These equations describe the rate of change of the probabilities of each state over time. We could solve them using various methods, such as matrix exponentiation or numerical simulation.
The Kolmogorov backward equations describe the probability of transitioning from one state to another in a stochastic process. In this case, we are interested in the probability of the two machines being in a certain state, given the mean lifetime and the rate at which the repairman can service them.
Let X1 and X2 represent the state of machines 1 and 2, respectively. We can define the states as follows:
- X1 = 0: Machine 1 is working
- X1 = 1: Machine 1 is broken
- X2 = 0: Machine 2 is working
- X2 = 1: Machine 2 is broken
The probability of transitioning from one state to another depends on the current state and the rates at which the machines fail and the repairman can fix them. Specifically, the rates of transition are:
- λ: The rate at which each machine fails (exponentially distributed with mean 1/λ)
- μ: The rate at which the repairman can fix a broken machine (exponentially distributed with rate μ)
Using these rates, we can set up the Kolmogorov backward equations as follows:
dP(X1=0,X2=0)/dt = -λP(X1=0,X2=0) + μ[P(X1=1,X2=0) + P(X1=0,X2=1)]
dP(X1=1,X2=0)/dt = λP(X1=0,X2=0) - (λ+μ)P(X1=1,X2=0) + μP(X1=0,X2=0)
dP(X1=0,X2=1)/dt = λP(X1=0,X2=0) - (λ+μ)P(X1=0,X2=1) + μP(X1=1,X2=0)
dP(X1=1,X2=1)/dt = (λ+μ)P(X1=1,X2=0) + (λ+μ)P(X1=0,X2=1) - 2μP(X1=1,X2=1)
These equations describe the rate of change of the probabilities of each state over time. We could solve them using various methods, such as matrix exponentiation or numerical simulation.
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This is a two part question. For the first blank, type the letter associated with with
the correct graph of this system. For the second blank, type the correct solution to
the system in point notation: (x,y).
Let
f(x) = (x − 2)² – 3
g(x) = -4x+1
==
A
C
B
D
The solutions to the system of equations in this problem is given as follows:
(0,1) and (0.25, 0).
The graph is given by the image presented at the end of the answer.
How to solve the system of equations?The equations that compose the system in this problem are given as follows:
f(x) = (x - 2)² - 3.g(x) = -4x + 1.We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.
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State the slope and x-intercept of the graph of y = 1/5x – 7.
Answer
slope: 1/5
x-intercept= 35
Step-by-step explanation:
0=1/5(X)-7
7=1/5x
7/1/5= 35
so
x-intercept is: (35,0)
8x−5y=−11 determine the intercepts
The x and y-intercepts of the given equation of line 8x - 5y = -11 are (-11/8,0) and (0,11/5) respectively.
What are the x and y-intercepts of the given equation of line?Given the equation of line in the question;
8x - 5y = -11
To find the x-intercept, substitute in 0 for y and solve for x.
8x - 5y = -11
8x - 5(0) = -11
8x - 0 = -11
8x = -11
x = -11/8
Hence, the x-intercept is (-11/8,0)
To find the y-intercept, substitute in 0 for x and solve for y.
8(0) - 5y = -11
0 - 5y = -11
-5y = -11
y = -11 / -5
y = 11/5
Hence, the y-intercept is (0,11/5).
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{41,57,77,83,95}
what is the set of even numbers that correspond to the given set of odd numbers that satisfy the function is
A. {42,58,78,84,96}
B. {44,60,80,86,98}
C. {82,114,154,166,190}
D. {84,116,156,168,192}
E. {86,118,158,170,194}
Which graph represents an exponential function?
Answer:
2
Step-by-step explanation:
What is the formula for the area A of a triangle with base b and height h?
The formula for the area of the triangle with based and height is bh/2, where b is base and h is height of triangle.
The base of the triangle is the line in the triangle parallel to x-axis. The height of the triangle is its altitude and vertical line parallel to y-axis. Do remember that base and altitude or height of triangle are always perpendicular to each other.
