A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 15 pounds each. There are 120 boxes in all. If the truck is carrying a total of 3800 pounds in boxes, how many of each type of box is it carrying?
If a delivery truck is transporting boxes of two sizes: large and small. The number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.
How to find the number of each type of box ?Let L represent the number of Large boxes.
Let S represent the number of Small boxes.
Total number of boxes = 120
L + S = 120
The two equations are:
L + S = 120
55×L + 15×S = 3800
L + S = 120 eliminate L by multiplying this equation by -55
-55×(L + S = 120)
The equations are:
55 ×L + ×15S = 3800
-55×L -55×S = -6600
0 - 40×S = - 2800
S = -2800/(-40)
S = 70
Plug S back into one of our equations.
L + S = 120
L + (70) = 120
L = 120 - 70
L = 50
So ,
L = 50 and S = 70
Therefore the number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.
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(x^3+5x^2-24x)/(x+8) Synthetic Division
The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is x² - 3x.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is given below:
(x³ + 5x² -24x) / (x + 8)
The divisor is -8
The coefficients are:
1 5 -24
Using synthetic division
the first coefficient is 1
the second coefficient = 1 * (-8) + 5
the second coefficient = -3
the third coefficient = -3 * (-8) + (-24)
the third coefficient = 0
Therefore, the solution = 1(x³/x) -3(x²/x) + 0(x/x)
The solution = x² - 3x
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the length of the diagonal AC and BD of a rhombus ABCD are 6m and 8cm, Find the length of each side of the rhombus
Length of side of the rhombus is 5cm.
Find the length of each side of the rhombus?A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.
step1
Diagonals of a rhombus bisect each other at right angles.
Let point of intersection of diagonals be O
So, OD = 3cm , OA = 4cm
From Right angled triangle △ AOD,
⇒ AD² = OA² + OD² (Pythagoras theorem)
⇒ AD² =4² + 3²
⇒ AD² = 16+9
⇒AD² =25
step2
⇒ AD² =25
⇒ AD=5 cm
AD is side of the rhombus.
So, length of side of the rhombus is 5cm
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If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), use Formula 5 of this theorem to find d/dt [u (t) x v (t). (3t sin(3 t) - cos(3 t) + 3cos(6 t), 3t- 3 sin(6 t), 3 t sin(3 t) - cos(3 t)
If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).
Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)
Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:
du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)
= (3 cos 3t, -3 sin 3t, 1)
dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)
= (1, -3 sin 3t, 3 cos 3t)
Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)
= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)
= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)
= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))
The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).
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A team of three is chosen randomly from an office with 2 men and 4 women. Let X be the number of women on the team. (a) Identify the probability distribution of X by name. (b) Give the probability mass function of X
The probability distribution of X by name is X/6 and the the probability mass function of X is X/6 - 4
The term probability mass function is defined as a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
Here we know that team of three is chosen randomly from an office with 2 men and 4 women.
And let us consider that X be the number of women on the team.
Total number of members in the term is calculated as,
=> 4 + 2 = 6
Then the the probability distribution of X by name is,
=> X/6
And the the probability mass function of X is written as,
=> x/6 - 4
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what is the answer? thanks
The solution for the expression given above would be = 31/40. That is option B.
What is a fraction?A fraction is defined as the part of a whole value which is written in the form of a numerator and a denominator.
The given fractions from the question;
2/5 + 3/8
Find the lowest common multiple of the figures below ( denominator) = 40
= 16 + 15/40
= 31/40
Therefore the correct fraction for the given expression = 31/40.
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Simplify 7+5(7+5n)
42+25n
2n+19
8n+6
8n+10
Answer:
42+25n
Step-by-step explanation:
[tex]7+5(7+5n)\\=7+35+25n\\=42+25n[/tex]
Eric bought a canoe for $333.75. The sales tax was 5.25%. What was his total cost?
factor the expression 15x - 10xy
Answer: 5x(3-2y)
Step-by-step explanation:
Step 1:
Find the greatest common factor (GCF):
Both values have 5x as the GCF.
Step 2:
Take out the GCF:
15x/5x=3
-10xy/5x=-2y
Step 3:
Write it out:
5x(3-2y)
Check:
Apply Distributive Property:
5x*3=15x
5x*-2y=-10xy
15x-10xy=15x-10xy
algebra 2-2
solve [tex]\sqrt{x}+3=-6[/tex]
√x+3=-6
The solution of equation is x=-3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given
The equation;√x+3=-6
Now,
√x=-6-3
√x=-9
x=-3
Therefore the answer of the given equation will be -3
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the probability that a student is taking a math class is 60%. the probability that a student in a math class is also taking a science class is 80%. what is the probability that a student is taking both math and science?
