Answer:
First, you distribute the 3 into the brackets,
3(x - 2) + 5x
=3(x) + 3(-2) + 5x
=3x - 6 + 5x
Adding the like terms, 3x and 5x, gives you
=8x - 6
Step-by-step explanation:
if the area of the triangle is 8 15/16ths and the base is 5 1/2, what is the height
Answer:
h=.34
Step-by-step explanation:
1/2(bh)=A
1/2(5.5*h)=8.9375
5.5h=1.875
h=.34
Anna wants to borrow $15,000 to buy a used sail boat. After looking at her financial situation, she realizes that she can only afford monthly payments of $300. The bank is offering financing at 6.1%. For how long will Anna need to finance the boat to stay within her monthly payment?
Answer:
47 months
Step-by-step explanation:
find 6.1% of 15k then divide that by 300
6.1% = 915
15,000 - 915 = 14085
14085 divided by 300 is 46.95 then rounded is 47
Company B needs to hire 30 new employees. Ten percent (10%) of applicants do not
meet the basic business requirements for the job, 12% of the remaining applicants
do not pass the pre-screening assessment, 23% of those remaining applicants do
not show up for the interview, and 5% of those remaining applicants fail the
background investigation. How many applicants need to apply in order to meet the
hiring target?
Company B needs approximately 55 applicants to apply in order to meet their hiring target of 30 new employees, taking into account the percentages of applicants who do not meet the requirements or pass the various stages of the hiring process.
Let's start with the total number of applicants needed to meet the hiring target of 30 new employees. We can call this number "x". We'll work backwards from there to find the number of applicants that need to apply in order to get 30 new employees.
We know that 5% of the remaining applicants fail the background investigation, which means that 95% pass. We also know that 23% of the remaining applicants do not show up for the interview, which means that 77% do show up.
Similarly, 12% of the remaining applicants do not pass the pre-screening assessment, which means that 88% do pass. Finally, 10% of all applicants do not meet the basic business requirements for the job, which means that 90% do meet the requirements.
Putting all of this information into the following equation;
0.9x × 0.88 × 0.77 × 0.95 = 30
Simplifying and solving for x, we get;
x = 30 / (0.9 × 0.88 × 0.77 × 0.95)
x ≈ 55.24
Therefore, Company B needs approximately 55 applicants.
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A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal area?
The dimensions of the region which enclose the maximal area will be 40.5 feet in length by width 27 feet.
How to find the dimensions of the areaGiven that the farmer has 162 feet of fencing, we will have:
2L + 3W = 162 feet
2L = 162 - 3W
L = 162 - 3W\2
L = 81 -3/2W Eqn 1
Given that the area of a rectangle is A = L × W we will call this equation 2
Now we substitute the first equation in the second one to give
A = (81 -3/2W) × W
A = 81W -3/2W²
When we take the derivative W will equal
81/3 = 27
Now we substitute in the second equation, we will have:
= 81 - 3/2(27)
= 81 - 40.5
= 40.5.
So the length will be 40.5 feet while the width will be 27 feet.
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At which values in the interval [0, 2π) will the functions f (x) = cos 2x + 1 and g(x) = sin x + 2 intersect?
x equals 0 comma pi over 6 comma 5 times pi over 6 comma pi
x equals 0 comma pi comma 7 times pi over 6 comma 11 times pi over 6
x equals pi over 2 comma 7 times pi over 6 comma 3 times pi over 2 comma 11 times pi over 6
x equals pi over 6 comma pi over 2 comma 5 times pi over 6 comma 3 times pi over 2
The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).
To find the intersection points, we set f(x) equal to g(x) and solve for x.
cos 2x + 1 = sin x + 2
Rearranging, we get:
cos 2x = sin x + 1
Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:
1 - 2sin²x = sin x + 1
Simplifying and factoring, we get:
2sin²x + sin x = 0
sin x(2sin x + 1) = 0
Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.
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A state's labor department conducted a study regarding the mean yearly earnings per household in the state. The department randomly selected 533 households in the state to be the sample. The population mean is $49,829.00. The department also found the standard deviation to be $933.00. What is the approximate standard error of the mean, assuming a 99.7% confidence level? 1.75 40.41 17.45 23.09
The approximate standard error of the mean, assuming a 99.7% confidence level is 40.41.
Given population mean (µ) = $49,829
population standard deviation (σ) = $933
the randomly selected households (n) = 533 households
the confidence level = 99.7%
To find the standard error of the mean at a 99.7% of confidence level, we will substitute the above values in the below equation,
Standard error of the mean = σ/√n = 933/√533 ≅ 40.41
From the above analysis, we can conclude that the standard error of the mean at a 99.7% confidence level is 40.41.
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Answer:
40.41
Step-by-step explanation:
Plato/Edmentum
What is 6+4 3/4+(-2.5)= explain your answer
The value of 6+4 3/4 +(-2.5) is 3 3/10
What is PEDMAS?PEDMAS is an acronym that shows the correct order of operations in mathematical problems. The full meaning of PEDMAS is ;
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
This order is followed when solving mathematical problems.
