When the thickness of a textbook is b mm the expressions for:
thickness of 5 stacked textbooks = 5b mm
thickness of each page, if the pages are numbered to 225 = b / 225
How to write the expressions for each conditionThe thickness for each of the condition is written as follows
For the thickness of 5 stacked textbooks
= b + b + b + b + b
= 5b
For thickness of each page, if the pages are numbered to 225
In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book
= b / 225
Learn more about division at:
https://brainly.com/question/941863
#SPJ1
(v-7)(v+5)(v-3)=0 solve the quadraticequation
A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3
Solving quadratic equations?The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given the quadratic expression below:
(v-7)(v+5)(v-3)=0
Required
The solution to the system of equation
Equate each expression to zero calculate the value of 'v' as shown:
v - 7 = 0
v = 0 + 7
v = 7
Also, v + 5 = 0
v = 0 - 5
v = -5
Similarly, v - 3 = 0
v = 0 + 3
v = 3
Hence the solution to the given equation is v = 7, -5 and 3
Learn more on quadratic equation here; https://brainly.com/question/1214333
#SPJ1
Factor completely 640-10x^2
Answer:
Step-by-step explanation:
640 - 10x^2 = (4x-10)(160 + 4x)
The factors of 640-10x^2 are (4x-10) and (160 + 4x).
A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 6
meters long and each piece of plastic pipe was 1 meter long. He bought 10 pieces of pipe.
The total length of the pipe was 35 meters. How many pieces of each type of pipe did the
plumber buy?
pieces of copper pipe
pieces of plastic pipe
Submit
The plumber bought 5 pieces of copper wire and 5 pieces of plastic wire.
What is an equation?
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Length of each piece of copper wire = 6 m
Length of each piece of plastic wire = 1 m
Total number of pipes bought = 10
Total length of pipes = 35 m
Let the number of copper pipes be x.
Let the number of plastic pipes be y.
The equation for number of pipes will be -
x + y = 10...(1)
The equation for length of pipes will be -
6x + y = 35...(2)
Subtracting equation (1) from (2) -
5x = 25
x = 5
Substituting the value of x in equation (1) -
5 + y = 10
y = 10 - 5
y = 5
Therefore, the number of copper and plastic wires is 5 each.
To learn more about equation from the given link
https://brainly.com/question/14107099
#SPJ1
Find the median and mean of the data set
below:
7, 47, 43, 47, 25, 16, 18
Median :
Mean :
Answer:
25 median. 29 mean.
Step-by-step explanation:
7, 16, 18, 25, 43, 47, 47
25 is the middle number when ordered by value, so 25 is the median
7 + 47 + 43 + 47 + 25 + 16 + 18 = 203
203 / 7 (amount of numbers in the set) = 29
29 mean
What is 1/5 x ( 7 x -4) =
Answer:
7x2−4x/5
Step-by-step explanation:
7x2−4x over 5
What happens to the perimeter of the frame
when it becomes a parallelogram?
The perimeter of the parallelogram is
less than the perimeter of the square.
The perimeter of the parallelogram is
the same as the perimeter of the square.
The perimeter of the parallelogram is
greater than the perimeter of the square.
The perimeter of the parallelogram is greater than the perimeter of the square.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".
Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".
Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.
Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,
Now, let's calculate perimeters of both the figures -
Square of side length " a " = a + a + a + a = 4a
Parallelogram of two base side length " a " and two parallel set lines of length √2a
= a + a + √2a + √2a
= 2a + 2√2a
= 2a [ 1 + √2 ]
Hence, the acquired perimeter of Parallelogram is greater than that of square
Learn more about perimeter from the given link
https://brainly.com/question/345835
#SPJ1
A polling agency showed the following two statements to a random sample of 2,150 adults in the United States.
Equal pay statement: The issue of equal pay should be given priority over increasing the minimum wage.
Minimum wage statement: Increasing the minimum wage should be given priority over the issue of equal pay.
The order in which the statements were shown was selected randomly for each person in the sample. After reading the statements, each person was asked to choose the statement that was most consistent with his or her opinion. The results are shown in the table.
Percent of Sample
Equal Pay Statement Minimum Wage Statement No Preference
50% 42% 8%
Part A: Assume the conditions for inference have been met. Construct and interpret a 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement. (5 points)
Part B: One of the conditions for inference that is met is that the number of those who chose the minimum wage statement and the number of those who did not choose the minimum wage statement are both greater than 10. Explain why it is necessary to satisfy this condition.
a) The 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement is given as follows: (0.3926, 0.4474).
