Brass is made from a mixture of copper and other elements. a mixture that is 80% copper is combined with a mixture that is 60% copper, resulting in 100 pounds of brass that is 65% copper. which equation can be used to find x, the amount of 60% mixture used to create the 65% mixture?
Answers
The equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture is:
0.60*x + 0.80*(100 - x) = 0.65*(100).
Which equation we should use?First, let's define two variables:
x = pounds of the 60% copper brass.y = pounds of the 80% copper brass.We know that we want to make 100 lb of 65% copper brass, then we must have that:
x + y = 100
And the percentage of copper before and after mixing must be the same, so we can write:
0.60*x + 0.80*y = 0.65*(x + y).
(where the percentages are written in decimal form).
Then we have a system of equations:
x + y = 100
0.60*x + 0.80*y = 0.65*(x + y).
To get a single equation, we can isolate the variable "y" on the first equation:
y = 100 - x
Now we replace that in the other equation:
0.60*x + 0.80*(100 - x) = 0.65*(100).
This is what we wanted to get, an equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
Related Questions
The
of a nonvertical line passing through two points is the ratio of the rise to the run.
Answers
Answer: Slope
Step-by-step explanation:
Slope is rise over run. It can be calculated by dividing the change in y (rise) over the change in x (run).
The slope of a non vertical line passing through two points is the ratio of the rise to the run.
What is slope of a line?
The slope of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.
1. Slope of Parallel Lines :
A set of parallel lines always has the same inclination angle. Assume we possess two parallel lines l1 and l2 in the reference plane, inclined at angles θ1 and θ2 with the x-axis, respectively, such that the, θ2 = θ1.
m1 = m2
Therefore, the slopes of the two given parallel lines are equal.
2. Slope of Perpendicular Lines :
A pair of perpendicular lines always form a 90° angle. Imagine we have two perpendicular lines l2 and l1 in the coordinate plane, inclined at angles θ1 and θ2 with the x-axis, respectively, so that the provided angles follow the external angle theorem, θ2 = θ1 + 90°
m₁ = tan θ₁
m₂ = tan (θ₁ + 90º) = - cot θ₁
m₁ × m₂ = -1
Therefore, the product of slopes of two given perpendicular lines is equal to -1
Hence , The slope of a non vertical line passing through two points is the ratio of the rise to the run.
To know more about the slopes click :
https://brainly.com/question/26446772
#SPJ2
11. There are 106 nails in one pound of 8d com-
mon nails. How many are in a 50-pound box?
Answers
Answer:
5300
Step-by-step explanation:
based on past experience, a bank believes that 7.6 % of the people who receive loans will not make payments on time. the bank has recently approved 240 loans. what must be true to be able to approximate the sampling distribution with a normal model? before proceeding, think about whether the conditions have been met. what are the mean and standard deviation of the sampling distribution of the proportion of people who will not make payments on time in samples of 240?
Answers
Therefore, the mean of the sampling distribution of the proportion is 0.076 and the standard deviation is approximately 0.0189.
To be able to approximate the sampling distribution with a normal model, we need the following conditions to be met:
Random Sampling: The 240 loans should be randomly selected from the population of all loans. This ensures that the sample is representative of the population.
Independence: The loans should be independent of each other. This means that the default status of one loan does not affect the default status of another loan.
Success-Failure Condition: The number of successes (people who do not make payments on time) and failures (people who make payments on time) in the sample should each be at least 10. This ensures that the sampling distribution can be approximated using a normal model.
Now, let's calculate the mean and standard deviation of the sampling distribution of the proportion:
The mean of the sampling distribution of the proportion is equal to the population proportion, which is 7.6% or 0.076.
The standard deviation of the sampling distribution of the proportion can be calculated using the formula:
σ = √((p * (1 - p)) / n)
where p is the population proportion and n is the sample size.
In this case, p = 0.076 and n = 240.