Let us take an example to find the area. Assume the height to be 5 cm and base to be 4 cm. Keep the values in formula -
Area = 1/2 × 5 × 4
Area = 5 × 2
Area = 10 cm²
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A traw i placed inide a rectangular box that i 6 inche by 6 inche by 1 inche, a hown. If the traw fit exactly into the box diagonally from the bottom left corner to the top right back corner, how long i the traw? Leave your anwer in implet radical form
The length of the straw placed inside the rectangular box is [tex]\sqrt{73}[/tex] inches.
A quadrilateral with parallel sides equal to one another and four equivalent vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel. The area of a rectangle is given as the product of the length and breadth of the rectangle.
The given parameters are:
Length (l) = 6 inchesWidth (w) = 6 inchesHeight (h) = 1 inchesThe straw is said to fit into the box diagonally from the bottom.
So, the length (s) of the straw is calculated as:
[tex]s=\sqrt{l^{2}+w^{2}+h^{2} }\\[/tex]
The equation becomes:
[tex]s=\sqrt{6^{2}+6^{2}+1^{2} }\\[/tex]
Evaluate the exponents:
[tex]s=\sqrt{73}[/tex] inches
=> s≈8.544 inches
Hence, the length of the straw is 8.544 inches.
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Calculate the number of full meals a bag of dog food makes. On average, each dog gets 180 g of food and the bag is 50 kg.
Answer:
277.777778 Or about 277 meals
Step-by-step explanation:
We can find this out by converting 50 kg into grams. There are 1000 grams in a kg. So to convert 50 kg into grams we have to multiply by 1000. 50 x 1000 = 50000 g. 50000g / 180 g = 277.777778 or about 277.
If UY= 3x - 6 and YV = x + 2, find UV.
(WY INTERSECTS UV AT Y)
WY intersects UV at Y and hence the value of UV is 8.
What is point of intersection?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.
Given that WY intersects UV at Y.
Hence, the value of UY = YV.
Substitute the value of UY and YV as follows:
UY = YV
3x- 6 = x + 2
3x - x = 2 + 6
2x = 8
x= 2
Now, the value of UV = UY + YV
Substitute the values:
UV = UY + YV
UV = 3x - 6 + x + 2
UV = 4x - 4
Substitute the value of x as follows:
UV = (4)(2) - 4
UV =8 -4
UV = 4
Hence, the value of UV is 8.
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Suppose your family is going to buy a new air conditioning unit. A more expensive brand cost $2600 to buy but only $50 a month to operate. Let “x” represent time in months.
a. write an equation for the cost of the cheaper brand
b. Write an equation for the cost of the more expensive brand.
c. What is the cost of running the cheaper unit for 36 months?
d. For how many months will the cost of both brands be equal?
An equation for the cost of the cheaper brand is y = 60x + 1,800.
An equation for the cost of the more expensive brand is y = 50x + 2,600.
The cost of running the cheaper unit for 36 months is $3,960.
The number of months for which the cost of both brands would be equal is 8 months.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign variables to the time and cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the time measured in months.Let the variable y represent the cost measured in dollars.Since a brand cost $1800 to buy with a monthly operation fee of $60, an equation for the cost of this cheaper brand is given by:
y = 60x + 1,800.
When x = 36 months, the cost of running the cheaper unit is given by:
y = 60(36) + 1,800.
y = $3,960.
For the more expensive brand, we have:
y = 50x + 2,600.
Next, we would determine the number of months for which the cost of both brands would be equal;
50x + 2,600 = 60x + 1,800
60x - 50x = 2,600 - 1,800
10x = 800
x = 800/10
x = 8 months.
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Complete Question:
Suppose your family is going to buy a new air conditioning unit. One brand costs $1800 to buy and $60 a month to operate. A more expensive brand cost $2600 to buy but only $50 a month to operate. Let “x” represent time in months.
a. write an equation for the cost of the cheaper brand
b. Write an equation for the cost of the more expensive brand.
c. What is the cost of running the cheaper unit for 36 months?
d. For how many months will the cost of both brands be equal?
Alonso's mother drives to the gas station and
fills up her tank. Then she drives to the market.
Sketch the graph that shows the relationship
between the amount of fuel in the gas tank of
her car and time.
(gal)
Therefore , the solution of the given problem of graphs comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.
