A) Where the calibration of the graph represents a unit each, the approximate coordinates of the points of intersection of the two graphs is (4.5, 3)
This means that after after a given number of days, the area covered by both types of mold were the same.
b) given the function, the number days it takes for the mold to cover 1000 square millimeters is 46 days.
How is this so?A) this is observed by exploring the graph.
b) Let A(d) = 1000
⇒ 1000 = 100 x [tex]e^{0.05d}[/tex]
If we divide both sides by 100 to simplify, we will get
[tex]e^{0.05d}[/tex] = 10
To solve for d we need to compute the natural log of both sides, so we get
ln [tex]e^{0.05d}[/tex] = ln (10)
Recall that ln (eˣ) = x so
ln [tex]e^{0.05d}[/tex] = ln (10)
⇒ 0.05d = ln (10)
Divide both sides by 0.05
d = ln10/0.05
d = 2.30258509299/0.05
d = 46.0517018599
d ≈ 46 days.
thus,
it will take about 46 days for the mold to cover 1000 millimeters.
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The function f(x)=-x^2-2x+15 is shown on the graph. What are the domain and range of the function?
Answer:
2nd choice down
Step-by-step explanation:
Domain is the set of all real numbers (no restrictions on x).
The vertex of the solid-line open-down parabola is at (-1, 16), therefore the range is y≤16 (maximum value of y is 16, at the vertex point (-1, 16). Range is {y|y≤16}
B
A
E
C
D
Which statement is true about the given information?
O ZCED measures 45°.
O ZCED measures 180°.
ZAEC measures 90°.
O
O ZAEC measures 45°.
The statement that is true of the information given is that C. Angle AEC measures 90°.
How to determine the angle givenThe picture of the diagram obtained from other sources shows aline CE that stands at a perpendicular angle to another line AED. These two lines meet at a point that corresponds to the summation of two 45° angles. Now we do our summation as follows:
45° + 45° = 90°.
So, we can arrive at the conclusion that angle AEC is a right-angle triangle with a dimension of 90°. Therefore, option C is correct.
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A rectangular prism is 6 feet wide and 6 feet high. Its volume is 180 cubic feet. What is the length of the rectangular prism?
Step-by-step explanation:
volume = L x W x H
180 ft^3 = L x 6 x 6 ft
180 / ( 6x6) = L = 5ft
PLS PLSPKS PLS HELP URGENT ❗️❗️❗️❗️
The true statement is that D. On average, Rosalie scored higher on her maths test that Marvin.
How to calculate the valueMean = (68+73+76+76+83+83+86)/7 = 77.14%
Therefore, this claim is untrue.
Rosaline's test results fall within a range of scores that is 11.
Q3 - Q1 = 16% is the interquartile range (IQR).
Therefore, this claim is untrue.
C) Marvin and Rosalie both had a wider range of test results.
The gap between the greatest and lowest scores is known as the range.
Range = 86 - 68 = 18% for Marvin.
Range = 97 - 70 = 27% for Rosalie
Therefore, this claim is untrue.
Rosalie performed better than Marvin on math exams on average.
Rosalie's test results' average were calculated as follows: Mean = (70+84+86+89+93+95+97)/7 = 87.14%
So, this assertion is accurate.
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which equation belongs to the same function family as the graph shown below?
The equation that belongs to the same function family as the graph shown below is given as follows:
C. h(x) = 2(5)^x.
What is an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The graphed function is a decreasing exponential function, belonging to the exponential function family.
Hence the correct option is given by option C, as it is the only exponential function among the options given.
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A corresponding diagonal of two similar trapizolds are in eatio of 1:7 what is the ratio of the areas
The ratio of the areas is 4:7.
If two trapezoids are similar, then their corresponding sides are proportional. The ratio of the corresponding diagonal is given as 1:7, so let us assume that the ratio of the corresponding bases is also 1:7.
