Answer:
P(A) = 0.58
Step-by-step explanation:
Using the total probability formula, we have:
P(A) = P(A|B)P(B) + P(A|B')P(B')
We know that P(B') = 1 - P(B) = 1 - 0.4 = 0.6
Substituting the given values, we get:
P(A) = (0.7)(0.4) + (0.5)(0.6) = 0.28 + 0.3 = 0.58
Therefore, P(A) = 0.58.
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Write a function in terms of $t$ that represents the situation.
Sales of $10,000 increase by 65% each year.
A function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
What is function?An element of one non-empty set and an element of another non-empty set are said to have a special relationship when they are connected by a function in mathematics.
An assignment of an element from set Y to each element of set X, where set X is the domain and set Y is the codomain, is what is meant when a function is applied from a set X to a set Y.
We have given that f(t) is given by the Sales of $10,000 increase by 65% each year, i.e.
As sales of $10,000 increase by 65% each year.
The situation is represented by an exponential growth function.
The initial amount a = 10,000
The rate of growth r = 65% = 0.65
Therefore, the function will be:
t = a(1 + r)ⁿ
Where,
t represents the final amount.
a represents the initial amount
r represents the rate of growth
1+r represents the growth factor
n represents the time.
⇒ t = a(1 + r)ⁿ
⇒ t = 10,000(1 + 0.65)ⁿ
⇒ t = 10,000(1.65)ⁿ
Thus, a function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
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What is the domain of f )= 4?
The domain of f(x) = 4 is the set of all real numbers.
The domain of any constant function (where the output is always the same) is the set of all real numbers. This is because any real number can be plugged into the function, and the output will always be 4.
The domain of f(x) = 4 is the set of all real numbers, including integers, rational numbers, irrational numbers, and any other types of real numbers.
The domain of f(x) = 4 is the set of all real numbers.
The domain of any constant function (where the output is always the same) is the set of all real numbers. This is because any real number can be plugged into the function, and the output will always be 4.
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Jacob is roller skating. He can skate 3/10 of a mile in 1/2 of a minute. What is Jacobs unit rate in miles per minute? please answer this is 100% of my grade TwT
Answer:
[tex]\frac{3}{5}[/tex] miles per minute
Step-by-step explanation:
3/10 ÷ 1/2
3/10 x 2 = 6/10 = 3/5
To indirectly measure the distance across a river, Arun stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Arun draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
The distance PR, representing the distance across the river, is given as follows:
PR = 294 ft.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.The two similar triangles for this problem are given as follows:
POC and PRE.
Hence the distance PR is symbolized as follows:
PR = x.
The equivalent side lengths form a proportional relationship, given as follows:
x/(x + 160) = 230/355.
Hence, applying cross multiplication, the distance PR is obtained as follows:
355x = 230(x + 160)
355x = 230x + 36800
125x = 36800
x = 36800/125
x = 294 ft.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Answer: The distance across the river is 181 ft.
Step-by-step explanation:
in photo
Write the equation of the line represented by the following graph
Answer:
Y=-[tex]\frac{1}{2}[/tex] + 4
Step-by-step explanation:
You will be using the equation of Y= Mx+B
First you must find the Y intercept, where the line crosses the Y axis, this is at positive four, this will be your B value. then you find the slope by picking 2 easily readable points on the graph, to do this i will choose (0,4) and (2,3), then you find the change in Y and put it in a fraction over the change in x, since this is going down the slope will have a negative infront of it, so your fraction is [tex]\frac{3-4}{2-0}[/tex] which equates to [tex]\frac{-1}{2}[/tex] so your slope is -1/2 (this is M value)
so lastly you plug it all in, Y= -1/2x+4
Find the Equation of the line that goes through (2,7) and (-1.1)
*Graphically and Algebraically
how to graph y=-2/3x-5
-2x+3y=-15
By plotting the given points (0,-5) , (1,-17/3 ) for y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.
What is linear equation ?
Linear equation can be defined as the equation in which highest degree is one.
Given Equation,
y=-2/3x-5 and -2x+3y=-15
So,
use the slope form is
y= mx+b , where m is slope and b is the y-intercept.
find the valued of m an b using the form y = mx+b
m = -2/3 and b=-5
The slope of line is the value of m and y-intercept the value of b
slope = -2/3
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.
create a table for x and y values.
x y
0 -5
1 -17/3
and soon
Similarly for -2x+3y=-15
x y
0 -5
1 -13/3
2 -11/3
and soon
And Hence plot the points in the graph.
Therefore, By plotting the given points (0,-5) , (1,-17/3 ) for y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.
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Given a polynomial function f(x) = 2x2 + 7x + 6 and an exponential function g(x) = 2x + 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [–4 , ∞)
Both f(x) and g(x) have the same x-intercepts of (–2, 0) and (–1.5, 0).
