Answers
By inclusion/exclusion,
[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]
We have
[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]
so that
[tex]n(P' \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]
Now,
[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]
and by inclusion/exclusion,
[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]
Decompose [tex]Q[/tex] into the union of two disjoint sets:
[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]
Since they're disjoint,
[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]
[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]
[tex]\implies 21 = 3n(P)[/tex]
[tex]\implies n(P) = 7[/tex]
From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that
[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]
Finally, we get for (a)
[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]
For (b), we have by inclusion/exclusion that
[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]
Related Questions
In the diagram below, if AB = 24, AC = 8, and BD = 6, then find the length of DC.
A) 8
B) 2
C) 12
D) 3
thank you :)
Answers
Answer: 2
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{8}{24}=\frac{DC}{6}\\\\DC=2[/tex]
The length of DC is 2
What is angle bisector theorem?Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Given:
AB = 24, AC = 8, and BD = 6
Now, using angle bisector theorem
AB/ AC = BD / DC
24 / 8 = 6 / DC
3 DC= 6
DC = 2
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2 Add the given fractions. Write the answers in the simplest form
A. 18/16 and 22/24 =
B. 23/13 and 42/15 =
C. 27/16 + 15/12 =
Answers
Answer:
A. 18/16 + 22/24 = 49/24
B. 23/13 + 42/15 = 297/65
C. 27/16 + 15/12 = 47/16
Step-by-step explanation:
18/16 + 22/24
= 54/48 + 44/48
= 98/48
= 49/24
…………………
23/13 + 42/15
=(23×15)/(13×15) + (42×13)/(13×15)
= 345/195 + 546/195
= 891/195 (divide both sides by 3)
= 297/65
……………………………………
27/16 + 15/12
= 81/48 + 60/48
= 141/48 (divide both sides by 3)
= 47/16
Which ordered pair below is a solution to the following system of equations?
3x − 5y = -1
2x − y = -3
Answers
The solution of the equation is given by (-2,-1), This is represented by option C.
What is a System of Equations?A system of equations is a set of equation that have a common solution.
The solution of the equations can be determined by using the Elimination and Substitution method
3x-5y = -1
2x-y = -3
-7x = 14
x = -2
Substituting this value in the equation
3 * (-2) -5y = -1
-6 -5y = -1
-5y = 5
y = -1
Therefore, the solution of the equation is given by (-2,-1), This is represented by option C.
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Reza paid $4,500 as a down payment on a car. she then made equal monthly payments of $250. reza paid a total of $10,500 for her car. how many months did she make payments on the car and which function can be used to find the answer?
Answers
Answer:
it took her 18 month
Step-by-step explanation:
if you divide 4500 with 250 you get the ans
Down payment = $4,500
Unknown no. Of payment months = X • 250
Therefore; $4,500 + $250 • X = $10,500
Then; $250X = $10,500 - $4,500
= $250X = $6000
Divide both sides by $250
Therefor; X = $6000/$250
X = 24
Therefore; no. Of months = 24
A ski slope is 1 km long and has an average slope of
13.4, what is the height of the mountain to the nearest metre?
Answers
Answer:
13400 m
Step-by-step explanation:
The slope is defined as:
[tex]Slope=\frac{Rise}{Run}[/tex]
Substitute slope=13.4, Run=1 km=1000 m :
[tex]13.4=\frac{Rise}{1000}[/tex]
Solve for Rise:
[tex]Rise=13.4\cdot 1000=13400 ~m[/tex]
find the remainder when f(x)=4x3-20x-50 is divided by x-3
Answers
Answer:
-2
Step-by-step explanation:
The hcp has ordered cefazolin 500 mg ivpb every 6 hours. the pharmacy sends cefazolin 500 mg in 50 ml of d5/w and it is to run over 1 hour via an infusion pump. the drop factor of the ivpb set is 60 gtt per ml. what is the hourly rate? __________ml/hr what would the hourly rate be if the hcp ordered the cefazolin to run over 30 minutes?_____________ ml/hr
Answers
It is to be noted that the flow rate is 50mL/h for the first instance, and;
100mL/h for the second instance.
What is flow rate?Flow rate (Fr) is computed with the following formula:
Fr (mL/h) = Volume (mL)/ Time (Hours)
Time = 1 hour
Volume = 50 mL
It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence,
Hourly flow rate = unknown
To compute for Flow Rate (Fr)
Recall that:
Fr (mL/h) = Volume (mL)/ Time (Hours)
Inserting the values we have
Fr = 50/1
Fr = 50mL/h
What would the hourly rate be if the hcp ordered the cefazolin to run over 30 minutes?
