, distribute 8 over the terms in the bracket:
[tex]\begin{gathered} =40+8(n)+8(-3) \\ =40+8n-24 \end{gathered}[/tex]Finally, collect like terms and simplify:
[tex]\begin{gathered} =40-24+8n \\ =16+8n \end{gathered}[/tex]An equivalent expression is 8n+16.
How much would a 5% tip be on a bill that cost $75.00?
Answers
Answer:
Step-by-step explanation:
it would be a 20% tip
Answer:
3.75
Step-by-step explanation:
5% of 75 is 3.75
5. What is the main doman and range of the roller coaster? (Hint: you should express these as a compound inequality or in interval notation
Answers
Answer:
If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section we will investigate methods for determining the domain and range of functions such as these.
Step-by-step explanation:
The height (h), in feet, of a balloon is calculated by using the equation h= 3+ + 2 where t is time, in seconds.What is the height of the balloon after 30 seconds?A. 60 ftB. 66 ftO C. 92 ftO D. 102 ft
Answers
Given data:
The given expression for height is h=3t+2.
Substitute 30 for t in the above expression.
[tex]\begin{gathered} h=3(30)+2 \\ =92\text{ ft} \end{gathered}[/tex]Thus, the height of the balloon after 30 seconds is 92 ft, so option (C) is correct.
PLEASE HELP URGENT!!!!
Answers
Answer:
Step-by-step explanation:
answer is the first one: square root property of equality
BTS zzz
Answer:
Reflexive property of equality
Step-by-step explanation:
look at the image
Describe the correlation:
r = -.009
strong positive
weak negative
weak positive
moderate negative
Answers
The correlation for r = -0.009 is B. weak negative.
What is correlation?The Pearson correlation coefficient (r) is the most commonly used metric for determining a linear relationship. It is a number ranging from -1 to 1 that indicates the strength and direction of a link between two variables. When one variable shifts, the other shifts in the same way.
Positive correlation is graded on a scale of 0.1 to 1.0. Weak positive correlation would be between 0.1 and 0.3, moderate positive correlation between 0.3 and 0.5, and strong positive correlation between 0.5 and 1.0. The stronger the positive correlation, the more probable the equities will move in unison. Having a minus means it's negative correlation.
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HELP HELP HELP What is the x-intercept of the line with this equation −5x+15y=15 ?
<3
Answers
Answer: (-3, 0)
Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.
0 = 1+1/3x
-1 = 1/3x
-3 = x
Answer:
x = - 3
Step-by-step explanation:
To get the x intercept, y has to be equal to 0.
- 5·x + 15·y = 15
- 5·x + 15·0 = 15
- 5·x = 15
x = 15/(- 5)
x = - 3
can you help me solve part A and B ASAP! THANKYOU
Answers
The shape comprises a semicircle, rectangle, and a trapezoid
A) The shape below will illustrate how the side length of the rectangle will be calculated
Part I is the semicircle of diameter
[tex]\begin{gathered} d=8\operatorname{cm} \\ r=\frac{d}{2} \\ r=\frac{8}{2}=4\operatorname{cm} \end{gathered}[/tex]From the diagram above
[tex]AB=r=4\operatorname{cm}[/tex]To find the missing side length of the rectangle , we will use the relation below
[tex]AB+BC+CD=12\operatorname{cm}[/tex]Where.
[tex]\begin{gathered} AB=4\operatorname{cm} \\ CD=3.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} AB+BC+CD=12\operatorname{cm} \\ 4+BC+3.5=12\operatorname{cm} \\ 7.5+BC=12\operatorname{cm} \\ BC=12-7.5 \\ BC=4.5cm \end{gathered}[/tex]The missing side length of the rectangle is = 4.5 cm
Hence,
The rectangle can be represented below as
The formula for the area of the rectangle is
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ \text{where,} \\ \text{length}=8\operatorname{cm} \\ \text{breadth}=4.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ A_{\text{rectangle}}=8\operatorname{cm}\times4.5\operatorname{cm} \\ A_{\text{rectangle}}=36\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Area of the rectangle = 36cm²
B) To calculate the area of the semicircle, we will use the formula below
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ \text{where,} \\ r=4\operatorname{cm} \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ A_{\text{semicircle}}=\frac{\pi\times4^2}{2}=\frac{16\pi}{2}=8\pi \\ A_{\text{semicircle}}=25.13\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the semicircle = 25.13 cm²
To calculate the area of the trapezoid, we will use the formula below
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ \text{where,} \\ a=8\operatorname{cm} \\ b=15\operatorname{cm} \\ h=3.5\operatorname{cm} \end{gathered}[/tex]The diagram below represents the trapezoid
By substituting the values, we will have
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ A_{\text{trapezoid}}=\frac{1}{2}(8\operatorname{cm}+15\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{1}{2}(23\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{80.5\operatorname{cm}}{2} \\ A_{\text{trapezoid}}=40.25\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the trapezoid is = 40.25cm²
To calculate the total area of the shape, we will use the formula below
[tex]\begin{gathered} \text{Total area=} \\ =A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Total area=}A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \\ \text{Total area}=25.13\operatorname{cm}+36\operatorname{cm}+40.25\operatorname{cm}^2 \\ \text{Total area}=101.38\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Total Area of the composite shape = 101.38cm²
find the dimensions of the page that will require the minimum amount of paper
Answers
Let's use the variable x to represent the length of the paper and y to represent the width of the paper.
