The coordinates of P' are (-√3, 1).
Given that P is located on a circle with a radius of two and an origin at its centre, the following trigonometric ratios can be used to determine P's coordinates:
Sin is equal to the opposite/hypotenuse and cos is equal to the adjacent/hypotenuse.
P's coordinates are as a result:
y = 2 sin = 2(1/2) = 1 and x = 2 cos = 2(3/2) = 3.
The x-coordinate of P' will be the opposite of the x-coordinate of P since P and P' are symmetrical about the y-axis, or x' = -3. P' will have the same y-coordinate as P, meaning that y' = 1. Hence, P's coordinates are (-3, 1).
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Parallel lines e and f are cut by transversal b. e=(2x+10)f=(3x-15)What is the value of x?a. 1b. 5c. 25d. 37
The value of x that makes lines e and f parallel and intersected by transversal b is x = 25. Answer choice (c) is correct.
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
When parallel lines e and f are cut by a transversal, the corresponding angles are congruent. Using this fact, we can set up an equation involving the angles formed by the intersection of lines e and f with transversal b:
2x + 10 = 3x - 15
Solving for x, we get:
x = 25
Therefore, the value of x that makes lines e and f parallel and intersected by transversal b is x = 25. Answer choice (c) is correct.
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the function f(x) is a quartic function and the zeros of f(x) are -5,-2,5 and 6. Assume the leading coefficient of f(x) is 1. write an equation of the quartic polynomial in standard form
The quartic polynomial in standard form is:
f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300
Quartic Polynomial Standard Form.Since the zeros of the quartic function are -5, -2, 5, and 6, we can write the function as:
f(x) = a(x + 5)(x + 2)(x - 5)(x - 6)
where a is the leading coefficient of f(x).
Since the leading coefficient of f(x) is assumed to be 1, we have:
f(x) = (x + 5)(x + 2)(x - 5)(x - 6)
To write this in standard form, we need to expand the product:
f(x) = (x^2 + 7x + 10)(x^2 - 11x + 30)
Multiplying out the terms, we get:
f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300
Therefore, the quartic polynomial in standard form is:
f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300
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Angel scores 17 , 19 , 13 , 24 , and 14 points in the first five game of a seven game basketball season of scoring leader in Angela’s league average 18 points per game how many points must angela score in the final two games combined to end the season with the highest scoring average in the league and have a higher scoring average than any other player
Answer:
Step-by-step explanation:
your friend finds the slope and y - intercept of the graph of the equation y= 4x -3
Is your friend correct?
Estimate the following difference by replacing each fraction with 0, 12, or 1.
78−611
Drag numbers to the boxes to complete your answer.
Numbers may be used more than once, or not at all.
The difference of the fraction expression 7/8 - 6/11 is 1/2.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To estimate the difference 7/8 - 6/11 by replacing each fraction with 0, 1/2, or 1 use the expression -
7/8 - 6/11
7/8 > 3/4 so round it to 1.
1/4 ≤ 6/11 ≤ 3/4 so round it to 1/2.
Now estimate the difference by replacing each fraction with 0, 1/2, or 1 -
7/8 - 48/88 ≈ 1 - 1/2 = 1/2
Therefore, it can be estimated that 7/8 - 6/11 is approximately equal to 1/2.
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How to analyzing qualtrics data in spss?
Once data has been collected through Qualtrics, it can be downloaded in a variety of formats, including a CSV file that can be imported into SPSS for data analysis.
Qualtrics is a popular web-based survey tool used to create and distribute online surveys.
To import Qualtrics data into SPSS, follow these steps:
Open SPSS and create a new data file.
Go to "File" > "Import Data" > "CSV File" and browse to find the Qualtrics data file you want to import.
In the import wizard, select the CSV file and choose the appropriate options for handling missing values and delimiters.
Specify the variable properties, including the variable name, label, and measurement level.
Click "Finish" to complete the import process.
Once the data has been imported into SPSS, you can use various statistical analyses to explore the relationships between variables, test hypotheses, and generate charts and tables to summarize the data.
The exact analysis methods used will depend on the research questions and the nature of the data, but common techniques include descriptive statistics, correlations, regression analysis, and factor analysis.
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Which statement is true?
1) Kai's bag definitely has more pink marbles than orange marbles.