Let the bases of the trapezoids be a and 7a, and let the heights be h1 and h2 respectively. We can use the formula for the area of a trapezoid, which is:
Area = (1/2) × (sum of bases) × height
The area of the larger trapezoid is:
A2 = (1/2) × (a + 7a) × h2 = 4a × h2
The area of the smaller trapezoid is:
A1 = (1/2) × (a + 7a) × h1 = 4a × h1
We know that the corresponding diagonal is in the ratio of 1:7, which means that the corresponding sides are also in the ratio of 1:7. This implies that the corresponding heights are in the same ratio, i.e., h1:h2 = 1:7.
Therefore, we can write h1 = (1/7)h2. Substituting this into the expression for A1, we get:
A1 = 4a × h1 = 4a × (1/7)h2 = (4/7)A2
So the ratio of the areas of the smaller trapezoid to the larger trapezoid is:
A1 : A2 = (4/7) : 1
Therefore, the ratio of the areas of the two similar trapezoids is 4:7.
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Quadrilateral HUK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm. Which could be the side lengths of a dilation of HUK?
The option that could be the side lengths of a dilation of HUK is (C) 18cm, 39cm, 21cm and 45cm.
What is the side lengths of a dilation?From the question, the quadrilateral HIJK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm.
If HIJK is said to be dilated with a scale factor of 1.5, the side lengths will thus be:
12 x 1.5 =18 cm
26 x 1.5 =39 cm
14 x 1.5 =21 cm
30 x 1.5 =45 cm
A dilation of HIJK with a scale factor of 1.5 will make us have the side lengths: 18cm, 39cm, 21cm and 45cm.
Therefore, The correct option is C.18cm, 39cm, 21cm and 45cm.
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See full text below
Quadrilateral HUK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm. Which could be the side lengths of a dilation of HUK?
(A)24cm,50cm,28cm, 60cm (B)6cm,15cm,7cm,15cm (C)18cm,39cm,21cm,45cm (D)30cm,78cm,35cm,75cm
Suppose all of the players on a basketball team had
the same height. Explain how you could use reasoning to find the
mean absolute deviation of the players' heights.
i need answer...............................
On plotting the equation on the graph the value of x is -1.25. The correct option is C.
A function is a rule in mathematics that links every element of one set, known as the domain, with precisely one element of another set, known as the range.
A function is, to put it simply, a relationship between two sets of numbers in which each input (domain value) has exactly one corresponding output (range value).
One method is to graph both sides of the equation and find the point of intersection. We can graph y = -4x-1 [tex]y = 5^x+4[/tex] on the same set of axes. The point of intersection will give us an approximate solution.
When the graph is plotted on the x-y axis the value of the x coordinate will be -1.28. Which is approximately equal to -1.25.
Therefore, the value of x will be -1.25. The correct option is C.
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I need help finding out if i have to factor this using GCF or the other way and why ? pls helpp
Answer:
Step-by-step explanation:
This is the difference of squares. There is no GCF to take out.
The first term is a "perfect square" and so is the second term
You can take the square root of both terms perfectly
[tex]\sqrt{4w^{2} }[/tex] = 4w
√1 = 1
format for factors:
(√ of 1st term + √ of 2nd term)(√ of 1st term - √ of 2nd term)
The order of + and minus doesn't matter which parenthesis it goes in
factor:
(4w+1)(4w-1)
PLEASE HELP ONLY HAVE 30 MINS WILL MARK BRANLIEST!!!!
Answer:
the question is not complete
Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
The classifications that must be the according to the figure are:
For RSUT
QuadrilateralParallelogramRectangleFor XVWY
QuadrilateralParallelogramRectangleFor ABCD
QuadrilateralParallelogramWhat is a rectangleA rectangle is a four sided polygon otherwise known as a quadrilateral that has other properties such as
Two opposite sides are equaltwo opposite sites are parallel to each otherThe diagonals are equal and bisect each otherFor ABCD, the third property mentioned here is failing as the diagonals are not equal.
