y = 3sin(πt). This function models the oscillation by representing the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds.
y = 3sin(πt). This function can be used to model the oscillation because it represents the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds. This means that for any given value of t, the value of y will be the sine of π multiplied by t, which will correspond to a certain distance from the equilibrium position. As the oscillation has a frequency of 1 cycle per second, the value of t will increase linearly, and the value of y will oscillate between a maximum and a minimum value. As the distance between the maximum and minimum points of the oscillation is 3 centimeters, the maximum and minimum values of y will be 3 when t is an integer multiple of π. Therefore, the function y = 3sin(πt) can be used to accurately model the oscillation.
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Use the table of random numbers to simulate the situation.
An amateur golfer hits the ball 48% of the time he attempts. Estimate the probability that he will hit at least 6 times in his next 10 attempts.
The estimate of the probability that he will hit at least 6 times in his next 10 attempts is given as follows:
80%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
An amateur golfer hits the ball 48% of the time he attempts, hence we round the probability to 50%, and have that the numbers are given as follows:
1 to 5 -> hits.6 to 10 -> does not hit.From the table, we have 20 sets of 10 attempts, and in 16 of them he hit at least 6 attempts, hence the probability is given as follows:
16/20 = 0.8 = 80%.
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Mark is training for a mini triathlon he rode his bike 3/4 Mille ran 2/4 milks and swam 1/4 mile each day how does the distance he biked in 3 days compare to the distance he swam in 3 days in 5 days in 6 days why
The comparison between the distance he biked and swam is 3 : 1.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.
Given, He rode his bike 3/4 miles and swam for 1/4 mile.
Therefore, The ratio of biking : swimming = 3/4 : 1/4.
Now, Multiplying by 4 to get rid of the denominator we have,
Biking : Swimming = 3 : 1.
As the days in both comparisons increase in the same manner the ratio will remain the same.
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Rewrite the following polynomial in standard form. -2x^3+1/7+x^4-x^2
The value conversion of polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² to standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.
To rewrite the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² in standard form, we need to arrange the terms in decreasing order of their degree, with the highest degree term first.
Rewrite the polynomial with the terms in descending order of degree:
[tex]x^4[/tex] - 2x³ - x² + 1/7
Combine any like terms:
There are no like terms to combine in this polynomial.
Rewrite the polynomial in standard form:
The polynomial in standard form is:
[tex]x^4[/tex] - 2x³ - x² + 1/7
Therefore, the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x^2 in standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.
It is important to remember to always arrange the terms in descending order of degree when writing a polynomial in standard form.
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Using completion of square find a general solution to ax^(2) + bx + 1 = 0. What are the conditions for both the solutions to be real and for both to be complex numbers.
To find a general solution to the equation ax^(2) + bx + 1 = 0 using the completion of the square, we need to follow these steps:
1. Divide the entire equation by a to get x^(2) + (b/a)x + 1/a = 0.
2. Move the constant term to the right side of the equation: x^(2) + (b/a)x = -1/a.
3. Complete the square by adding (b/2a)^(2) to both sides of the equation: x^(2) + (b/a)x + (b/2a)^(2) = -1/a + (b/2a)^(2).
4. Factor the left side of the equation: (x + b/2a)^(2) = -1/a + (b/2a)^(2).
5. Take the square root of both sides of the equation: x + b/2a = ±√(-1/a + (b/2a)^(2)).
6. Solve for x: x = -b/2a ± √(-1/a + (b/2a)^(2)).
This is the general solution to the equation.
The conditions for both solutions to be real are that the discriminant, -1/a + (b/2a)^(2), is greater than or equal to 0. This means that b^(2) - 4a >= 0.
The conditions for both solutions to be complex numbers are that the discriminant, -1/a + (b/2a)^(2), is less than 0. This means that b^(2) - 4a < 0.
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Please show your work.
In the triangle DEF the measure of angle E is obtained as (183 - 9x)°.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In the triangle DEF the value for ∠D = (4x + 1)°.
In the triangle DEF the value for ∠F = (5x - 4)°.
According to the properties of a triangle, the sum of angles of a triangle is equal to 180°.