How do graphs work?Graphs are used by mathematicians to rationally represent or chart facts or values. Typically, a graph tip will show a connection amongst two or more objects. A graph is a type of non-linear data structure that is made up of nodes, and vertices, and edges. affix the nodes, also referred as as vertices. This graph includes elements E=3,2,14,5 , having (2.5) and vertex V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistics charting (bar charts, charts, line charts, etc.). the form of a triangle-shaped logarithmic graph
Here,
If she is first driving toward the gas station, then the graph will be declining.
She fills up her tank at the gas station, which causes the graph to move upward.
After that, the graph will start to decline as she approaches the market.
From the information,
we can simply deduce that the graph will initially start out declining, then quickly increase, and finally have a continuous reduction until we achieve our target.
Therefore , the solution of the given problem of graph comes out to be we can simply deduce that the graph will initially start out declining, then quickly increase.
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How do you get the answer on answering the multiplication of integers?
Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
What is an integer ?All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.
A straight line of numbers is shown visually as a number line.
This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.
The collection of integers can be shown on a number line much like other sets of numbers..
Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
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Which of the following are solutions to the equation below?
Check all that apply.
4x²2²-12x+9=5
□ A. x= √5-3
□ B. x= -√4-3
C. x=--√5 + 3
□ D. x = √5 +
□ Ex= √4-3
□ F. x= -√5-3
Equation 4x222-12x+9=5 has a solution of x= -√4-3. It is said to be linear when an equation has the form y=mx+b .
what is equation ?In algebra, a linear equation is one with the form y=mx+b. B is the slope, and m is the y-intercept. Because y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are those with two variables. There are various examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
4x²2²-12x+9=5
8x2 - 12x +4 = 0
8x2 - 6x - 6x +4 = 0
2x(4x - 3) - 2(3x +2) = 0
Equation 4x222-12x+9=5 has a solution of x= -√4-3 . It is said to be linear when an equation has the form y=mx+b .
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2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check left Side of both equations
The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.
Answer:
2(3b+6) =78 : b=11
-2(6c-3) = -72 : c=6.5
Step-by-step explanation:
They are correct
The function f is defined by f(x) = x^2 +
3x – 10. If f(x - 2) = x^2 + bx + c, what
are the values of b and c?
(Please explain too, I want to know how to do this)
The value of c is -12
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given: f(x) = x² +3x – 10 and f(x - 2) = x²+ bx + c
f(x - 2)= (x-2)²+3x-6-10
= x² -4x+4+3x-16
=x²-x-12
Thus comparing it to the given equation we get c=-12
Hence, the value of c is -12
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A family wants to rent a car to go on vacation. Company A charges $55.50 and 15¢ per mile. Company B
charges $50.50 and 9¢ per mile. How much more does Company A charge for x miles than Company B?
Company A charges $5.00 and 6 cents much more for x miles than Company B. The solution is obtained using arithmetic operations.
What are arithmetic operations?There are four basic operations which are listed as follows: Addition(‘+’): This operation deals with finding the sum. Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product. Division(‘÷’): This operation deals with finding the quotient.
In order to find how much more does company A charge than company B, we need to subtract the charges of company B from that of Company A.
So, on subtracting we get,
$55.50 and 15 cents - $50.50 and 9 cents = $5.00 and 6 cents per mile.
For x miles, we multiply $5.00 and 6 cents by x miles.
Also, we could convert dollars to cents by multiplying it by 100.
as $1 =100 cents.
5565 - 5059 cents = 506 cents.
For x miles, 506x cents.
Hence, Company A charges $5.00 and 6 cents much more for x miles than Company B.
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PLEASE HELP ASAP!!!!!
Answer:
Factored completely is: 3x^2 (x+3)(x-2)
according to your question - probs (x-2), no other choice
Step-by-step explanation:
have fun friend & have a good day friend :)
Suppose the cost of a new computer is $650 and the sales tax is 7.5%. What is the total cost of this computer, including the tax?
Answer: $698.75
Step-by-step explanation: 7.5% of 650 is $48.75. 650 plus 48.75 = 698.75
Consider the following frequency table representing the scores on a test. . Scores on a Test Class Frequency 20-38 7 39-57 5 58-76 9 77-95 5 96-114 3
The answer is :
a) The lower class boundary for the fifth class is 96.
b) The upper-class boundary for the second class is 57.
c) The class width is 18.
d) Number of scores between 19.5 and 95.5 is 26.
a) Fifth class is 96-114.
