Answer:
50(115-y) + 25y = 4125 [from eq2]
5750 - 50y + 25y = 4125 [distribute]
5750 - 25y = 4125
-25y = -1625
y = 65 [divide both sides by (-25)]
There are 65 small boxes.
Put that value into either equation (now, which is easier?) to solve for x:
x = 115 - y
x = 115 - 65
x = 50
There are 50 large boxes.
- Mring0506
The required number of boxes that the truck contain is 55 small boxes and 65 large boxes.
Given that, the large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all, the truck is carrying a total of 4300 pounds.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the number of large boxes will be l and the number of small boxed be s,
According to the question,
l + s = 120
l = 120 - s - - - - - (2)
Again,
45l + 25s = 4300
put l in the above equation,
45[120 - s] + 25s = 4300
5400 - 45s + 25s = 4300
20s = 1100
s = 1100/20
s = 55
Now,
l = 120 - 55
l = 65
Thus, the required number of boxes that the truck contain is 55 small boxes and 65 large boxes.
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write each ratio in simplest form:
3:6
10:5
16:24
Answer:
1:2
2:1
2:3
Step-by-step explanation:
3:6
Divide each side by 3
3/3: 6/3 1:2
10:5
Divide each side by 5
10/5 : 5/5 2:1
16:24
Divide each side by 8
16/8: 24/8 2:3
4x + 3y = 6
-4x + 2y = 14
solve the system of equations
Answer:
I believe it is
x = -3/2 (-1.5)
y = 4
Answer:
A) 4x + 3y = 6
B) -4x + 2y = 14
Add the equations
5 y = 20
y = 4
Putting y into A)
A) 4x + 3*4 = 6
A) 4x = -6
x = -1.5
Step-by-step explanation:
a scientist has 400ml of a 8% solution. how much water needs to be added to lower it to a 2% solution?
1200 ml of water needs to be added to lower it to a 2% solution.
Step-by-step explanation:
Given that,
A scientist has 400ml of a 8% solution.
you need to find how water is required to lower the 400 ml to 2% solution.
Let 'x' be the amount of water added to lower it 2% solution.
The formula is given by,
volume of the liquid × % of solution = volume of the new liquid × new %
This can be denoted in chemical relationship ⇒ c₁v₁=c₂v₂ where c is concentration and v is volume .
Now, to find the total volume of new liquid in ml :
400 ml = v₁
0.08= c₁
0.02=c₂
v₂=?
400 × 0.08 =v₂ × 0.02
v₂=1600 ml
To find the x value :
Amount to be added = volume of new liquid - volume of liquid before.
⇒ x =1600-400
⇒ x =1200 ml
∴ 1200 ml of water needs to be added to lower it to a 2% solution.
Drag and drop a statement or reason to each box to complete the proof. Given: parallelogram EFGH Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ . Parallelogram E F G H with diagonals E G and H F intersecting at point K. Statement Reason parallelogram EFGH Given EF¯¯¯¯¯∥HG¯¯¯¯¯¯ When two parallel lines are cut by a transversal, alternate interior angles are congruent. The opposite sides of a parallelogram are congruent. △EKF≅△GKH ASA Congruence Postulate CPCTC EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .
By proving triangle HKE and triangle GKF congruent, it is proved EG bisects HF and HF bisects EG.
Given that, parallelogram EFGH.
Prove that, EG bisects HF and HF bisects EG.
Parallelogram EFGH with diagonals EG and HF intersecting at point K.
Proof:
Consider, ΔHKE and ΔGKF
∠HKE=∠GKF (Vertically opposite angles are equal)
∠FHE=∠GFH ( Alternate angles between the parallel line EF and HG)
∠GEH=∠FGE ( Alternate angles between the parallel line EF and HG)
By AAA congruency, ΔHKE and ΔGKF are congruent
By CPCT,
KE=GK
JF=HK
So, EG bisects HF and HF bisects EG.
Hence, proved.
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Final answer:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH, we can use the statements and reasons provided.
Explanation:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH with diagonals EG and HF intersecting at point K, we can use the following statements and reasons:
Statement: parallelogram EFGHKevin is going to purchase sod for his backyard (see diagram below). How many square feet of sod will Kevin need?