So, the equation will be -
(4x + 1)° + (5x - 4)° + ∠E = 180°
Evaluate the expression -
(9x - 3)° + ∠E = 180°
∠E = 180° - (9x - 3)°
∠E = 180° - 9x + 3°
∠E = (183 - 9x)°
Therefore, the value for angle E is (183 - 9x)°.
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Angie used a twenty-dollar bill to pay for a bottle of water. The cashier gave her back 1 ten-dollar bill, 7 one-dollar bills, 3 quarters, and 2 pennies as change. How much did Angie's bottle of water cost?
$
Answer:
$2.23
Step-by-step explanation:
To find the cost of the bottle of water, we need to subtract the amount of change that Angie received from the twenty-dollar bill that she used to pay. The cashier gave her back $10 in one ten-dollar bill, $7 in seven one-dollar bills, $0.75 in three quarters, and $0.02 in two pennies.
Therefore, the total change that Angie received was: $10 + $7 + $0.75 + $0.02 = $17.77
To find the cost of the bottle of water, we need to subtract this amount from the twenty-dollar bill: $20.00 - $17.77 = $2.23
Therefore, the bottle of water cost $2.23.
sharah has 35 coins in her pocket, all of which are dimes and quarters. if they are worth a total of $5.30, how many of each kind dose she have?
The number of each kind of coins Sharah have is 23 dimes and 12 quarters.
Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:
x + y = 35 (the total number of coins)
0.10x + 0.25y = 5.30 (the total value of the coins)
We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:
x = 35 - y
Now we can substitute this into the second equation:
0.10(35 - y) + 0.25y = 5.30
3.50 - 0.10y + 0.25y = 5.30
0.15y = 1.80
y = 12
Now we can use this value of y to solve for x:
x = 35 - 12 = 23
So Sharah has 23 dimes and 12 quarters.
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LINEAR EQUATIONS AND INEQUALITIES Translating a phrase into a two-step expression Translate this phrase into an algebraic expression. 15 more than twice Chrissy's savings Use the variable c to represent Chrissy's savings.
The algebraic expression that translates the given phrase is 2c + 15, where c is the amount of Chrissy's savings.
To translate the phrase "15 more than twice Chrissy's savings" into an algebraic expression:
1. First, we need to identify the variable. In this case, the variable is c, which represents Chrissy's savings.
2. Next, we need to identify the operations and numbers involved in the phrase. The phrase "twice Chrissy's savings" means that we need to multiply c by 2.
3. The phrase "15 more than" means that we need to add 15 to the result of the multiplication.
4. Putting these steps together, we get the algebraic expression 2c + 15.
So the final answer is 2c + 15.
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Tell whether (-1,9) is a solution to inequality. Hint: plug in the point. 2x+y<-3
No, (-1,9) is not a solution to the inequality 2x+y<-3.
What is inequality?Inequality is when something is not equal in terms of rights, resources, opportunities or outcomes between different groups or individuals.
To determine if a point is a solution to an inequality, we can plug in the x and y values of the point into the inequality and see if it is true.
In this case, we plug in x=-1 and y=9 into the inequality:
2(-1)+9<-3
Simplify:
-2+9<-3
7<-3
This is not true, so (-1,9) is not a solution to the inequality.
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NEED HELP ON THIS ASAP
The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function
[tex]h(x) = 6x + 66x^2 + 17[/tex].
What are expressions in standard form?A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].
The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.
The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.
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Abstract Algebra (6408 Math) Homework (3) Let \( R \) be a ring. Question 1 Show that \( 0_{R} x=0_{R} \) for all \( x \in R \). Question 2 If \( a, b \in R \), show that \( -(a b)=(-a) b \). Best wis
Abstract Algebra
By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.
Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.
Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.
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A venue sells seated, standing and VIP tickets.
The seated and standing tickets are in the ratio 1:2
The standing and VIP tickets are in the ratio 6:1
What percentage of the tickets sold are standing?
The percentage of those standing is 60%
How to determine the percentage of those standingFrom the question, we have the following parameters that can be used in our computation:
The seated and standing tickets are in the ratio 1:2The standing and VIP tickets are in the ratio 6:1Using the above as a guide, we have the following:
Seated : Standing = 1 : 2
Standing : VIP = 6 : 1
Multiply Seated : Standing = 1 : 2 by 3
Seated : Standing = 3 : 6
Standing : VIP = 6 : 1
Combine the ratios
Seated : Standing : VIP = 3 : 6 : 1
So, we have
Standing = 6/(3 + 6 + 1) * 100%
Evaluate
Standing = 60%
Hence, the percentage is 60%
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Work out (h+4)/(2)-(h+5)/(7) Give your answer as a single fraction in its simplest form.
