Answer:
Step-by-step explanation:
The correct equation that shows a step in the process of completing the square on the given quadratic y = x^2 + 8x – 3 is y = x^2 + 8x + 16 – 3 – 16. Completing the square involves adding and subtracting a constant term in order to create a perfect square trinomial. In this case, the constant term added is (8/2)^2 = 16, which is half the coefficient of the x-term squared. This step transforms the quadratic into the form (x + a)^2 + b, where a represents half of the x-term coefficient and b represents the constant term.
By adding 16 to the equation to create a perfect square trinomial, we need to subtract 16 afterward to maintain the equation’s balance. Thus, the equation becomes:
y = x^2 + 8x + 16 - 3 - 16
Simplifying further:
y = (x + 4)^2 - 19
Therefore, the correct equation is:
y = (x + 4)^2 - 19
(q14) Ron is studying the income of people in a particular state. He finds out that the Lorenz curve for that state can be given as L(p)=p^4/3. Find the gini coefficient.
The Gini coefficient is 2(−13/30) = -13/15.
The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).
In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.
The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.
The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.
The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=
∫[0,1](p^4/3−p)dp
=(1/15)−(1/2)
= -13/30
The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.
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Which of the following graphs shows the image of the figure below after a dilation with a scale factor of 2, centered at (-2, -2)?
NO LINKS!
The answer choice which shows the image of the given figure after a dilation with a scale factor of 2, centered at (-2, -2) is as attached.
What is dilation?It follows from the task content that the graph which correctly shows the image of the figure after a dilation with a scale factor of 2, centered at the point (-2, -2) is to be identified.
Recall that the image point in such case would be such that the distance of each vertex would be twice what it was from (-2, -2) as in the pre-image.
Hence, the correct representation of the image is as attached.
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Use the image to determine the line of reflection.
A. Reflection across the x-axis
B. Reflection across the y-axis
C. Reflection across y = -2
D. Reflection across x = 2
Answer:
D. Reflection across x = 2
Step-by-step explanation:
We see that it reflect across x = 2 because if you look at the graph, we see the left side rectangle is 3 points away to the left, and the rectangle on the right is 3 point to the right.
Find the perimeter of pentagon ABCDE. Round to the nearest tenth.
The perimeter of the pentagon ABCDE is 12.8 units
How do we find the perimeter of the five sided pentagon?To solve for the perimeter of the pentagon, we need to find the length of each side and add them up.
The length of a line segment in a coordinate plane can be found using the distance formula which is derived from the Pythagorean theorem:
D = √(x2-x1)² + (y2-y1)²
[tex]AB: \sqrt(-6-(-4))^2 + (-3-(-2))^2 = \sqrt5 = 2.236[/tex]
[tex]BC: \sqrt(-5-(-6))^2 + (-6-(-3))^2 = \sqrt10 = 3.162[/tex]
[tex]CD: \sqrt(-2-(-5))^2 + (-5-(-6))^2 = \sqrt10 = 3.162[/tex]
[tex]DE: \sqrt(-2-(-2))^2 + (-3-(-5))^2 = \sqrt4 = 2[/tex]
[tex]EA: \sqrt(-4-(-2))^2 + (-2-(-3))^2 = \sqrt5 = 2.236[/tex]
2. 236 + 3.162 + 3.162 + 2 + 2.236 = 12.796
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An employee started a new job and must enroll in a new family health insurance plan. One of the plans involves prescription drug coverage. The employee estimates that the entire family will fill 10 prescriptions per month, totaling $1,250. The employee has two options to choose from:
Option A: $75 monthly premium; 80% coverage for all prescription costs
Option B: $45 monthly premium; 75% coverage for first $600 in prescription costs, then 85% coverage for all prescription costs over $600
Which option would result in the highest overall cost for the employee, and by how much?
Option A has the highest overall cost by $77.50.
Option B has the highest overall cost by $77.50.
Option A has the highest overall cost by $32.50.
Option B has the highest overall cost by $32.50.
The employee can choose between Option A or Option B.Option A and B have different prescription drug coverage policies.
When an employee starts a new job, they are usually eligible for a range of benefits, including health insurance. An employee in such a situation has to enroll in a new family health insurance plan.
For instance, the employee estimates that the entire family will fill ten prescriptions per month, which would cost $1,250.Each option has a different cost associated with it.