Solving 6+4 3/4 +(-2.5)
= 6+ 19/4 - 5/2
= ( 24+19-10)/4
= 33/10
= 3 3/10
Therefore the value of 6+4 3/4 +(-2.5) is 3 3/10
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What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?
The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.
What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept
Given that; the line passing through the point (-3,-4) and parallel to the x-axis.
A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.
Hence;
The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.
To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:
-4 = b
Note that: y = b, where b is a constant.
y = -4
Therefore, the equation of the line y = -4.
Option C) y = -4 is the correct answer.
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Solve for 10 and 12 please and thank you
Answer:
10. 120 Degrees 12. 60 Degrees
Step-by-step explanation:
#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.
#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.
Answer:
Step-by-step explanation:
10. somewhere between 126 and 129, i feel its 128
12. between 60 and 65
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
the answer for this question is x=8
A chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?
Answer:10-x
Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.
what are the answers to these questions?
The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Given that;
Expression is,
e²ˣ = - 2x - 1
Hence, Function is,
⇒ f (x) = e²ˣ + 2x + 1 = 0
⇒ f' (x) = 2e²ˣ + 2
Now, By newton's method;
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₂ = x₁ - f (x₁) / f' (x₁)
⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)
⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)
⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)
⇒ x₂ = - 68 / 7.2
⇒ x₂ = - 9.4
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₃ = x₂ - f (x₂) / f' (x₂)
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Thus, The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
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A new car sells for 25000 the value of the car decreases by 15% each year what is the approximate value of the car 5 years
The answer is $11,092.63.
This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.
After 1st year:
$25,000 : 100% = x1 : 85%
x1 = $25,000 · 85% ÷ 100%
x1 = $21,250
After 2nd year:
$21,250 : 100% = x2 : 85%
x2 = $21,250 · 85% ÷ 100%
x2 = $18,062.5
After 3rd year:
$18,062.5 : 100% = x3 : 85%
x3 = $18,062.5 · 85% ÷ 100%
x3 = $15,353.12
After 4th year:
$15,353.12 : 100% = x4 : 85%
x4 = $15,353.12 · 85% ÷ 100%
x4 = $13,050.15
After 5th year:
$13,050.15 : 100% = x5 : 85%
x5 = $13,050.15 · 85% ÷ 100%
x5 = $11,092.63
Therefore, the value of the car 5 years after it is purchased is $11,092.63.
Help please Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons. What kind of reasoning is Jared using?
A)Inductive Reasoning
B)Deductive Reasoning
If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.
Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.
The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.
In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.
Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.
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In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC
In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.
Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.
Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.
We know that AB = 10, AD = 16, and DE = 22.
Let x be the length of AC. Then, we have
AB/AD = CE/EA (by similarity of triangles ABD and ACE)
10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)
5/8 = CE/(x-6)
CE = (5/8)(x-6)
We also know that
BD/DE = AB/AE (by similarity of triangles ABD and ADE)
BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)
CE = (220 - 10x)/(x-22)
Since CE is equal in both expressions, we can equate them and solve for x
(5/8)(x-6) = (220 - 10x)/(x-22)
5x² - 196x + 1320 = 0
x² - 39.2x + 264 = 0
Using the quadratic formula, we get
x = 30.96 or x = 8.54
The length of AC must be positive, so we choose x = 30.96.
Therefore, the length of AC is approximately 30.96 units.
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--The given question is incomplete, the complete question is given
" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--
Las ecuaciones de la demanda y la oferta de cierto producto están dadas por espacio 4 q al cuadrado más p al cuadrado igual 1405 y p igual q más 10 donde p está en dólares por unidad y q está en unidades. Para un precio de 27 dólares por unidad, determine el gasto real del consumidor.
The actual consumer spending at a price of $27 per unit is $268.26.
How to calculate the priceSubstitute the given price into the supply equation to get the corresponding quantity supplied:
p = q + 10
27 = q + 10
q = 17
Substitute q = 17 into the demand equation to get the corresponding price:
4q² + p² = 1405
4(17)² + p² = 1405
p² = 1405 - 1156
p² = 249
p = 15.78
The actual consumer spending can be calculated by multiplying the quantity demanded by the price:
Actual consumer spending = quantity demanded x price per unit
= 17 x 15.78
= $268.26
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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.
What is the difference between a formal and informal proof?
A) A formal proof is much shorter, whereas an informal proof is longer.
B) A formal proof provides the reasons for steps, whereas an informal proof does not.
C) A formal proof uses equations, whereas an informal proof only uses text.
D) A formal proof uses a table or a list of steps, whereas an informal proof uses paragraphs.
Answer: D
Step-by-step explanation: formal proofs deeply uses tables or a list of steps where informal proofs are proven in paragraphs.
What is the solution of x=9y and 3y - 3x =24
Answer:
Step-by-step explanation:
The solution to the system of equations `x=9y` and `3y - 3x =24` can be found by substituting the value of `x` from the first equation into the second equation. This gives us `3y - 3(9y) = 24`, which simplifies to `-24y = 24`. Solving for `y`, we get `y = -1`. Substituting this value of `y` into the first equation, we get `x = 9(-1) = -9`. So the solution to the system of equations is `(x,y) = (-9,-1)`.
