The quotient of the given rational expressions, when reduced to its lowest terms, is [tex]${\frac{(x+2)(x-2)}{x+1}}$.[/tex]
The given rational expressions are:
[tex]$\frac{x^2-4}{x+3}$[/tex] and[tex]$\frac{4x+4}{4x+12}$[/tex]
Factoring numerator and denominator of the expression
[tex]$\frac{x^2-4}{x+3} = \frac{(x+2)(x-2)}{x+3}$ $\frac{4x+4}{4x+12} = \frac{4(x+1)}{4(x+3)}$\\[/tex]
Invert the second fractionAfter inverting, the second fraction becomes
[tex]$\frac{4(x+3)}{4(x+1)}$[/tex]
Multiply the two fractions together
By multiplying the fractions together, we get
[tex]$$\frac{(x+2)(x-2)}{x+3} \cdot \frac{4(x+3)}{4(x+1)}$$[/tex]
Simplifying the expression we get,
[tex]$$\frac{4(x+2)(x-2)(x+3)}{4(x+1)(x+3)} = \frac{(x+2)(x-2)}{x+1}$$[/tex]
Reduce the resulting fraction to its lowest terms.Rewriting the above expression in factored form, we get
[tex]$\frac{(x+2)(x-2)}{x-(-1)}$[/tex]which becomes [tex]$\frac{(x+2)(x-2)}{x+1}$[/tex]
Therefore, the main answer is [tex]$\boxed{\frac{(x+2)(x-2)}{x+1}}$.[/tex]
Thus, the quotient of the given rational expressions, when reduced to its lowest terms, is [tex]$\boxed{\frac{(x+2)(x-2)}{x+1}}$.[/tex]
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Question 16 of 20 True or false: An experiment repeated 3 times would be less reliable than an experiment repeated 10 times.
An Experiment is repeated 10 times compared to just 3 times, the results from the 10 repetitions would generally be considered more reliable.
True.
In general, conducting an experiment multiple times increases the reliability of the results. The more times an experiment is repeated, the greater the opportunity to collect data and observe patterns or trends. This allows for a more robust analysis and reduces the impact of random variations or errors that may occur in a single trial.
When an experiment is repeated multiple times, it helps to reduce the effects of outliers or anomalies that may occur in a single trial. By averaging the results over multiple repetitions, the overall outcome tends to be more representative and reliable.
In the context of statistical analysis, increasing the sample size (number of repetitions) can lead to more precise estimates of parameters and reduce the margin of error. It provides a better understanding of the underlying phenomenon being studied and allows for more confident conclusions.
Therefore, if an experiment is repeated 10 times compared to just 3 times, the results from the 10 repetitions would generally be considered more reliable. The larger sample size provides a stronger basis for drawing conclusions and making inferences about the population or phenomenon under study.
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Please help me vote you brainiest
Answer:
s-b-t-s-w
Step-by-step explanation:
Answer: answer is B
Step-by-step explanation: I took the test.
which of the following statements is true of pie charts? group of answer choices they are ineffective in showing quantitative totals. they are ineffective in showing percentages. they present data in columns and rows. they make it easier to understand processes.
Pie charts are effective in conveying percentages and are commonly used in data analysis and presentations.
The true statement about pie charts is that they are effective in showing percentages. Pie charts are a common data visualization tool used to represent proportions or percentages of a whole.
The chart is divided into slices, with each slice representing a specific category or data point. The size of each slice is proportional to the percentage it represents within the whole.
This visual representation makes it easier for viewers to understand the distribution and relative proportions of different categories or variables. Pie charts are therefore frequently used in data analysis and presentations because they are good at communicating percentages.
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1) what is the proportion of children with significance social activity in children with ALL and what is the proportion of children with significant social activity in children wifhout ALL?
2)what is the uppwr bound of 95% confidencd interval?
1) The proportion of children with significant social activity in children with ALL is 0.805 (1020 out of 1272). The proportion of children with significant social activity in children without ALL is 0.858 (5343 out of 6238).