Other figures makes us the desired properties of a rectangle
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you solved for x in a triangle that has angles with the following measures: (x2 + 34)°, (6x + 4)°, and (10x + 10)°. Find the measure of the smallest angle in this triangle.
The value of measure of the smallest angle in this triangle is, 40 degree
Since,
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Here, The measure of three angles of triangle are given;
⇒ (x²+34)°, (6x+4)°, and (10x+10)°.
Hence,
(x²+34)°+(6x+4)°+(10x+10)°=180°
x²+16x+48=180
x²+16x-132=0
Using splitting middle term method, we get
x²+22x-6x-132=0
x(x+22)-6(x+22)=0
(x+22)(x-6)=0
x-6=0
x=6
Therefore, the value of of measure of the angle in this triangle is,
⇒ x² + 34 = 6² + 34 = 36 + 34 = 70
⇒ (6x + 4) = 6 × 6 + 4 = 40
⇒ (10x + 10) = 10 × 6 + 10 = 70°
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• Point M (12, -5) • Point N (6,11) • Point P (-9,9) • Point Q (10,9) • Plant R (-1, -13) Consider the distance between the origin and each point Determine whether each point is less than 13 units, greater than 13 units, or exactly 13 units from the origin. Drag the letter of each point to the proper column in the table. Greater than 13 units
The table of distance of points from the origin is:
Less than 13 units Equals to 13 units Greater than 13 units
M N, P Q, R
We know that in Cartesian Coordinate Plane, the distance between the point (a, b) and the origin (0, 0) is given by,
D = √(a² + b²)
Coordinates of Point M = (12, -5)
So the distance of the point M to the origin
= √(12² + (-5)²)
= √(144 + 25)
= √169
= 13 units
Coordinates of Point N = (6, 11)
So the distance of the point N to the origin
= √(6² + 11²)
= √(36 + 121)
= √157
= 12.53 units (approximated to two decimal places)
< 13 units
Coordinates of Point P = (-9, 9)
So the distance of the point P to the origin
= √((-9)² + 9²)
= √(81 + 81)
= √162
= 12.73 units (approximated to two decimal places)
< 13 units
Coordinates of Point Q = (10, 9)
So the distance of the point Q to the origin
= √(10² + 9²)
= √(100 + 81)
= √181
= 13.45 units (approximated to two decimal places)
> 13 units
Coordinates of Point R = (-1, -13)
So the distance of the point R to the origin
= √((-1)² + (-13)²)
= √(1 + 169)
= √170
= 13.04 units (approximated to two decimal places)
> 13 units
hence the table is,
Less than 13 units Equals to 13 units Greater than 13 units
M N, P Q, R
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pls help this was due last week!!!
Answer:
Triangle A is correct since 87° + 23° + 70° = 180°.
Nicole bought 7 shirts for a total of $136. Fancy shirts cost $28 and plain shirts cost $8. How many of each type of shirt did she buy?
Answer:
Nicole bought 4 fancy shirts and 3 plain shirts.
Step-by-step explanation:
I multiplied 28 x 4 to get $112
then I multiplied 8 x 3 to get $24
You add $112 and $24 to get $136.
Nguyen has opened a new bake shop in town selling pies. Nguyen
sells each pie for $8 and has spent $918 on rent and maintenance, this
month. How many pies did Nguyen sell if he made $602 profit this
month?
RICH VS. MARCUS
For this simulcam race, Rich is given a 10 yard head start. Write the function rules for
both players, then graph both equations and fill in the approximate table values.
Rich's function R(t) = function rule?
T R(t)
0 10
1 ?
2. ?
3. ?
4. ?
5. ?
Marcus' is M(t) = function rule?
T. R(t)
0. 0
1. ?
2. ?
3. ?
4. ?
5. ?
