a. The expressions for c and d in terms of a and b are
c = -2b³/[(a⁴ - b⁴)a] + 1/(a - b) and d = -2b²/(a⁴ - b⁴)b. The inverse of (2,1) is (13/15, -4/15)
The question has to do with binary operation.
What is a binary operation?A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.
a. How to find the expression for c and dSince The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).
Let (e, e') be the identity element.
We know that for any binary operation * on a given set, a*e = a where e is the identity element.
So, (a,b)*(e,e') = (a,b)
So, (a,b)*(c,d) = (ac - bd, ad + bc)
(a,b)*(e,e') = (ae - be, ae' + be')
Since (a,b)*(e,e') = (a,b)
(ae - be, ae' + be') = (a, b)
So,
ae - be = a (1) and ae' + be' = b (2)e = a/(a - b) and e' = b/(a + b)
So, (e, e') = (a/(a - b), b/(a + b))
Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.
Since (c,d) is the inverse of (a,b), we have that
(a,b)*(c,d) = (e, e')
So, (a,b)*(c,d) = (ac - bd, ad + bc)
= (a/(a - b), b/(a + b))
So,
ac - bd = a/(a - b) (3) and ad + bc = b/(a + b) (4)From (3), c = bd/a + 1/(a - b)
Substituting c into (4), we have
ad + bc = b/(a + b)
ad + b[bd/a + 1/(a - b)] = b/(a + b)
ad + b²d/a + b/(a - b) = b/(a + b)
ad + b²d/a = b/(a + b) - b/(a - b)]
(a + b²/a)d = b[1/(a + b) - 1/(a - b)]
[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)
[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)
[(a² + b²)/a]d = b(-2b)/(a² - b²)
d = -2ab²/[(a² - b²)(a² + b²)]
d = -2ab²/(a⁴ - b⁴)
Substitutind d into c, we have
c = bd/a + 1/(a - b)
c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)
c = -2b³/(a⁴ - b⁴) + 1/(a - b)
So, the expressions for c and d in terms of a and b are
c = -2b³/[(a⁴ - b⁴) + 1/(a - b) and d = -2ab²/(a⁴ - b⁴)b. What is the inverse of (2,1)Since (c,d) is the inverse of (a,b) is
c = -2b³/(a⁴ - b⁴)+ 1/(a - b) and d = -2ab²/(a⁴ - b⁴)So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)
= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)
= -2/(16 - 1) + 1/1
= -2/15 + 1
= (-2 + 15)/15
= 13/15
So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)
= -2(2)(1)²/(2⁴ - 1⁴)
= -4(1)/(16 - 1)
= -4/15
So, the inverse of (2,1) is (13/15, -4/15)
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Help please!
A collection of numbers M consists of all positive integers less than 20. If a collection of numbers N is a collection created by randomly choosing five numbers from M. Which of the following must be true about M?
i. The range must be at least 4
ii. The median must be at least 3
iii. The mean can be above 17
a. i only
b. ii only
c. i and ii only
d. i and iii only
The answer choice which represents statements which are correct regarding the datasets described in the task content is; Choice C; i and ii only.
Which of the answer choices represents statements which are true about the dataset described?It follows from the task content that the universal set M is described to contain all positive integers less than 20 while the collection of numbers N is created randomly by choosing five numbers from it.
Consequently, it follows that since 5 number are to be chosen, the range must be at least 4 as this follows from the extreme case scenario of selecting consecutive numbers. Hence, statement i is correct.
Also, the median must be at least three as the extreme case scenario in which numbers 1,2,3,4 and 5 are chosen still renders the median to be 3.
The mean of the five numbers cannot be above 17 because, when when numbers, 15,16,17,18 and 19 are chosen, the mean is 17 and does not exceed 17. Hence, statement iii is incorrect.
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Determine the number of different groups of 5 items that can be selected from 12 distinct items.
There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
According to the given question.
Total number of items, n = 12
Total numbers of items to be selected, r = 5
Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the total number of permutations.
n is the total number of objects.
r is teh total number of objects to be selected.