The interpretation is that we are 99% sure that the true population proportion is in this interval.
b) The condition has to be satisfied as the confidence interval is constructed considering an assumption of normality, and by the Central Limit Theorem, at least 10 successes and 10 failures are needed for the sampling distribution of sample proportions to be normal.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The sample size and the estimate are given as follows:
[tex]n = 2150, \pi = 0.42[/tex]
Hence the lower bound of the interval is given as follows:
[tex]0.42 - 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.3926[/tex]
The upper bound of the interval is given as follows:
[tex]0.42 + 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.4474[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Given a set A={1,2,3,4,5,6,7}
Define a relation induced by the partition of set A and that partition must contain of at least 3 subsets.
Given a set A={1,2,3,4,5,6,7}, a relation induced by the partition of set A is
(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}
What is a set?Generally, A set comprises elements or members that may be mathematical objects of any sort, including numbers, signs, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical formula for a collection of various things.
A relation induced by a partition of a set is a relation that defines a way of grouping elements in the set into subsets, called "blocks" or "cells". In this case, the set
A={1,2,3,4,5,6,7}
can be partitioned into at least 3 subsets. For example, one possible partition is
A={1,2,3}, {4,5}, {6,7}.
The relation induced by this partition is a relation that assigns to each element in one of the 3 subsets, i.e.
(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}
Read more about set
https://brainly.com/question/8053622
#SPJ1
help me pleace!!!!!!!
Step-by-step explanation:
For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.
For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.
For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.
Because 2×3=6
Is this equation an identity?
k - 4 = 4 + k
Yes or No
Answer:
no
Step-by-step explanation:
An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.
That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.
If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.
[tex]k - 4 = 4 + k[/tex]
[tex]0 - 4 \stackrel{?}{=} 4 + 0[/tex]
[tex]-4 \ne 4[/tex]
We have found one value for k that results in an inequality. Thus, this equation is not an identity.
a flower bed is the shape of a triangle with one side twice the length of the shortest side and the third side is
25 feet more than the length of the shortest side. find the dimensions if the perimeter is 133 feet
The dimensions of the sides of the triangular flower bed are 27ft, 54ft and 52ft.
What are the dimensions of the triangular flower bed?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
Given the data in the question;
Let the shortest side b x.
Shortest side = xSecond side = 2xThird side = x + 25Perimeter = 133 ftSince a triangle has three side, the perimeter of the triangle will be;
Perimeter = side 1 + side 2 + side 3
Plug in the values and solve for x
133 = x + 2x + x +25
133 = 4x + 25
133 - 25 = 4x
108 = 4x
4x = 108
x = 108/4
x = 27
Therefore, the dimensions of the flower bed are;
Shortest side = x = 27ft
Second side = 2x = 2( 27) = 54 ft.
Third side = x + 25 = 27 + 25 = 52 ft
Learn more about of triangles here: https://brainly.com/question/27490624
#SPJ1
NO LINKS!!
1. Underline the hypothesis and circle the conclusion in the following conditional statement. Then rewrite the conditional statement in if-then form.
a. All 120° angles are obtuse angles.
2. Write the negation of the following statement:
a. It is raining
Answer:
1. Hypothesis: "All 120° angles"
Conclusion: "are obtuse angles"
If-then statement: If an angle measures 120°, then it is an obtuse angle.
2. It is not raining.
Step-by-step explanation:
Question 1Conditional statement
"If this happens, then that will happen."
Hypothesis: The part after the "if".Conclusion: The part after the "then".For the statement "All 120° angles are obtuse angles":
Hypothesis: "All 120° angles"Conclusion: "are obtuse angles"Therefore, the statement written in the if-then form is:
If an angle measures 120°, then it is an obtuse angle.Question 2Given statement:
"It is raining"The definition of a negation of a statement is the opposite of the given statement. For example, the negation of statement "p" is "not p."
Therefore, the negation of the given statement is:
"It is not raining"Complete the regression equation below.
F(x)=
The regression equation, given the line of best fit and the points on the line, would be F ( x ) = 30x + 685
How to find the regression equation ?To find the regression equation, you first need to find two points on the line on the graph. Those two lines would be ( 3, 775) and ( 4 , 805).
The next step would be to find the slope of the line :
= ( Y₂ - Y ₁ ) / ( X ₂ - X ₁ )
= ( 805 - 775 ) / ( 4 - 3 )
= 30 / 1
= 30
Then use the points to find the y - intercept :
y = mx + y- intercept
775 = 30 ( 3 ) + y - intercept
y - intercept = 775 - 90
y - intercept = 685
The regression equation is:
F ( x ) = 30x + 685
Find out more on regression equation at https://brainly.com/question/25987747
#SPJ1
Find a counterexample to show that the statement is false. (Select all that apply.)
X >
none of these
X> 2
-1 < x < 0
0 < x < 1
XS-1
X> 1
X
A building has a number of floors of equal helght, as well as a thirty-foot spire above them all. If the
height of each floor In feet is h, and there are n floors in the building, which of the following represents
the building's total height In feet?