The answer is (5h+18)/(14).
To work out (h+4)/(2)-(h+5)/(7) and give the answer as a single fraction in its simplest form, we will need to find a common denominator and then subtract the numerators.
Step 1: Find a common denominator. The common denominator of 2 and 7 is 14.
Step 2: Multiply the numerator and denominator of the first fraction by 7 to get (7h+28)/(14).
Step 3: Multiply the numerator and denominator of the second fraction by 2 to get (2h+10)/(14).
Step 4: Subtract the numerators: (7h+28)-(2h+10) = 5h+18.
Step 5: Place the difference over the common denominator: (5h+18)/(14).
Step 6: Simplify the fraction if possible. In this case, the fraction cannot be simplified further.
Therefore, the answer is (5h+18)/(14).
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(a) [Marks=5] Construct a one replicate of a 24 factorial design in factors A, B, C and D in blocks of size 4 by confounding the interactions ABC and ACD with the blocks. Show your steps clearly. Listing the contents of two blocks, one of which contains the treatment combination (1) and the other contains treatment combination a, will suffice the purpose.
(b) [Marks=1] What other interactions, if any, are confounded with the blocks.
Other interactions that are confounded with the blocks are BCD and BCD.
(a) Constructing a one replicate of a 24 factorial design in factors A, B, C, and D in blocks of size 4 by confounding the interactions ABC and ACD with the blocks:
1. Number the blocks from 1 to 4.
2. Assign the factor levels to each block, so that the interactions ABC and ACD are confounded. One possible way to do this is as follows:
3. List the contents of two blocks, one of which contains the treatment combination (1) and the other contains treatment combination a.
(b) Other interactions that are confounded with the blocks are BCD and BCD.
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i need help with finding the domain and range for this will give brainliest
For the given function we have:
domain [0, 76,867] and range [$0, $12,375,587]
How to find the domain and range?We know that x represents the number of people in atendance, then:
R(x) = 161*x
Represents the revenue.
The domain is the set of possible inputs, and it will go between 0 and 76,867 (total number of seats).
The range will go between:
R(0) = 161*0 = 0
R(76,867) = 76,867*161 = 12,375,587
Then the domain is all the integers in [0, 76,867] and the range is [$0, $12,375,587]
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Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?
Answer:
3 pages per minuet 90pages/30min=3 pages per min
Step-by-step explanation:
Answer:
3 pages
Step-by-step explanation:
Create a ratio:
30 minutes is equal to 1 hour
90 pages/30 minutes
Divide 90/30
90/30=3
Alya reads 3 pages per minutes
Hope this helped you!
Stay safe and have a good day/night! :)
Jack is ten years older than Anna. Seven years from now Jack will be twice as old as Anna. How old is Jack now?
Jack is 13 years old now.
To solve this problem, we can use algebra to set up an equation and solve for Jack's age. Let's let J represent Jack's age now, and A represent Anna's age now.
According to the problem, Jack is ten years older than Anna, so we can write:
J = A + 10
Seven years from now, Jack will be twice as old as Anna, so we can write:
J + 7 = 2(A + 7)
Now we can substitute the first equation into the second equation to solve for A:
A + 10 + 7 = 2(A + 7)
A + 17 = 2A + 14
A = 3
Now that we know Anna's age, we can plug it back into the first equation to find Jack's age:
J = 3 + 10
J = 13
So Jack is 13 years old now.
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Is 6x-2 equivalent to 2-6x
Answer:
No
Step-by-step explanation:
6x-2
Factor out -1
( - -6x + -2)
- ( -6x +2)
- ( 2 -6x)
This is not equal to (2+6x) because of the negative sign out front.
A bee population of 3000 increases by 40% every year.
Answer:
That is the answer
Step-by-step explanation:
how old am i if 400 reduced by 2 times my age is 300?
Answer:
You are 78 years old.
Answer:
Naw bro you're 0
Step-by-step explanation:
What is the value of X?