σ = √((0.076 * (1 - 0.076)) / 240)
= √(0.07095 / 240)
≈ 0.0189
To know more about mean,
https://brainly.com/question/29586760
#SPJ11
what is the solution to the equation 14 x + 3 = 21?
Answers
Answer:
x=9/7
Step-by-step explanation:
14x+3=21
14x=21-3
14x=18
14x/14=18/14
x=9/7
14(9/7)+3=21
2*9+3=21
18+3=21
21=21
if you have any question about this you can ask me
currently, the rate for new cases of diabetes in a year is 4.3 per 1000 (based on data from the centers for disease control and prevention). when testing for the presence of diabetes, the newport diagnostics laboratory saves money by combining blood samples for tests. the combined sample tests positive if at least one person has diabetes. if the combined sample tests positive, then the individual blood tests are performed. in a test for diabetes, blood samples from 10 randomly selected subjects are combined. find the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes. is it likely that such combined samples test positive?
Answers
A data of cases of diabetes from the centers for disease control and prevention, the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes is equals to 0.04218.
We have a data from the centers for disease control and prevention.
The rate of new cases of diabetes
= 4.3 per 1000
So, probability ( diabetes) =\( \frac{4.3}{1000}\) = 0.0043
Using complement rule, Probability for no diabetes people, P( no diabetes)
= 1 - 0.0043 = 0.9957
Now, blood samples from 10 is randomly selected. It is assumed that each of these different people having diabetes is independent events. Using multiplcation rule for independent events, P( All 10 have no diabetes )
= P( no diabetes)× P( no diabetes)×....× P( no diabetes) ( 10 times)
= ( P( no diabetes))¹⁰ = 0.9957¹⁰
= 0.957823
Using complement rule, P ( atleast 1 the 10 people having diabetes) = 1 - P( All 10 have no diabetes ) = 1 - 0.957823
= 0.04218
Since, probability value is small so it is unlikely that a combined sample test. Hence, required probability is 0.04218.
For more information about probability, refer:
https://brainly.com/question/25870256
#SPJ4
solving a word problem using a one step linear inequality
Answers
To solve a word problem using a one-step linear inequality, follow these steps: identify the given information, translate it into an inequality, isolate the variable, and write the solution. For example, if a store sells T-shirts for $15 each and you have at most $100 to spend, the number of T-shirts you can buy is represented by the inequality x ≤ 6, which means you can buy at most 6 T-shirts.
To solve a word problem using a one-step linear inequality, follow these steps:
Read the word problem carefully and identify the information given.Translate the given information into an inequality. Use the appropriate inequality symbol (<, >, ≤, ≥) based on the problem.Isolate the variable on one side of the inequality symbol by performing the same operation on both sides of the inequality. If you multiply or divide by a negative number, remember to reverse the inequality symbol.Write the solution to the inequality using interval notation or set notation, depending on the problem.For example, let's say you have the word problem: 'A store sells T-shirts for $15 each. You have at most $100 to spend. Write an inequality to represent the number of T-shirts you can buy.'
Step 1: Identify the given information. The store sells T-shirts for $15 each and you have at most $100 to spend.
Step 2: Translate the given information into an inequality. Let x represent the number of T-shirts. The inequality is 15x ≤ 100, since the total cost of the T-shirts should be at most $100.
Step 3: Isolate the variable. Divide both sides of the inequality by 15 to get x ≤ 6.67. Since you can't buy a fraction of a T-shirt, round down to the nearest whole number. The solution is x ≤ 6.
Step 4: Write the solution. The number of T-shirts you can buy is represented by the inequality x ≤ 6, which means you can buy at most 6 T-shirts.
Learn more about linear inequality
https://brainly.com/question/21857626
#SPJ11
On a world map, the distance between city A and city B is 10.125 inches. The two cities are actually 3038 miles apart. On the same map, what would be the distance between city C and city D, two cities that are actually 3445 miles apart? Use a proportion to solve this problem.On the map, the distance between city C and city D is _____ inches.(Round to three decimal places as needed.)
