To find out the number of groups of 1/5 in 3, we need to divide 3 by 1/5.
We can also write this as a fraction: 3 / (1/5)
To divide fractions, we flip the divisor and then multiply. This gives us:3 / (1/5) = 3 x 5/1 = 15So there are 15 groups of 1/5 in 3.To show this on a number line, we can first mark 0 and 3 on the number line.
Then we can draw 15 equally spaced tick marks between 0 and 3. Each tick mark represents 1/5, so 15 tick marks represent 15 groups of 1/5.
We can also label the tick marks with fractions to show that each tick mark represents 1/5.
The number line should look something like this:0 ------- 1/5 ------- 2/5 ------- 3/5 ------- 4/5 ------- 1 ------- 6/5 ------- 7/5 ------- 8/5 ------- 9/5 ------- 2 ------- 11/5 ------- 12/5 ------- 13/5 ------- 14/5 ------- 3
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To make a specific hair dye a hairstylist uses a ratio of one and 1/8 oz of red tone 3/4 oz of Gray tone and 5/8 oz of Brown tone if the stylist needs to make 20 oz of dye how much of each dye color is needed?
Answer: To make 20 oz of hair dye, the hairstylist needs to use 1 and 1/8 oz of red tone, 3/4 oz of gray tone and 5/8 oz of brown tone.
We can use proportionality to figure out how much of each dye color is needed.
Let's call the amount of red dye needed x, the amount of gray dye needed y and the amount of brown dye needed z.
According to the proportionality, we can write the following equation:
(1 + 1/8)x + (3/4)y + (5/8)z = 20
To find the amount of each dye color needed, we can solve this equation for x, y and z.
First, we can clear the fractions by multiplying all terms by 8:
(8 + 1)x + (6)y + (5)z = 160
Now we can solve for x:
9x + 6y + 5z = 160
x = (160 - 6y - 5z)/9
Similarly, we can solve for y and z:
y = (160 - 9x - 5z)/6
z = (160 - 9x - 6y)/5
Now we can substitute the desired amount of 20 oz into the equation and solve for x, y and z
Step-by-step explanation:
What is the formula for finding the area of a sector of a triangle?
The formula for a sector's area is: 1. A = (sector angle / 360 ) * (pi *r2)
2. A = (sector angle / (2*pi)) * (pi * r2) 3. A = (fraction of the circle) * (pi * r2)
The ratio used to find the area of the sector is that of how to know what fraction of the circle is the sector.
Ratio = (θ/360°)
θ is the angle subtended at the center of the circle by the arc, measured in degrees.
For this question,
θ = 60°
Ratio = (θ/360°) = (60°/360°) = (1/6)
Area of a circle is given as
Area of a circle = πr²
where
π = pi
r = radius of the circle = 8
Area of the circle = πr²
Area of the circle = π (8²) = 64π square units
Area of the sector is given as
Area of the sector = (Ratio) × (Area of the circle)
Ratio = (1/6)
Area of the circle = 64π square units
Area of the sector = (Ratio) × (Area of the circle)
Area of the sector = (1/6) × (64π) = (64π/6) = (32π/3) square units
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Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60. What percent did she leave?
answer = _____%
The percentage of the tip that she leaves will be 20.02%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60.
Then the percentage is given as,
P = [2.6 / 12.99] x 100
P = 0.2002 x 100
P = 20.02%
The percentage of the tip that she leaves will be 20.02%.
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i need help, i feel like i know how to do it but when i try it makes no sense. can someone explain this to me with steps?
Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.
What exactly is an X2?X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .
heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!
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What do you call the total distance around a polygon, or 2-D shape?
A .area
B .perimeter
C .volume
D .width
Answer:
It is called the perimeter
Step-by-step explanation:
A ratio of 4 to 7 maybe written as the following, except 4:7 8:14 7/4 8/14 12:21
Answer:
except 7/4
Step-by-step explanation:
The ratio of 4 to 7 is the same as the fraction 4/7
7/4 is not equal to 4/7 and therefore they cannot be written in the same way.
Can someone help me with this please?