The measure of angle x is 19.5
What is Angle Sum Property?Octagon interior angles sum is equal to 1080 degrees. Also, the sum of all eight exterior angles is equal to 360 degrees.
We have Polygon of 8 side called Octagon.
Also, a Regular Octagon have all of its angles equal
So, Using Angle Sum Property
sum of all internal angle of Octagon = 1080
8 x 6(x+3)= 1080
6(x+3) = 1080/8
6x+ 18 = 135
6x = 135- 18
6x = 117
x= 19.5
Thus, the value of x is 19.5
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Find the value of AC and BD
The values are given as follows:
AC = 25.BD = 12.4.How to obtain the values?The value of AC can be obtained applying the Pythagorean Theorem, as follows:
(AC)² = 20² + 15²
AC = sqrt(20² + 15²)
AC = 25.
Then there are two similar triangles, with dimensions given as follows:
BC = 15 and DC = x.AB = 20 and AD = 25 - x.Then the value of x is obtained as follows:
15/20 = x/(25 - x)
3/4 = x/(25 - x)
4x = 3(25 - x)
7x = 75
x = 10.7.
Then the altitude BD is obtained with the geometric mean theorem as follows:
BD² = 10.7 x (25 - 10.7)
BD² = 153
BD = sqrt(153)
BD = 12.4.
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[(0)/(1) Points ] DETAILS PREVIOU. Simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8))
The simplified the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)) is (x+9)/(x+7).
To simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)), we can follow the following steps:
Step 1: Find the common denominator for the fractions in the numerator and denominator. In this case, the common denominator is (x+8).
Step 2: Multiply the numerator and denominator of the expression by the common denominator to get rid of the fractions. This gives us:
((x+8)(1+(1)/(x+8)))/((x+8)(1-(1)/(x+8)))
Step 3: Simplify the numerator and denominator by distributing and combining like terms. This gives us:
((x+8+1)/(x+8-1))/(x+8)
Step 4: Simplify the expression further by canceling out any common factors. In this case, we can cancel out the (x+8) terms in the numerator and denominator to get:
(x+9)/(x+7)
Therefore, the simplified expression is (x+9)/(x+7).
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PLEASE HELP WITH THESE 4 QUESTIONS!!! 70 POINTS!!!
Answer:
1: x=2
Step-by-step explanation:
Do you know the pythagorean theorem?
a2 + b2 = c2
1) We will square all the sides:
2[tex]\sqrt{2}[/tex] -squared- 2(4)=8
x squared= [tex]x^{2}[/tex]
[tex]x^{2} +x^{2} =2x^{2} =8[/tex]
[tex]2x^{2} =8[/tex]
[tex]x^{2} =4[/tex]
x=2
2: [tex]\sqrt{3}[/tex] we will square to make 3
same with x to [tex]x^{2}[/tex]
and y to [tex]y^{2}[/tex]
3+[tex]x^{2}[/tex]=[tex]y^{2}[/tex]
Since the ratio of the sides is 1: 2: 3
Imma continue typing later srry gtg
Given: /\ABC, KM|| AC
a) AB=10, KB=2, KM=1
AC-?
b) KM=3, AC=6,BC=9
BM-?
c)BC=25, MC=10, AC=5
KM-?
d)AK=10,KB=4,BC=21
BM-?,MC-?
As we see, triangle ABC is congruent to triangle BMK so, a) length of AC = 5
b) length of BM = 4.5
c) length of KM = 3
d) length of BM = 3.42 , MC = 17.58
We have a triangle ABC and KM, a segment is parallel to AC, i.e., KM || AC. First we show that triangle ABC is congruent to triangle BMK. AC and AB are transversals that intersect parallel lines. Since the two pairs of corresponding angles created by this intersection are equal, that is,
∠ BKM =∠ BAC and ∠ BMK = ∠ BCA
By Angle-Angle congruence rule, ∆ ABC is similar to triangle BMK, i.e., ∆ABC ~ ∆BMK. When two triangles are similar, the ratios of the lengths of their corresponding sides are equal, KB/AB = KM/AC --(1) or
BM/BC = KM/AC --(2)
a) AB = 10, KB = 2, KM = 1, determine AC=?
from equation (1), KB/AB = KM/AC
=> 2/10 = 1/AC
Cross multiplication
=> 2 AC = 10
=> AC = 5
b) KM= 3, AC = 6,BC = 9, determine BM= ?
from equation (2), BM/BC = KM/AC
=> BM/9 = 3/6
Cross multiplication
=> 6 BM = 27
=> BM = 9/2
=> BM = 4.5
c)BC = 25, MC = 10, AC = 5, determine KM= ?