A.) n+h+30
B.)nh+30
C.)30n+h
D.)30h+n
The total height of the building would be nh + 30.
Option (B) is correct.
What is a simplification in mathematics?
In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.
The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.
So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:
= n * h + 30
=nh + 30
This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.
Hence, the total height of the building would be nh + 30.
To learn more about the simplification, visit:
https://brainly.com/question/28595186
#SPJ1
The cab charges in a metro city include a fixed charge plus the charges for the distance covered. Linus traveled 11 miles and paid $88. For the ride of 16 miles, he paid $108. How much would Linus have to pay to travel 6 miles?
$268.00
$128.00
$98.00
$68.00
Answer:
Step-by-step explanation:
The problem can be solved by using the information provided to set up a system of equations and then solving for the unknown variable, which in this case is the fixed charge.
Let x be the fixed charge.
We know that the total cost of the 11-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:
x + 11y = 88 (1)
We also know that the total cost of the 16-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:
x + 16y = 108 (2)
Where y is the cost per mile
We can solve for y by subtracting equation (1) from equation (2), so:
16y - 11y = 108 - 88
5y = 20
y = 4
Now we know that cost per mile is 4$, we can substitute it in equation (1)
x + 11(4) = 88
x = 24
Now we know the fixed charge is 24$ and cost per mile is 4$, we can calculate the fare for 6 miles
24 + 6(4) = $48
Therefore, Linus would have to pay $48 to travel 6 miles.
[tex]x^{2} +5x-14[/tex]
[tex] \sf {x}^{2} + 5x - 14 \\ \sf {x}^{2} - 2x + 7x - 14 \\ \sf x(x - 2) + 7(x - 2) \\ \sf \: (x - 2)(x + 7) = 0 \\ \sf \: x = 2 \: and \: x = - 7[/tex]
I need help with this
Using the above equation 1/i is equal to 2/(9-5j^2+3k)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given; 2i+5j^2-3k=9
2i+5j^2-3k=9
2i=9-5j^2+3k
i=(9-5j^2+3k)/2
1/i=2/(9-5j^2+3k)
Therefore, the value of 1/i according to the given equation will be
2/(9-5j^2+3k)
Learn more about quadratic equations;
https://brainly.com/question/17177510
#SPJ1
PLS HELP
Use the product rule to simplify
The expression √5x × √30x is simplified using the product rule to give 12.25x
What is square root?Square root of a number can be defined as the inverse operation of the square of a number.
It is the number obtained by finding a number that when squared would give the original number.
Square root is represented using the symbol '√ '. The symbol is called a radical.
Also, the number under the symbol is called the radicand.
To multiply two square roots, we have to multiply the radicands and leave the radical sign.
From the information given, we have;
√5x × √30x
Multiply the radicands and retain the square root symbol, we have;
√150x²
Find the square root
12.25x
Hence, the value is 12.25x
Learn more about square root here:
https://brainly.com/question/3617398
#SPJ1
Dominic fills some jars with chutney that
he has made.
Each jar weighs 230 g when it is empty
and can contain 300 cm³ of chutney.
8 full jars of chutney weigh a total of
5.68 kg.
Calculate the density of the chutney, in
g/cm³.
If your answer is a decimal, give it to
1 d.p.
Answer:
1.6 g/cm³
Step-by-step explanation:
230g = 0.23 kg
0.23 kg x 8 = 1.84 kg
So, the weight of chutney in the 8 jars is 5.68kg - 1.84kg = 3.84kg or 3840g.
So, 1 jar weight is 3840g/8 or 480g of chutney.
Density = 480/300 or 1.6 g/cm³
Answer:
2.36
Step-by-step explanation:
5.68 kg into grams = 5680 and 300*8 is 2400
5680/2400 is 2.36
On April 11, George Jimerson had $6,521.37 in his savings account. The account pays 5.5% interest
compounded daily. How much interest will the money earn by June 30?
The interest George Jimerson would earn by June 30 be $83368.21
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let y represent the amount of money in Jimerson savings account after x days.
The account pays 5.5% interest compounded daily, hence:
y = 6521.37(1.055)ˣ
In June 30, the number of days from April 11 is 49. Hence;
y = 6521.37(1.055)⁴⁹ = 89889.58
The interest = 89889.58 - 6521.37 = 83368.21
The interest would be $83368.21
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Assume a total current of 2 amperes flows in a circuit with three resistorsR1 has a value of 1400 ohms, R2 has a value of 200 ohms and R3 has a value of 100 ohms , producing a total resistance of 80 ohms for the circuit. What is the amount of the current flow through resistor R3?
Answers:
(A)0.114
(B)0.800
(C)1.600
(D)0.228
1.600 amps of current flow through resistor r3 are measured.