Answer:
450 square feet
Step-by-step explanation:
Think of the shape as a complete rectangular
The area of the rectangular shape would be 25×30 = 750 square feet
Now find the area of the missing space and subtract it from 750
it would be 15×20 = 300 square feet
750 - 300 = 450 square feet
Determine any data values that are missing from the table, assuming that the data represent a linear function.
Answer:
D
Step-by-step explanation:
Are the expressions equivalent? Use j = 3 and j = 8 to determine if they are. 7(j – 2) 4j – 5 No, because when j = 8, the values of the expressions are different. Yes, because when j = 3, the value of both expressions is 7 and when j = 8, the value of both expressions is 42. Yes, because when j = 3, the value of both expressions is 7. Yes, because when j = 8, the values of the expressions are different.
Answer:
No, because when j = 8, the values of the expressions are different.
for a shorter answer, A
Step-by-step explanation:
No, because when j = 8, the values of the expressions are different. Therefore, option A is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 7(j-2)4j-5.
Here, j=3 ad j=8
When j=3, we have
7(3-2)4×3-5
= 7×1×4×3-5
= 84-5
= 79
When j=8, we have
7(8-2)4×8-5
= 7×5×4×8-5
= 1115
Therefore, option A is the correct answer.
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A scientist estimated that a mixture would need 5 millimeters of a chemical to balance. The actual amount d was 7 millimeters. What was the percent error of the scientists estimation?
Answer:
29%
Step-by-step explanation:
If 7 is 100% correct then 5 would only be a portion of it
So you need to divide 5 by 7
So 5 divided by 7 is .714 or .71
this means the error was 29%
Please can you help me with this question
Mr Tan invested $5000 in an endowment fund for
5 years. The fund pays an interest compounded
yearly. At the end of 5 years, he received a total of
$5800. Find the interest rate.
Answer:
Compound Interest Formula Solved For Rate:
log (1 + rate) = {log(total) -log(Principal)} ÷ Years
log (1 + rate) = {log(5,800) -log(5,000)} ÷ 5
log (1 + rate) = [3.7634279936 -3.6989700043] / 5
log (1 + rate) = 0.0644579893 / 5
log (1 + rate) = 0.0128915979
Then we raise 10 to the power of 0.0128915979 which equals
1.0301289629 = 1 + rate
Therefore, rate = .0301289629 and we multiply by 100 to make a percentage:
3.01289629 %
Source: https://1728.org/compint2.htm
https://1728.org/compint.htm
Step-by-step explanation:
Using the compound interest formula and the provided values, the interest rate for Mr Tan's investment is calculated to be approximately 3.02%.
Explanation:The subject problem belongs to the topic of Compound Interest in mathematics. The formula used for compound interest is A = P (1 + r/n)^(nt), where A represents the total amount received, P represents the principal (initial investment amount), r represents the rate of interest, n represents the number of times interest is compounded per time period, and t represents the time period.
In this problem, Mr Tan's initial investment, P, is $5000. The total amount, A, he received after 5 years is $5800. The interest is compounded annually meaning that n is 1. We rearrange the compound interest formula to solve for the interest rate: r = [(A/P)^(1/nt) - 1]n .
Using Mr Tan's values, the calculation becomes: r = [(5800/5000)^(1/5) - 1]*1. Thus, the interest rate is approximately 0.0302 or 3.02%.
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A investor has an account with stock from two different companies. Last year her stocking company A was worth $4600 in her stocking company B was worth $1000. Stocking company a has decreased 25% since last year in stock and Company B has decreased 22%. What was the total percentage decrease in the investor stock account round your answer to the nearest 10
Answer: 24.5%
Step-by-step explanation:
Last year her stock in company A was worth $4600. If her Stock in company A has decreased by 25% since last year in stock, then the amount by which it decreased is
25/100 × 4600 = $1150
The present worth is
4600 - 1150 = $3450
Also, her stock in company B was worth $1000. If her Stock in company B has decreased by 22% since last year in stock, then the amount by which it decreased is
22/100 × 1000 = $220
The present worth is
1000 - 220 = $780
The total worth of both stocks last year was
4600 + 1000 = $5600
The total worth of both stocks this year was
3450 + 780 = $4230
The amount by which it decreased is
5600 - 4230 = 1370
the total percentage decrease in the investor stock account is
1370/5600 × 100 = 24.5%
If the circumference of a circle is 50. How many inches long is it’s radius?