We have been given the following:
Time = 0.5 hours (30 minutes = 0.5 hours)
Volume = 50mL
It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence
Fr = 50/0.5
Fr = 100 mL/h
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please answer asap I would really appreciate it <3
Answers
The toroid formed by rotating the rectangular figure gives;
a. A toroid
b. 374•π
c. 400•π
d. The surface area will be 4 times the initial surface area
The volume will be 8 times the initial volume
How can the shape formed and it's characteristics be found?Taking the distance from the y-axis as 8
Width of the rectangle; 2.5
Length; 6
We have;
a. The solid of revolution is a toroid, having sharp corner edges
b. The surface area is found using the surface area of a hollow cylinder as follows;
Outer radius = 8 + 6 = 14
Inside radius = 8
Width = 2.5
Outer area = 2• π × 14 × 2.5 = 70•π
Inner area = 2• π × 8 × 2.5 = 40•π
[tex]{\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi[/tex]
The surface area of the figure is therefore;
70•π + 40•π + 2×132•π = 374•πc. The volume of the solid of revolution is found as follows;
[tex]{\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi[/tex]
The volume of solid is 400•πe. When the dimensions are doubled, we have;
The linear scale factor = 2
The area scale factor = 2^2 = 4
Therefore;
The surface area of the solid, S' = 4 × 374•π = 1496•π (4 times initial surface area)The volume scale factor = 2^3 = 8
The volume of the solid following the enlargement, is therefore;
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5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
Answers
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
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Please answer the question below
Answers
The value of x in the given sector is determined as 7.1.
Area of the sectorTotal area of the sector = area of the shaded + area of the unshaded
Since shaded and unshaded areas are equal, the value of x is calculated as follows;
πr²θ/360 = πx²60/360 + πx²60/360
πr²θ/360 = 2(πx²θ/360)
πr² = 2(πx²)
r² = 2x²
x² = r²/2
x² = (10²)/2
x² = 50
x = √50
x = 7.1
Thus, the value of x in the given sector is determined as 7.1.
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If f(x) and g(x) are polynomial functions, what is the domain of f(x) + g(x) ?
Answers
Answer:
all real numbers or [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.
Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.
Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ
I have an answer written down but i'm not sure if I am right. I require assistance because proofs are confusing
Answers
Using the above conditions ; If m ∠LOM = m ∠JKI, if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.
What are congruent angles about?An angle is known to be Congruent if its angles do have equal measure."
Note that question, In the said figure of the angles (image attached),
m ∠LOM = m ∠JKI (congruent angles) taken as 1
m ∠MON = m ∠IKH (congruent angles) taken as 2
The one should sum up both the side angle of m ∠MON in (1) we obtain;
m ∠LOM + m ∠MON = m ∠JKI + m ∠MON
Then one should replace angle m ∠MON = m ∠IKH from (eqn. 2) on right hand side and then it will be:
m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH taken as (3)
Then:
m ∠LOM + m ∠MON = m ∠LON ( M is said to be the interior point of ∠LON) taken as (4)
Since m ∠JKI + m ∠IKH = m ∠HKJ ( I is said to be the interior point of ∠HKJ) taken as number (5)
Using Number (3) , (4) and (5) in the image attached, we obtained:
m ∠LON = m ∠HKJ (Congruent angles)
Therefore, Using the above conditions ; If m ∠LOM = m ∠JKI, if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.
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-4,12-5-22,24-100,37 ordenar de menor a mayor
Answers
Answer:
24-100, 12-5-22, -4, 37
Step-by-step explanation:
12 - 5 - 22=-15
-4
37
La orden es:
-76, -15, -4, 37
A researcher conducts a power analysis for a study in which there was no difference between control and experimental group scores and identifies a power level of 0.75 and a level of significance of 0.05. What will this researcher do
Answers
Consider repeating the study using a larger sample.
Too small a sample may prevent the findings from being extrapolated, whereas too huge a sample may additionally increase the detection of differences, emphasizing statistical variations that are not clinically relevant.
Selecting the proper sample length will increase the chance of detecting an impact, and ensures that the look is both ethical and value-powerful. Repeated measures designs are widely used due to the fact they have got blessings over pass-sectional designs.
Larger sample sizes provide extra accurate mean values, perceive outliers that would skew the information in a smaller pattern and provide a smaller margin of blunders.
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Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results: Mean Grade Standard Deviation Professor 1 79.3 22.4 Professor 2 82.1 12.0 What are the degrees of freedom for the numerator of the F ratio
Answers
The degrees of freedom for the numerator of the F ratio can be calculated to be 9.
How many degrees of freedom is the numerator of the F ratio?The degrees of freedom for the numerator can be found to be:
= number of exams graded - 1
Solving gives:
= 10 - 1
= 9
In conclusion, the degrees of freedom for the numerator of the F ratio is 9.