Both f(x) and g(x) have the same y-intercept of (0, 6).
Both f(x) and g(x) have the same range of (–∞, 0].
The solution is Option C.
The functions f ( x ) and g ( x ) have the same y-intercept of ( 0 , 6 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first function be represented as A
Let the second function be represented as B
Now , the value of A is
f ( x ) = 2x² + 7x + 6 be equation (1)
Now , the value of B is
g ( x ) = 2ˣ + 5 be equation (2)
Now , on simplifying the equation , we get
To find the y-intercepts of the function ,
Substitute the value of x = 0 in the equation , we get
f ( 0 ) = 2 ( 0 )² + 7 ( 0 ) + 6
On simplifying the equation , we get
y = 6
Now , g ( x ) = 2ˣ + 5
Substitute the value of x = 0 in the equation , we get
g ( 0 ) = 2⁰ + 5
g ( 0 ) = 1 + 5
g ( 0 ) = 6
Hence , the y intercepts of the functions f ( x ) and g ( x ) is ( 0, 6 )
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What quadrant is 0degrees?
0 degrees is located in Quadrant I of the Coordinate Plane.
Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive. 0 degrees is the angle formed by the positive x-axis, and it is located in Quadrant I.
A coordinate plane is divided into four sections called quadrants, which are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.
This quadrant is defined by angles between 0 and 90 degrees and is generally associated with positive values on both the x- and y-axes.
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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 - θ).
Describe trigonometry.Correlations between triangles' angles and sides are studied in the mathematics discipline known as trigonometry. Since every straight-sided form can be reduced to a collection of triangles, trig can be found throughout geometry. The relationships between trigonometric and other branches of mathematics, in particular calculus, either real or complex, integrals, square root, and integrals, are astonishingly complicated.
Here,
Below is a list of the trigonometric values that are missing:
Angle A = θ-90.
28° sin = 62° cos
Cos 33° equals Sin 57°.
Cos 31° equals Sin 59°.
Sin( θ) = Cos(90 - θ).
Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 - θ).
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Why do people say geometry is hard?
Due to the lack of spatial thinking instruction in most math classes, people say geometry is hard. People should acquire geometrical ideas easily instead.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
Everyone finds it difficult to dive into the issue of proofs. Children must realize that this issue affects everyone, even the mathematically skilled. Because they have trouble seeing how 3D, and 2D, forms, angles, and lines connect from various viewpoints, most youngsters struggle with geometry issues. Even kids who are really good at solving sum problems in math might be utterly stumped by this.
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Due to the lack of spatial thinking instruction in most math classes, people say geometry is hard. People should acquire geometrical ideas easily instead.
Who named geometry?Euclid, the inventor of geometry, was a master mathematician. The words "ge" and "metria," both of which denote "measuring," are where geometry got its start. The way the Greeks approached geometry has been the basis for geometry for more than 2000 years.
Geometry is the study of different mathematical or real-world shapes, sizes, and figures. Geometry teaches us about numerous angles, transformations, and similarities among forms. The primary components of geometry are the point, line, and plane.
Everyone finds it challenging to explore the topic of proofs. Children need to understand that this problem impacts everyone, even those who are good at arithmetic. Most kids have problems with geometry because they have trouble recognizing how 3D and 2D shapes, angles, and lines link from different views. Even children who excel at math sum problems may be completely baffled by this.
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Which of the following could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor
The units (derived unit) for dy/dx will be option C i.e. square millimeter per milimeter.
What are units?
Unit is a quantity of constant magnitude which is used to measure the magnitudes of other quantities of the same manner.
There seven SI base units, which are comprised of:
Length - meter (m)
Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)
Derived units - A derived unit is a unit of measurement in the International System of Units (SI) that is derived from one or more of the seven base units.
As
Surface area(y) is mm^2
and radius(x) is mm
so, dy/dx will be mm^2/mm.
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What is the two steps in solving inequality?
Two steps in solving the inequality: simplify the algebraic expressions by combining like terms and isolating the target variable, then applying the mathematic operators.
Steps in solving the inequality:- Simplify the expression by: open the parentheses of algebraic expression, combine the terms like, and isolate the target variable.
- Use mathematic operators such as: addition, subtraction, multiplication, and division. All mathematic operations must be done on both sides. Addition and subtraction do not change the inequality. Multiplication and division with positive numbers will not change the inequality.
Multiplication and division with negative numbers will change the sign of the inequality.
Example:
Solve the inequality: 3x + 2 < 5x - 8
Step one: Subtract both sides with 5x and 2, this operation does not change the inequality sign
3x + 2 - 5x - 2 < 5x - 8 - 5x - 2
-2x < -10
Step two: Divide both sides with (-2). Since we divide with negative numbers, flip the inequality sign.