Answer:
48%
Step-by-step explanation:
0.6*0.8 = 0.48 = 48%
When Mamadou goes bowling, his scores are normally distributed with a mean of 175 and a standard deviation of 13. Using the empirical rule, what percentage of the games that Mamadou bowls does he score between 136 and 214?
The percentage of games that Mamadou scores between 136 and 214 is given as follows:
99.7%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.For this problem, we have that
136 = 175 - 39 = 175 - 3 x 13.214 = 175 + 39 = 175 + 3 x 13.Hence the percentage is of 99.7%, as the measures are within three standard deviations of the mean.
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A function is shown f(x)=-(13)/(5)x+k if f(30)=-1 what is the vallue of k?
The value of the variable , k is -385/13
What is a function?A function can be described an expression, equation, law or rule explaining the relationship between two variables.
These variables are known as;
Dependent variableIndependent variableFrom the information given, we have the function;
f(x)=-(13)/(5)x+k
Also, for the value of f(30), the function is equivalent to -1
Now, substitute the value of x as 30 and equate the function to -1. we have;
-1 = -13/(5)30 + k
Divide both sides by the cofficient of 30 + k
30 + k = -1 × -5/13
Multiply the values
30 + k = 5/13
Now, collect like terms
k = 5/13 - 30
k = -385 /13
Thus, the value is -385/13
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13. You need to make 18 one-cup bags of trial mix for a class trip. The recipe calls for peanuts,
chocolate chips, and raisins in the extend ratio of 5:1:4. How many cups of each item do you
need? You will get some decimal answers.
The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.
How to calculate the number of cups of each item that is needed?From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4
Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.
5x- peanuts
1x- chocolate chips
4x- raisins
5x + 1x + 4x= 18
10x= 18
x= 18/10
x = 1.8
Chocolate = 1.8 cups
Raisins = 4x
= 4 × 1.8
= 7.2 cups.
Peanut = 5x
= 5 × 1.8
= 9 cups
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severe difficulty in making mathematical calculations as a result of a brain disorder
Dyscalculia is a learning disorder that affects a person’s ability to do the math.
A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.
The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.
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How do you solve this type of problem?
It's a fact that the sum of the angles of a triangle add up to 180º.
So, 55º + 85º + (3x+4)º = 180º.
That's the equation you need to solve:
55 + 85 + 3x+4 = 180 (combine like terms)
144 + 3x = 180 (subtract 144 from both sides)
3x = 36 (divide both sides by 3)
x = 12 (you've got x)
When does king become the most emotional ? What is the message at this moment?
King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.
In what ways does Dr. King use emotion in his speech?Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.
When does king become the most emotional?King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.
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How many possible centers of rotation will produce an image of a left-pouting arrow?
The number of center of rotations to produce the image is (d) infinite
How to determine the number of centers?An arrow pointing to the left is symmetric around its central axis.
This means that any point along the central axis of the arrow can serve as a center of rotation to produce an image of a left-pointing arrow.
The central axis is a straight line that runs through the middle of the arrow from the tip to the base, and also extend through the arrow's depth.
Hence, the number of possible centers of rotation that will produce an image of a left-pointing arrow is infinite.
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Why does 5xy³ have a degree of 4? (Hint: Look at the exponents on the variables.)
by number of forme
Answer:
The degree is 4 because the term shown has TWO variables, while y has an exponent of 3, x has an exponent of 1, add the exponents of the variables to find the degree
Step-by-step explanation:
A men's health magazine would like to conduct a survey using a simple random sample of 900 men who practice yoga. One of the goals of the survey is to create a confidence interval to estimate the proportion of all men practicing yoga who report low stress levels. Since the intended survey method requires face-to-face interaction, some of the magazine executives are concerned about the cost of the survey and suggest sampling a smaller group of 100 men instead of 900 men. Assuming the sample proportion doesn't change, which of the following best describes the anticipated effect on the width of the confidence interval if the magazine were to survey a random sample of 100 men who practice yoga, rather than 900 men? A) The width of the interval based on 100 men would be about nine times the width of the interval based on 900 men.
B) The width of the interval based on 100 men would be about three times the width of the interval based on 900 men. C) The width of the interval based on 100 men would be about the same width as the interval based on 900 men. D) The width of the interval based on 100 men would be about one-third the width of the interval based on 900 men. E)
The width of the interval based on 100 men would be about one-ninth the width of the interval based on 900 men.
The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.
What is the width of the interval?
The width of a confidence interval for a proportion is proportional to the standard error of the sample proportion, which is proportional to the square root of the sample size.
The standard error is defined as the standard deviation of the sampling distribution of the sample proportion, which is estimated by the standard deviation of the Bernoulli distribution (square root of the sample proportion times (1 - sample proportion) divided by the sample size).
So, if the sample size is reduced by a factor of 9 (from 900 to 100), the standard error (and hence the width of the confidence interval) would increase by a factor of 3 (square root of 9).