Answer: N/A
Step-by-step explanation: In a race between Rich and Marcus, Rich is given a 10-yard head start. Assuming that Rich runs at a constant speed and Marcus runs at a faster constant speed, we can write their positions as functions of time:
Rich's position function is R(t) = 10 + r*t, where r is Rich's speed in yards per second.
Marcus's position function is M(t) = m*t, where m is Marcus's speed in yards per second.
We can use these functions to fill in a table of approximate values for the distance each runner travels at different times:
Time (t) Rich's Distance (R(t)) Marcus's Distance (M(t))
0 10 0
1 10 + r m
2 10 + 2r 2m
3 10 + 3r 3m
4 10 + 4r 4m
5 10 + 5r 5m
To graph these functions, we can plot the points from the table and connect them with a straight line. The graph shows the distance each runner travels as a function of time. Note that the value of r is not given in the problem, so we cannot calculate the exact positions of Rich at each time interval.
Marcus has scores of 92, 87, 85 and 88 on four algebra tests. What score must he make on his exam to receive a "B" in the course, if the final exam counts as two tests? A "B" in the course is earned if the final average is between 83 and 91. Write a compound inequality to represent this situation
The compound inequality can be written as 83 ≤ x ≤ 91
How to write the inequalitywe can write a compound inequality to represent this situation as:
83 ≤ (92 + 87 + 85 + 88 + 2x) / 6 ≤ 91
where x represents Marcus's score on the final exam (which counts as two tests).
To solve for x, we can start by multiplying both sides of the inequality by 6 to eliminate the denominator:
498 ≤ 352 + 2x ≤ 546
Next, we can subtract 352 from all sides of the inequality:
146 ≤ 2x ≤ 194
Finally, we can divide all sides of the inequality by 2:
73 ≤ x ≤ 97
Therefore, Marcus must score between 73 and 97 on his final exam to earn a "B" in the course.
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You earn $13 per hour plus a commission equal to x percent of your sales as a cell phone sales representative.
What is your commission percentage (x ) if you work 8 hours with sales of $1200 worth of merchandise and your total earnings for the day is $140?
The commission percentage for the sales is 3%.
What is function and equation?A mathematical statement known as an equation, typically with an equal sign, illustrates the relationship between two expressions. To determine the values of the variables that make an equation true, equations can be solved.
On the other hand, a function is a collection of ordered pairs where each input value (also known as the independent variable) and each output value (also known as the dependent variable) have a precise correspondence. Although equations are frequently used to write functions, this is only one approach to express a function.
Given, your commission percentage is x.
Now, for commission x percent of the sales we have:
$140 = ($13 x 8) + (x/100 x $1200)
$140 = $104 + 12x
$36 = 12x
x = 3
Hence, the commission percentage for the sales is 3%.
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£1400 is put into an account. It gathers simple interest at a rate of 7% per year. a) How much money is added to the account each year? b) How much money will be in the account after two years? Give your answers in pounds (£).
Part(a),
The amount added to the account each year will be £98.
Part(b),
After two years, there will be £1602.86 in the account.
a) Apply the basic interest formula to determine how much is added to the account annually:
I = Prt
where I stands for interest, P for principal, r for the interest rate expressed as a decimal per year, and t for the period of time in years.
P = £1400, r = 0.07, and t = 1 in this instance (since we are calculating the interest for one year). When these values are added to the formula, we obtain:
I = 1400 × 0.07 × 1 = £98
Therefore, £98 is added to the account each year.
b) The interest earned in the first year must be added to the principal to determine the balance in the account after two years, and the interest earned in the second year must be determined using the same formula:
Year 1: Interest = £98, Total amount = £1400 + £98 = £1498
Year 2: Interest = 1498 × 0.07 × 1 = £104.86, Total amount = £1498 + £104.86 = £1602.86
Therefore, after two years, there will be £1602.86 in the account.
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Ryan's backyard deck cost $87. 85 per square yard to build. The deck is 8 yards wide and 12 yards long. How much did it cost to build the deck?