If there are margins of 1 inch along the sides and 3 inches along the top and bottom, and the area with printer matter is 27 in², we can write the equation:
[tex](x-2)\cdot(y-6)=27[/tex]Solving for x, we have:
[tex]\begin{gathered} x-2=\frac{27}{y-6} \\ x=\frac{27}{y-6}+2 \end{gathered}[/tex]Then, the equation that we want to minimize is the area equation, so:
[tex]\begin{gathered} A=x\cdot y \\ A=(\frac{27}{y-6}+2)\cdot y \\ A=(\frac{27+2(y-6)_{}}{y-6})y_{} \\ A=(\frac{27+2y-12}{y-6})y \\ A=(\frac{2y+15}{y-6})y \\ A=\frac{2y^2+15y}{y-6} \end{gathered}[/tex]The critical points of this function are:
y = 0 (one of the roots)
y = -15/2 (one of the roots)
y = 6 (function is not defined)
how can i find the angle of elevation of the sun to nearest degree?
Answers
SOLUTION
From the diagram at the right of the question, a right-angle has been formed already. So we will use SOHCAHTOA to find angle A. Looking at angle A, the opposite side is 140 ft and the adjacent side is 173 ft.
Using TOA, we have
[tex]\begin{gathered} TOA,tanA=\frac{opposite}{adjacent} \\ tanA=\frac{140}{173} \\ tanA=0.80924855 \\ A=tan^{-1}0.80924855 \\ A=38.98146539 \end{gathered}[/tex]Hence the answer is 39 degrees
What is the complete factorization of 6x2 + 9x - 6?
A. 3(2x - 1)(x + 2)
B. (3x + 2)(2x - 3)
C. 3(x-2)(2x + 1)
D. 3(x-2)(2x - 1)
Answers
Answer: A. 3(2x−1)(x+2)
NEED HELP ASAP 9TH Grade
Answers
The equation that passes through the given points is the 3 option which is y = -3/2 x + 5
What are linear equation?A x + B y = C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x + 3y = 5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx +b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax + b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has only one solution. 2x + 3 = 8, for instance.
According to the given points
x = -1
So
y = (-3/2)(-1) + 5
y = 6.5
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Evaluate express your answer in exact simplest form9P4=
Answers
The formula for Permutation is,
[tex]^nP_r=\frac{n!}{\left(n-r\right)!}[/tex]The expression given is,
[tex]^9P_4[/tex]Given:
[tex]n=9,r=4[/tex]Plug in n = 9, r = 4
[tex]\frac{9!}{\left(9-4\right)!}[/tex]Simplify
[tex]\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}=9\times8\times7\times6=3024[/tex]Hence, the answer is 3,024.
Rectangle A is 5 in by 7 in. If the scale factor is 4, what is the area of the new rectangle B? How does it compare with the first rectangle?
Answers
The area of rectangle B is 560 square inches.
What is the area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.
Given that,
Scale factor = 4
Rectangle A has
length = 5 inches
breadth = 7 inches
Area of a rectangle A = length×breadth
= 5×7
= 35 square inches
Scale factor is 4 so length and width of a new rectangle is
length = 5×4 = 20 inches
breadth = 7×4 = 28 inches
Area of a rectangle B = length×breadth
= 20×28
= 560 square inches
Hence, The area of rectangle B is 560 square inches.
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A triangle on a sphere could have ___ degrees.
OA. 160
OB. 200
OC. 180
OD. any number of
Answers
Answer:
the anwser is 180
Step-by-step explanation:
1013 nearest thousand
Answers
Answer: The answer is 1013, it is already rounded as much as it can go.
Step-by-step explanation:
Solve for x. Just write the number. Triangle btw
1 + 6x
70°
55°
Answers
70+55=125
A Triangle is 180
180-125=55
55-1=54
54/6=9
the ratio of bots to girls in a school is nine : ten. what does this ratio mean. if there are 300 girls at the school, how many total students are at the school.
Answers
The number of the total students that are at the school is 570 if the ratio of boys to girls in a school is nine: ten and there are 300 girls at the school.
What is the ratio formula?The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
Given that a and b are separate amounts for two quantities, the combined total quantity is denoted as (a + b).
How are these ratio difficulties solved?Three steps are necessary to determine the ratio of three numbers:
Step 1: Add the ratio's numbers together to determine the total number of pieces.
Step 2: By dividing the given sum by the total number of parts, determine the value of each component in the ratio.
Step 3: Divide the original ratio by the sum of each component's values.
The ratio is given as 9:10 as boys to girls.
Number of girls = 300
Thus, girls will be 10x and boys will be 9x
then 10x = 300
⇒x = 30
Then we can calculate the number of boys as
9x = 9*30
=270
Thus, the total number of students in the school
= exact number of girls + exact number of boys
= 300 + 270
= 570
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What are the solutions to the inequality (x-3)(x=5)greater than or equal to 0
Answers
The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals
(-∞,3] or [5,∞) that is x ≥5 or x≤3
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
Given inequality (x-3)(x-5) ≥ 0
It generates two cases either case1 is true or case 2.
Case1. (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0
⇒(x-3) ≥0 and (x-5)≥0
⇒ x ≥ 3 and x ≥ 5
⇒ x ∈ [3,∞) and x∈ [5,∞)
⇒ x ∈ [3,∞) ∩[5,∞)
⇒ x ∈ [5,∞)
∴ x is greater than or equal to 5
Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0
⇒(x-3) ≤0 and (x-5)≤0
⇒ x ≤3 and x ≤ 5
⇒ x ∈ (-∞,3] and x∈ (-∞,5]
⇒ x ∈ (-∞,3] ∩ (-∞,5]
⇒ x ∈ (-∞,3]
∴ x is less than or equal to 3
Solution of the given inequality is case 1 or case 2
⇒ x ∈ [5,∞) or x ∈ (-∞,3]
⇒ x x ∈ (-∞,3] ∪ [5,∞)
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