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-5 4 3 2 -1
5
4
32
42
-3
-4
-5
2 3
4
5
Use the graph and table to write the equation that
describes the line graphed.
X
-2
-1
0
1
2
The equation of the line is
y
1
2
3
4
5
Answers
**ahh**
NEED HELP ASAP!!
This graph shows the total number of patients seen by a doctor over the course of a 5-day workweek.
What are the domain and range of this relationship??
Answers
Answer: its the last one
Step-by-step explanation:
i guessed and got it right
g The two general approaches to forecasting are: historical and associative. qualitative and quantitative. judgmental and qualitative. precise and approximation. mathematical and statistical.
Answers
The two general approaches are qualitative and quantitative.
What is Forecasting?Forecasting is a technique that uses past data as inputs to make future predictions by determining the direction of trends in the future.
What is Qualitative forecasting?It is an estimation methodology that uses judgment, other than numerical analysis. This type of forecasting depends upon the knowledge of most experienced employees and consultants to provide predictions for future outcomes.
What is Quantitative forecasting?It is a data-based math process that teams use to understand performance and predict future based revenue on the data and the patterns. Forecasting results gives businesses the ability to make informed decisions on strategies and processes to ensure continuous success
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help asap grade 5 math.
Answers
Answer:
A and C
Step-by-step explanation:
multiplying the value by a fraction < 1 will give a value less than the original value.
multiplying the value by an integer greater than 1 will give a value greater than or equal to the original value
A and C have 6,766 multiplied by a fraction < 1 , then
A and C have a value less than 6,766
Answer: A and C
Step-by-step explanation: Every time you multiply a fraction by a whole number, you get less than the whole number
You have a bag of marbles that has 12 red, 5 green, 6 yellow, and 4 blue. If you draw one at random, what is P(red or green)? (What is the percentage)
Answers
[tex]|\Omega|=12+5+6+4=27\\|A|=12+5=17\\\\P(A)=\dfrac{17}{27}\approx63\%[/tex]
Please help me I am confused on how to do these.
Answers
1. There's so much wrong with the suggested solution that it's hard to pinpoint the exact error. The "logic" is inconsistent - why do the [tex]x[/tex] and constant term stay in the denominator but the [tex]x^2[/tex] term does not?
What should be done is factorization in the numerator and denominator:
[tex]x^2 + 2x - 8 = (x + 4) (x - 2)[/tex]
[tex]x^2 + 6x - 16 = (x + 8) (x - 2)[/tex]
Then in the quotient, the factors of [tex]x-2[/tex] cancel so that
[tex]\dfrac{x^2+2x-8}{x^2+6x-16} = \dfrac{(x+4)(x-2)}{(x+8)(x-2)} = \boxed{\dfrac{x+4}{x+8}}[/tex]
2. Use the same strategy: factorize everything everything you can, then cancel anything you can.
[tex]x^2 - 9 = (x-3) (x+3)[/tex]
[tex]x^2+x-2 = (x+2)(x-1)[/tex]
[tex]x^2+x-12 = (x+4)(x-3)[/tex]
[tex]x^2+6x+8 = (x+4)(x+2)[/tex]
Then using the algebraic properties of multiplication/division, we have
[tex]\dfrac{x^2-9}{x^2+x-2} \div \dfrac{x^2+x-12}{x^2+6x+8} = \dfrac{x^2-9}{x^2+x-2} \times \dfrac{x^2+6x+8}{x^2+x-12} \\\\ ~~~~~~~~= \dfrac{(x-3)(x+3)(x+4)(x+2)}{(x+2)(x-1)(x+4)(x-3)} \\\\ ~~~~~~~~= \boxed{\dfrac{x+3}{x-1}}[/tex]
if the ratio of red to blue circles is 1:3 how many more red circles need to be added to make it a ratio of 3:1
Answers
Answer:
8Step-by-step explanation:
if the ratio of red to blue circles is 1:3 how many more red circles need to be added to make it a ratio of 3:1
add 8 red =
9/3 = 3/1
Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.
Answers
The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.
What is the approximation about?From the question:
Mars: F(x) = 2/3[tex]\sqrt{64x}[/tex]
Therefore, If x = 15
Then:
f (15) = 2/3 [tex]\sqrt[8]{15}[/tex]
= 16/3[tex]\sqrt{15}[/tex]
= 20.7ft/s
Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.
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A worker at a farm supply company in Franklin County is mixing up a 420-kilogram batch of its special grain blend for horses, which costs $5.80 per kilogram to make. If the mixture includes oats that cost $9.40 per kilogram and feed corn that costs $3.40 per kilogram, how many kilograms of each should the worker include in the mixture?