Therefore,
The number of different groups or permutaions of 5 items that can be selected from 12 distinct group
[tex]^{12} P_{5}[/tex]
[tex]= \frac{12!}{(12-5)!}[/tex]
[tex]= \frac{12!}{7!}[/tex]
[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]
= 12 × 11 × 10 × 9 × 8
= 95040
Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
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what is 1016/86.89 include all your steps
Answer:
11.692945103
Step-by-step explanation:
take out a calculator divide 1016 by 86.89
C is the point on the line y = 2x + 1 where x = 2
Find the co-ordinates of the mid-point of BC.
Based on the calculations, the coordinates of the mid-point of BC are (1, 4).
How to determine coordinates of the mid-point of BC?First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:
At the origin x₁ = 0, we have:
y = 2x + 1
y₁ = 2(0) + 1
y₁ = 2 + 1
y₁ = 3.
When x₂ = 2, we have:
y = 2x + 1
y₂ = 2(2) + 1
y₂ = 4 + 1
y₂ = 5.
In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).
Midpoint on x-coordinate is given by:
Midpoint = (x₁ + x₂)/2
Midpoint = (0 + 2)/2
Midpoint = 2/2
Midpoint = 1.
Midpoint on y-coordinate is given by:
Midpoint = (y₁ + y₂)/2
Midpoint = (3 + 5)/2
Midpoint = 8/2
Midpoint = 4.
Therefore, the coordinates of the mid-point of BC are (1, 4).
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Annel sells a phone which costs $180 and earns $9 commission. If he sells $640
worth of phones the following day, how much will he earn on commission?
Answer:
he will earn 32$ worth of commision
Step-by-step explanation:
so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$ which is 32$
Answer this question please
NO FAKE ANSWERS OR I WILL REPORT
Answer:
D
Step-by-step explanation:
the figure is composed of a rectangle and a right triangle ( top )
calculate the hypotenuse h of the right triangle using Pythagoras' identity
h² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
h = [tex]\sqrt{100}[/tex] = 10
the base of the rectangle is equal to h , then perimeter (P) of pentagon is
P = 10 + 4 + 6 + 8 + 4 = 32 cm
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ the dimensions or the perimeter of the pentagon
What information do we need to find the perimeter:
⇒ the unknown side length
Let's find the unknown side length:
[tex]\hookrightarrow \text{split the pentagon into two shapes as shown in the image below}\\\hookrightarrow \text{the hypotenuse of the right triangle is equal to the length of the unknown side}\\\hookrightarrow\text{hypotenuse}=\sqrt{6^2+8^2}= \sqrt{36+64}=\sqrt{100}=10\\[/tex][tex]\hookrightarrow \text{the unknown side length is 10}[/tex]
Perimeter = 6 + 8 + 4 + 4 + 10 = 32
Answer: 32 or (D)
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the length of a new rectangular playing field is 3 yards longer than quadruple the width. if the perimeter of the rectangular playing field is 586 yards, what are its dimensions?
Answer:
length = 235 yd
width = 58 yd
Step-by-step explanation:
Let the width be W.
L = 4W + 3
perimeter = 2(L + W)
perimeter = 2(4W + 3 + W)
perimeter = 2(5W + 3) = 10W + 6
We are told the perimeter = 586 yd
10W + 6 = 586
10W = 580
W = 58
L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235
length = 235 yd
width = 58 yd
What is the margin of error for 95% confidence for a sample of size 700 where p = 0.65?
A. 0.0455
B. 0.0303
OC. 0.0651
D. 0.0353
Answer:
D 0.0353
Step-by-step explanation:
a= 0.05. p= 0.65. n=700
S N P = 700 × 065 = 45575
1 n ( 1 - p ) = 700× ( 1 - 0.65 ) = 24575
get the sample is big ,. p~ N ( π. √ π ( 1-π ) p - π
-----------. ------- ~ ( o. 1
n Ñ 1 ~ñ
the margin of error ∆ = Z a
-----. =. √ π ( 1 - π )
2 --------
n
according to the standard normal distribution,
Z d
---. = zo.o25 = 1.96
2
∆=1.96×√p ( 1 - p ). =. 1.96 × √ 0.65× ( 1 - 65)
---------. ---------
π. 700
= 0.0353
Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
Which two of the following expressions can be simlified by using the Quotient of Powers Property?
