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.
Please help me with this question.
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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What is the amplitude of the sinusoidal function
Answer: 3
Step-by-step explanation:
The vertical distance between the sinusoidal axis and the maximum or minimum value of the function.
Trust
Help pls simplify the following expression (attached to image )
Answer:
[tex]\frac{1}{343}[/tex]
Step-by-step explanation:
[tex]7^{-3}[/tex] = [tex]\frac{1}{7^{3} }[/tex] = [tex]\frac{1}{7x7x7}[/tex] = [tex]\frac{1}{343}[/tex]
Un numeral aumentado en el triple de su cifra de decenas resulta 93. Hallar la suma de sus cifras
El número de este problema es 72, y la suma de sus cifras da 9.
¿Como hallar la suma de sus cifras?En este problema tenemos un numero de dos cifras, que podemos escribir como:
a*10 + b
Donde a y b son numeros enteros entre 0 y 9, y son las cifras de nuestro número.
Sabemos que si a este número le aumentamos 3 veces la cifra de decenas, resulta en 93, entonces podemos escribir:
a*10 + b + 3*a = 93
a*13 + b = 93
Ok, ahora simplemente devemos reemplazar los valores de b por numeros enteros y resolver la ecuación para a, asi hasta que el resultado de a tambien de un numero entero.
si b = 5
a*13 + 5 = 93
a*13 = 93 - 5
a*13 = 88
a = 88/13 = 6.7
No es una solucion.
si b = 2
a*13 + 2= 93
a*13 = 93 - 2
a*13 = 91
a = 91/13
a = 7
Esta es la solución.
Las cifras son a = 7 y b = 2, y su suma da:
7 + 2 = 9
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In order to increase the circumference of a circle from 12 pie cm to 18 pie cm, by how much must the diameter increase
Answer: Circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is a constant.
We know that the diameter is twice the radius (d = 2r).
So when we increase the circumference of the circle from 12π cm to 18π cm, we are increasing the radius from r to r'.
To find the increase in diameter, we can use the formula for the diameter, and subtract the original diameter from the new diameter.
d' = 2r' and d = 2r
d' - d = 2r' - 2r
We know that the relationship between circumference and radius is C = 2πr.
So we can write:
12π = 2πr and 18π = 2πr'
r = 6/π and r' = 9/π
then
d' - d = 2r' - 2r = 2(9/π) - 2(6/π) = 18/π - 12/π = 6/π
Therefore, the diameter must increase by 6/π cm in order to increase the circumference of the circle from 12π cm to 18π cm.
Step-by-step explanation:
Jenny drew a figure in art class. Does it have rotational symmetry? If yes, what is the angle of rotation.
Answer : Yes, it has rotational symmetry. The angle of rotation is, 60 degree.
What is Rotational symmetry?It is a shape that has Rotational Symmetry when it still the same after the rotation.
here, we have,
The given figure is hexagon and it has rotational symmetry because it still the same after the rotation.
As there are 6 sides of hexagon geometry and the degree of rotation is, .
So, the angle of rotation = 360/60
=60 degree
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Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(-4,-1) and C(2,5)
The coordinates are ( , ) and ( , )
Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information we have been given about the diagonal AC and its vertices. The diagonal AC has been given as having the vertices A(-4, -1) and C(2, 5). Since a square has right angles, we know that the other two vertices of the square must form a right angle with the diagonal AC.
To find the coordinates of vertex B, we know that it must have the same y-coordinate as vertex A, but a different x-coordinate. Since the x-coordinate of vertex A is -4, we can deduce that the x-coordinate of vertex B must be the same as the x-coordinate of vertex C, which is 2. Therefore, the coordinates of vertex B are (2, -1).
To find the coordinates of vertex D, we know that it must have the same x-coordinate as vertex A, but a different y-coordinate. Since the y-coordinate of vertex A is -1, we can deduce that the y-coordinate of vertex D must be the same as the y-coordinate of vertex C, which is 5. Therefore, the coordinates of vertex D are (-4, 5).
In summary, the coordinates of the remaining vertices of square ABCD are B(2, -1) and D(-4, 5)
Step-by-step explanation:
what type of polynomial is -10x^(4)-7
Answer:
biquadratic polynomial
Step-by-step explanation:
The given polynomial is
[tex]-10x^4 - 7\\\\[/tex]
The degree of this polynomial (the highest power) is 4
Such a polynomial is called a quartic polynomial. If all the terms have even degree, which in this case is true since there is only one term and its degree is 4 it is called a biquadratic polynomial
If polynomial has degree 1 ex 4x + 3 it is called a linear polynomial
If it has degree 2 --> quadratic
If it has degree 3 --> cubic
Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200. First the share of Mr. Christopher if they share a profit #2000 according to the amount contributed.
The profit for Mr Christopher is #1000.
What is profit?Profit is the money that is earned in trade or business after paying the costs of producing and selling goods and services.