2) If Piper chooses 15 more marbles, she can expect 3 to be orange.
3) Each bag must contain at least 20 marbles.
4) There are definitely no green marbles in Kaia's bag.
The true statement is, 3) Each bag must contain at least 20 marbles.
What is the expected value?We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory.
The anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
1. From the table, Piper's bag has definitely more pink marbles than Kai's.
2. If Piper chooses 15 more marbles he can expect (4/30)×15 = 2 orange marbles.
3. There can be green marbles in Kai's bag as the process is repeated only 20 times.
4. So, The true statement is each bag must have at least 20 marbles,
As the sum of different colored marbles is 20.
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Answer:
If Piper chooses 15 more marbles, she can expect 3 to be orange.
A manager's salary of N600 is increased by 12%. What is his new salary?
Answer:
672
Step-by-step explanation:First you need to change the percent into 12 over 100 times 600.then the result is 72.after that it says increased so you plus 600 plus 72 and that is the answer
Lashonda does a weekly exercise program consisting of cardiovascular work and weight training. Each week, she exercises for at least 7 hours. She spends at most 5 hours on weight training. She spends at most 11 hours doing cardiovascular work. Let × denote the time (in hours) that Lashonda spends doing cardiovascular work. Let y denote the time (in hours) that she spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
The region (labelled A) corresponding to all values of x and y that is added as an attachment
How to determine the regionBased on the given information, we can write the following system of inequalities:
Lashonda exercises for at least 7 hours:
x + y ≥ 7
She spends at most 5 hours on weight training:
y ≤ 5
She spends at most 11 hours doing cardiovascular work:
x ≤ 11
So the system of inequalities can be written as:
x + y ≥ 7
y ≤ 5
x ≤ 11
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Given trapezoid ABCD, what is the length of XY ?
B
X
A
6s+1
4s-2
S
D
с
Y
int
It should be noted that the geometrical constraint is that the average of the top and bottom lines will be the middle line thus the value of length XY is 18 units.
How to calculate the valueA quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.
The average of the top and bottom lines will be the middle line.
So, (6s + 1 + s)/2 = (4s - 2)
7s + 1 = 8s - 4
5 = s.
So,
XY = 4(5) - 2
= 20 - 2
= 18.
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(Student Loans LC) A student is graduating from college in 18 months but will need a loan in the amount of $7,855 for the three remaining semesters. The student may either receive an unsubsidized or subsidized Stafford Loan. The terms of each loan are: Unsubsidized Stafford Loan: annual interest rate of 3.7%, compounded monthly Subsidized Stafford Loan: annual interest rate of 4.7%, compounded monthly What is the difference in the balance of the two loans at the time of graduation?
- 427.60
- 302.57
- 890.95
- 447.57
The difference between original loan and unsubsidized loans at the time of graduation is = 8302.57 - 7855 = $447.57
What is meant by a loan?
A loan is a type of debt that a person or other entity incurs. The lender advances the borrower a certain amount of money, typically on behalf of a business, financial institution, or government. The borrower accepts a specific set of terms in return, which may include any economic costs, interest, a repayment schedule, and other requirements.
The lender may occasionally need collateral to protect the loan and guarantee repayment. Major purchases, investments, renovations, debt reduction, and company endeavours are just a few uses for loans. Loans aid in the expansion of already existing businesses. The growth of an economy's total money supply and fostering competition are made possible by loans to new enterprises.
Given,
Time to graduate = 18 months
Amount of loan for 3 semesters = $7855
Unsubsidized loan
rate of interest = 3.7%
Subsidized Stafford Loan
rate of interest = 4.7%
Amount after 6 months for each loan
P = $7855
r1 = 3.7%
r2 = 4.7%
t (in years) = 18 months = 1.5 years
Number of times compounded in a year n = 12
Amount of Unsubsidized loan at the time of graduation
= [tex]P(1 + \frac{r}{n})^{nt}[/tex]
= [tex]7855(1 + \frac{0.037}{12})^{12*1.5}[/tex] = $8302.57
Amount of the Subsidized Stafford Loan at the time of graduation
= [tex]P(1 + \frac{r}{n})^{nt}[/tex]
= [tex]7855(1 + \frac{0.047}{12})^{12*1.5}[/tex] = $8427.60
Therefore the difference between the balance amount of the original loan and the unsubsidized loan at the time of graduation is
= 8302.57 - 7855 = $447.57
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Ambers dinner bill is $36. 00 if amber leaves a 17% tip, how much tip will amber leave?