Answer:
[tex]\frac{15x^{4}y^{3}}{5x^{3}} \ \ \text{and }\ -10x^{5}\div 2x^{3}y[/tex]
Step-by-step explanation:
the Quotient of Powers Property :
let a be a number where a ≠ 0
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
……………………
[tex]\frac{15x^{4}y^{3}}{5x^{3}}[/tex]
[tex]= \frac{3 \times 5x^{3}\times x \times y^{3}}{5x^{3}}[/tex]
[tex]= \frac{3 \times x \times y^{3}}{1}[/tex]
[tex]= 3 x y^{3}[/tex]
=============
[tex]-10x^{5}\div 2x^{3}y[/tex]
[tex]= [-5 \times (2x^{3}) \times x^2] \div [(2x^{3}) \times y][/tex]
[tex]= -5 \times x^2 \div y[/tex]
[tex]= -5 x^2 \div y[/tex]
A plate of vegetables and white rice. jace is a vegetarian, eating at a local restaurant. he chooses a grilled tofu salad that includes vegetables. what change can he request to make his meal healthier? he can ask for the tomatoes to be left out. he can ask for brown rice instead of white rice. he can ask for his tofu to be fried instead of grilled. he can ask for fewer sprouts, peas, and cucumbers.
What is the numerical value of mswithin when sswithin= 70, the sample size = 17 and the number of groups = 3? group of answer choices mswithin = 70
The numeric value of ms within is = 19.
What is a numeric value?A real number, regardless of its sign, has a numerical value. A definite quantity is a defined amount measurement.To find the numeric value of ms within:
Given: Swithin = 70, sample size = 17 and number of groups = 3.
So, 17 × 3 = 51
70 - 51 = 19
Therefore, the numeric value of ms within is = 19.
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What are the coordinates of point J'? (-2,-4) (-2,-6) (Negative nine-halves, negative 4) (Negative nine-halves, negative 9)
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Quadrilateral FGHJ is dilated according to the rule Do,Two-thirds(x,y) to create the image quadrilateral F'G'H'J', which is not shown. Quadrilateral FGHJ has points F(-5, -4), G(-3, -2), H(-1, -4) and J(-3, -6).
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
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Answer:
(-2,-4)
Step-by-step explanation:
Geometry B E2020!! :3
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
According to the statement
we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.
So, for this purpose,
we know that the best method show the relationship is a slope intercept form.
So,
The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
And
Using the coordinate points on the plane (0, 6) and (10, 28)
now we Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
And then Determine the y-intercept
6 = 2.2(0) + b
b = 6
And now we have to put in the general form of the slope intercept form which is y = mx + b
Then the equation become
y = 2.2x + 6
So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
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20. A trader took a loan of 1,800.00 at an interest of 12 percent per annum. It was agreed that the loan and the interest must be paid in one year equal monthly instalments.
a) Calculate
i) the interest on the loan.
ii) the amount to be paid at the end of the year.
iii) the monthly instalment.
b) Another trader took a loan at the same rate interest and conditions. If she had to pay $200.00 monthly instalment, find to the nearest cedi, how much she took.
Step-by-step explanation:
i)I=PRT/100
I=1800*12*1/100
I=$216
ii) amount to be paid =1800+216
=$2016
iii) monthly installments=2016/12
=$168
b)I=PRT/100
I=
If a trader took a loan of 1,800.00 at an interest of 12 percent per annum
a. Interest on the loan is $216.
Amount to be paid at the end of the year is $2016
Monthly Installment is $168
b. She took $2184 to the nearest dollar.