Given that, Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200, they share a profit #2000,
Let the ratio of their contribution = 5x : 3x : 2x
Therefore,
5x + 3x + 2x = 2000
10x = 2000
x = 200
Their profit share =
Mr. Christopher = 200 x 5 = 1000,
Miss Uche = 200 x 2 = 200
and
Mrs. Amaka = 200 x 3 = 600
Hence, the profit share of Mr. Christopher is #1000,
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Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(-3, 2) and C(0,5)
The coordinates are ( , ) and ( , )
The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).
What is meant by coordinates?A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.
To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.
Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC :
Let the equation be Distance [tex]$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex] substitute the values in the above equation, we get
[tex]$\mathrm{AC}=\sqrt{\left((2-(-2))^2+(4-1)^2\right)}$$[/tex]
simplifying the equation, we get
[tex]$A C=\sqrt{ }(4+9)=\sqrt{ }(13)$$[/tex]
We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).
Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))
Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.
The complete question is:
Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are and D.
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here are 15 European cities that Yolanda would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.)
The number of different schedules are possible is given by the permutation and the equation is P = 2,730 schedules
What are Permutations?A permutation is an ordered arrangement.
The number of ordered arrangements of r objects taken from n unlike objects is:
Permutation ⁿPr = n! / ( n - r )!
Given data ,
Let the total number of schedules be P
Let the total number of European cities be n = 15
Let the number of cities Yolanda can visit in time r = 3 cities
So , the total number of different schedules is calculated by permutation and ,
The total number of different schedules = ⁿPr = n! / ( n - r )!
Substituting the values in the equation , we get
¹⁵P₃ = ( 15 ) ! / ( 15 - 3 ) !
¹⁵P₃ = ( 15 ) ! / ( 12 )!
¹⁵P₃ = 15 x 14 x 13
¹⁵P₃ = 2,730 schedules
Hence , the value of P is 2,730 schedules
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can you please help me?
Answer:
5,3,3-1 the box are illustrate the the number of the triangle
Verify that [n+3]!\n!=(n+1
Answer:
To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:
[n+3]! = (n+3) * (n+2) * (n+1) * n!
And we can cancel out n! from both sides of the equation:
(n+3) * (n+2) * (n+1) = n+1
Which is true, and thus [n+3]! / n! = (n+1) holds true.
Another way to verify this is by simplifying the RHS and LHS
(n+1) = (n+1)
And the LHS,
(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!
which is also equal to (n+1)
So, [n+3]! / n! = (n+1) is true.
The rule C=6.3r gives the approximate circumference C of a circle as a function of its radius r. Identify the independent and dependent variables in this relationship. Explain your reason.
Answer:
below
Step-by-step explanation:
The INdependent variable is 'r'
'C' DEPENDS on the value of 'r'...it is the dependent variable
After school Sasha likes to make snack by mixing raisins and nuts in the ratio 3:5 when she checked cupboard today there were only 60g of raisins and 75g of nuts left.what is the largest snack sasha can make while still using the correct ratio of ingredients
The largest snack Sasha can make while still using the correct ratio of ingredients is 555g.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that after school Sasha likes to make snacks by mixing raisins and nuts in a ratio of 3:5 when she checked the cupboard today there were only 60g of raisins and 75g of nuts left.
The largest snack Sasha can make while still using the correct ratio of ingredients is calculated as,
E = ( 60 x 3 + 75 x 5 )
E = 180 + 375
E = 555 g
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which graph represents the function y=-2cos(2πx)
Answer:
Step-by-step explanation:
When it comes to graphing a trigonometric function we use the amplitude, period, vertical shift and these values all help our graph come together to give us our final answer.
In this case,
The amplitude=2
period=1
and there is no phase / vertical shift.
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
x =
°
Answer:
30
Step-by-step explanation: 30-60-90 theorem
Show me you work!
Subtract: 2 1/4 - 1 2/3 =
A) 1 7/12
B) 1/3
C) 5/12
D) 7/12
Answer:
D) 7/12
Step-by-step explanation:
The first thing we want to do is find a like denominator for the fraction
Both 4 and 3 go into the multiple 12, so we'll use that
4x3=12
3x4=12
and what you do to one side, you must do to the other so we have
1/4x3= 3/12
2/3x4= 8/12
With that you get 2 3/12 and 1 8/12, which is subtractable
Take one from 2 so that you can make 3/12 15/12
15/12-8/12=7/12
This gives us our answer 7/12
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2 1/4 - 1 2/3
2 1/4 to an improper fraction is 9/4
1 2/3 to an improper fraction is 5/3
to get the same denominator multiply 9/4 by 3 and 5/3 by 4.
27/12 - 20/12
7/12 IS YOUR ANSWER.
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Oreana's 150 g bag of trail mix is x% raisins. Brandon's 250 g bag of trail mix is y% raisins. They combine the two mixes together in one bowl.
Write an expression which shows how many grams of raisins are in the bowl
The expression which shows how many grams of raisins are in the bowl will be
(0.01x) * 150 + (0.01y) * 250
What is the expression that shows the raisin?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The expression which shows how many grams of raisins are in the bowl will be:
= (x% × 150) + (y% × 250)
= (0.01x) * 150 + (0.01y) * 250
This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.