The total cost of the plan with Option A is higher by $77.50 compared to Option B. On the other hand, Option B has a total cost that is higher by $32.50 compared to Option A.
It is important to note that both plans have different deductibles and copays.An employee should choose a plan that suits them and their family's medical needs.
They should also consider other factors such as the cost of each plan and whether they can afford it. In case of confusion, an employee can always seek guidance from their employer's human resource department.
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Show your work please help me please
Answer:
10
Step-by-step explanation:
[tex]\displaystyle \biggr(2\frac{3}{8}+1\frac{3}{4}\biggr)+5\frac{7}{8}\\\\2\frac{3}{8}+1\frac{6}{8}+5\frac{7}{8}\\\\(2+1+5)+\biggr(\frac{3}{8}+\frac{6}{8}+\frac{7}{8}\biggr)\\\\8+\frac{16}{8}\\\\8+2\\\\10[/tex]
Make sure to have all fractions have the same denominator so it's easier to add.
I need help with this problem in statistics
(a) The null hypothesis, H₀, and the alternative hypothesis, H₁, that should be used for the test are as follows:
H₀: μ = 90 (The mean SI score for the population of all smokers is 90)
H₁: μ < 90 (The mean SI score for the population of all smokers has decreased)
How to explain the hypothesis(b) If the psychologist decides not to reject the null hypothesis, she might be making a Type II error. A Type II error occurs when the null hypothesis is not rejected, but it is actually false. In this case, it would mean that the psychologist fails to detect a decrease in the mean SI score for smokers, even though it has truly decreased.
(c) A Type I error would be rejecting the hypothesis that μ = 90 when it is actually true. In other words, it would mean concluding that the mean SI score for all smokers has decreased (H₁) when, in reality, it has not changed or remains at 90 (H₀).
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..................................................................................................
Hi :)
Answer:
The quotient will be decreased by 10
Step-by-step explanation:
720 ÷ 9 = 80
630 ÷ 9 = 70
Hope this helps :) !!!
Answer:
the quotient will decrease by 10 because when you divide 720 by 9 you will get 80 and when you divide 630 by 9 you will get 70. If you minus 8-0 and 70 you will get 10 hope this helps
If the cos 42° = one half, then the sin 48° = _____. Group of answer choices two thirds, because the angles are complementary 2 over 1, because the angles are supplementary one half, because the angles are complementary 1, because the angles are complementary
The sine of 48 Degrees is equal to one-half.
The cosine of an angle is equal to one-half when the angle is 60 degrees. Therefore, if the cosine of 42 degrees is one-half, it means that the angle of 42 degrees is complementary to the angle of 60 degrees.
Since the angles are complementary, the sine of one angle is equal to the cosine of the other angle. In this case, the sine of 48 degrees will be equal to the cosine of its complementary angle, which is 42 degrees.
Therefore, the sine of 48 degrees is equal to one-half.
The correct answer is: 1/2, because the angles are complementary.
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For each of the following annuities, calculate the annuity payment.
(Future Value=25,850, Year= 8, interest rate=8% annuity payment =?)
(Future Value=1,130,000, Year= 43, interest rate=10% annuity payment =?)
(Future Value=976,000, Year= 29, interest rate=11% annuity payment =?)
(Future Value=149,000 Year= 16, interest rate=7% annuity payment =?)
Step-by-step explanation:
To calculate the annuity payment for each of the given scenarios, we can use the formula for the present value of an ordinary annuity:
Annuity Payment = Future Value / [(1 - (1 + r)^(-n)) / r]
Where:
Future Value = Future value of the annuity
r = Interest rate per period (in decimal form)
n = Total number of periods
Let's calculate the annuity payment for each scenario:
Scenario 1:
Future Value = $25,850
Year = 8
Interest rate = 8% (0.08 as a decimal)
Annuity Payment = $25,850 / [(1 - (1 + 0.08)^(-8)) / 0.08]
Scenario 2:
Future Value = $1,130,000
Year = 43
Interest rate = 10% (0.10 as a decimal)
Annuity Payment = $1,130,000 / [(1 - (1 + 0.10)^(-43)) / 0.10]
Scenario 3:
Future Value = $976,000
Year = 29
Interest rate = 11% (0.11 as a decimal)
Annuity Payment = $976,000 / [(1 - (1 + 0.11)^(-29)) / 0.11]
Scenario 4:
Future Value = $149,000
Year = 16
Interest rate = 7% (0.07 as a decimal)
Annuity Payment = $149,000 / [(1 - (1 + 0.07)^(-16)) / 0.07]
After performing the calculations, you will obtain the annuity payment for each scenario.