The lower class boundary for the fifth class is 96.
b) Second class is 39-57.
The upper-class boundary for the second class is 57.
c) Class width = 38- 20 = 18, 57-39 = 18, 76- 58 = 18, 95-76 = 18, 114 - 93=18
So, the class width is 18.
d) Number of scores between 19.5 and 95.5 is = 7 + 5 +9 +5 = 26
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The complete question is:
Consider the following frequency table representing the scores on a test. . Scores on a Test Class Frequency 20-38 7 39-57 5 58-76 9 77-95 5 96-114 3
Required:
a. Determine the lower class boundary for the fifth class.
b. Determine the upper-class boundary for the second class.
c. Determine the class width of each class.
d. Determine the number of scores between 19.5 and 95.5
Help? This be mad confusing
Answer:
Angle EFP = 115
Step-by-step explanation:
3x + 2.5 = 4x - 35
2.5 = x - 35
x = 37.5
3(37.5) + 2.5
= 112.5 + 2.5
= 115
Graph this line:
y + 1=(x-4)
Therefore ,as a result, the solution of the given problem of equation is left side of the line's run is taken into consideration because the slope is positive.
Describe equation.A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two variable on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.
Here,
provided: y + 1= (x-4)
The slope in this case turns out to be =>
=>y = x -5
We obtain m = 1 and an intercept of c = -5 when comparing with the equation y= mx + c.
As a result, the left side of the line's run is taken into consideration because the slope is positive.
We can swap the point for plot the graph by bringing the piece down by -5.
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Micah paint birdhoue to ell at a fair. The table how the amount of paint he ue. I thi a proportional relationhip? If o, find the contant of proportionality and write an equation for the relationhip
The constant of proportionality is 12. The equation to represent the relationship is : b = 12p.
Constant proportional:
A constant of proportionality is a constant value for the ratio of two proportional quantities. If the ratio or product is constant, the two variables are proportional. The value of the constant of proportionality depends on the type of relationship between the two given quantities (positive versus inverse variation).
According to the question:
From the above mentioned , the individual ratio of number of birdhouse (b) cans of paints is:
Now,
For 1st pair,
b/ p = 3/ 1/4
⇒ b / p = 3 ×4 /1
⇒ b/ p = 12
Again,
For 2nd pair,
b /p = 9/0.75
⇒ b /p = 12
For 3rd pair,
b /p = 18/3/2
⇒ b /p = 18× 2/3
⇒ b/ p = 12
Finally,
For 4th Pair =
⇒ b/ p = 20/2.5
⇒ b/ p = 12
As all the ratios are equivalent, the relationship between number of birdhouse (b) and cans of paints (p) is proportional. The constant of proportionality is 12. The equation to represent the relationship is :
b = 12p.
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A metal bar has a length of 3. 0 cm, a width of 3. 0 cm, and a height of 2. 0 cm. What volume of water, in liters, would the bar displace?.
The metal bar would displace 0.018 liters of water.
Volume is the measure of the amount of space occupied by an object or substance. It is often represented by the symbol 'V' and is typically measured in units such as liters (L), cubic meters (m^3), or gallons (gal). In three-dimensional space, the volume of an object is calculated by multiplying its length, width, and height (or depth). In two-dimensional space, the area of an object can be calculated by multiplying its length and width.
The volume of the metal bar is 3 cm x 3 cm x 2 cm = 18 [tex]cm^3[/tex]. The density of water is 1 g/[tex]cm^3[/tex]. To find the volume of water displaced, we need to convert the volume of the bar from cubic centimeters to liters.
1L = 1000[tex]cm^3[/tex]
So the volume of water displaced would be 18 [tex]cm^3[/tex] / 1000 = 0.018 L.
In summary, the metal bar would displace 0.018 liters of water.
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What’s question a? PLEASE HELLPPPP!!!
By using the given formula and solving we get, the original value of the vase is 5000 pounds.