A: Classify the triangle above by its sides
B: Classify the triangle above by its angles
C: Explain your answer to part a and b
The nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?
The nearest whole number to which the new height of the image is enlarged is 9cm.
What is scaling?By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are what we call scaled figures.
Given that the original size was in the ratio 4: 3.
When the image is enlarged the enlarged image will be in the similar ratio to the original size.
Hence, the ratio in which the enlarged image will be increased is 4x : 3x.
The new width is given as 12,
The value of 4x = 12
x = 3
Then the new height of the image is:
3 (3) = 9cm.
Hence, the new height of the image is 9cm.
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What is the formula for square units?
The formula for the area of a square is A = s², where A is the area of the square and s is the length of one of its sides.
To calculate the area of a square, multiply the length of one side by itself. For example, if the side of a square is 5 meters, the area of the square would be 25 square meters (5² = 25). If the side of a square is 8 feet, the area of the square would be 64 square feet (8² = 64). The area of a square is always equal to the length of one side multiplied by itself.
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What are the types of substitute?
Answer:
"Substitution comes in three flavors: nominal, verbal or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
Algebra i need help asap
Answer:
Below
Step-by-step explanation:
Solutions are where the graphs intersect....they are equal at these points
(2,-3) and (4,-1)
There is likely one more point of intersection down and to the left which is not shown on the graph
the length of a rectangle is 6 feet longer than the width. the perimeter is 28 feet. find the dimensions of the regtangle
The length of rectangle :10 feet
The width of rectangle : 4 feet
Given
perimeter of the rectangle :28 feet
let width of the rectangle be :x
and length of the rectangle be : 6+x (as per given condition)
therefore
perimeter = 2(length +width)
28 = 2(6+x+x)
28 = 2(6+2x)
28 = 12+4x
28-12 = 4x
16 = 4x
x = 4
as width of rectangle is : 4
similarly length : 6+x
6+4
:10
The dimensions of the rectangle are : length =10
width = 4
verification :
perimeter =2(l+w)
28 = 2(10+4)
28 = 28
What can you conclude about the following figure?
What we can conclude by the given triangle about similarity is;
ΔPQR ∼ ΔPST
How to Identify Triangle similarity theorem?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Now, there are three types of similarity theorems for triangles namely;
Angle Angle(AA) Similarity
Side Angle Side(SAS) Similarity
Side Side Side(SSS) Similarity
We see that both triangles PQR and PST have equal angle R and angle T which are both 36 degrees. Thus, they are both similar by the AA Similarity theorem
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a function pairs each teacher with 30 students
On solving the provided question we can say that when each teacher is matched with 30 students, t is not a function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
When each teacher is matched with 30 students, t is not a function.
This is true since it demonstrates a one-to-many link.
Therefore, this is the case because it shows a many-to-one relationship and multiple weights can have the same cost.
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Which function has the lowest minimum value, and what are its coordinates?
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
B. Function 1 has the lowest minimum value, and its coordinates are (0, 1).
C. Function 2 has the lowest minimum value, and its coordinates are (−1, 0).
D. Function 2 has the lowest minimum value, and its coordinates are (0, 2).
Answer:
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
Step-by-step explanation:
To find the minimum value for f(x), set its first derivative to 0 and solve for x.
First derivative of f(x) is
f'(x) = 8x + 8 + 0 = 8x + 8
Setting this equal to 0 gives
8x + 8 = 0
8x = -8
x = -1
Plugging in this value for x in 4x² + 8x + 1 gives
f(x) = 4(-1)² + 8(-1) = 4 · 1 - 8 + 1
= 4 - 8 + 1
-4 + 1
= -3
So minimum for f(x) occurs at (-1, -3)
For g(x) the minimum is 0 and is at x = -1
So f(x) has minimum of -3 at x = -1
g(x) has minimum of 0 and occurs at x = -1
Answer:
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $4 hour and your sales job pays $8 per hour. You need to earn at least $120 each week to pay your bills. Write and graph a system of inequalities that shows the various numbers of hours you can work at each job.
Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box. If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
The total number of books that Jarrod packed into boxes can be represented by 84 + x*12.