I hope I was helpful
3x+4
12. Simplify +
x+2
x²+2x
2x+4
Answer:
[tex]\dfrac{x^2+8x+8}{2x+4}\\\\[/tex]
Step-by-step explanation:
Simplify:
[tex]\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}[/tex]
Multiply the denominator and the numerator of the first term by 2,
[tex]=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}[/tex]
[tex]\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\[/tex]
Write the next whole number after 3355 in the base-six system.
Find y and x need to get the answer asap
Answer:
x = 30
y = 120
Step-by-step explanation:
okay so , 3x - 30 = 60 (opposite each other)
60 + 30 = 90
90 / 3 = 30
x = 30
all angles have to equal 360
we already have two 60 degrees
60 + 60 = 120
360 - 120 = 240
240 / 2 = 120
y = 120
Clarence walks 3.1 miles around Lake Johnson every day for five days.
If it takes him a total of 6 hours to walk the 15.5 miles, what is his
average time per day?
minutes per day.
Answer:
Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day
Step-by-step explanation:
To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.
Let's calculate his average time per day:
Average time per day = Total time / Number of days
Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:
Average time per day = 6 hours / 5
Average time per day = 1.2 hours per day
To convert hours to minutes, we'll multiply the average time per day by 60:
Average time per day = 1.2 hours * 60 minutes
Average time per day = 72 minutes per day
Therefore, Clarence's average time per day is 72 minutes.
Rajani is studying in class X in a school. Her age consisting of two digits equal to 4 times its sum and 6 times the product of her digits.How old is she?
Rajani's age is calculated to be 24 years old.
How to find Rajani''s ageLet's assume the two-digit number representing Rajani's age is written as AB,
where
A represents the tens digit and
B represents the units digit.
According to the given information, Rajani's age, AB, is equal to:
4 times the sum of its digits: 4 * (A + B)6 times the product of its digits: 6 * (A * B)Based on this information, we can form the equation:
10A + B = 4(A + B) + 6(A * B)
10A + B = 4A + 4B + 6AB
rearranging the terms:
10A - 4A = 4B + 6AB - B
6A = 3B + B(6A - 4)
6A = 3B + 2B(3A - 2)
Dividing both sides by 3A - 2:
6A / (3A - 2) = 3B / (3A - 2) + 2B
at this point, we need to check the possible values for A and B that satisfy this equation. Since the problem states that Rajani's age consists of two digits, A and B must be integers ranging from 0 to 9.
By trying different values for A and B, we find that A = 2 and B = 4 satisfy the equation:
6 * 2 / (3 * 2 - 2) = 3 * 4 / (3 * 2 - 2) + 2 * 4
12 / 4 = 12 / 4 + 8
3 = 3 + 8
The equation is true for A = 2 and B = 4.
Therefore, Rajani's age is 24 years old.
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mention three example situation that run project for human rights mention three example in situation The Strand projects for human rights campaign's
The three example situation that run project for human rights are;
Amnesty International securing a live of a citizen in another country when her right is been violatedHuman Rights Watch that fight for the oppressedCivil Rights Defenders that fight for individuals rightWhat does the term "human rights" mean?All people have the right to human rights, regardless of their ethnicity or nationality.Human rights cover a wide range of rights, such as the freedom from slavery and torture, the right to life and liberty.
Human rights cover a wide range of rights, such as the freedom from slavery and torture, the right to life and liberty, the freedom of speech, the right to a job and an education, among many more.
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Investor E decided to use a hard money(short-term) loan to purchase a condo that costs $80,000 with a $30,000 down payment, 6.00% annually fixed rate for a 30 months term, and one payment per month. What is the monthly payment for this mortgage?
Step-by-step explanation:
In the case of a hard money or short-term loan, the calculation for the monthly payment is slightly different. Typically, hard money loans have interest-only payments during the loan term, and the principal amount is due at the end of the term.