What is percentage?A percentage is a way to express a number as a fraction of 100. It is often denoted by the symbol "%". For example, 25% means 25/100 or 0.25. Percentages are often used to express rates of change or proportions.
What is rate?A rate is a ratio that compares two quantities of different units, such as distance and time, or weight and volume. It is often represented as a fraction or a decimal and can be converted to a percentage by multiplying by 100.
The given formula tells us how the value of the vase changes over time, with the value increasing by a factor of 1.28 (28% increase) every year.
To find the original value of the vase, we need to know the value of the vase when n = 0.
Substituting n = 0 into the formula, we get:
value in pounds = 5000*1.28^0
When n = 0, 1.28^0 = 1, so the original value of the vase is:
value in pounds = 5000*1 = 5000 pounds
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How do you find the area of a triangle in Class 10?
Answer:
1/2 x b x h
Step-by-step explanation:
b = length of the base of the triangle.
h = height of the triangle.
Therefore, the area of the triangle = 1/2 x b x h
Help please! Triangle Proofs are so hard!
The required two-column proof that the triangles are congruent is explained below.
Properties of a congruent triangles.A triangle is a three sided plane shape whose the sum of internal angles is 180^o. Thus two or more triangles are said to be congruent when their corresponding sides and measure of internal angles are equal.
When two triangles are congruent, it can be proven in all respect that they are thus equal (considering their corresponding length of sides and measure of internal angles).
The two-column proof required in the question is given below:
STATEMENT JUSTIFICATION
1. <WXZ ≅ <YXZ Property of an angle bisector.
2. <XZW ≅ <XZY Definition of a perpendicular bisector.
3. WX ≅ YX Congruent sides of a triangle.
4. WZ ≅ YZ Definition of a midpoint.
Therefore,
ΔWXZ ≅ ΔYXZ Angle-Angle-Side theorem
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What is median of a triangle Class 7?
A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.
A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.
It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.
A triangle's median is a straight path that joins a vertices to the midpoint of the following sectors across from it.
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The quadratic number pattern: 4; p; 11; q; 22; ... 4.1 Show that p = 7 and q = 16.
The quadratic pattern with value of p and q has been proved.
Why is quadratic referred to as quadratic?A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word for square, is where the word "quadratic" originates.
Here,
Given : 1st difference
p−4;
11−p;
q−11;
22−q;
2nd difference−2p+15;
q+p−22;
33−2q−2p+15=1−2p=−14p
=733−2q
=1q+p−22
=1−2q=−32or/of
q+7−22=1
q=16
Therefore , the solution of the given problem of quadratic comes out to be q =16
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Sarah walks laps around spring lake park. she can walk 4 laps in 108 minutes. a single walk around is 1.5 miles. Sarah walks at a constant rate.
It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
Sarah walks laps around spring lake park. she can walk 4 laps in 108 minutes.
1 lap = 1.5 miles
4 lap = 6 miles
walking rate = 6 / 108 = 0.056 miles per minute
Now,
time = distance/walking rate
time = 7.5/0.056 = 136.36 minutes
Thus, It would take Sarah 136.36 minutes to walk 7.5 miles around spring lake park.
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M gyo apd o
Solve.
1. Hana is putting the fruit she bought into
bowls. She bought 8 melons, (12 pears,
and 24 apples. She puts
the same number
of pieces of fruit in each bowl and puts
only one type of fruit in each bowl/How
many pieces can Hana put in each bowl?
Hana can put 4 fruits in each bowl. We can solve the given problem by finding the highest common factor using prime factorization.
The highest common factor is what?The Highest Common Factor (HCF) of two numbers is the largest possible number that divides both numbers equally.
There are various methods for calculating the highest common factor between two numbers. The prime factorization method can be used to quickly determine the HCF of two or more numbers.
Examine the many attributes and components of HCF to learn more about it. Find the solutions to questions like what is the highest common factor for a collection of integers, how to quickly calculate the highest common factor, how to compute HCF using the prime factorization, and more to learn more fascinating details about them.
We found that the Highest common factor is 4
then 8 melons can be placed in 2 bowl having 4 melons in each bowl
12 pears can be placed in 3 bowls having 4 pears in each bowl
and lastly, 24 apples can be placed in 6 bowls having 4 apples in each bowl.
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