A test for divisibility by 11 is to see if the digits taken in order and alternately added and subtracted produce a number which is divisible by 11. Consider 5-digit numbers of the form "abcde'. Show that "abcde' will be divisible by 11 if and only if a - b+c-d+e is divisible by 11.
Answers
An test for divisibility that a 5-digit number "abcde" will be divisible by 11 if and only if "a - b + c - d + e" is divisible by 11.
To show that a 5-digit number "abcde" is divisible by 11 if and only if "a - b + c - d + e" is divisible by 11, the concept of modular arithmetic.
The 5-digit number "abcde" as a sum of its digits multiplied by their respective place values:
"abcde" = a × 10000 + b × 1000 + c × 100 + d × 10 + e
Then express "a - b + c - d + e" in terms of the digits:
a - b + c - d + e = a × (10,000 mod 11) - b × (1,000 mod 11) + c × (100 mod 11) - d × (10 mod 11) + e
examine the patterns of the modulos:
10,000 mod 11 = 1
1,000 mod 11 = 10
100 mod 11 = 1
10 mod 11 = 10
Substituting these values back into the expression,
a - b + c - d + e = a × 1 - b ×10 + c × 1 - d × 10 + e
Simplifying further:
a - b + c - d + e = a - b + c - d + e
observe that the expression "a - b + c - d + e" is equivalent to the original 5-digit number "abcde." This means that if "abcde" is divisible by 11, then "a - b + c - d + e" will also be divisible by 11.
Conversely, if "a - b + c - d + e" is divisible by 11, it implies that the expression and the 5-digit number "abcde" have the same remainder when divided by 11. Since they are equivalent, "abcde" must also be divisible by 11.
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Related Questions
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 7500 and estimated standard deviation σ = 1750. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. (a) What is the probability that, on a single test, x is less than 3500? (b) Suppose a doctor uses the average x(sample mean) for two tests taken about a week apart. What can we say about the probability distribution of x(sample mean)? What is the probability distribution of x(sample mean) < 3500? (c) Repeat part (b) for n = 3 tests taken a week apart. (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities increased as n increased. If a person had x ( sample mean)< 3500 based on three tests, what conclusion would draw as a doctor or nurse?
Answers
The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.
a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.
Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.
(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.
The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.
(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.
The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.
In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.
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Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
Answers
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
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Ms. Augello is making tie-dyed shirts with her students. Each gallon of hot water needs 2/3 cup of dye. If Ms. Augello has 5 1/4 cups of dye, how many batches of solution will she be able to make?
Answers
Answer:
The answer is 7 7/8.
Step-by-step explanation:
Divide the hand on cups Augello has with the required cups it needs to make a batch.
5 1/4 ÷ 2/3
21/4 · 3/2
63/8 = 7 7/8
Answer:
The answer is if i am doing my math right u could make 7 batches
Step-by-step explanation:
dont have one sorry i did this off the top of my head
7968 divided by 22 estimating
Answers
Answer:
363
Step-by-step explanation:
The quantities xxx and yyy are proportional. xxx yyy 222 222222 777 777777 999 999999 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x. r =r=r, equals
Answers
Answer:
If the table is:
x=2 y=22
x=7 y=77
x=9 y=99
you can see that 22/2=11 same with 7/77 and 9/99
r=11
Step-by-step explanation:
pretty simple but i probably explained it horribly
The constant of proportionality (r) is 11 for the given variables in the table.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
The table is given in the question consists as:
The value of variable x = 2 when variable y = 22
The value of variable x = 7 when variable y = 77
The value of variable x = 9 when variable y = 99
We have to determine the constant of proportionality (r)
the constant of proportionality (r) = y / x
Substitute the values in the above equation,
the constant of proportionality (r) = 22/2 = 7/77 = 9/99 = 11
the constant of proportionality (r) =11
Thus, the constant of proportionality (r) is 11 for the given variables in the table.