To calculate the monthly payment for an interest-only loan, you can use the following formula:
Monthly Payment = Loan amount * (Annual interest rate / 12)
Given:
Condo cost = $80,000
Down payment = $30,000
Loan amount = Condo cost - Down payment = $80,000 - $30,000 = $50,000
Annual interest rate = 6.00%
Loan term = 30 months
First, calculate the monthly interest rate:
Monthly interest rate = (Annual interest rate / 100) / 12 = (6.00 / 100) / 12 = 0.005
Next, substitute the values into the formula:
Monthly Payment = $50,000 * 0.005
After performing the calculations, the monthly payment for this hard money loan is $250.
I hope I was helpful
2. Jordan Alexander bought an all-in-one printer that regularly sells for $249.99 at the markdown rate of
32%.
The required price of an all-in-one printer that regularly sells for $249.99 at the markdown rate of 32% is $169.99.
Here, we have,
given that,
Jordan Alexander bought an all-in-one printer that regularly sells for $249.99 at the markdown rate of 32%
now, we have,
32% of $249.99
= 32% × $249.99
=$79.99
so, we have,
the price =$249.99 - $79.99
= $169.99
Hence, The required price of an all-in-one printer that regularly sells for $249.99 at the markdown rate of 32% is $169.99.
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Harrison, Anny and Ekua shared GH4000 in the ratio 1:3:6 calculate each person's share
Answer:
To calculate each person's share, we first add up the parts of the ratio, which is 1+3+6=10.
Next, we divide the total amount shared, GH4000, by the ratio sum (10):
GH4000/10= GH400
Finally, to find each person's share, we multiply the ratio part by GH400:
- Harrison's share: 1 part out of 10 parts = 1/10 * GH4000 = GH400
- Anny's share: 3 parts out of 10 parts = 3/10 * GH4000 = GH1200
- Ekua's share: 6 parts out of 10 parts = 6/10 * GH4000 = GH2400
Therefore, Harrison's share is GH400, Anny's share is GH1200, and Ekua's share is GH2400.
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
Simplify the following expression.
Answer:
[tex]\displaystyle \frac{cd^6}{a^4b^2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}[/tex]
Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with [tex]e^{-7}[/tex]) and became positive, and vice versa with those originally in the numerator went in the denominator (like with [tex]a^{-4}b^{-2}[/tex]) and also became positive.
Step-by-step explanation:
a‐⁴b‐²cd⁶
_______
e‐⁷
cd⁶e⁷
_____
a⁴b²
You want to buy a new sports coupe for $75,500, and the finance office at the dealership has quoted you a loan with an APR of 7.9 percent for 72 months to buy the car. Effective Annual Rate is 8.14.
What will your monthly payments be?
Loan amount (P): $75,500
Annual Percentage Rate (APR): 7.9%
Loan term (n): 72 months
Monthly interest rate = APR / 12 = 7.9% / 12 = 0.0079
M = P * (r * (1+r)^n) / ((1+r)^n - 1)
M = 75500 * (0.0079 * (1+0.0079)^72) / ((1+0.0079)^72 - 1)
$1,217.17
The ratio of the number of Mary's beads to the number of Jane's beads is 4 : 7. The ratio of the number of Jane's beads to the number of Pauline's beads is 5 : 2. If Mary has 6 more beads than Pauline, how many beads does Jane have?
Jane have 35 beads in total.
We have, ratio of the number of Mary's beads to the number of Jane's beads is 4 : 7.
The ratio of the number of Jane's beads to the number of Pauline's beads is 5 : 2.
We can Write the ratios as
Mary : Jane : Pauline
4 : 7
5 : 2
Now, Jane is common in both then
Mary : Jane : Pauline
20 : 35 : 14
Thus, Jane have 35 beads in total.
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solve the system of linear equation by inverse method
x + 2y - z = 7
2x - 3y - 4y = -3
x + y +z = 0
The solution to the system of equations is:
x = -36,
y = 23,
z = -10.
To solve the system of linear equations using the inverse method, we first need to represent the system in matrix form.