Answer:
7.9617
Step-by-step explanation:
r=c/2pi so 50/2(3.14)
Answer: about 7.9617 !
Step-by-step explanation: you to divide 50 by 3.14 to get the diameter, then divide the diameter by 2 to get the radius, then round it!
What is the slope of the line that contains these points?
x
12
13
14
15
y
-4
2
8
14
Answer:
6x-76
Step-by-step explanation:
If you graph it out, you'll realize it makes a line that cuts the y-intercept at -76, thus the last value. The slope also has a gradient of 6, thus the coeffecient of x.
Final answer:
The slope of the line through the points given is 6, calculated using the slope formula with the rise over run between the two points.
Explanation:
The slope of a line is calculated by finding the ratio of the vertical change (the rise) to the horizontal change (the run) between two points on the line. Using the coordinates provided (12, -4) and (15, 14), we can apply the slope formula slope (m) = (y_2 - y_1) / (x_2 - x_1). Plugging in the values gives us (14 - (-4)) / (15 - 12) = 18 / 3 = 6. Therefore, the slope of the line that contains these points is 6.
Solve the system of equations using the substitution method.
-5x − 3y = 16
y = x
Answer:
-5x - 3x = 16
-8x = 16
x = -2
y = x
Step-by-step explanation:
Answer:
(-2, -2)
Step-by-step explanation:
Make use of the 2nd equation to eliminate x or y in the 1st equation:
-5x - 3(x) = 16
Then -8x = 16, and x = -2. Since we are told that y = x, y = -2.
The solution is (-2, -2).
1. Find g(x), where g(x) is the translation 7 units up of f(x) = x.
2. Find g(x), where g(x) is the translation 5 units left of f(x) = x2.
3. Find g(x), where g(x) is the translation 3 units right and 4 units up of f(x) = x2.
4. Find g(x), where g(x) is the translation 1 unit left and 5 units down of f(x) = |x|.
Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.
Explanation:To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.
Translation 7 units up of f(x) = x results in g(x) = x + 7.For the translation 5 units left of f(x) = x2, we use g(x) = (x + 5)2.The translation 3 units right and 4 units up of f(x) = x2 gives us g(x) = (x - 3)2 + 4.Translation 1 unit left and 5 units down of f(x) = |x| leads to g(x) = |x + 1| - 5.In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.
Write the standard form of the equation of the circle with its center at (-3,0), and a radius of 6.
What is the equation of the circle in standard form?
Ok i'm so sorry but if you could answer this for me? nobody else will! >0<
Enter the equation of the circle described below.
Center (-3, 0), radius /5
Answer:(X+3)^2 +y^2 =25
This is the correct answer, i just found it out
What is the midpoint of ?
A: (2p – 2t, r)
B: (t + p, r)
C: (p, r)
D: (p – t, r)
The midpoint of a line segment is given by the formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2). After applying this formula to the given options, the correct midpoint is (p, r).
Explanation:The midpoint of a line segment with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Applying this formula to the given options:
A: Midpoint = (2p - 2t, r)B: Midpoint = (t + p, r)C: Midpoint = (p, r)D: Midpoint = (p - t, r)After substituting the values, we find that the correct answer is Option C: (p, r).
NEW YORK
The standard configuration for a New York license
plate is 3 digits followed by 3 letters.
Source: New York State Department of Motor Vehicles
How many different license plates are possible
if digits and letters can be repeated?
234 ABC
O 1757600
1577600
12812904
11232000
The total number of possible New York license plates is 17,576,000.
The number of different license plates possible for a standard configuration in New York, where a license plate is composed of 3 digits followed by 3 letters, can be determined through combinatorial math.