Answers
We will use the proportional method to solve the question
Since the distance on the map of actual distance 3038 miles is 10.125 inches
Since we need to find the distance on the map of the actual distance of 3445 miles
Then by using the proportional method
\(\frac{10.125}{x}=\frac{3038}{3445}\)By using the cross-multiplication
\(\begin{gathered} x\times3038=10.125\times3445 \\ \\ 3038x=34880.625 \end{gathered}\)Divide both sides by 3038
\(\begin{gathered} \frac{3038x}{3038}=\frac{34880.625}{3038} \\ \\ x=11.481\text{ inches} \end{gathered}\)On the map, the distance between city C and city D is 11.481 inches
A city doubles its size every 24 years. If the population is currently 145,000, what will the population be in 48 years?
Answers
Answer:
145000x2
=answer
then
answer×2
= final answer
Answer:
580,000 people
Step-by-step explanation:
First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.
48÷24=2
The population will double 2 times.
Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.
145,00022=580,000
That calculation could also be written with exponents:
145,000 x 2^2=580,000
After 48 years, the population will be 580,000 people.
\(\sqrt{100}\)
Answers
Because 10x10=100
For square roots you try to find what number multiplied by itself equals the number on the inside.
in general, the strictest standards with the lowest acceptable levels are the
Answers
Answer:
Step-by-step explanation:
are the what???
A tire in Abduls car has just sprung a leak and is losing pressure at a rate of 5% every hour. If the tire pressure is currently 280 kilopascal, what will it be in 18 hours? If necessary round your answer to the nearest tenth
Answers
.05•18=.9
Multiply 280, your initial number, by .9
280•.9=252
In 18 hours, the tire pressure will be 252 kPa
Figure II is a translation image of Figure I. Write a rule to describe the translation.
The translation rule is (x,y)→(x+ __ , y+ __ )
Answers
The translation rule is (x, y) → (x + (-2) , y + 4)
We have,
From the figure,
We see the coordinates of Figure I.
(4, -5), (2, 1), and (-3, -3) _____(1)
We see that the coordinates of Figure Ii.
(2, -1), (0, 5), and (-5, 1) _____(2)
Now,
From (1) and (2),
Taking the corresponding coordinates.
(4, -5) and (2, -1)
(2, 1) and (0, 5)
(-3, -3) and (-5, 1)
We see that,
x coordinates is substrated by 2 and y coordinate is added by 4.
So,
The translation rule is (x, y) → (x + (-2) , y + 4)
Thus,
The translation rule is (x, y) → (x + (-2) , y + 4)
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ1
The diameter of a circle is 8 meters. What is the circle's circumference?
Answers
Answer:
25.13 square meters
Step-by-step explanation:
The formula for finding the circumference of a circle is πd or pi times the diameter
Diameter = 8 meters
Pi = 3.14
3.14 times 8 = 25.13
Write a linear equation representing the information shown in the table.
A) y= -5/2x-5
B) y=-2/x-5
C) y=5/2x-5
D) y = 2/x-5
Answers
Answer:
A
Step-by-step explanation:
This is how I write
y=kx+m
but I have seen some write it like this:
y=mx+b
Well both of them are the same thing, I'll use the first one because I'm more comfortable with it.
y=kx+m
To find out what k
\(k = \frac{y2 - y1}{x2 - x1} \)
So you first need to choose two points.
I'll go for (0,-5) and (2,0)
\(k = \frac{0 - 5}{2 - 0} \)
\(k = \frac{ - 5}{2} \)
Now you could insert k into the equation and it will look like this.
\(y = \frac{ - 5}{2}x + m\)
To find out what m is just pick one point and insert it into the equation. So if I pick (0,-5). 0=X therefore it should be replaced by x and -5=y therefore it should also be replaced by y.