Let's rewrite the system of equations:
1x + 2y - 1z = 7 ...(1)
2x - 3y - 4z = -3 ...(2)
1x + 1y + 1z = 0 ...(3)
We can express this system in matrix form as AX = B, where:
A = [[1, 2, -1],
[2, -3, -4],
[1, 1, 1]]
X = [[x],
[y],
[z]]
B = [[7],
[-3],
[0]]
Now, to solve for X, we need to find the inverse of matrix A. If A is invertible, we can solve for X by multiplying the inverse of A with B:
X = A⁻¹ × B
Let's calculate the inverse of matrix A:
A⁻¹ = [[-3, 5, -1],
[2, -3, 1],
[-1, 1, 0]]
Now, we can solve for X:
X = A⁻¹B
X = [[-3, 5, -1],
[2, -3, 1],
[-1, 1, 0]] [[7],
[-3],
[0]]
Multiplying the matrices, we get:
X = [[-3×7 + 5(-3) + (-1)0],
[2×7 + (-3)(-3) + 10],
[-1×7 + 1(-3) + 0*0]]
Simplifying further:
X = [[-21 - 15 + 0],
[14 + 9 + 0],
[-7 - 3 + 0]]
X = [[-36],
[23],
[-10]]
Therefore, the solution to the system of equations is:
x = -36,
y = 23,
z = -10.
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HELP PLEASEI NEED HELP FATS FATS FATS IT SO EASY BUT I DONT GET IT!!!
Answer:
1x3
2x3
2x2
3x2
Step-by-step explanation:
with the 1x3 you get 3 and with 2 x 3 you get 6 which means for the first one you get 3/6 .
for the second one 2x2 =4 and 3x2=6 which equals 4/6
What is the cos A?Will give 15 points.
Answer:
Step-by-step explanation:
cos A = [tex]\frac{\sqrt{8} }{3}[/tex]
A manufacturer is producing metal rods, whose lengths are normally distributed with a mean
of 75.0 cm and a standard deviation of 0.25 cm. If 3000 metal rods are produced, how many
will be between 74.5 cm and 75.5 cm in length?
Therefore, we can expect that approximately 95.45% of the 3000 metal rods produced will fall between 74.5 cm and 75.5 cm in length. To find the actual number, we multiply 0.9545 by 3000, yielding approximately 2864 rods.
To determine how many metal rods will be between 74.5 cm and 75.5 cm in length, we can use the properties of the normal distribution.
Given that the lengths of the metal rods are normally distributed with a mean of 75.0 cm and a standard deviation of 0.25 cm, we can calculate the probability of a rod falling within the specified range.
First, we find the z-scores for the lower and upper limits of the range. The z-score for 74.5 cm is
[tex]\frac{ (74.5 - 75.0) }{ 0.25} = -2,[/tex]
and the z-score for 75.5 cm is
[tex]\frac{(75.5 - 75.0)} { 0.25} = 2.[/tex]
Using a standard normal distribution table or a statistical calculator, we can determine the area under the curve between these z-scores, which represents the probability.
The area between -2 and 2 is approximately 0.9545.
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The track below has two straight lengths and two curved ends. What is the area of the field inside the track? Round your answer to the nearest meter.
Answer:
(63.69)(100) + π(31.695^2)
= about 9,495 square meters
Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84 m3 . The manufacturer wants the length of the container to be one meter longer than the width, and the height to be one meter greater than twice the width. What should the dimensions of the container be?
The dimensions of the container in the shape of a rectangular solid are 3.41 m by 4.41 m by 7.81 m.
How to determine dimensions?Let the width of the container be w.
The length of the container is w + 1.
The height of the container is 2w + 1.
The volume of the container is 84 m3.
Set up the following equation to represent the volume of the container:
w(w + 1)(2w + 1) = 84
Solve for w by expanding the left-hand side of the equation:
2w³ + 3w² + w - 84 = 0
Then use the quadratic formula to solve for w:
w = (-3 ± √(3² - 4 × 2 × (-84))) / (4 × 2)
w = (-3 ± √(9 + 672)) / 8
w = (-3 ± √681) / 8
w = (-3 ± 26.09) / 8
w = 3.41 or -5.59
Since w is the width of the container, it must be positive. Therefore, w = 3.41.
The length of the container is w + 1 = 3.41 + 1 = 4.41.
The height of the container is 2w + 1 = 2 × 3.41 + 1 = 7.81.
Therefore, the dimensions of the container are 3.41 m by 4.41 m by 7.81 m.
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