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Big points if you get these answers correct. Will mark brainliest for fist correct answer. URGENT
Answers
Answer:
1. ≈37.7
2. ≈47.75
3. ≈69.12
4. ≈31.42
5. =17.6
6. =48
7. =40
8. =8
9. =18
10. =14
11. ≈71.63
12. ≈23.88
13. =44
14. =32
15. ≈25.13
16. ≈34.56
17. ≈25.76
18. ≈43.98
19. =28.8
20. =28
A shipping container will be used to transport several 60-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 24500
kilograms. Other shipments weighing 14600 kilograms have already been loaded into
the container. Write and solve an inequality which can be used to determine 2, the
number of 60-kilogram crates that can be loaded into the shipping container.
Answers
Answer:
c ≤ 330
Step-by-step explanation:
Given that:
Greatest weight = 23000 kg
Weight per crate = 60kg
Weight of other shipment already loaded = 3200kg
Total Number of 60kg crates, c that can be loaded
((Weight per crate * number of crates) + weight of other loaded shipment) ≤ greatest weight
((60 * c) + 3200 ≤ 23000
60c ≤ 23000 - 3200
60c ≤ 19800
c ≤ 19800 / 60
c ≤ 330
Solve for n.
-5/7n + 1 =21
Answers
N in (-oo:+oo)
(-5/7)*n+1 = 21 // - 21
(-5/7)*n-21+1 = 0
-5/7*n-20 = 0 // + 20
-5/7*n = 20 // : -5/7
N = 20/(-5/7)
N = -28
N = -28
hope it worked out, since i'm not entirely sure.
10)
Solve:
1-x + 5) = -2
.
Answers
-1x+5=2
_5. -5
-1x=7
-1. -1
x=-7
What interval in which both f(x)and g(x) are positive?
Or
(-infinity,-2) U(-2,-infinity)
Answers
We conclude that both functions f(x) and g(x) are positive on the interval (4, ∞)
In which interval both functions f(x) and g(x) are positive?
On the image we can see two graphs, the blue one is the graph of f(x) and the red one is the graph of g(x).
A function is positive when its graph is above the horizontal line.
For the case of f(x), it is positive on the intervals:
(-∞, -2) and (1, ∞)
And for function g(x), we can see that it is positive on the interval:
(4, ∞)
Now, the interval where both functions are positive is in the intersection between the intervals (in this case is the smaller of the intervals, so it is the correspondent to g(x)), which is (4, ∞)
We conclude that both functions f(x) and g(x) are positive on the interval (4, ∞).
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A triangle has sides with lengths of 5 meters, 12 meters, and 13 meters. Is it a right triangle?
Answers
Answer:
yes :
use the following formula :
a^2 +b^2 = c^2
now apply it to the problem :
5^2+12^2=13^2
do the exponent :
25 + 144 =169
now add
169 =169
if they are equal , then it is a right triangle .
1.44 x 106
In standard form
Answers
Answer: The way you would write this in standerd form would be like this one point fourty four times one hundered six. Let me know if this correct or not.
Step-by-step explanation:
!!!!!!HURRY!!!!!!
Which scenario can be represented using the inequalities below?
1.25 ≤ x ≤ 1.5
A- A container of milk costs at least $1.25 but less than $1.50.
B- A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
C- A tip added to a restaurant bill is less than or S equal to 25% or less than or equal to 50%.
D- The point value of a test item is more than 1.25 points and less than 1.5 points.
Answers
Answer:
B. A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
Step-by-step explanation:
1.25 ≤ x ≤ 1.5 means x = 1.25 or more than 1.25
and x < 1.5 or x = 1.5.
{ 1.25 and 1.5 are contained }
_______________________
Option A: " Less than $1.50 " : doesn't contain 1.5
Option C: " 25% " = 0.25, " 50% " = 0.5
D: " More than 1.25 and less than 1.5 " doesn't contain 1.25 and 1.5.