Step-by-Step Solution:
There are 10 possible digits (0-9) and 26 possible letters (A-Z).Since repetitions are allowed, we calculate the total number of combinations for digits and letters separately.The number of ways to choose 3 digits is 10 3 = 10 × 10 × 10 = 1000.The number of ways to choose 3 letters is 26 3 = 26 × 26 × 26 = 17576.Multiplying these two results together gives the total number of possible license plates: 1000 × 17576 = 17576000.Is (1,1) a function?
Answer:
I don't think it is a function
A function is a set of ordered pairs where a x-value is paired with only one y-value.
As long if the x-value (1) is sharing only one y-value then it makes it a function.
which term means 1/1000 decimeter, millimeter, kilometer, decameter
Answer:
millimeter
Step-by-step explanation:
1/1000
James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 22 2 2 cm. One tray makes 66 6 6 spheres.
Answer:
James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.What is the total volume of ice the tray can make at one time?
Total volume of the tray James have = 201.06 cm^3
Step-by-step explanation:
Given:
Radius of the spherical ice cube = 2 cm
No. of spheres in the ice cube = 6
We have to find the total volume of the ice tray that can make at one time.
Let the total volume be "V".
Formula to be used:
Volume of sphere = [tex]\frac{4\pi r^3 }{3}[/tex] cubic unit.
Total volume = [tex]n\times \frac{4\pi r^3 }{3}[/tex] cubic unit.
So,
Total volume of the ice tray (V) :
⇒ [tex]V=n\times \frac{4\pi r^3 }{3}[/tex]
⇒ Plugging n = 6 and r = 2
⇒ [tex]V=6\times \frac{4\pi (2)^3 }{3}[/tex]
⇒ [tex]V=6\times \frac{4\pi (8) }{3}[/tex]
⇒ [tex]V=6\times \frac{32\pi }{3}[/tex]
⇒ [tex]V=\frac{32\times 6\pi }{3}[/tex]
⇒ [tex]V=32\times 2\pi[/tex]
⇒ [tex]V=201.06\ cm^3[/tex]
So,
The total volume of ice the tray can make at one time = 201.06 cm^3
NEED HELP ON THIS WILL GIVE CROWN
Matt buys 14 jars of paint. Each jar contains 300 milliliters of paint.
How many liters of paint in all is there in the jars?
4.2 L
42 L
420 L
4,200 L
In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes
Answer:
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
Step-by-step explanation:
Conditional probability:
Let A and B any two events connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B has occurred, denoted by P(A|B), is defined as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Given that,
In a city school, 70% of students have blue eyes, 45% have dark eyes and 30% have blue eyes and dark hair.
A= students have blue eyes
B= Students have dark hair.
P(A)= 70% [tex]=\frac{70}{100}[/tex] [tex]=\frac7{10}[/tex]
P(B)=45% [tex]=\frac{45}{100}[/tex] [tex]=\frac9{20}[/tex]
P(A∩B)=30%[tex]=\frac{30}{100}[/tex] [tex]=\frac3{10}[/tex]
∴P(B|A)
[tex]=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{0.3}{0.7}[/tex]
[tex]=\frac37[/tex]
=0.429
=0.429×100 %
≈43%
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
Answer:
The median is - C
The minimum is - A
The maximum is - E
The lower quartile (Q1) is - B
The upper quartile (Q3) is - D
The median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
What is median?The value that divides the mathematical numbers or expressions in half is known as the median. The middle data point is known as the median value. Then, organize the data points in ascending order before calculating the median.
As per the given data, whiskers range from A to E.
The middle point of whisker is C.
Hence, the median is given by C.
And the whisker ranges to maximum E.
And range starts from A.
So the minimum is A.
Quartiles are three values that split sorted data into four parts, each with an equal number of observations.
The lower quartile is B and upper quartile is D.
Therefore, the answers of the median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
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cost of x articles at 2 dollars each
Answer:
2x
Step-by-step explanation:
Cost of x articles at 2 dollars each = 2x
A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspection. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected
In hypothesis testing for this scenario, the null hypothesis (H-0) is that the proportion of rejected screens remains 12 percent (H-0: p = 0.12). The alternative hypothesis (Ha) is that the proportion of rejected screens is less than 12 percent (Ha: p < 0.12). A sample is taken and a significance test (such as a z-test for proportion) is conducted to decide if the null hypothesis can be rejected.