What is the Interest?a) i) Interest on the loan:
Interest = Principal × Rate × Time
Interest = $1800 × 0.12 × 1
Interest = $216
ii) Amount to be paid at the end of the year:
Amount = Principal + Interest
Amount = $1800 + $216
Amount = $2016
iii) Monthly installment:
Number of monthly installments = 12
Monthly Installment = Total Amount / Number of Installments
Monthly Installment = $2016 / 12
Monthly Installment ≈ $168
b) Let's X represent the amount she took
Total Payment = Monthly Installment × Number of Months
Total Payment = $200 × 12
Total Payment = $2400
So
Total Payment = X + $216
$2400 = X + $216
Subtract $216 from both sides:
$2400 - $216 = X
$2184 = X
Therefore she took approximately $2184 to the nearest dollar.
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Solve the compound inequality. 5x – 11 < –11 or 4x + 2 > 14
Answer:
5x-11<-11
group like terms
5x<11+11
5x<22
divide both sides by 5
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3 write an equation to determine the area, a, of the patio that will be painted. a = (x 18)(x 35) a = (x 15)(x 25) 30 a = (x 5)(x 22) a = (x 25)(x 15) − 30
The correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
What is Geometrical figure?Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.
According to the given Information:Length of the rectangular patio is (x+25).
Width of the rectangular patio is (x+15).
Length of bench is 5.
Width of the bench is 1.
Area of rectangle:Area of a rectangle is:
A = Length x Width
Area of rectangular patio is:
A[tex]_1[/tex] = (x + 25)(x + 15)
Area of bench is:
A[tex]_2[/tex] = 10 x 3
= 30
The painting area is:
A = A[tex]_1[/tex] - A[tex]_2[/tex]
A = (x + 25)(x + 15) - 30
Therefore, the correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
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In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a total of $258, how much did Seedevi spend?
The amount spent by Seedevi is $66
How to determine the amount spent by Seedevi?From the question, the given parameters are:
Seedevi = half as much money as Georgia,
Seedevi = $6 more than Amy
The three of them = $258
To solve this question, we use the following representations
x = Seedevi
y = Georgia
z = Amy
So, we have the following equations
x = 0.5y
x = 6 + z
x + y + z = 258
Make y and z the subjects
y = 2x
z = x - 6
Substitute y = 2x and z = x - 6 in x + y + z = 258
x + 2x + x - 6 = 258
Evaluate the like terms
4x = 264
Divide by 4
x = 66
Hence, the amount spent by Seedevi is $66
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The function — is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. What are the domain and range of the function h(t)? Round values to the nearest hundredth.
The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].
What are the domain and range of the function as given in the task content?It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.
Also, the range of a function is the set of all possible output values for such function.
On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].
While the range is the difference between the minimum and maximum height attained and can be computed as follows;
At minimum height, t = 0; hence, h(t) = 0.
At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.
Hence, h(1.92) = 18.05.
The range is therefore; [0, 18.05].
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-3p+6p
help simplify
Step-by-step explanation:
-3p+6p is 3p
-3 + 6 = 3
So when you simplify the equation you get 3p
A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The correct answer is D.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given:
A rhombus with horizontal diagonal length 25 millimeters,
and vertical diagonal length 8 millimeters.
Let d₁ = 25 mm and, d₂ = 8 mm.
Let A be the area of rhombus.
To find the area of rhomus:
Using diagonals,
A = (1/2) × d₁× d₂.
Substituting the values of diagonals,
A = 1/2 x 25 x 8
A = 200/2
A = 100 mm².
Therefore, 100 mm² is the area of the rhombus.
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What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
A. 33
B. 57
C. 45
D. 8
Answer: A. 33
Step-by-step explanation:
Practice another write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 4 0, t ≥ 4
Using the Laplace transform to solve the given integral equation f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is [tex]\frac{4(1-2e^-5s)/}{s}[/tex]
explanation is given in the image below:
Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.
The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.