_?__ Kilograms of oats
_?__ Kilograms of feed corn
Answers
Answer:
168 kg oats and 252 kg corn
Step-by-step explanation:
2 equations and 2 unknowns
eq 1: x + y = 420
x is the amount of oats
y is amount of corn
eq 2: 9.4x + 3.4y = 5.8*420
solve equation 1 for x
x = 420 - y
substitute the value of x in eq 2
9.4(420-y) + 3.4y = 2436
y = 252
substitute y in eq 1
x + 252 = 420
x = 168
i knew how to do this but now i forgot the steps, can someone explain it to me?
Answers
The probability that a customer spends 10+ hours or have below $40,000 is 0.6034
How to solve the probability?Let A represent spending 10+ hours, and B represent having below $40,000
The probability is then calculated using:
P(A or B) = P(A) + P(B) = P(A and B)
This gives
P(A or B)= (476 + 621 - 131)/1601
Evaluate the sum and difference
P(A or B)= 966/1601
Divide
P(A or B)= 0.6034
Hence, the probability is 0.6034
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An angle measures 22.4° more than the measure of its complementary angle. What is the measure of each angle?
Answers
The first angle is 33.8° and second angle is 56.2°.
What is Complementary angle?
If the sum of the two angles is equal to the measurement of a right angle then the pair of angles is said to be complementary angles.
Complementary angles are the angles whose sum makes 90⁰.
Let's say our first angle is x:
x = first angle
According to the question,
The other angle is 22.4° more than the complementary angle.
Therefore, 22.4° will be added to the other angle.
first angle = x
second angle = x + 22.4°
Since, complementary angle is equal to the sum of the two angles to be 90°.
∴ x + x + 22.4° = 90°
2x = 90 ° - 22.4°
2x = 67.6°
x = 67.6° / 2
x = 33.8°
Thus, the first angle is 33.8° and second angle is 56.2°.
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A woman is sitting in a chair with her cat. When she stands up and tells the cat "Let's go. I'll give
you a treat!", the cat runs to the cabinet where his food is stored (a distance of 12 meters) and then to
his bowl (a distance of 5 meters). For how many second will the cat be waiting and meowing at his
bowl if he can run 10 meters per second and the woman can walk 1 meter per second? Consider that
the woman also needs 2 seconds to take the treat from the cabinet plus 3 more seconds to open the
package and put the treat in the cat's bowl.
Answers
The cat will be waiting and meowing at his bowl for 18.3 seconds.
How to calculate the total time taken?The time it takes the cat to reach the bowl = 3.7 seconds (17/10 + 2)
The time it takes the woman to reach the bowl = 17 seconds (17/1)
The total time it takes the woman to put the food = 22 seconds (17 + 3 + 2)
Waiting time = 18.3 seconds (22 - 3.7)
Data:Distance to the cabinet = 12 meters
Distance to the bowl = 5 meters
Total distance to be covered = 17 meters
Speed of the cat = 10 meters/s
Speed of the woman = 1 meter/s
Thus, since the time it takes is dependent on the speed of both, the cat will be waiting and meowing at his bowl for 18.3 seconds.
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60,120,130 without a reminder
Answers
Step-by-step explanation:
what is the question. what am I to do with those random numbers without a question, I'm just writing all this because they said at least 20 characters so don't get offended but pls give a detailed question
Consider the paragraph proof.
Given: D is the midpoint of AB, and E is the midpoint of AC.
Prove:DE = One-halfBC
On a coordinate plane, triangle A B C is cut by line segment D E. Point D is the midpoint of side A B and point E is the midpoint of side A C. Point A is at (2 b, 2 c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c).
It is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot, can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = StartRoot (2 a minus 0) squared + (0 minus 0) squared EndRoot, which simplifies to 2a. The length of DE can be determined with the equation DE = StartRoot (a + b minus b) squared + (c minus c) squared EndRoot, which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.
Which is the missing information in the proof?
a
4a
a2
4a2
Answers
Applying the distance formula, DE = a. Therefore, the missing information is: A. a.
What is the Distance Formula?Distance Formula for determining the distance between two points on a coordinate plane is given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
In the proof given, applying the distance formula to find DE, we have:
DE = √[(a + b - b)² + (c - c)²}
Simplifying this, we would have:
DE = √(a² + 0²) = √(a²)
DE = a
Therefore, the missing information in the proof is: A. a.
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Answer:
A. a
Step-by-step explanation:
got it right on edge23
A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym, and has an area of 7000ft^2. write an equation to represent the area of the gym and track together in terms of width
Answers
The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²
Let x be the width of the rectangle.
As the area of track along the walls of the gym is 7000ft²
(x - 12)(3x - 12) = 7000
After simplifying:
3x² - 48x + 6856 = 0
Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.
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