B: 1 hour 15 min = 1 hour + 15/60 hour 1 hour + 1/4 hour = 1.25 hour
1 hour 30 min = 1.5 hour
Answer:
B
Step-by-step explanation:
Question 3(Multiple Choice Worth 2 points)
(Scale Factor LC)
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long
What scale factor was used to produce Figure 2 from Figure 1?
7 over 3
3 over 7
7
3
Answers
The scale factor used to produce Figure 2 from Figure 1 is: 7/3. The correct option is 1.
A scale factor is a number in mathematics that scales or multiplies some quantity.
The scale factor in geometry refers to the ratio of the lengths of two corresponding sides of two similar geometric figures.
The scale factor is the ratio of two similar figures' corresponding sides. The two triangles in this case are similar because they have the same shape but different sizes.
Figure 2's legs are 7 units long, which is 7/3 the length of Figure 1's legs, which are 3 units long.
Thus, the scale factor used to generate Figure 2 from Figure 1 is 7/3.
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What is 241m as a fraction of 5.4km
Answers
Answer:
i think 223/499
Step-by-step explanation:
Quadrilateral ABCD is similar to quadrilateral A'B'C'D'. Write a proportion that would have to be true, involving the side lengths of the quadrilaterals
(Hint: use the / key to get fractions!)
Answers
The true proportion of the side lengths of the quadrilaterals is A'B'/AB
How to determine the true proportion of the quadrilaterals?From the question, we have the following parameters that can be used in our computation:
Quadrilaterals ABCD and A'B'C'D
These quadrilaterals are similar
So, it means that the corresponding side lengths are proportional
So. we have
Side length = AB
Corresponding side length = A'B'
The true proportion is then represented as
k = Corresponding side length/Side length
Substitute the known values in the above equation, so, we have the following representation
k = A'B'/AB
Hence, the proportion is A'B'/AB
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explain to me how we obtain the answer below, because i am not getting the same figure on my calculator.Electric field charge dinsity (G) is ________
E=σ/2πϵ_0d
Answers
The Electric field charge density (G) is 4.10 × 10^5 V/m.
To obtain the answer for Electric field charge density (G), use the formula below:
E = σ/2πϵ₀d
Where:E is electric fieldσ is the surface charge density d is the perpendicular distance between the point and the surface.ϵ₀ is the permittivity of free space.
In most textbooks, it is taken as 8.85 × 10^-12 C² N^-1 m^-2.
σ is a scalar quantity and has units of C/m². G is a scalar quantity and has units of V/m.
A scalar quantity is defined as a physical quantity with magnitude only and no direction.
To obtain the answer for Electric field charge density (G), use the formula below:
E = σ/2πϵ₀d
Now let's assume that the value of σ is 15 µC/m² and the value of d is 7 cm which is 0.07 m.
And the value of ϵ₀ is 8.85 × 10^-12 C² N^-1 m^-2.
Therefore, Electric field charge density (G) will be given as follows:G = Eσ=σ/2πϵ₀dG = (15 × 10^-6 C/m²)/(2π × 8.85 × 10^-12 C² N^-1 m^-2 × 0.07 m)G = 4.10 × 10^5 V/m
Therefore, the Electric field charge density (G) is 4.10 × 10^5 V/m.
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2x + 2y= -6
-2x + y =12
its elimination method
Answers
2x + 2y = -6
-2x + y = 12
3y = 6
/3 /3
y = 2
(-2x and 2x cancels out)
Now we substitute y(2) into one of our equations (2x + 2y = -6 or -2x + y = 12)
2x + 2y = -6
2x + 2(2) = -6
2x + 4 = -6
- 4 -4
2x = -10
/2 /2
x = -5
(x,y) -> (-5, 2)
Check your answer:
2x + 2y = -6
2(-5) + 2(2) = -6
-10 + 4 = -6
-6 = -6
This statement is true, which makes our answer correct.
Hope this helps!
Select THREE expressions that are equivalent
to 15x + 9y.