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3s + a = 38 and 3s + 2a =52
Step-by-step explanation:
answer is (a,s) = (14,8)
Please look at the picture and answer the question thank you
Answer:
f(-4) = -36
Step-by-step explanation:
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.
Therefore, the value of the function when the value of x is -4 can be calculated as shown below,
F(x) = 3x² - 10x + 4
F(-4) = 3(-4)² - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Hence, the value of the function when the value of x is -4 is 92.
Hectors school is holding a fitness challenge
Answer: What is the question ?
Step-by-step explanation:
Answer: 2 7/8 hours per week
hectors rate is greater
Step-by-step explanation:
Caitlyn wants to determine what percent of her trail mix is chocolate pieces, so she counts out exactly how many eacch item are in her bag. There are 28 raisins 28 chocolate pieces and 24 peanuts what percent of pieces in the trail mix are chocolate?
well, there are 28 + 28 + 24 = 80 pieces total, or namely that's the 100%, and we know that 24 of those are chocolates
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 24& x \end{array} \implies \cfrac{80}{24}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 10 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30[/tex]
To figure out what percentage of the trail mix is chocolate, we add up all the pieces, divide the number of chocolate pieces by the total and multiply by 100. In this case, we find that 35% of the trail mix is chocolate.
Explanation:In order to figure out the percent of chocolate pieces in Caitlyn's trail mix, we first need to determine the total number of pieces. Caitlyn counts 28 raisins, 28 chocolate pieces, and 24 peanuts, which gives us a total of 80 pieces in the mix. Then, since there are 28 chocolate pieces, we divide 28 (chocolate pieces) by 80 (total pieces). This will give us the decimal representation of the portion of the mix that is chocolate. To convert this into a percentage, we multiply by 100. Hence, the calculation will be (28/80)*100 = 35%. So, 35% of the trail mix is chocolate.
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Toby has a strawberry lace that is 36 cm long ar He needs pieces 18 mm long to decorate a cake. How long is the lace in mm? How many 18 mm pieces can he cut from the lace? help⭐⭐⭐⭐⭐
Answer:
The lace is 36 cm long and 1 cm = 10 mm. So, 36 cm = 360 mm.
He can cut the lace into 18 mm pieces, so he can cut 360 mm / 18 mm = 20 pieces of 18 mm lace from the 36 cm lace.
Which expression represents the total area of the rectangle. (look at picture)
Find The Missing Number
1. 1:2=4N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
The missing number of all the ratios are given below.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
The ratios are given.
1. 1:2=4:N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
p:q can be written as p/q.
To find the missing number:
1. 1:2=4:N
1/2 = 4/N
So, N = 8
2: 3:8=N:16
So, N = 6
3.15:20=30:N
So, N = 40
4.N:25=2:5
So, N = 10
5.10:N=40:80
N = 20
Therefore, all the missing numbers are given above.
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Help please
The answer is ____
Answer:
The answer is 3x-11
Step-by-step explanation:
x+x+x-11 = 3x-11. I'm assuming the answer is an algebraic equation.
Marco budgets $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$1,008
$908
$1,142
$1,029
Marco pays $64 for credit card, $272 for Groceries and $672 for rent
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Marco budgets $1,600 a month for expenses.
According to the graph he pays 4% of credit card
Now let us find 4% of 1600
4/100×1600
0.04×1600
$64 Marco pays for credit card.
From graph, he pays 17% for groceries
17% of 1600
17/100×1600
0.17×1600=$272
$272 Marco pays for Groceries.
From graph, he pays 42% for rent
42/100×1600
0.42×1600=672
$672 Marco pays for Rent.
Hence, Marco pays $64 for credit card, $272 for Groceries and $672 for rent
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A snack mix recipe calls for 2
1
4
cups of chips and
1
5
cup of dip.
Xander wants to make the same recipe using 1 cup of dip. How many cups of chips will Xander need?
i do not know the answer either
At an amusement park, only 17 people are allowed on a ride at the
same time. There are 157 people waiting in line. How many groups
of riders will there be?
Show your work.
Answer:
To find out how many groups of riders there will be, we need to divide the total number of people waiting in line (157) by the maximum number of people allowed on the ride at one time (17).
157 people / 17 people/group = 9.235 groups (approx)
But since the groups must be in whole numbers, we have to round up the value 9.235 groups to the next whole number, which is 10 groups.
So, the number of groups of riders will be 10.
Answer: 9 groups of riders.
Step-by-step explanation:
To find out how many groups of riders there will be, you need to divide the total number of people waiting in line by the maximum number of people allowed on the ride at one time.
157 (total people in line) ÷ 17 (people allowed per ride) = 9.235 (groups of riders)
Because you can't have a fraction of a group, you need to round down to get the whole number of groups.
So the answer is 9 groups of riders.