\( - 5 = \frac{ - 5}{2} \times 0 + m\)
m=-5
Try it with another point to see if you get the same answer. this time I'll pick (-6,10)
\( 10= \frac{ - 5}{2} \times( - 6)+ m\)
m= -5
The equation will be y=-5/2x-5)
Select all the ratios equivalent to 8:6.A. 4:3B. 6:8C. 16:12D. 10:8E. 7:5
Answers
Dividing the given ratio by 2, we get
8:6 = 8/2 : 6/2 = 4:3
Multiplying the given ratio by 2, we get
8:6 = 8*2 : 6*2 = 16:12
Then, the correct choices are A and C
A box-shaped vessel 65 m x 10 m x 6 m is floating
upright on an even keel at 4 m draft in salt water. GM = 0.6 m.
Calculate the dynamical stability to 20 degrees heel.
Answers
The dynamical stability of the box-shaped vessel at a 20-degree heel is approximately 5,510,350 Nm.
To calculate the dynamical stability of the box-shaped vessel at a 20-degree heel, we need to consider the changes in the center of buoyancy (B) and the center of gravity (G) due to the heeling angle.
Given:
- Length (L) = 65 m
- Breadth (B) = 10 m
- Depth (D) = 6 m
- Draft (T) = 4 m
- GM = 0.6 m (metacentric height)
To determine the dynamical stability, we need to calculate the righting moment (RM) at a 20-degree heel. The formula for calculating the righting moment is:
RM = (GZ) * (W)
Where:
- GZ is the righting arm, which is the horizontal distance between the center of gravity (G) and the vertical line passing through the center of buoyancy (B)
- W is the weight of the vessel
First, let's calculate the weight of the vessel (W):
W = Density of water * Volume of the immersed portion of the vessel
W = Density of water * Length * Breadth * Draft
Assuming the density of saltwater is approximately 1025 kg/m³, we can calculate the weight as follows:
W = 1025 kg/m³ * 65 m * 10 m * 4 m
W = 26,650,000 kg
Next, we need to calculate the righting arm (GZ) at a 20-degree heel. The formula for calculating GZ is
GZ = GM * sin(heel angle)
GZ = 0.6 m * sin(20°)
GZ ≈ 0.207 m
Finally, we can calculate the dynamical stability (RM) using the formula mentioned earlier:
RM = GZ * W
RM = 0.207 m * 26,650,000 kg
RM ≈ 5,510,350 Nm (Newton-meters)
Therefore, the dynamical stability of the box-shaped vessel at a 20-degree heel is approximately 5,510,350 Nm.
for more such question on dynamical visit
https://brainly.com/question/32952661
#SPJ8
(5x^2+4x-7)+(-5x^2-4x+7)
Answers
Answer:
0
Step-by-step explanation:
(5x^2+4x-7) + (-5x^2-4x+7)
= 5x² + 4x - 7 - 5x² - 4x + 7
= 4x - 7 - 4x + 7
= - 7 + 7
= 0
Find the value of x to the nearest tenth.
Answers
Answer:
x ≈ 16.2
Step-by-step explanation:
tan56° = \(\frac{24}{x}\) ( multiply both sides by x )
x × tan56° = 24 ( divide both sides by tan56° )
x = \(\frac{24}{tan56}\) ≈ 16.2 ( to the nearest tenth )
if f(x)=x^2+1 and g(x) =3x+1, find f(2) + g(3).