Answer:
$42.12
Step-by-step explanation:
if tip is 17% then she should pay 117% (this is 1.17)
$36 * 1.17 = $42.12
Olivia makes and sells bracelets and necklaces. She can make up to 60 pieces per week, but she can only make up to 40 bracelets and 40 necklaces. Write and graph a system of inequalities that shows the combination of bracelets and necklaces that she can make if she wants to sell at least 30 items per week. If necklaces sell for $80 each and bracelets sell for $5 each, what is the most amount of money she can make in a week?
We wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.
What is meant by inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Let x be the number of bracelets and y be the number of necklaces.
Given Olivia can make up to 60 pieces per week.
So the inequality is: x + y ≤ 60
She can make less than or equal to 40 bracelets.
So the inequality is : x ≤ 40
She can make less than or equal to 40 necklaces as well in a week.
So the inequality is : y ≤ 40
She wants to sell at least 30 items per week.
x + y ≥ 30
x+y ≤60 can be written as
We can draw the inequalities as shown below.
x + y ≤ 60 as red
x ≤ 40 as green
y ≤ 40 as violet
x + y ≥ 30 as blue
The overlapping region of all inequalities is yellow.
The money made per week: 5x + 80y
We have to find the maximum money made.
The vertices of the yellow region are:
(0,30),(0,40),(30,0),(40,0),(20,40),(40,20)
The coordinates with negative values are neglected.
From this, 5*20 + 80 * 40 = $3300 is the maximum amount.
Therefore we wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.
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what is binomial theorem calculator
A binomial theorem calculator is an online tool that calculates the expansion of a binomial expression raised to a power
The binomial theorem, also known as the binomial expansion, describes the algebraic expansion of a binomial expression, which is a mathematical expression that consists of two terms. A binomial theorem calculator is an online tool or a software program that calculates the expansion of a binomial expression raised to a power. The binomial theorem calculator can quickly and easily perform this expansion for any given binomial expression and power.
For example, if we have the binomial expression (a + b) raised to the power of 3, the binomial theorem calculator will provide the expanded form:
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
This expansion can be useful in many mathematical calculations and applications, such as probability theory, combinatorics, and algebraic equations.
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1 microcentury is equal to how many minutes
Answer:
53 minutes
Step-by-step explanation:
c. The area of a rectangular body is (x²-16) sq.cm. If its breadth is(x-4) cm, find its length.
Step-by-step explanation:
hence proved.The answer is mentioned in above pdf. so for bad handwriting
PLEASE NEED HELP
(SAT Prep) Find the value of x
The measure of angle x is 70°
Triangle Exterior Angle Theorem:
For a triangle, the exterior angle is the angle formed by extending one of the sides of the triangle
The Triangle Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Here we have
A triangle where 105° is an exterior angle
And 'x' is an interior angle
Name the given triangle as given below
If we take AC as Transversal which cuts AB and DC
=> ∠A = 35° [ Alternate Interior Angles ]
In a triangle,
The measure of an exterior angle will equal to the sum of measures of opposite interior angles.
=> x° + 35° = 105°
=> x° = 105° - 35°
=> x° = 70°
Therefore,
The measure of angle x is 70°
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What are algebraic equations?
Answer:
An algebraic expression is a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations.
Step-by-step explanation:
An example could include x^3 + 1, or something more complicated, like (y^4x^2 + 2xy – y)/(x – 1) = 12
Answer:
Step-by-step explanation:
These are equations which have an = sign and have a variable that needs to be found.
E.g x + 3 = 24
I need help quick pleaseee
The slope of the tangent line to the graph g(x) = 2x⁴ at (-2,32) is -64.
What is the slope of the tangent to the graph of the given function?Given the function in the question;
g(x) = 2x⁴
Slope of the tangent line at (-2,32) = ?
Since 2 is constant with respect to x, the derivative of 2x⁴ with respect to x will be;
2 d/dx [x⁴]
Now, differentiate using power rule.
d/dx[ xⁿ ] = nxⁿ⁻¹ where n = 4
2( 4x³ )
8x³
Next, evaluate the derivative at x = -2
8( -2 )³
8 × -8
-64
Therefore, the slope of the tangent line is -64.