It cost $8,428.80
The first step to solving this problem is to find the area of the deck in square yards. We can do this by multiplying the length by the width:
Area of the deck = Length x Width = 8 yards x 12 yards = 96 square yards
Next, we can find the total cost of building the deck by multiplying the area by the cost per square yard:
Total cost = Area of the deck x Cost per square yard
Total cost = 96 square yards x $87.85 per square yard
Total cost = $8,428.80
Therefore, it cost $8,428.80 to build Ryan's backyard deck.
Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)
(4.99)3
using differentials using a calculator
Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251.
To use differentials to approximate the value of the expression (4.99)3, we can use the formula:
Δy ≈ dy = f'(x)Δx
Where f'(x) is the derivative of the function f(x) = x3 evaluated at x = 5, since we are approximating around x = 5, and Δx is the change in x from 5 to 4.99, which is -0.01.
f'(x) = 3x2
f'(5) = 3(5)2 = 75
Δy ≈ dy = 75(-0.01) = -0.75
So, the approximate value of (4.99)3 using differentials is:
(4.99)3 ≈ (5 + Δx)3 ≈ 53 + 3(53)(-0.01) = 124.2575
Rounding to four decimal places, we get:
(4.99)3 ≈ 124.2575
Using a calculator, we get:
(4.99)3 = 124.251
Comparing the two values, we see that the approximation using differentials is very close to the value obtained using a calculator. The difference is only in the third decimal place, which is likely due to rounding errors in both calculations.
Step 1: Choose a base point
Since 4.99 is close to 5, we will choose 5 as our base point (x = 5).
Step 2: Find the expression's value at the base point
At x = 5, the expression is (5)³ = 125.
Step 3: Calculate the derivative of the expression
For the expression x³, the derivative is 3x².
Step 4: Find the derivative's value at the base point
At x = 5, the derivative is 3(5)² = 3(25) = 75.
Step 5: Calculate the differential
Δx = 4.99 - 5 = -0.01.
Step 6: Approximate using differentials
Δy ≈ dy = (derivative) * Δx = 75 * (-0.01) = -0.75.
Step 7: Add the differential to the base point value
Approximate value = 125 + (-0.75) = 124.25.
Now, let's compare this with a calculator result.
Using a calculator:
(4.99)³ ≈ 124.251
In conclusion:
Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251. Both values are rounded to four decimal places.
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Linear equations:
What is the is the slope and the y-intercept for y=3x+75
Answer:
m = 3
Y-intercept: 75
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = Y-intercept
We see
m = 3
b = 75
So, the slope is 3 and the intercept is 75
The answer of the given question based on the Linear equations is , the slope of the line is 3 and the y-intercept is 75.
What is Slope?Slope is measure of steepness of line on a graph. It describes rate at which line rises or falls as it moves from left to right, and it is defined as ratio of vertical change (rise) to horizontal change (run) between any two points on line.
In the equation y = 3x + 75, the coefficient of x is 3, which represents the slope of the line. Therefore, the slope of line is 3.
The equation is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The y-intercept is value of y when x is 0. In this case, when x is 0, y is:
y = 3(0) + 75
y = 75
So the y-intercept of the line is 75.
Therefore, the slope of the line is 3 and the y-intercept is 75.
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a graph titled monthly sales and advertising costs has advertising costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. a line goes through points (6.4, 117) and (6.6, 120). the slope of the trend line is 15. what does that mean in regard to the data of the scatterplot? check all that apply. the slope represents the rate of change of the data. advertising costs increase $15,000 as sales increase by $1,000. sales increase $15,000 as ads increase by $1,000. a positive slope infers a negative correlation. a positive slope infers a positive correlation.
A graph titled "Monthly Sales and Advertising Costs" has advertising costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. The line goes through points (6.4, 117) and (6.6, 120) with a slope of 15.