-2x/(-2) > -10/(-2)
x > 5
Hence, the solution is x> 5
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The art class lasts 90 minutes. The teacher explains the project for 25 minutes and allows 15 minutes for questions and discussion. He talks to each student about their project for 5 minutes.Write an expression to show how many students are in the class.
The expression for the students in the class is 5N + 25 + 15 = 90 or N = 10
How to write an expression to show how many students are in the class?
An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
Let the number of students in class be N.
Therefore, from the information provided, the expression for the students in the class can be written as:
5N + 25 + 15 = 90
5N + 40 = 90
5N = 90 - 40
5N = 50
N = 50/5
N = 10
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Is the square of a sum the same as the sum of squares?
A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.
Why is it called sum of squares?A statistical method called the sum of squares (SS) is used in regression analysis to determine how well the data can fit the model and how dispersed the data are. Since it is determined by adding up the squared differences, the sum of squares is how it is calculated.
A sum's square is equal to the product of its summands' squares and its double products' sums of summands in twos.
So, it is not always true that the square root of a sum is equal to the sum of the square roots.
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What is the value of x in the triangle? an isosceles right triangle with two legs of length 10 and hypotenuse of length x.
After using the Pythagorean theorem, the hypotenuse of the length x is 14.14 cm
In this case, we are given that:
The isosceles right triangle has two legs with length 10 cm
Let’s assume leg 1 as “a” = 10 cm, and leg 2 as “b” = 10 cm
The length of hypotenuse is “c”
To find the value of the hypotenuse or the longest side of a right triangle, we can use Pythagorean theorem:
a² + b² = c²
10² + 10² = c²
200 = c²
c = √200 = 14.14 cm
Therefore, the length of the hypotenuse would be 14.14 cm
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Magnolia ha a net aet of P142,234. 00 after liabilitie of P53,435. 00 at the end of the
year. What i it equity at year end?
Magnolia ha a net aet of P142,234. 00 after liabilitie of P53,435. 00 at the end of the year. Then the equity at year end become 88799
magnolia ha a net aet of P142,234. 00 after liabilitie of P53,435. 00 at the end of the
year. What i it equity at year end?
The ideal current ratio for a company is between 1.2 and 2, which indicates that it has two times as many current assets as liabilities to cover its debts.
If the current ratio is less than 1, the company's liquid assets are insufficient to cover its current liabilities.
equity = assets - liabilities
= 142234-53435
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Lana want to encloe a garden plot each ide of the garden will be 9 feet what i the area of the garden
The area of the garden is 81 square feet (9 x 9).
Since each side of the garden plot is 9 feet, then the area of the garden plot can be calculated by multiplying 9 feet by 9 feet, which is equal to 81 square feet.
To calculate the area of the garden plot, we need to know the length and width of the plot. Since the length and width of the garden plot is both 9 feet, then the area of the garden plot can be calculated by multiplying the length and width together. 9 feet multiplied by 9 feet is equal to 81 square feet, which is the area of the garden plot.
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What is a 4 polygon?
A 4 polygon is a two-dimensional shape with four sides and four angles.
What is polygon?Polygon is a closed figure in a plane made up of straight lines or curved lines that intersect in pairs. A polygon has at least three sides and angles. The sides can be of any length and the angles can be of any measure. Polygons are classified according to the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), etc. Polygons are used in many fields, from mathematics to engineering.
It is a type of quadrilateral, which is a polygon with four sides. Examples of 4 polygons include squares, rectangles, rhombuses, and trapezoids. All 4 polygons have four sides of equal length, and all their interior angles add up to 360 degrees.
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true or false : A fair coin is flipped 5 times.
The probability of getting more heads than tails is 1/2
The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.
True
The probability of getting more heads than tails is the same as the probability of getting an equal number of heads and tails, because the two outcomes are equally likely. The probability of getting an equal number of heads and tails is 1/2, so the probability of getting more heads than tails is also 1/2.
The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2, which is the same as the probability of getting an equal number of heads and tails.
The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.
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MAKE THE ANSWER IS RIGHT!!! 100 points + Brainliest. 100 points + Brainliest Let C represents the cost in dollars and R represents the revenue in dollars. What is the break-even point? Use a table to help if necessary.
C=36x+200
R=76x
Break-even point: (,)
Answer: accidentally did that sorry
Step-by-step explanation:
Use the Product or Quotient Rule to differentiate the function. 1. y =(x^2-3x)(x^2 + 1); 2. s(t) = (sqrt t+3) (4-t^2) 3. f(x)=x^4 sin x
The derivatives of the functions are as follows: y' = 4x^3+2x-3x^2-3 , s'(t) =[tex]2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex] , f'(x) = 4x^3sin x + x^4cos x
1. y' = (2x-3)(x^2+1) + (x^2-3x)(2x) = 4x^3+2x-3x^2-3
2. s'(t) = [tex](1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t) = 2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex]
3. f'(x) = 4x^3sin x + x^4cos x
1. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.
y' = (2x-3)(x^2+1) + (x^2-3x)(2x)
2. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.