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find the equation of a line that passes through the point (4, 3) and is parallel to the line 2x-2y=11
Answer:
The slope of the line would be y=x-1
Step-by-step explanation:
y=x-1
Subsite
3=4-1
3=3 True,
Thus y=x-1
Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 are labeled negative x and 2 are labeled negative. 3 tiles are in the factor 2 spot: 2 are labeled x and 1 is labeled negative. 12 tiles are in the product spot: 4 are labeled negative x squared, 4 are labeled negative x, 2 are labeled x, and 2 are labeled . which is true regarding adi’s use of algebra tiles?
Answer:
3 tiels are in the factor 2: 2 are labeled x and 1 is labeled negative
Answer: B
Step-by-step explanation:
Practising
and Applying
1. Write each radial in simplified form.
a) √48
b) √ 1000
Answer:
[tex]\Large\boxed{a)~4\sqrt{3} }[/tex]
[tex]\Large\boxed{b)~10\sqrt{10} }[/tex]
Step-by-step explanation:
Question a). √48Given term
[tex]\sqrt{48}[/tex]
Factorize 48 inside the radical sign
[tex]\sqrt{2\times2\times2\times2\times3}[/tex]
Combine terms to form squares
[tex]\sqrt{2^2\times2^2\times3}[/tex]
Simplify the radical sign
[tex](2\times2)\sqrt{3}[/tex]
[tex]\Large\boxed{4\sqrt{3} }[/tex]
Question b) √1000Given term
[tex]\sqrt{1000}[/tex]
Factorize 1000 inside the radical sign
[tex]\sqrt{2\times2\times2\times5\times5\times5}[/tex]
Combine terms to form squares
[tex]\sqrt{2^2\times5^2\times2\times5 }[/tex]
Simplify the radical sign
[tex](2\times5)\sqrt{2\times5}[/tex]
[tex]\Large\boxed{10\sqrt{10} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which function in cryptography takes a string of any length as input and returns a string of any requested variable length?
The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.
According to the statement
we have to explain about the function in which cryptography takes a string of any length as input and returns a string of any requested variable length.
So, For this purpose,
we know that the
A sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length.
So from definition and its working process it is clear that for this purpose the sponge function is used.
this function returns the string of any variable length.
So, The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.
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5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution.
Answer:
Ten thousands place
Step-by-step explanation:
84 530 216
Frm here u can see that the 3 is in the ten thousands place
use the present value formula to determine the amount to be invested now, or the present value needed.
The desired accumulated amount is $50,000 after 14 years invested in an account with 7% interest compounded annually
The amount to be invested now, or the present value needed, is ???
(Round to the nearest cent as needed.)
The amount to be invested now, or the present value needed, is $22873.75
How to find the present value?We solve the problem using the compound interest formula for amount
A = P(1 + r)ⁿ where
P = present value, r = interest rate and n = number of years.What is the present value?Making P subject of the formula, we have
P = A/(1 + r)ⁿ
Given that
A = $50,000, r = 7% = 0.07 and n = 14Substituting the values of the variables into the equation, we have
P = A/(1 + r)ⁿ
P = 50000/(1 + 0.07)¹⁴
P = 50000/(1.07)¹⁴
P = 50000/1.7317
P = 22873.75
So, the amount to be invested now, or the present value needed, is $22873.75
Learn more about present value here:
https://brainly.com/question/20813161
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Orlando is 12 years older than Omar. Carl is three times older than Orlando. The sum of their ages is 68.Find the ratio of Omar’s age to Carl’s age to Orlando’s age.
Step-by-step explanation:
let's name the variables for the age of the people as the people themselves :
orlando = omar + 12
carl = 3×orlando
carl + orlando + omar = 68
using the first equation in the second equation, and then that result and the first equation in the third equation :
carl = 3×(omar + 12)
3×(omar + 12) + (omar + 12) + omar = 68
3×omar + 36 + omar + 12 + omar = 68
5×omar + 48 = 68
5×omar = 20
omar = 4
orlando = omar + 12 = 4 + 12 = 16
carl = 3×orlando = 3×16 = 48
the ratio omar : carl : orlando
4 : 48 : 16 = 1 : 12 : 4