Explanation:The question is looking for you to conduct a hypothesis test to investigate whether a new process in manufacturing cell phone screens has led to a reduced proportion of rejected screens. When conducting such a hypothesis test, you'll need to consider a null hypothesis and an alternative hypothesis.
The null hypothesis (H-0) is often the initial claim about a population proportion. In this case, the null hypothesis would be that 12 percent of the screens (0.12) are still being rejected: H-0: p = 0.12.
The alternative hypothesis (Ha) is what you might believe to be true if the null hypothesis is proven to be incorrect. Here, the alternative hypothesis would be that less than 12 percent of screens are being rejected with the new process: Ha: p < 0.12.
To clarify, if the new process is effective, a lower proportion of screens should be rejected. Thus, the hypotheses to be tested are:
H-0: p = 0.12Ha: p < 0.12Lastly, after selecting the sample, compute the sample proportion. Here a total sample size of 100 screens with only 6 being rejected means the sample proportion (p) = 6/100 = 0.06.
From here, you would proceed to conduct a significance test (possibly a z test for proportion) and determine a p-value to make a decision regarding the null hypothesis.
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The hypotenuse of a right triangle is 12, and one of the legs is 4, what’s the missing leg
Answer:
About 11.31
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + b^2 = 12^2
16 + b^2 = 144
-16 -16
b^2 = 128
Take the square root of both sides
b= approximately 11.31
The cereal box shown below is a rectangular prism. Find the surface area of the cereal box.
Answer:
= 1700 :)
Step-by-step explanation:
-multiply all the sides,
-add them,
- then double the answer (or times it by 2):
1) 30 times 20 = 600
30 times 5= 150
20 times 5 =100
2) Add them:
600+150+100 = 850
then times 850 by 2
850 times 2 = 1700
Hope that helped :)
Answer:
Guys for this one the 30, 20, 5 is 1700
Step-by-step explanation:
what is the area of a 3in by 3in square
Final answer:
The area of a 3in by 3in square is calculated by squaring the side length. The area is 9 square inches.
Explanation:
The area of a 3in by 3in square can be calculated by multiplying the length of one side by the length of another side since the sides are equal in a square. In this case, both sides measure 3 inches.
The formula for the area of a square is:
Area = side × side
Applying the formula for our 3in by 3in square:
Area = 3in × 3in = 9 square inches
This straightforward calculation represents how the surface area of a square object changes when the sides of the square are altered. When the sides of a square are scaled down by a fraction, the area changes by the square of that fraction (e.g., scaling down by 3/4 leads to an area that is 9/16 of the original).
Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)
Answer:
ength (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3Step-by-step explanation:
Let x is the side of identical squares
By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:
length (l) : (10-2x)width(w): (10-2x)height(h): xThe volume will be:
V = (10-2x) (10-2x) x
<=> V = (10x-2[tex]x^{2}[/tex]) (10-2x)
<=> V = 100x -20[tex]x^{2}[/tex] - 20[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
<=> V = 4[tex]x^{3}[/tex] - 40[tex]x^{2}[/tex] + 100x
To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume
dV/dx = 12[tex]x^{2}[/tex] -80x + 100
<=> 12[tex]x^{2}[/tex] -80x + 100 =0
<=> x = 5 or x= 5/3
You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3
=>
length (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. The dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
Explanation:To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. Let's assume the side length of the square to be x inches. The length and width of the resulting box will be 10 - 2x inches and 10 - 2x inches, respectively. The height of the box will be x inches. To find the dimensions of the largest box, we need to find the value of x that maximizes the volume of the box.
The volume of the box is given by V = (10 - 2x)(10 - 2x)(x). We can write this as V = 4x^3 - 40x^2 + 100x. To find the value of x that maximizes the volume, we can take the derivative of V with respect to x and set it equal to 0. Differentiating V, we get dV/dx = 12x^2 - 80x + 100. Setting this equal to 0 and solving for x, we find x = 1.67 inches (rounded to two decimal places). Therefore, the dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
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