The slope of the trend line represents the rate of change of the data. In this case, the slope is positive, which means there is a positive correlation between advertising costs and sales. For every $1,000 increase in advertising costs, the sales increase by $15,000. So, the correct statements are:
1. The slope represents the rate of change of the data.
2. Sales increase $15,000 as ads increase by $1,000.
3. A positive slope infers a positive correlation.
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PLEASE HELP I BEG YOU GUYS:(
06.06 Transitioning to the End Worksheet
Prompt 1: There is one door you pass every day that is always locked. However, one day, you pass by and it's slightly ajar. You decide to walk in. Plan a narrative about what you find and what happens when you enter.
Determining which plot element is the most challenging to write can pose difficulties for writers, largely depending on their individual style and the story they are crafting.
How to explain the informationOne of the more difficult plot elements can be the climax, which requires careful buildup and execution to deliver on achieving a satisfying payoff for readers due to escalating tensions throughout the narrative.
Writers tend to employ two common narrative approaches in their writing- dialogue and sensory details. Dialogue helps establish characters' drive, emotions, and motivations, while also advancing the plot and providing critical information to readers. Sensory details create immersive scenes with vivid imagery that allow readers to become invested into the story's ambiance and location.
In sum, by utilizing sensory details, authors capture readers' senses and render stories more tangible, while dialogue helps readers grasp characters' actions and feelings.
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Find the length of a side of a square if its area is: x units
Answer:
square root of x.
If the area is "x" the length must be the square root of x because all sides of a square are equal and the square root of x times itself equals x
Fulgurites are pieces of glass in the shape of a cylinder produced when lightning strikes sand. A student found a fulgurite with a height of 21 inches and a diameter of 6 inches. Which equation can be used to find V, the volume of the fulgurite in cubic inches?
Question 9 .
[tex]V = \pi(3)^2(21)[/tex] is the equation that shows the volume of the given cylinder.
The following formula may be used to determine a cylinder's volume:
[tex]V=\pi r^2h[/tex]
Where r is the radius of the cylinder's base, h is its height and is a mathematical constant that denotes the ratio of a circle's circumference to its diameter.
We must first determine the radius of the cylinder's base in order to utilize this formula to calculate the fulgurite's volume. The radius is equal to half of the base's diameter, or 3 inches since we know it to be 6 inches.
When we enter the values we are aware of into the formula, we obtain:
[tex]V = \pi(3)^2(21)[/tex]
Therefore, the expression that represents the volume is [tex]V = \pi(3)^2(21)[/tex]
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4x^2+12x+4y^2-8y=87
what is the center and radius?
Answer:
C = (-3/2, 1)
r = 25
Step-by-step explanation:
4x² + 12x + 4y² - 8y = 87 divide both sides by 4
x² + 3x + y² - 2y = 87/4 rearrange the equation
(x² + 3x + h) + (y² - 2y + k) = 87/4 + h + k complete the square
h = (3/2)² = 9/4
k = (-2/2)² = 1
(x² + 3x + 9/4) + (y² -2y + 1) = 87/4 + 9/4 + 1
(x² + 3x + 9/4) + (y² -2y + 1) = 25
(x + 3/2)² + (y - 1)² = 25
r² = 25
r = √25 = 5
C = (h, k) = (-3/2, 1)
the fee to check luggage with a new airline is based on the weight of each bag. Brett paid $7.14 to check a 42 pound g how much will eileen ppay of her bag weighs 63 pounds
For 63 pounds of the bag, Eileen will have to pay $10.71.
Given is that the fee to check luggage with a new airline is based on the weight of each bag. Brett paid $7.14 to check a 42 pound.
Brett paid $7.14 to check a 42 pound.
Then, for 1 pound, Brett will have to pay $(7.14/42) or $0.17.
So, for 63 pounds of the bag, Eileen will have to pay -
63 x 0.17
10.71
Therefore, for 63 pounds of the bag, Eileen will have to pay $10.71.
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