A. 15(x + 9y)
B. 3(5x + 3y)
C. 5(3x + 3y)
D. 9(15x + y)
E. 5x + 5x + 5x + 5y + 4y
F. x + 3x + 6x + 5x + y + 6y + y + y
Answers
ADF
Thats not the answer those are just my favorite letters
of For the function f(x)= In (x + 2), find t''(x), t"O), '(3), and f''(-4). 1"(x)=0 (Use integers or fractions for any numbers in the expression) = Homework: 12.2 Question 6, 12.2.23 HW Score: 0% of 10 points Part 1 of 6 Points: 0 of 1 Save The function () ---3-gives me distance from a starting point at time tot a partide moving along a inn. Find the velocity and contration function. Then find the velocity and acceleration att and 4 Assume that time is measured in seconds and distance is measured in contimeter. Velocity will be in motors per second (misc) and coloration in centimeter per second per second errusec) HD The verseny function in 20- (Simplify your wor)
Answers
- f''(-4) = -1/4.
To find the second derivative t''(x), the value of t''(0), t'(3), and f''(-4) for the function f(x) = ln(x + 2), we need to follow these steps:
Step 1: Find the first derivative of f(x):f'(x) = d/dx ln(x + 2).
Using the chain rule, the derivative of ln(u) is (1/u) * u', where u = x + 2.
f'(x) = (1/(x + 2)) * (d/dx (x + 2))
= 1/(x + 2).
Step 2: Find the second derivative of f(x):f''(x) = d/dx (1/(x + 2)).
Using the quotient rule, the derivative of (1/u) is (-1/u²) * u'.
f''(x) = (-1/(x + 2)²) * (d/dx (x + 2))
= (-1/(x + 2)²).
Step 3: Evaluate t''(x), t''(0), t'(3), and f''(-4) using the derived derivatives.
t''(x) = f''(x) = -1/(x + 2)².
t''(0) = -1/(0 + 2)² = -1/4.
t'(3) = f'(3) = 1/(3 + 2)
= 1/5.
f''(-4) = -1/(-4 + 2)²
2)
= 1/5.
f''(-4) = -1/(-4 + 2)² = -1/4.
In summary:- t''(x) = -1/(x + 2)².
- t''(0) = -1/4.- t'(3) = 1/5.
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can i get a lil help here, lollolll
Answers
Answer:
5 + 2 = 7
4 squared = 16
16 - 7 = 9
value = 9
Determine f(4) for the function f(x)=2/5x+11
Answers
Answer:
63/5 in improper form and 12 and 3/5 in mixed form
Step-by-step explanation:
f(x) = 2/5x + 11
Substitute in value of x for the equation
f(4) = 2/5(4) + 11
f(4) = 8/5 + 11
f(4) = 8/5 + 55/5
f(4) = 63/5 or 12 and 3/5
So, the answer should be 63/5 in improper form and 12 and 3/5 in mixed form.
Answer:
Step-by-step explanation:
f(x) = \(\frac{2}{5}x + 11\)
f(4) = \(\frac{2}{5}*4 +11\\\)
\(=\frac{8}{5}+11\\\\=\frac{8}{5}+\frac{11*5}{1*5}\\\\=\frac{8}{5} + \frac{55}{5}\\\\=\frac{63}{5}\\\\=12\frac{3}{5}\)
Which is the better buy: 12 cans of soda for $9 or 4 cans for $3?
And, Why?
Answers
Answer:
12 for 9$
Step-by-step explanation:
Because you get more cans.
Benny's arcade has five video game machines. The average time between failures (i.e. the average time between jobs) is 34 hours. The maintenance engineer can repair a machine in about 13 hours. Assume the failure time and repair times are both exponentially distributed. What is the average time in HOURS from when a machine breaks until it is fixed?
Answers
The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.
Given,
Benny's arcade has five video game machines
The average time between failures = 34 hours
The maintenance engineer can repair a machine in about = 13 hours
The failure time and repair times are both exponentially distributed
The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.
In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,
λ_f = 1/34λ_r = 1/13
Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.