Is there anything else you would like to know?
What is the maximum possible product of two numbers that have a sum of -8?
The maximum possible product of two numbers that have a sum of -8 is 16.
How to find the maximum possible product of two numbers that have a sum of -8Let us name the two numbers "x" and "y".
We are aware of the following: x + y = -8
We're looking for the greatest possible product of x and y.
The number we're looking that are as near together as feasible and have a sum of -8.
-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.
The sum of these two figures is:
x * y = (-4) * (-4) = 16
So, the maximum possible product of two numbers that have a sum of -8 is 16.
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Solve the Pythagorean theorem for a, assuming a, b, and c are positive.
Answer:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
The correct answer is D.
one two 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Answer:
31
Step-by-step explanation:
the next number is 31 in this series
Last week Kristen spent 4 hours gardening over a period of 7 days .she spent the same amount of time gardening each day.about how much time did she spend gardening each day last week
Answer:
28
Step-by-step explanation:
i did 7 times 4
The volume of a rectangular prism is 5,890.625cm3 . if the height is 14.5 cm and the length is 25 cm, with is the value of the width ?
A. 16.25 cm B. 16.5 cm C. 16.75cm D. 16.97cm
Answer:
Step-by-step explanation:
The answer is A. 16.25cm.
Explanation:-
We know,
The Volume of Prism =height*width*length;
Here, In the question Height and length is given.
So We have to do a simple calculation to find,width=
(Vol of Prism)/Heigth*length;=> 5890.625/(14.5*25)
=>16.25 cm .
We don't need to worry about dimensions because all are in the same cm dimensions.
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Answer:
A. 16.25 cm
Step-by-step explanation:
To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:
"l" is the base length
"w" is the base width
"h" is the height of the prism
In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.
5,890.625 = (14.5)(25)w
To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.
(5,890.625)/(14.5) = (14.5)(25)w/(14.5)
406.25 = (25)w
Next, we can divide each side of the equation by 25 to get our answer.
406.25/25 = (25)w/25
w = 16.25 cm
What remainder is found when dividing 2x^2+7x-4 by x-3?
The remainder that is found when dividing 2x^2+7x-4 by x-3 is 35
Calculating the remainder that is found when dividing 2x^2+7x-4 by x-3?From the question, we have the following parameters that can be used in our computation:
Dividing 2x^2+7x-4 by x-3
This means that
Dividend = 2x^2 + 7x - 4
Divisor = x - 3
Set the divisor to 0
So, we have
x - 3 = 0
Evaluate
x = 3
Substitute 3 for x in the dividend equation, so, we have the following representation
Remainder = 2(3)^2 + 7(3) - 4
Evaluate
Remainder = 35
Hence, teh remainder is 35
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I need some assistance with this ? Please
Answer:
I am sorry this is just so new for me like what even is an "imaginary" solution, i am in 6th grade wth
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3
B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5
How to Solve Polynomial Expressions?A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.
Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.
3x² - 2 + x² + 2xy + 5
Combine like terms:
4x² + 2xy + 3
Part B: Number of canned food still remaining to be collected is calculated below.
(6x² - 2xy + 8) - (4x² + 2xy + 3)
Open bracket:
6x² - 2xy + 8 - 4x² - 2xy - 3
Combine like terms:
2x² - 4xy + 5
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Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C
What are algebraic expressions?Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.
Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;
BracketDivisionSubtractionMultiplicationParenthesesAdditionFrom the information given, we have that;
24 is the constant
Let the number be represented as n
Then, the expression is given as;
24 = 31.4(n) - 8.4
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A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects.
Before treatment, 23 subjects had a mean wake time of 105.0 min. After treatment, the 23 subjects had a mean wake
time of 82.1 min and a standard deviation of 23.3 min. Assume that the 23 sample values appear to be from a
normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a
population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before
the treatment? Does the drug appear to be effective?
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
what is mean ?In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.
given
For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
When we enter the provided values, we obtain:
s = 23.3
n = 23
t0.025,22 = 2.074
The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:
82.1 ± 2.074 * (23.3/√23)
which is equivalent to:
(71.4, 92.8)
The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.
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If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.
What is the range?The right interval to utilize for this set of numbers depends on the aim of the analysis.
If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.
So, in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.
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See full question below
If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
101, 203, 407, 512, 98, 642
Drag numbers to the table so it shows a proportional relationship between x and y.
The table is completed as follows:
x = 0.6, y = 6.x = 1.8, y = 18.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the first row, when x = 0.2, y = 2, hence the constant is given as follows:
k = y/x
k = 2/0.2
k = 10.
Hence the equation is:
y = 10x.
Then the numeric values are given as follows:
x = 0.6, y = 10 x 0.6 = 6.x = 1.8, y = 10 x 1.8 = 18.More can be learned about proportional relationships at https://brainly.com/question/7723640
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