One box of dog food costs $7, while one can of cat food costs $8.
What is an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It illustrates that the expressions printed on the left and right sides have an equal relationship.
Some of the components of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. When expressing an equation, the "=" symbol and terms on both sides are a need.
Given data ,
Let the price of a single box of dog food at x.
Let's say the price of one can of cat food is y.
The cost of 1 box of dog food and 2 cans of cat food is = $ 23
One can of cat food and two boxes of dog food cost $22, total.
So , the equation will be
1x + 2y = 23 ....... (1)
2x + 1y = 22 ....... (2)
Equation (1) is multiplied by 2 to get
2x + 4y = 46 ....... (3)
When equation (2) is subtracted from equation (3), we obtain
3y = 24
value of y is obtained by dividing both sides by 3,
y = $ 8
Equation (1) can be solved by substituting the value of y.
x + [tex]2*8[/tex] = 23
x + 16 = 23
16 is subtracted from both sides, giving us
x = $ 7
Therefore , the value of x is $ 7 and value of y is $ 8
Thus, one package of dog food costs $7, while one can of cat food costs $8.
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Evaluate x² + 2y + 3x for x = 5, y = 8
robin is twice as old as earl and adam is 8 years younger than earl. in 6 years robin will be three times as old as adam. find their present ages
The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.
Let us consider the present age of Earl to be x years.
According to the given question, the present age of Robin is twice that of Earl = 2x
And since it is given that Adam is 8 years younger than Earl, then his age
= x - 8
After 6 years, the age of Earl will be x + 6
Robin's age will be = 2x + 6
Adam's age will be = x - 8 + 6 = x - 2
According to the given question, Robin's age will be thrice the age of Adam.
Hence, 2x + 6 = 3 (x - 2)
⇒ 2x + 6 = 3x - 6 ⇒ 6 + 6 = 3x - 2x ⇒ 12 = x
Thus, the present age of Earl is 12 years,
Robin's age = 2x = 2 x 12 = 24 years
Adam's age = x - 8 = 12 - 8 = 4 years
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Please help, I’ll give brainliest!!!!!!!!!!!!
Answer: (2, -1)
Step-by-step explanation:
Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 204 square meters. Solve for the dimensions (length and width) of the field
The dimension of rectangular piece of land is 17 x 12 square units in size.
The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.
The space occupied by a flat shape or an object's surface can be referred to as the area.
What is the rectangular area formula?
Rectangle area equals length x width
Let the rectangle plot's length and breadth be x and y, respectively.
Juliet has a 58-meter fence.
The rectangular piece of land's perimeter is 58 meters.
2(length + width) = 58
x + y = 58\2
⇒ x + y = 29
Moreover, the plot's total area is 204 square units.
x × y = 204
⇒ x × (29 - x) = 204
[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]
(x-12) (x-17) = 0
x = 12, x = 17
When, x= 17
y = 29 - 17 = 12m
when x = 12
y = 29 - 12 = 17m
As a result, the rectangular land parcel has dimensions of 17 x 12 square units.
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An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?
(A) 30√2 m
(B) 45 m
(C)30√3 m
(D)60√3 m.
The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.
We have,
In an equilateral triangle,
- all three sides are of equal length
- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.
Let's denote the side length of the equilateral triangle as "s."
When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."
The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).
So,
Using the Pythagorean theorem, the value of "s":
s² = (s/2)² + 15²
s² = s²/4 + 225
4s² = s² + 900
3s² = 900
s² = 300
s = √300 = 10√3
Now,
Perimeter = 3 * side length
Perimeter = 3 * 10√3
Perimeter = 30√3 meters
Thus,
The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.
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Compact fluorescent light (CFL) bulbs reduce energy waste. The amount of energy
waste that is reduced each day in a certain community can be estimated by -b² + 8b
where b is the number of bulbs. Divide by b to find the average amount of energy
saved per CFL bulb.
Add twice the weight in kilograms to the volume in litres and multiply the result by one thousandth of the distance the parcel is sent in kilometres (1 litre equals 1000 cubic centimetres).
This gives the postal cost in dollars.
A customer wishes to post a parcel which measures 50cm x 50cm x 20cm and weighs 40kg to a city 200km away. How much will it cost?