Answers
Answer:
15 brainliest please
Step-by-step explanation:
f(x)=x^2+1
f(2)=(2)^2 +1
= 5
g(x)=3x+1
g(3)=3(3)+1
= 10
5+10= 15
Please please ASAP ASAP please ASAP thank you so
No links or files
Answers
Answer:
c
Step-by-step explanation:
Assume that the recovery time for an individual from an infectious disease can be modeled as a normal distribution. (a) Calculate the time, d, in days for an individual to recover from being initially infected, with a 95% confidence level, assuming that the likelihood of recovering at any time is modeled as a normal distribution with a mean of 5 days and a standard deviation of 0.5 days. (b) Use the SIR model that you constructed previously. Assume that a city of 10 million people is confronted with a potential infectious epidemic. A ship arrives at the international airport carrying 100 individuals who are infected, but are unaware that they are infected. While contagious, infected individuals come into transmission contact with another individual once every 2 days. The recovery process is modeled using the Poisson process from Part (a). Assume that recovered individuals that survive develop immunity to the disease. Plot the fraction of susceptible individuals, infected individuals, and recovered individuals as a function of time throughout the epidemic. (c) What fraction of the total population will have ultimately come down with the infectious disease once the epidemic is over? How many days after the ship docking did this number finally reach steady state (i.e.,the epidemic is completely over). (d) What is the basis for this structured model (i.e.,scale, time, etc.)? What is/are the major assumptions associated with the structure?
Answers
Upper
daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.
(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.
Given:
Mean (μ) = 5 days
Standard deviation (σ) = 0.5 days
The confidence interval can be calculated as follows:
Lower limit = Mean - (1.96 * Standard deviation)
Upper limit = Mean + (1.96 * Standard deviation)
Lower limit = 5 - (1.96 * 0.5)
= 5 - 0.98
= 4.02 days
Upper limit = 5 + (1.96 * 0.5)
= 5 + 0.98
= 5.98 days
Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.
(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.
(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.
(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:
Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.
Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.
Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.
No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.
These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.
Learn more about Normal distribution here: brainly.com/question/15103234
#SPJ11
PLEASE HELP ME !! ILL GIVE YOU BRAINLIEST
Answers
A movie theater sold 5 child tickets. The other 45 tickets it sold were adult tickets. What is the ratio of the number of adult tickets to the number of child tickets?
a) 10:45
b) 45:5
c) 5:45
d) 50:5
Answers
Answer: 9/1
Step-by-step explanation: We can write a ratio using the word "to", using a colon, or using a fraction bar.
The problem asks us to compare the number of
adult tickets to the number of child tickets.
We know that there are 45 adult tickets
and 5 child tickets so we have 45/5.
However, 45/5 is not in lowest terms so we divide
the numerator and denominator by 5 to get 9/1.
So the ratio of adult tickets to child tickets is 9/1.
How do you know if there is no solution or infinite solutions?
Answers
There are countless possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable. If we try to solve an equation and receive a variable or a number equal to itself, there are infinitely many solutions to the equation.
Single-solution equations:
Some equations only have one precise solution. The variable in these equations can only take on one value in order for the equation to be true. When you solve an equation and the result is a variable equal to a number, you know that the equation only has one solution.
Example: For x, find the solution to the equation 6x-3=21.
6x \s= 24
To both sides, add 3.
x \s= 4
Subtract 6 from both sides.
For a single value of the variable, x=4, the equation is true. Consequently, there is only one solution to the equation 6x-3=21
Non-solvable equations:
There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.
Example: Solve the equation 4x+12=2x+12+2x.
4x+12
= 2x+12+2x
4x+12
= 4x+12 Combine like terms 2x and 2x.
12
= 12 Subtract 4x from both sides.
Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.
Equations that have infinitely many solutions:
The number of solutions to some equations is limitless. When a variable is used in these equations, any value makes the equation true. If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions.
Solve the equation 4x+12=2x+12+2x.
4x+12
= 2x+12+2x
4x+12
= 4x+12 Combine like terms 2x and 2x.
12
= 12 Subtract 4x from both sides
Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.
To learn more about no solution or infinite solution:
https://brainly.com/question/17764456
Evaluate this function at X = 6.express your answer as an integer or a simplified fraction that is the function is undefined at the given value, indicate “undefined”.