2) The upper bound of the 95% confidence interval for the odds ratio of ALL associated with significant social activity is 1.32. This means that there is a 95% chance that the true odds ratio is between 1.32 and infinity.
In other words, the study found that children with significant social activity were more likely to develop ALL than children without significant social activity. However, the study was observational, so it cannot be concluded that significant social activity caused ALL. There may be other factors that explain the association between significant social activity and ALL. For example, children who are more outgoing may be more likely to be exposed to germs, which could increase their risk of developing ALL.
Here are some additional details about the study:
The study was conducted by Gilham et al. (2005).The study included 1272 children with ALL and 6238 children without ALL.The children were followed for an average of 10 years.The study found that children with significant social activity were more likely to develop ALL than children without significant social activity.The study was observational, so it cannot be concluded that significant social activity caused ALL.Learn more about Confidence Intervals in Z-Test here:
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What is the coefficient of the second term of the expression 3x^4 + x^2?
Answer:
1
Step-by-step explanation:
because no number Is beside it except 1 because 1 x anything will give it back
The coefficient of the second term of the expression 3x⁴ + x² will be 1. Then the correct option is B.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
⇒ 3x⁴ + x²
The number which is associated with the variable is known as the coefficient of that variable.
In the expression 3x⁴ + x², the coefficient of x⁴ is 3 and the coefficient of x² is 1.
The coefficient of the second term of the expression 3x⁴ + x² will be 1. Then the correct option is B.
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WILL MARK BRAINLIEST IF RIGHT!
If quadrilateral ABCD rotates 90° counterclockwise about the origin, what are the coordinates of A′ in quadrilateral A′B′C′D′ ?
A. (2, 1)
B. (-2, -1)
C. (-2, -2)
D. (-2, 0)
Answer:
B. (-2, -1)
Step-by-step explanation:
Step-by-step explanation:
Answer option B - ( -2, -1)
Nicola is multiplying 1/6 by 3/2
Use the drop-down menu to complete the statement
Graph the line y=kx+1 if it is known that the point M belongs to it: m(1,3)
Answer:
y = 2x +1
Step-by-step explanation:
y=kx+1
Substitute the point into the equation
3 = k(1) + 1
3 = k+1
Subtract 1 from each side
3-1 = k
2 = k
y = 2x +1
The slope is 2 and the y intercept is 1
Question 2, 4+4=8 marks. Consider the paraboloid paremterized by o(u, v) = (u,v,u²+ v²). 1. Find the second fundamental form of o. 2. Compute the normal curvature and the geodesic curvature of the circle (t) = (sint, cost, 1) on the above paraboloid.
The second fundamental form of the paraboloid parameterization is computed by finding the coefficients L, M, and N using the derivatives of the position vector. The normal curvature of the circle on the paraboloid is given by (2 sin t) / √(1 + 4u² + 4v²), while the geodesic curvature is zero..
1. To find the second fundamental form of the paraboloid parameterization, we start by computing the partial derivatives of the position vector o(u, v) with respect to u and v. The first-order partial derivatives are:
o_u = (1, 0, 2u)
o_v = (0, 1, 2v)
Next, we compute the coefficients of the second fundamental form using the following formula:
L = o_{uu} ⋅ N, M = o_{uv} ⋅ N, N = o_{vv} ⋅ N
where N is the unit normal vector. Taking the cross product of o_u and o_v, we find that N = (2u, 2v, -1) / √(1 + 4u² + 4v²). Evaluating the partial derivatives of N, we obtain:
N_u = (2, 0, -4u) / √(1 + 4u² + 4v²)
N_v = (0, 2, -4v) / √(1 + 4u² + 4v²)
Substituting the values into the formula, we have:
L = (1, 0, 2u) ⋅ (2u, 2v, -1) / √(1 + 4u² + 4v²)
M = (1, 0, 2u) ⋅ (0, 2, -4v) / √(1 + 4u² + 4v²)
N = (0, 1, 2v) ⋅ (0, 2, -4v) / √(1 + 4u² + 4v²)
Simplifying the dot products, we get:
L = 2u / √(1 + 4u² + 4v²)
M = -4v / √(1 + 4u² + 4v²)
N = -4u² - 4v² / √(1 + 4u² + 4v²)
Therefore, the second fundamental form of the paraboloid parameterization is given by:
II = [L, M; M, N]
2. To compute the normal curvature and geodesic curvature of the circle (t) = (sin t, cos t, 1) on the paraboloid, we substitute the circle's parametric equations into the formulas for normal curvature and geodesic curvature.