The postal cost is $26
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
twice the weight = 2(40) = 80 kg
volume = 50cm x 50cm x 20cm = 50,000 cm³ = 50 litres
80 + 50 = 130
distance = 200 km
one thousandth = 0.001
one thousandth of the distance = 0.001 * 200 = 0.2
Multiply 130 by 0.2 as given
130*0.2 = 26
The postal cost is $26
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Quadrilateral ABCD~ Quadrilateral WXYZ, AB= 15, BC= 27, WX= 10
The scale factor is 3/2. The length of XY is 18.
What are similar Quadrilaterals?
Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape. Real-world examples of congruent figures or objects include, for instance, both of a person's hands, both of a car's front wheels, etc.
If the corresponding angles and sides of two quadrilaterals are equal, then the two quadrilaterals are similar.
Given that Quadrilateral ABCD is similar to Quadrilateral WXYZ.
Thus
AB/WX = BC/XY = CD/YZ = AD/WZ ....(i)
The length of AB = 15, BC= 27, WX= 10
The scale factor is
AB/WX = BC/XY = CD/YZ = AD/WZ
= 15/10
= 3/2 [Divide the denominator and numerator by 5]
Take first two ratios of (i):
AB/WX = BC/XY
15/10 = 27/XY
3/2 = 27/XY
XY = 27 × (2/3)
XY = 18
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The length of a rectangular parking lot is 4 yards more than 5 times the width. Find the area of the parking lot.
The required expression by distributing the w on the right side, we get: A = 5w^2 + 4w
Explain about Rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.
According to question:Let's call the width of the parking lot "w". According to the problem, the length is 4 yards more than 5 times the width, so we can write the length as 5w + 4.
The formula for the area of a rectangle is A = length × width. Substituting in our values, we get:
A = (5w + 4) × w
Simplifying this expression by distributing the w on the right side, we get:
A = 5w^2 + 4w
This is the formula for the area of the rectangular parking lot in terms of its width. To find the actual area, we need to know the width. Once we have that, we can plug it into the formula and solve for A.
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How do you score 102 students play at least once by there is 40% of the students at the school how many students are at the school
If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school
Let's assume that the total number of students in the school is "x".
40 percentage of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.
We also know that the number of students who play at least one sport is 102. Therefore, we can write:
0.4x = 102
Move 0.4 to the right hand side of the equation
x = 102 / 0.4
Divide the numbers
x = 255
Therefore, there are 255 students at the school.
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i need help………………………………
The domain and the range of the piecewise function for this problem are given as follows:
Domain D: All real values.Range R: [-2, ∞).How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the values of x of the function.The range of a function is the set that contains all the values assumed by the values of y of the function.For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.
The range is obtained as follows:
Up to x = 3: Positive infinity to y = -2, which is the least value assumed at x = 3.From x = 3 to x = 5: values from y = 3 to y = 5, which are already in the range for the above interval.x = 5 and greater: constant at y = -1, which is already in the range.Hence the range is given as follows:
[-2, ∞).
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Write a linear equation in slope intercept form y=mx+b that passes through (-6,-1) and is parallel to y=-2/3x+1
On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8
What is slope intercept?In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.
When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.
the line is y = -2/3x+1
so the slope, m = -2/3
since it parallel , new slope = 3/2
the slope intercept of line is
y +1 = 3/2(x+6)
y + 1= (3/2)x + 9
y = (3/2)x + 9 - 1
y = (3/2)x + 8
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HELP!!!!!!!!!!!! NEED ANSWER ASAP!!!!! :(
What is 40% of $20? Show your work. (2 points)
Answer:
40%/100×20=8
the answer is $8
the general rule of thumb is that it takes a driver 3/4 of a second to percieve the need to stop her car. it then takes another 3/4 of a second to react and move her foot from the accelerator to the brake and begin streeing out of the way. how far will a car traveling at 60 miles per hour travel (in feet) before the driver reacts to an obstacle?
A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.
To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).
Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.
Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:
distance = rate x time = 88 feet/second x 3/4 second = 66 feet
Hence,
A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.
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Janie has $180 m. She spends 50% of her money on a new pair of ice skates. How much does she spend on ice skates?