BM = BC - MC = 25 - 10 = 15
from equation (2), BM/BC = KM/AC
=> 15/25 = KM/5
Cross multiplication
=> 25 KM = 15×5
=> KM = 75/25
=> KM = 3
d)AK = 10, KB = 4, BC = 21, determine BM=? and MC= ?
AB = AK + KB = 10 + 4 = 14
from equations (1) and (2),BK/AB = BM/BC
=> 4/14 = BM/21
Cross multiplication
=> 14 BM = 21 × 4
=> BM = 84/14 = 24/7
=> BM = 3.42
so, MC = BC - BM = 21 - 3.42 = 17.58
Hence, required value is 3.42..
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Complete question:
Given: ∆ABC, KM|| AC. See the above figure.1.
a) AB=10, KB=2, KM=1
AC-?
b) KM=3, AC=6,BC=9
BM-?
c)BC=25, MC=10, AC=5
KM-?
d)AK=10,KB=4,BC=21
BM-?,MC-?
Jan is researching the average annual income that people earn in her state based on the level of education they have received.
Based on the table, how much more would someone with a bachelor’s degree earn compared to someone with a high school diploma over a period of 30 years?
Step-by-step explanation:
well, we don't need to look for any fancy calculation tricks.
all we need to do is calculate the amounts in both cases and then calculate the difference.
bachelor's degree income in 30 years :
59,100×30 = $1,773,000
high school diploma income in 30 years :
35,250×30 = $1,057,500
the difference is
$1,773,000 - $1,057,500 = $715,500
a person with a bachelor's degree would earn
$715,500
more over a period of 30 years than a person with only a high school diploma.
this is not considering the changes of the income levels over the period of 30 years (that adds insult to injury ...).
What does it equal?
-8=z/14
If you are solving for z:
-8=z/14
multiply by 14 on both sides:
z = -112
2. Kobe scored 85 points in a basketball game. That was 1/8 of the points that he scored
for the season. How many points did Kobe score in the season?
The length of an arc RV of circle M with a radius of 6 units is 3pi/2 units. What is the approximate measure of angle RMV?
the options are
A- 15
B- 45
C-66
D-231
Answer:
The formula for the length of an arc of a circle is given by:
length of arc = (central angle/360) x 2πr
where r is the radius of the circle and the central angle is measured in degrees.
In this problem, we know the length of arc RV is 3π/2 units and the radius of circle M is 6 units. Therefore, we can solve for the central angle using the formula above:
3π/2 = (central angle/360) x 2π(6)
3π/2 = (central angle/180) x π x 6
3/2 = (central angle/180) x 6
central angle = (3/2) x (180/6) = 45 degrees
So the approximate measure of angle RMV is 45 degrees, which corresponds to option B.
Three partners luc, Deborah and Melanie R176 496,R29 416 and R102 956
Among Luc, Deborah, and Melanie, the ratio in which the profit was shared is 2:3:7.
Let us assume that the ratio in which the profit shared among the three partners is L:D:M,
We know that the total profit for the year is = R176496,
We also know that Luc received R29416 and
Melanie received R102956.
So, Deborah profit share is calculated as;
⇒ Deborah's share = Total profit - Luc's share - Melanie's share
⇒ Deborah's share = R176496 - R29416 - R102956
⇒ Deborah's share = R44124,
So, now we know that the ratio of the profit shared among the three partners is:
⇒ L:D:M = R29416 : R44124: R102956
To simplify this ratio, we can divide all the amounts by R14708,
We get,
⇒ L:D:M = 2:3:7
Therefore, the profit was shared in the ratio of 8:1:28 among Luc, Deborah, and Melanie.
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The given question is incomplete, the complete question is
Three partners Luc, Deborah and Melanie, share the profits of a business. The profit for the year is R176496. If Luc receives R29416 and Melanie receives R102956, determine the ratio in which the profit was shared.