The normal curvature (k_n) is given by the formula:
k_n = (o_{uu} ⋅ T) / |o_u|
where T is the unit tangent vector of the curve. Evaluating the derivatives and simplifying, we find:
o_{uu} = (0, 0, 2)
o_u = (1, 0, 2u)
T = (sin t, cos t, 0) / √(sin² t + cos² t + 4u²)
o_{uu} ⋅ T = 2 sin t / √(sin² t + cos² t + 4u²
)
|o_u| = √(1 + 4u²)
Hence, the normal curvature becomes:
k_n = (2 sin t) / √(1 + 4u² + 4v²)
The geodesic curvature (k_g) is given by the formula:
k_g = (o_{tt} ⋅ N) / |o_t|
where o_t is the derivative of the position vector o with respect to t. Evaluating the derivative and simplifying, we find:
o_{tt} = (0, 0, 0)
o_t = (cos t, -sin t, 0)
N = (2u, 2v, -1) / √(1 + 4u² + 4v²)
o_{tt} ⋅ N = 0
|o_t| = 1
Therefore, the geodesic curvature is zero:
k_g = 0
the second fundamental form of the paraboloid parameterization is computed by finding the coefficients L, M, and N using the derivatives of the position vector. The normal curvature of the circle on the paraboloid is given by (2 sin t) / √(1 + 4u² + 4v²), while the geodesic curvature is zero.
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The mass of planet Earth is about 5.98 x 1024 kilograms. When this number is written in standard notation, how many zeros are in the
number
Answer:
7. nn. jn. mm m. m .............
Answer:
In scientific notation, Earth's mass is 5.97×1024 kg. The 5.97 part is called the coefficient; the 24 is called the exponent.
Step-by-step explanation:
i dont know if this answered your question.
PLEASE HELP will give brainliest
HELP HELP HELP HELP
A parachutist is 500 feet above the ground. After she opens her parachute, she
falls at a constant rate of 5 feet per second. Which of these equations gives her
height (h) above the ground in terms of seconds (t).?
(Hint: She is descending)
A. y = 500x +5
B.y = -500x +5
C. y = 5x +500
D.y = -5x+500
Answer:
if it explaining it you will have to add the answer then add the x
Step-by-step explanation:with your answer whiches A
Dale made $132 for 11 hours of work.
At the same rate how many hours would he have to work to make $216
Answer:
18 hours
Step-by-step explanation:
Divide the total amount by the hours worked to find the dollars per hour rate. Next, take the amount of money you're looking for hours for and divide it by the dollars per hour rate and the quotient is the hours necessary to work to earn the money
Answer:
18 hours
Step-by-step explanation:
We can use a ratio to solve
132 dollars 216 dollars
---------------- = ------------------
11 hours x hours
Using cross products
132 x = 216 *11
132x=2376
Divide by 132
132x/132 = 2376/132
x = 18
Discuss the type of this operational problem and identify the
decision variables and objective function. Discuss the type of this
operational problem and identify the decision variables and
objective Product 1 would require a metal sheet of 0.250 {~m}^{2} , a glass sheet of 0.120 {~m}^{2} and 3 units of electrical components. Product 2 would require a metal sheet of 0.1
The given operational problem relates to production or manufacturing, with decision variables representing the quantities of the two products to be produced and an objective function representing the specific goal to be achieved (such as maximizing profit or minimizing costs).