The total number of books that Jarrod packed into boxes can be found by multiplying the number of boxes he packed with the number of books per box.
In this case, Jarrod packed 6 boxes of science textbooks with 14 books per box, so the number of books in the science boxes is 614 = 84. He also packed math textbooks with 12 books per box, so the number of books in the math boxes can be represented by x*12, where x represents the total number of boxes he packed.
So the total number of books that Jarrod packed into boxes can be represented by 84 + x*12.
Therefore, the equation that can be used to find the total number of books that Jarrod packed into boxes is: 84 + x*12 = Total number of books.
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What is final value theorem Mcq?
The steady state value of the system is determined using the final value theorem.
The main characteristics of the Laplace transform are the initial and final value theorems. Pierre Simon Marquis De Laplace, a French mathematician and scientist, presented these theorems. Limiting theorems refer to both the initial and final value theorems.
The final value theorem asserts that one can compute a system's ultimate value using. The function's Laplace transform is
[tex]\lim_{t\rightarrow\infty}f(t) = \lim_{s\rightarrow0}sF(s)[/tex]
(1) Final value theorem prerequisites are the functions f(t) and f(t)' should be Laplace transformable.
(2) sF(s), where F(s) is the Laplace transform of f(t), has no pole on the j-w axis and right half plane.
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Can someone help me with this please?
By using the triangle inequality theorem, the possible side lengths for the third side is equal to: D. 4 < c < 42.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < a < b + c
23 - 19 < a < 23 + 19
4 < a < 42.
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PLEASE HELP!!! I NEED HELP WITH MY HOMEWORK!!!!
(GEOMETRY)
WILL MARK BRAINLIEST!!!!!
Answer:U: 1.98 V: 1.4 And also the other side, square root symbol: 1.4
Step-by-step explanation:
I hope this helps man, i havnt done this stuff in a while...
If f(x)=6x-4 and f(x)=14, what is the value of x?
Answer:
Since, 6x -4 and 14 both are values of f(X)then,
6x-4=14
or,6x=14+4
or,X=18/6
:.X=3
*mark me brainliest
Answer: X=3 :)
Step-by-step explanation:
f(x)= 6x-4 and f(x)=14
6x-4=14
6x=4+14
6x=18
Divide both by 6
x=3
Please help me find the value and the kind of angel this is?
Answer: the only line crossed is called a transversal line. x +3 would be vertically opposite to the other angle,and 2x-61 would also be vertically opposite. if you look at alternate and corresponding angles you would find the exact answer. this angle does not have a kind i guess.
hope it helps you!!!
Step-by-step explanation:
Write the coordinates of the vertices after a dilation with a scale factor of 1/3, centered at the origin.
The coordinates of the vertices after a dilation with a scale factor of 1/3 centered at the origin is E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Given that center of the dilation is origin.
Any coordinate (x, y) when dilated to a scale factor k is (kx, ky).
The coordinates of the quadrilateral are E(0, -6), F(9, -6), G(9, 3) and H(0, 3).
Dilation is with a scale factor of 1/3.
So all the coordinates become (1/3x, 1/3y).
E(0, -6) becomes E'(0, -2)
F(9, -6) becomes F'(3, -2)
G(9, 3) becomes G'(3, 1)
H(0, 3) becomes H'(0, 1)
Hence the coordinates are E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).
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Aira got 76, 85, 81 and 77 in her four quizzes. What average score must she get in her next two quizzes to obtain an average of 83?.
Aira should must score a total of 179 combined in her next two quizzes in order to make the average of all the marks of the quizzes as 83.
Aira has got 76, 85, 81 and 77 marks in her 4 quizzes.
I have to give two more quizzes and the marks obtained in those two quizzes should be such that the average of all the quizzes should be 83.
We know that we can find the average of the data by taking the sum of all the given values and dividing that particular value by the number of data given to us.
Here in this case let assume that she obtained X marks in her next to test combined. Now this way total number of observation are 6.
Now, we can simply apply the formula to find the average of the data.