So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13
= 0.0885 hours⁻¹ (approximately)
Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).
Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.
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What is the answer to this question?
Answers
The perimeter of the square BCDE is 8√2 cm.
How to find perimeter of a square?A square is a quadrilateral that has all its sides equal to each other. All the angles in a square are also equal.
Therefore, the perimeter of a square is the sum of the whole sides of the square.
perimeter of the square BCDE = 4l
area of triangle ABC = 2cm²
area of triangle ABC = 1 / 2 bh
2 = 1 / 2 bh
The diagonal of square bisect each other.
The base and height of the triangle ABC are the same.
bh = 4
b² = 4
b = √4
b = 2 cm
Therefore,
BC = √2² + 2²
BC = √8
BC = 2√2 cm
Hence,
perimeter of the square BCDE = 4(2√2)
perimeter of the square BCDE = 8√2 cm
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. Solve the following problems. Show your complete solution. 1. The sum of two numbers is 9and the sum of
their squares is 45. Find the numbers. 2. The difference of the cubes of two numbers is 37. The sum of their
squares is 25. Find the numbers.
Answers
The two numbers are approximately (3.583, 1.990) and (3.062, -1.990).
1. Let's assume the two numbers as x and y.
We are given two conditions:
1st condition: The sum of two numbers is 9.
x + y = 9
2nd condition: The sum of their squares is 45.
x² + y² = 45
To solve this system of equations, we can use the method of substitution. Rearrange the first equation to express x in terms of y:
x = 9 - y
Substitute this value of x into the second equation:
(9 - y)² + y² = 45
Expanding and simplifying:
81 - 18y + y² + y² = 45
2y² - 18y + 36 = 0
Divide the equation by 2 to simplify:
y² - 9y + 18 = 0
Factorize the quadratic equation:
(y - 3)(y - 6) = 0
Setting each factor to zero, we get:
y - 3 = 0 or y - 6 = 0
Solving for y:
y = 3 or y = 6
Now substitute these values back into the equation x + y = 9 to find x:
For y = 3, x + 3 = 9, x = 6
For y = 6, x + 6 = 9, x = 3
Therefore, the two numbers are (3, 6) or (6, 3).
2. Let's assume the two numbers as x and y.
We are given two conditions:
1st condition: The difference of the cubes of two numbers is 37.
x³ - y³ = 37
2nd condition: The sum of their squares is 25.
x² + y² = 25
Again, we can use the method of substitution to solve this system of equations. Rearrange the first equation to express x in terms of y:
x³ = y³ + 37
x = \((y^3 + 37)^{1/3}\)
Substitute this value of x into the second equation:
\([(y^3 + 37)^{1/3}]^2 + y^2 = 25\)
Simplifying:
y² + \(37^{2/3}\) + y² = 25
2y² = 25 - \(37^{2/3}\)
2y² = 25 - 17.074
2y² ≈ 7.926
y² ≈ 3.963
y ≈ ±1.990
Now substitute these values back into the equation x³ - y³ = 37 to find x:
For y ≈ 1.990, x³ - (1.990)³ = 37
x³ - 7.920 = 37
x³ ≈ 44.920
x ≈ ∛(44.920)
x ≈ 3.583
For y ≈ -1.990, x³ - (-1.990)³ = 37
x³ + 7.920 = 37
x³ ≈ 29.080
x ≈ ∛(29.080)
x ≈ 3.062
Therefore, the two numbers are approximately (3.583, 1.990) and (3.062, -1.990).
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P(Ω)
P(A)
0.4
0.1
P(B)
0.2
0.3
Answers
Answer:
i dont even have the first one on my computer
Step-by-step explanation:
Someone help me out plzz
Answers
Answer:
with what? You forget to attach the problem lol
Step-by-step explanation:
Answer: What is the question you need help with??
Step-by-step explanation:
Find the area of the shaded polygons
Answers
Answer:
Is there a picture?
Step-by-step explanation:
How much material is needed to make the popcorn container?