Answer:
$90
Step-by-step explanation:
180 - 50% or 180 x .50 = $90
A mother is 24 years older than her daughter. a. If the daughter is w years old, how old is the mother? b. If the ratio of their ages is 5:2, find the age of the daughter.
6. A triangle has two side lengths
3 feet. Select all the measures that could be the
length of the third side.
3 ft
9.2 ft
4.6 ft
8 ft
7.4 ft
2 ft
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Any two parts of a triangle can be added together to have a length larger than the third side.
A triangle has two side lengths of 3 feet. Let 'x' be the third side.
By the theorem, the inequality is given as,
x < 3
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
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the weight distribution of packages sent in a certain manner is normal with mean value 12 lb and standard deviation 3.5 lb. the package service wishes to establish a weight value c beyond which there will be a surcharge. what value of c is such that 99% of all packages are at least 1.0 lb under the surcharge weight?
The surcharge weight should be set at 12.25 lb, since 99% of all packages are at least 1.0 lb under this weight.
In this problem, we are given that the weight distribution of packages sent in a certain manner is normal, with a mean value of 12 lb and a standard deviation of 3.5 lb. The standard deviation is a measure of how much the data varies from the mean.
Now, the package service wishes to establish a weight value c, beyond which there will be a surcharge. We want to find the value of c such that 99% of all packages are at least 1.0 lb under the surcharge weight. This means that we are looking for a weight value that is exceeded by only 1% of all packages.
To find this weight value, we can use the properties of the normal distribution. We know that the area under the normal curve represents the probability of an event occurring. In this case, we want to find the weight value c that corresponds to the 1% probability.
To do this, we first need to standardize our normal distribution by converting it to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by subtracting the mean (12 lb) from our target weight value c, and then dividing by the standard deviation (3.5 lb). This gives us a z-score, which represents the number of standard deviations away from the mean our target weight value is.
Next, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the 1% probability. This is approximately -2.33.
Finally, we can solve for c by reversing the standardization process. We multiply the z-score (-2.33) by the standard deviation (3.5 lb) and add the mean (12 lb) to get our target weight value c.
Therefore, c = -2.33 x 3.5 + 12 ≈ 0.25 lb.
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15
Determine if lines a and b are parallel, perpendicular or neither.
(1 Point)
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
O parallel, they have the same slope
perpendicular, their slopes are opposite reciprocal
neither
parallel, their slopes are opposite reciprocal
perpendicular, their slopes are the same
Both slope are equal so we can say that both lines are parallel
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
and line
Line a: 2x + y = 10
= slope of line A is
2x + y = 10
y = -2x+10
slope = -2
- 6x – 3y = 3
-3y = 6x +3
x = -2y -1
slope = -2
in this case both slope are equal so we can say that both lines are parallel
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i need the answers to the marked answers! please help me!! :)
The results are given below.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
Consider the first triangles,
Given, L is the midpoint of KN and MP.
To find ΔMKL ≅ΔPNL
Using side-angle-side congruency ,
Here, the corresponding sides , KM and MP, KL and LP are equivalent.
But the angle ∠L is not an included angle.
So this triangles are non congruent.
Consider the next triangles.
BD bisects ∠ABC ∠BAD≅∠BCD
To find ΔABC≅BCD
By side- side-side congruency,
The corresponding sides AB and BD, AD and DC, BD are equivalent.
Therefore this ΔABC≅BCD proved.
Hence the proof.
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In 2004, $6,000 was invested in a mutual fund that earned 9% interest per year.
a) Tell whether the model represents an exponential growth or decay and create a function that models it
b) How much was in the account in 2012?
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
What is the function model?
In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.
a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:
A(t) = 6000(1 + 0.09)ᵗ
where A(t) is the amount in the account after t years.
b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:
A(8) = 6000(1 + 0.09)⁸
= 6000(1.09)⁸
≈ $11,737.51
Therefore, the amount in the account in 2012 was approximately $11,737.51.
Hence,
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
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pls help due tomorrow!!!
Answer:
[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]
[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]
pls help me
pls homework
I need help in both questions
The complete question:
A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?
Solution:
The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.
The total area of the floor is:
= 12m x 8m
= 96 square meters.
The area of the margin is:
= 2 x (12m + 8m) x 1m
= 40m.
Therefore, the area of the carpet is:
= 96m² - 40m²
= 56 meter²
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Example 7) Find three consecutive even integers such that the sum of the first and two times the
largest equals 20.