Average = (76 + 85 + 81 + 77 + X)/6
83 = (76 + 85 + 81 + 77 + X)/6
X = 179
So, Aira should obtain 179 marks in her next to quizzes in order to make the average of all the score equal to 83.
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Do all exponential functions pass through 0 1?
All exponential functions pass through (0, 1)
We know that the exponential function f with base b is defined as:
f(x) = b^x
where b > 0 and b is not equal to 1
and x is any real number.
For x = 0,
f(0) = b^0
f(0) = 1
This means, the graph of function f(x) passes through (0, 1)
For example consider an exponential function f(x) = 2^x
For x = 0,
f(0) = 2^0
f(0) = 1
the graph of f(x) = 2^x passes through (0, 1)
so, the characteristics of the graphs of all exponential functions:
The graphs contain the point (0, 1).
The x-axis is an asymptote.
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Triangle PQR was transformed to create the congruent triangle STU. Which describes how triangle PQR could have been transformed.
The term "congruent" refers to having exactly the same shape and size. Even if we flip, turn, or rotate the shapes, the shape and size should remain the same.
What exactly is SSS SAS RHS AAS?SSS (Side-Side-Side) (Side-Side-Side) SAS (Side-Angle-Side) (Side-Angle-Side) ASA (Angle-Side-Angle) (Angle-Side-Angle) AAS (Angle-Angle-Side) (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side) (Right angle-Hypotenuse-Side)
What is the distinction between SSS SAS and ASA postulates?The first two postulates, Side-Angle-Side (SAS) and Side-Side-Side (SSS), emphasise the side aspects, whereas the following lesson discusses two additional postulates that emphasise the angles. The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates are what they are.
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Which method of solving for the variable could be used instead of cross multiplication?.
Answer: multiplying by denominators
Step-by-step explanation: not sure if this is the right answer in this context but i hope it helps
technically cross multiplying basically is multiplying by denominators, but depending on the math level they are sometimes considered different methods
again, this may not be correct so if you want a more clear answer could you provide a bit of context? sorry, hope it helps anyway though.
Pls, Help!! My assignment is due tomorrow!
Mina will receive $13.33 after converting her 18 Pounds GBP to Dollars USD
What is conversion?A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used
To change 18GBP to USD at the current exchange rate of 1.35GBP to 1 USD
Divide the Amount being converted by the exchange rate
that is, 18GBP/1.35
=13.33USD
Hence, 13.33USD is the amount that Mina will receive after converting her 18 GBP
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What is 14/10 reduced??
The reduced form of 14/10 is 7/5. The answer is obtained using the method of simplifying fractions.
What is meant by simplifying fractions?
Making a fraction as simple as possible is referred to as simplifying (or reducing) a fraction.
To do this, we divide the denominator and numerator by the biggest number that can be divided exactly into both numbers. In other words, we choose the biggest common number between the top and bottom and divide it by that.
In a fraction, the numerator and denominator are referred to as the "terms." Thus, when we simplify a fraction, we cast it in its most basic mathematical form.
Now, to reduce 14/10, we will find the highest common factor of 14 and 10.
The highest common factor is 2 i.e. both numerator and denominator are divisible by 2.
So, on dividing both the terms by 2, we get
(14÷2)/(10÷2)= 7/5
Hence, the reduced form of 14/10 is 7/5.
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Find the sum of the measures of the angles in quadrilateral ABCD. (Hint: Draw diagonal AC. How can you use the figures you have formed to find the sum?)
The measure of four angles of quadrilateral is 360°.
What is quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles.
It is a type of polygon.
In order to create it, four non-collinear points are joined.
Quadrilaterals always have a total interior angle of 360 degrees.
A polygon with four sides, four angles, and four vertices is called a quadrilateral.
The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.
A quadrilateral is shown in the above image as an example.
A quadrilateral is a polygon with four vertices and four sides that each contain four angles, the sum of which is 360 degrees.
Two triangles are created when we draw a diagonal to a quadrilateral. These two triangles have a 180° angle sum.
As a result, the quadrilateral's total angle sum is 360°.
Hence, the measure of four angles of quadrilateral is 360°.
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