Therefore, The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.
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Shane bought a package of 12 bagels. He gave b of them to his friends. Write an expression that shows the number of bagels Shane has left.
The expression that shows the number of bagels Shane has left is 12-b.
What is an expression?Expression in math is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given;
Shane bought a package of 12 bagels
He gave b of them to his friends
Now;
Shane bought 12 bagels
Expression= 12
Shane gave b
Expression=12-b
Therefore, the expression will be 12-b.
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I can't figure this out and yet it's just a simply question. Not the best at math so please help me
[tex]6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}[/tex]
Write an exponential function to model the situation. Tell what each variable represents. A price of $130 increases 5% each year.
The exponential function to model the situation is f(x) = 130(1.05)ˣ⁺¹⁶
How to find the exponential function?First of all, note that each variable represents number of years the price increases in each year
We are given,
The initial number of population = 130
Rate of growth = 5% = 0.05
Number of years = 16.
Thus, we get that the growth in population for 16 years is given by,
f(x) = 130(1.05)¹⁶
⇒f(x) = 130(1.05)¹⁶i
This gives us that the population after 16 years will be given by,
f(x) = 130(1.05)ˣ⁺¹⁶
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Bottles Glue Glitter
1 3.8 1.9
This means,
1 bottle = 3.8 oz of glue and 1.9 oz of glitter
Now,
1 bottle = 3.8 oz of glue
Multiply 4 on both sides.
4 bottle = 4 x 3.8 oz
4 bottle = 15.2 oz
1 bottle = 1.9 oz of glitter
Multiply 4 on both sides.
4 bottle = 7.6 oz
Thus,
15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
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The amount of sand left in a 600 mL vase can be modeled by the equation s = – 1 5 t + 600, where s is the amount of sand left in the vase and t is time in minutes since the sand started leaking out. The vase is full of sand. Sand leaks out of the vase until the vase is empty. Determine the domain and range of this scenario
As per the given equation, the domain is [0, 3000] and the range is [0, 600].
In the term domain is defined as the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.
Here we know that the amount of sand left in a 600 mL vase can be modeled by the equation that is written as,
=> s = – 1/5 t + 600
here s refers the amount of sand left in the vase and t refers time in minutes since the sand started leaking out
Here we also know that the vase is full of sand and sand leaks out of the vase until the vase is empty.
Then in order to find the domain we have to put the value of s as 0, then we get the domain as,
=> 0 = -1/5t + 600
=>1/5t = 600
=> t = 3000
Then the domain is [0, 3000].
Similarly, in order to find the value of range we have to put the value of t as zero, then we get
=> s = -1/5(0) + 600
=> s = 600
Then the range is [0, 600]
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if one addend of x is c, what is the other addend?
If one addend of x is c, the other addend is x-c.
How to find the other addend?An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.
The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.
In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x
Therefore, If one addend of x is c, the other addend is x-c.
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Is the function represented by the table linear?
x
y
10
–6
11
1
12
6
13
12
The function is not linear because the rate of change in not constant.
What is Linear Function?Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.
Given:
x y
10 -6
11 1
12 6
13 12
So, the rate of Change
= 10/ (-6)
= -5/2
and, again = 11/1 = 11
As, the rate of change is not constant.
But, in linear function the rate of change is same.
Hence, the function is not linear.
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Can someone please help me with problem 6 of this assignment? I included the measurements of the triangle so that you are able to solve it accurately.
Geometry Topic: 6.1 - 6.4 Constructing Parts and Centers
Problem 6 Directions: Remember! Triangle centers may be outside the triangle. Locate the orthocenter of each triangle by finding the intersection of the altitudes.
Answer:
let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work. Then repeat for B and C. Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Step-by-step explanation:
Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Answer:
see attached
Step-by-step explanation:
You want to construct the orthocenter of the given triangle.
OrthocenterThe orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.
Perpendicular through an external pointA perpendicular to a line through a point not on the line is constructed in a few simple steps:
Using the external point as a center, draw an arc that intersects the line in 2 places.Using each of those points as a center, draw intersecting arcs with the same radiusThe line through that point of intersection and the original point is perpendicular to the lineThe attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.
Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.
__
Additional comment
The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.
It may appear that point Z is a reflection of point C in line AB, but it is not.
PLEASEE HELPPP
A line has a slope of –1/3 and a y-intercept of 5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
The answer in intercept form will be
-1/3=5/3x+c
The sequence of the other length of the rectangles is represented by the equation: an=8+(n−1)4 a) Determine two side lengths of the tenth rectangle in the sequence. b) You are given the following areas of rectangles: 392in2, 128in2, 576in2, and 968in2 Determine which of the areas is not possible in the given sequence and explain why.
Answer:
a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.
b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.
Step-by-step explanation:
The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.