Describe the resistor.A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.
Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.
The parameters are determined by the query:
total current = 2 amperes
Total resistance = 80 ohms
Total current = voltage * Resistance
Total current = 2* 80
= 160V.
Consequently, the current passing through resistor R3 will be
V= IR (Ohms law)
where I (current)= V/R
current = 160/ 100
Current flowing through R3 =1.600 amperes.
To know more about Resistors visit:-
https://brainly.com/question/29052966
#SPJ1
An object moves along a straight and horizontal path with a constant acceleration. If the velocity increases from rest to 11.53m/s in 5.44s, determine the acceleration of the object.
Just before Henderson Laboratories opened for business, Eugene Henderson, the owner, had the following assets and liabilities. Cash $ 39,900 Laboratory equipment 75,000 Laboratory supplies 6,200 Loan payable 14,500 Accounts payable 9,725
If Just before Henderson Laboratories opened for business. The totals that would appear in the firm’s fundamental accounting equation is $96,875
How to find the total that will appear in the accounting equation?Using this formula
Assets = Liabilities + Owner’s Equity
Total Owners Equity = Assets - Liabilities
Where:
Assets:
Assets = Laboratory Equipment + Laboratory supplies+ Cash
Assets=$75,000 + $6,200 + $39,900
Asset= $121,100
Liabilities:
Liabilities= Loan Payable+ Accounts Payable
Liabilities = $14,500 + $9,725
Liabilities= $24,225
Let plug in the formula
Total Owners Equity = Assets - Liabilities
Total Owners Equity =$121,100 - $24,225
Total Owners Equity= $96,875
Therefore the totals that would appear in the firm’s fundamental accounting equation is $96,875.
Learn more about accounting equation here:https://brainly.com/question/17611757
#SPJ1
The complete question is:
Just before Henderson Laboratories opened for business, Eugene Henderson, the owner, had the following assets and liabilities. Cash $ 39,900 Laboratory equipment 75,000 Laboratory supplies 6,200 Loan payable 14,500 Accounts payable 9,725. Determine the totals that would appear in the firm’s fundamental accounting equation (Assets = Liabilities + Owner’s Equity).
Find the circumcenter of the triangle.
The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The line's equation is x=-2.5.
Explain about the circumcenter of the triangle?The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).
This intersection represents the point on the triangle's perimeter. Distance d = (a - ax)2 + (b - bx)2 is the geometry formula for distance. "d" represents the separation between a vertex and the circumference, where x = 1, 2, 3.
The junction of the perpendicular bisectors of each side of the triangle, or the lines that are perpendicular to each side's midpoint, is where the triangle's circumcenter can be located.
To determine it, we locate the intersection of the circumcenter and the first name of the triangle, which is the point at which each line intersects the other
(-4,0) B=(-4,-4) C=(-1,-4) (-1,-4) (-4, -2),
y=-2 is the perpendicular line to AB's midpoint.
The intersection of the line at (-2.5,-2) and (-5/2,-2)
where BC's midpoint is located.
The line's equation is x=-2.5.
To learn more about circumcenter of the triangle refer to:
https://brainly.com/question/29398242
#SPJ1
Lucy paid $3.20 for 4 pounds of coffee beans. How much did she pay for each pound of coffee beans?
NASA’s research center has seven crates of hard-shell space suits. Each crate has two suits. If three suits crack during pressure testing, how many suits are left that are NOT cracked?
Sarah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $54 for parts. The total was $585.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The cost of labor per hour is $125.
What is the cost of labor per hour?The equation that can be used to solve for the cost of labor per hour is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of the linear equation is:
Total cost = cost of the parts + (cost per hour x total hours worked)
$585.25 = $54 + (4.25 x d)
$585.25 = $54 + 4.25d
In order to determine the value of x, take the following steps:
Combine similar terms:
$585.25 - $54 = 4.25d
Add similar terms
$531.25 = 4.25d
Divide both sides of the equation by 4.24
d = 531.25 / 4.25
d = 125
To learn more about linear equations, please check: https://brainly.com/question/29776996
#SPJ1
I will give brainliest, if you get this correct
1) What is the probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the I.D's of five students from among ten students of which four are not of legal age?
Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.
Step-by-step explanation:
he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.
The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
x = the number of successful outcomes (in this case, the number of minors refused service)
n = the total number of trials (in this case, the number of IDs checked)
p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)
In this case:
x = 3 (the number of minors refused service)
n = 5 (the number of IDs checked)
p = 4/10 (the probability that a randomly chosen student is a minor)
So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:
P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288
Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.
It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.
Write the formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input.
Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:
(r+g+b)/3, (r+g+b)/3, (r+g+b)/3
Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.
To calculate this average value we use the formula: (r+g+b)/3
So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.
Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.