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Thobeka wants to order a book that costs $56,56 the rand to dollar exchange rate is R17,25 to a dollar what is the price of the book in rands
Answer:
Step-by-step explanation:
The book is $56.56.
The rand to dollar exchange rate is R17.25 = $1
To find the price of the book in rands, simply multiply 56.56 x 17.25
= 975.66
The book would be R975.66 in rands.
Complete the equations. 95x10^3= ,95x 10^4= , 95x10^5=
The following equation after completion gives us the result which are given below :
95 x 10³= 9500095 x 10⁴= 95000095 x 10⁵= 9500000An equation is made up of two expressions joined by an equal sign ("="). The two expressions on each side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. This will not limit generality since we can balance it by subtracting the right-hand side expression from the expressions on both sides.
Algebra examines two major groups of equations: polynomial equations and linear equations. P(x) = 0, where P is a polynomial and axe + b = 0 is the generic form of linear equations, can be used to write polynomial equations with one variable. a and b are parameters in this case. To solve these equations, we can use geometric or computational approaches from linear algebra or mathematical analysis. There are also several sorts of equations, such as:
Linear equationsQuadratic equationsCubic equationsQuartic equationsDifferential equationsParametric equationsLearn more about Equations:
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pls explain how to do this!!!
The explanation is in the picture
In circle E, the length of FG=5/3pi and measure angleFEG=50°. Find the area shaded below. Express your answer as a fraction times pi
The area of the shaded region is 5π
Area of the Sector:The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:
Area of sector = (θ/360) x πr²where θ is the central angle (in degrees) of the sector, r is the radius.
Here we have
The length of arc FG = 5/3 π and measure of ∠FEG = 50°
As we know Arc Length = θ × (π/180) × r
=> Length of arc FG = 50 × (π/180) × r
From the given data,
=> 50 × (π/180) × r = 5π/3
=> 5 × (1/18) × r = 5/3
=> (1/6) × r = 1
=> r = 6 units
Hence, the radius of the circle is 6 units
By using the formula,
Area of a Sector of Circle = (θ/360°) × πr²
Area of shaded region = (50/360) × π(6)²
= (5/36) × π(36)
= (5/36) × π(36)
= 5π
The area of the shaded region is 5π
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Amber plans to build a scale model of the Washington Monument. She will use a scale of for her model. The actual height of the monument is 555 feet. What should be the height of Amber's scale model?200
The height of Amber's scale model of the Washington Monument should be 2.775 feet.
According to given conditions :To find the height of Amber's scale model, we need to multiply the actual height of the Washington Monument by the scale factor:
Scale factor = 1/200
Height of Amber's model = (1/200) * 555 feet
Height of Amber's model = 2.775 feet
Therefore, the height of Amber's scale model of the Washington Monument should be 2.775 feet.
What is scale ?In mathematics, scale refers to the ratio between measurements of the real world and measurements of a model or a drawing. It is a way of representing an object or a phenomenon that is too large or too small to observe directly, by creating a scaled-down or scaled-up representation of it.
For example, in maps, the scale represents the ratio between distances on the map and distances in the real world. A scale of 1:50,000 means that 1 unit on the map represents 50,000 units in the real world. Similarly, in architectural drawings, the scale represents the ratio between the size of the drawing and the size of the actual building.
Scales are used in many fields, including engineering, architecture, cartography, and model making. They allow us to represent objects and phenomena in a way that is more manageable and easier to visualize, while preserving the important proportions and relationships between the different elements of the object or phenomenon.
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Which sequence of transformations proves that shape I is similar to shape II?
A.
a 90° clockwise rotation about the origin, and then a dilation by a scale factor of 2
B.
a reflection across the x-axis, and then a dilation by a scale factor of 1.5
C.
a 90° counterclockwise rotation about the origin, and then a dilation by a scale factor of 1.5
D.
a reflection across the x-axis, and then a dilation by a scale factor of 2
E.
a reflection across the y-axis, and then a dilation by a scale factor of 2
Please, Help me with this question.... This is the same question in two pics but it doesn't show the full word question so I put two pics with a shortened questions. please compare them and you will understand what I am trying to say.