Answers
Since this is a pieciwise function we need to determine which expression to use for the value of x given. For the definition of the function we notice that for every x grater than 4 we need to use the function:
\(-2x-6\)Since in this case we want to evaluate the function at x=6 and this value is greater that four we need to use this expression.
Then we have that:
\(\begin{gathered} f(6)=-2(6)-6 \\ =-12-6 \\ =-18 \end{gathered}\)Therefore the value of the function at x=6 is -18
Find the sum.
4/5r+10/3r
Answers
Answer:
i hope this helps
Step-by-step explanation:
calculate the partial derivative ∂∂ using implicit differentiation of 6 7 2 2=0.
Answers
The partial derivative of 6x^7y^2 = 0 with respect to x is ∂y/∂x = -7/2x.
Assuming you meant to write 6x^7y^2 = 0, we can use implicit differentiation to find ∂y/∂x:
Taking the partial derivative of both sides with respect to x, we get:
(42x^6y^2)dx + (12x^7y)dy = 0
Now we can solve for ∂y/∂x:
(12x^7y)dy = -(42x^6y^2)dx
dy/dx = -(42x^6y^2) / (12x^7y)
dy/dx = -7/2x
So the partial derivative of 6x^7y^2 = 0 with respect to x is ∂y/∂x = -7/2x.
To know more about partial derivative refer here:
https://brainly.com/question/31397807
#SPJ11
A graphing calculator costs $85. The sales tax on the calculator is 8%. What is the total cost of
the
calculator? *
Answers
Answer:
$65
Step-by-step explanation:
*97 POINTS*
Use the numerals representing cardinalities in the Venn diagram, shown on the right, to give the cardinality of the set
A' ∩ B' ∩ C. '
n(A' ∩ B' ∩ C')= ___________
Answers
Answer:
19
Step-by-step explanation:
A' represents everything out A
B' represents everything out B
C' represents everything out C
So only the outside is left hope this helps
PLEASE HELP ME OUTT!
Answers
The rectangle on top with side lengths of 6 and 8 has an area of 48 in.^2 because 6 x 8 = 48.
The two squares with side lengths of 6 and 6 both have the area of 36 in.^2 because 6 x 6 = 36.
The two triangles have the area of 18 in.^2 because 6 x 6 / 2 = 18.
When you add up the areas of all the shapes you get 48 + 36 + 36 + 18 + 18 = 156 in.^2
Hope this helps :D
Answer:
156 \(in^{2}\)
Step-by-step explanation:
The surface area is, as said by the name, the area of the surface. So, we have to add up all the areas of all the planes. Look at the attachement I edited from the pic you provided.
Planes B and C are both the exact same area, which means the area of one of them is
1/2 * b * h
Now as the area is for both of them, we multiply the above expression by 2 to cancel it out.
2 * 1/2 * b * h
b * h
In this case, our bases and heights for planes B and C are both 6 inches.
So together, planes B and C area
6 * 6 inches square
36 inches square. Remember this.
We will also see that planes A and E have the same area, both being squares as shown from the unfolded version and from the sidelengths of the folded triangular prism.
The area of one plane is b*h, so 2 planes that have the same area would have the area of 2*b*h.
Our base and height for planes A and E are yet again, 6 inches.
So the combined area of the planes are
2*6*6
2*36
72 inches square. Remember this.
Now we have our last plane left, plane D.
This one is a basic plane, just a rectangle.
The area of a rectangle is b * h.
In this case, our area would be
8 * 6
48 inches square. Remember this.
Now for our final answer.
The surface area, using my edited version, would be the following sum:
plane A + plane B + plane C + plane D + plane E
We know that plane B + plane C is equal to 36 inches square.
So, so far we have:
36 + plane A + plane D + plane E
We now that plane A and plane E have a sum that totals to 72 inches square.
Now we have:
36 + 72 + plane D
Substitute the value of plane D and we get:
36 + 72 + 48
36 + 120
156 square inches as our answer