Based on the information provided, it appears that the given scenario relates to a production or manufacturing problem. The problem involves the production of two different products, Product 1 and Product 2, and requires specific quantities of different resources or components.
Decision Variables:
The decision variables in this operational problem could include the quantities or amounts of each product to be produced. For example, let's denote the quantity of Product 1 as x and the quantity of Product 2 as y.
Objective Function:
The objective function represents the goal or objective of the problem. In this case, the objective could be to maximize or minimize a certain aspect, such as profit, production efficiency, or resource utilization. The specific objective function would depend on the specific goal of the problem. For example, if the objective is to maximize profit, the objective function could be expressed as a linear combination of the quantities produced and the associated costs and revenues.
Since the specific objective function is not provided in the question, it is not possible to determine it accurately. However, it could involve maximizing profit, minimizing production costs, or maximizing resource utilization efficiency, among other possibilities.
In summary, the given operational problem relates to production or manufacturing, with decision variables representing the quantities of the two products to be produced and an objective function representing the specific goal to be achieved (such as maximizing profit or minimizing costs).
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the eiffel tower is about 301 meters tall. cooper is making a scale model of it using the scale factor 1:750. to the nearest tenth of a meter, what will be the height of the scale model?
Cooper's Eiffel Tower scale model is about 0.4 meters tall, rounded to the nearest tenth of a meter, using the scale factor 1:750.
The Eiffel Tower is approximately 301 meters tall. Cooper is building a scale model of it using the scale factor of 1:750. To the nearest tenth of a meter, what will be the height of the scale model?
To begin, we'll need to compute the scale factor:1:750. When we look at the scale factor, we see that the model is 750 times smaller than the actual structure.
As a result, we can divide the height of the Eiffel Tower by the scale factor to obtain the height of the scale model.301 / 750 ≈ 0.40133.
We can say that the height of the scale model will be 0.4 meters, rounded to the nearest tenth of a meter. So, Cooper's Eiffel Tower scale model will be about 0.4 meters tall.
The Eiffel Tower is approximately 301 meters tall. Cooper is building a scale model of it using the scale factor of 1:750. To the nearest tenth of a meter, what will be the height of the scale model?
The actual structure of the Eiffel Tower is incredibly tall and impressive, measuring around 301 meters high. This structure is so large that it can be challenging to fathom, and Cooper has decided to build a scale model of it to assist in better understanding it.
Cooper intends to use the scale factor 1:750, which means that the scale model will be 750 times smaller than the actual structure's size. As a result, we must compute the height of the model by dividing the height of the actual tower by the scale factor.301 / 750 ≈ 0.40133.
Since the height of the Eiffel Tower is 301 meters and the scale factor is 750, we divide the two to obtain the height of the model. When we divide, we obtain an answer of roughly 0.40133.
We can round this to the nearest tenth of a meter, which is 0.4 meters, which is Cooper's Eiffel Tower scale model's approximate height.
Cooper's Eiffel Tower scale model is about 0.4 meters tall, rounded to the nearest tenth of a meter, using the scale factor 1:750. To better understand the Eiffel Tower's sheer size and beauty, it is a fantastic idea to construct a scale model that is easier to manage and comprehend.
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WILL MARK BRAINLEST!!
Answer:
Perpendicular Line : y = -3x + 6
Step-by-step explanation: Find the negative reciprocal of the slope of the original line and use the point-slope formula y-y1 = m (x-x1) to find the line perpendicular to x-3y=3.
I hope this helps you out. If not, I am really sorry.
Answer:
Perpendicular Line : y = -3x + 6
Step-by-step explanation:
Which numbers can be classified as rational? Select all that apply.
A. 56
B. 11−−−√
C. 6.565656…
D. 0.23
E. 0.32416…
F. −538
Answer:
the answer is A, D, and F
The numbers can be classified as rational are 56, 6.56, 0.23,0.32416 and -538.