[tex]s'(t) = (1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t)[/tex]
3. Begin by applying the quotient rule to differentiate the function. The quotient rule states that the derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions minus the product of the two functions divided by the square of the denominator.
f'(x) = 4x^3sin x + x^4cos x
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Five friends together earned $165 raking leaves. They divided the money evenly among the 5 of them. Maria earned another $10 walking a neighbor's dog. How much money did Maria earn in all?Enter your answer in the box.
I need help with this pls.
The number of sessions will be 5 and the cost is $249.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that for the first plan, the initial cost is $39 and the cost per session is $42 and for the second plan, initial cost is $54 and per session is $39.
The number of sessions for same cost of two plans will be calculated as,
39 + 42S = 54 + 39S
42S - 39S = 54 - 39
3S = 15
S = 5
For 5 sessions the cost will be calculated as,
Cost = 39 + 42S
Cost = 39 + ( 42 x 5 )
ost = 39 + 210
Cost = $249
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Which of the angles measures more than 90 but less than 180?
Answer:
Isosceles triangle
Step-by-step explanation:
Isosceles triangle has more than 90 but less than 180, which means Isosceles triangle is equal to 120.
How do you calculate the x-intercept of a line written in Standard Form?
A. Set y = 0 and solve for x.
B. Convert to Slope-Intercept Form and use the value of b.
C. The x-intercept is the coefficient of the x-term in the equation.
D. Set x = 0 and solve for y.
The y intercept of a line written in the standard form is calculated by
D. Set x = 0 and solve for y.How to solve for the interceptA linear function consists of functions where the variables has exponents of 1. The relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
To solve for the intercept in the equation y = mx + c x is set to zero
y = mx + c
y = m(0) + c
y = 0 + c
y = c
hence the intercept is equal to c when x is zero
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Select all statements that are TRUE about the graph.
A.) The pre-image is in quadrant III.
B.) The orientation of the vertices changed.
C.) The reflection can be represented by (-x, y).
D.) The line of reflection is the x-axis.
E.) The pre-image and image are congruent
HELP ASAPP
The true statements are,
A.) The pre-image is in quadrant III.
B.) The orientation of the vertices changed.
D.) The line of reflection is the x-axis.
What is orientation of the vertices?It is determined by the order in which a figure's vertices are labeled. It refers to the sequence of points after a transformation has been applied to a geometric figure. The order may be clockwise or counterclockwise.
Here, we have,
from the given figure ,we get,
the true statements are,
A.) The pre-image is in quadrant III.
B.) The orientation of the vertices changed.
D.) The line of reflection is the x-axis.
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What is the slope of 5y =- 10?
The slope of line equation 5y = -10 is m = 0.
There are three type of the equation of line:
- slope-intercept form.
The equation of line is: y = mx + b
Where:
m = slope
b = y-intercept
- point-slope form
The equation of line is: y - y₁ = m(x - x₁)
Where:
m = slope
(x₁,y₁) = a point on the line
- standard form
Ax + By + C = 0
Where A, B, C are constant
The given equation of line is: 5y = -10
Convert it first to slope-intercept form. Divide both sides by 5:
5y/5 = -10/5
y = -2
Then, compare with slope intercept form: y = mx + b
Note that y = -2 can be written as:
y = 0 ·x - 2
Hence, the slope = m = 0
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Why is it called equation?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
what is equation?Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The slope-intercept form, standard form, and point-slope form are the three primary forms of linear equations. A mathematical expression known as an equation contains the equals sign. Algebra is a significant component of many equations. When you don't know the exact number to compute in math, you use algebra.
given
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Consider the equation 3x + 7 = 14, where 3x + 7 and 14 are two expressions that are separated by the symbol "equal."
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Brooklyn divides 2.84 kilograms of fruit salad equally among 4 serving bowls.she wants to know how many kilograms of fruit salad to put in each bowl.she uses the decimal grids shown
By taking a quotient between the mass of salad fruit and the number of bowls, we will see that she needs to put 0.71 kg of salad fruit on each.
How much she needs to put in each bowl?
Here we know that Brooklyn wants to divide 2.84 kilograms of fruit salad equally among 4 serving bowls.
So, to see the mass of fruit salad that she needs to put in each bowl is equal to the quotient between the total mass of frit salad and 4, then we will get:
N = 2.84kg/4
N = 0.71 kg
So she needs to put 0.71 kilograms of salad fruit on each one of the 4 bowls.
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