The consecutive even integers are 4,6 and 8.
What are the consecutive even integers?An even number is a number that can be perfectly divided by 2. An example of an even number is 10. A consecutive even number is an even number that follows each other on the number line.
Let the first even number be represented with x
The second even number : x + 2
The third even number : x + 4
x + 2(x + 4) = 20
x + 2x + 8 = 20
3x = 20 - 8
3x = 12
x = 12 / 3
x = 4
The second even number : 4 + 2 = 6
The third even number : 4 + 4 = 8
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Help im having trouble
Answer:
3 square units
Step-by-step explanation:
You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).
TriangleThe plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.
AreaThe area formula for a triangle is ...
A = 1/2bh
For base b=3 and height h=2, the area is ...
A = 1/2(3)(2) = 3 . . . . . square units
The area of the triangle is 3 square units.
You receive 23 out of 25 points on an exam. What is your score as a percent?
Answer:
Your score as a percent is **92%**. Here is how I calculated it:
To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign
In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".
23 ÷ 25 = 0.92
0.92 × 100 = 92
92 + "%" = 92%
Therefore, your score as a percent is 92%.
Step-by-step explanation:
if $m$ is a real number and $x^2 mx 4$ has two distinct real roots, then what are the possible values of $m$? express your answer in interval notation.
The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:
m ∈ (-∞, -4) ∪ (4, ∞).
The quadratic formula tells us that the quadratic equation's roots
[tex]x^2 + mx + 4 = 0[/tex]
are provided by:
[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]
The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:
Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.
Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.
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For the pair of similar solids, find the value of the variable
A 12 mm
B 48 mm
C 20 mm
D 3 mm
the value of the variable x that makes these two solids similar is 12mm. and explained as
Let's assume that the sides x, 24 belong to one of the solids and the sides 4, 8 belong to the other similar solid. To find the value of the variable x that makes these two solids similar, we can set up a proportion using the corresponding sides:
x/24 = 4/8
We can simplify this proportion by cross-multiplying:
8x = 24 x 4
Simplifying the right-hand side of the equation, we get:
8x = 96
Dividing both sides of the equation by 8, we get:
x = 12
Therefore, the value of the variable x that makes these two solids similar is 12. We can also use this value to find the missing side of the first solid:
x/24 = 4/8
Substituting x = 12, we get:
12/24 = 4/8
Simplifying both sides of the equation, we get:
1/2 = 1/2
This confirms that the two solids are indeed similar. We can also use the ratio of corresponding sides to find the missing side of the second solid:
x/4 = 24/8
Substituting x = 12, we get:
12/4 = 24/8
Simplifying both sides of the equation, we get:
3 = 3
This confirms that the two solids are similar and that the corresponding sides are in the same ratio. Therefore, the missing side of the second solid is 3 times its corresponding side, which is 8. Therefore, the missing side is 24.
In conclusion, the value of the variable x that makes these two solids similar is 12. The missing side of the first solid is 4 and the missing side of the second solid is 24.
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Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥8) , n=9 , p=0. 8
The probability of getting 8 or more successes in 9 trials, with given success rate in each trial is 0.8, is 0.9520.
To find the probability , we can use the cumulative distribution function (CDF) of the binomial distribution:
P(X ≥ 8) = 1 - P(X < 8) = 1 - P(X ≤ 7)
Using a binomial calculator or a binomial probability distribution table, we can find:
P(X ≤ 7) = 0.0480 (rounded to four decimal places)
Therefore,
P(X ≥ 8) = 1 - 0.0480 = 0.9520
So the probability of getting 8 or more successes in 9 trials, given the probability of success in each trial is 0.8, is 0.9520 (rounded to four decimal places).
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If these two shapes are similar, what is the measure of the missing length h?
In similar triangles, 15.07 miles is the measure of the missing length h .
What does "similarity" for triangles mean?
Triangles are said to be comparable if two of their angles have measurements that are the same as those of two other triangles' angles. In proportion, and with the same measure, are the equivalent sides and angles of identical polygons.
To test whether two triangles are similar, use one of the three triangle similarity theorems, Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS).
35/65 = 28/h
h = 35 * 28/65
h = 15.07 miles
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