Roots of the given quadratic equation are
x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9
What is quadratic equation?A quadratic equation is a second-order algebraic equation in x. The quadratic equation in standard form is ax² + bx + c = 0.
where a and b are the coefficients, x is the variable, and c is the constant term.
Given, equation
9x² + 10x + 16 = 2x + 9
taking 2x + 9 to left side
9x² + 10x + 16 - 2x - 9 = 0
Subtracting like terms
9x² + 8x + 7 = 0
here, a = 9, b = 8, c = 7
Quadratic formula for the solution
x = (-b ± √(b² - 4ac))/2a
x = (-8 ± √(8² - 4 . 9 . 7))/2 . 9
x = (-8 ± √(64 - 252))/18
x = (-8 ± √- 188)/18
x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9
Hence, x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9
are the roots of the given equation.
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How do you solve systems of equations with back substitution?
To use back substitution to solve a system of equations, work backwards from the last equation to the first.
Back replacement is a strategy for settling frameworks of conditions by working in reverse from the last condition to the first. To settle an arrangement of conditions utilizing back replacement, follow these means:
Begin with the last condition in the framework and tackle for the variable with the biggest coefficient.
Substitute this worth into the second-to-last condition and tackle for the relating variable.
Keep subbing values from the tackled conditions into the excess conditions, working in reverse until all factors are settled.
Actually look at the arrangement by subbing the qualities into the first conditions.
Back replacement is a valuable technique for tackling frameworks of conditions, particularly when the conditions are in three-sided structure or when Gaussian disposal has been applied. Be that as it may, it may not be the most proficient technique for bigger frameworks, and different strategies, for example, grid reversal or Cramer's standard might be more suitable
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Which expressions can be used to find the volume of the pyramid? Select three choices
The correct answer regarding the volume of the pyramid has been explained and given below.
The volume of the pyramid shape is given by the product of its base area and its height and then the product is divided by 3.
i.e.V = (1/3)a²h
So, the options which are correct are, (a) XY and ST , (b) VU and TW and (d) TX and WX.
From the given figure we can clearly see that,
a=XY=YZ=ZU=UV=VW=WX
h=ST
Firstly, the volume of the pyramid can be easily determined by XY and ST.
and also, VU and WX can be used to calculate the area of the base and YZ and TX can be used to calculate height.
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The graph shows two functions, f(x) and g(x). If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options. domain: x ≥ –2 domain: x ≥ 2 The point (2, 2) is on h(x). The point (–2, 0) is on h(x). The point (0, –3) is on h(x).
If functions h(x)= f(x)+g(x), the point (2, 2) is on h(x) and The point (–2, 0) is on h(x).
What does function mean?In mathematics, a function is a rule or a set of rules that assigns a unique output to each input of a given set of inputs. It is a type of mapping or transformation in which each member of one set (the inputs) is associated with a unique member of another set (the outputs). Functions are often represented by equations or graphs, and they can be used to describe relationships between different variables.
For example, the equation y = x2 describes the function that assigns to each number x its square y.
The domain of the combined graph h(x) is x ≥ –2 since the domain of both f(x) and g(x) are x ≥ –2. The point (2, 2) is on h(x) because when x = 2, the function f(x) takes the value 2 and the function g(x) takes the value 0. When these two values are added together, they equal 2, which is the y-value of the point (2, 2). The point (–2, 0) is on h(x) because when x = –2, the function f(x) takes the value 0 and the function g(x) takes the value –3. When these two values are added together, they equal –3, which is the y-value of the point (–2, 0). The point (0, –3) is not on h(x) because when x = 0, the function f(x) takes the value –1 and the function g(x) takes the value –2. When these two values are added together, they equal –3, which is not the y-value of the point (0, –3).
The point (2, 2) is on h(x) since h(x) = f(x) + g(x) = 2 + 0 = 2. The point (–2, 0) is on h(x) since h(x) = f(x) + g(x) = 0 + 0 = 0. The point (0, –3) is not on h(x) since h(x) = f(x) + g(x) = 0 + 2 = 2, which does not equal –3.
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How to convert 750ml to cups?
To value of volume 750 ml after converting to cups is 3.17 cups.
The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.
To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.
So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).
Therefore, volume of 750ml is equivalent to 3.17 cups.
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