It is required to choose the numbers can be classified as rational.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
A rational number can be expressed as p/q, where p and q are both integers and q ≠ 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on. if it is a decimal number then it should not be repeating and terminating. Therefore, all the rational numbers are 56, 6.56, 0.23,0.32416 and -538.
Therefore, the numbers can be classified as rational are 56, 6.56, 0.23,0.32416 and -538.
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52÷25
What is the answer :)
Answer:
2.08 this is answer
Plz help quick! And thank you to whoever helps :)
Answer:
Option c- should have added from both sides
k= 9.7
Step-by-step explanation: I dont know if i am right but hope it is xd
The Hernandez family paid $190 for 4 adult tickets and 1
child ticket to visit the Seattle Space Needle.
-The Lee family paid $130 for 2 adult tickets and 3 child
tickets for the same visit. How much was a child ticket?
How many centimeters are there in a meter?
Answer:
there are 100 centimetre in a meter.
Step-by-step explanation:
hope this
will help
you!
Answer:
100
Step-by-step explanation:
..................
Can someone tell me the answer and explanation plz I’ll give brainlist points
Answer:
5
Step-by-step explanation:
to cancel out the bottom part of the fraction, we multiply by 3. so now we have y+1= 6. we subtract 1, and get y=5
You notice you are growing awfully fast lately. You have been growing at a rate of 3 inches per year. If you are 5 feet tall now, and you continue to grow at the same rate, how many years will it take you to before you catchup to your brother who is 6 feet tall now and only growing 1 inch per year?
Answer:
4 years
Step-by-step explanation:
FYI this sounds like a personal problem
3x - 5 = 2x + 10 what is the value of x
Answer:
x = 15
Step-by-step explanation:
add 5 on both sides
subtract 2 on both sides
divide 1 on both sides
then x = 15
7/2x + 1/2x = 10 1/2 + 5/2x
Answer:x in (-oo:+oo)
(7/2)*x+(1/2)*x = (5/2)*x+101/2 // - (5/2)*x+101/2
(7/2)*x+(1/2)*x-((5/2)*x)-(101/2) = 0
(7/2)*x+(1/2)*x+(-5/2)*x-101/2 = 0
3/2*x-101/2 = 0 // + 101/2
3/2*x = 101/2 // : 3/2
x = 101/2/3/2
x = 101/3
x = 101/3
Step-by-step explanation:
Use the number line below, where RS = 8y +4, ST = 4y + 7, and RT = 107.
a. What is the value of y?
b. Find RS and ST.
Answer:
a) Finding value of y:
8y+4+4y+7=107
12y+11=107
12y =107-11
12y =96
y = 96/12
y = 8
b) RS= 8y+4
= 8(8)+4
= 64+4
= 68
ST= 4y+7
= 4(8)+7
= 32+7
= 39
A normal population has a mean of 21 and a standard deviation of 6. Use Appendix B.3. a. Compute the z value associated with 24. (Round your answer to 2 decimal places
In statistics, the "z-score" is used to determine how far away from the mean a data point is. It indicates how many standard deviations the data point is from the mean.
The formula for calculating the z-score is given below:
z = (x - μ) / σ
where: x = data point
μ = population mean
σ = population standard deviation
Given a normal population with a mean of 21 and a standard deviation of 6, we can compute the z-score associated with 24 as follows:
z = (x - μ) / σz = (24 - 21) / 6z = 0.50
To compute the z-value associated with 24, we use Appendix B.3 which gives the area under the normal distribution curve for different z-scores.
Looking at Appendix B.3, we find that the area to the left of z = 0.50 is 0.6915 (rounded to 4 decimal places). Therefore, the z value associated with 24 is 0.50.
Note: The answer has been provided in less than 100 words, but the computation involved has been thoroughly explained.
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HOW DO YOU SEE IT? Does the graph of $f$ represent inverse variation or direct variation?
A function labeled f is plotted on a coordinate plane. The x-axis is extended from negative 2 to 2, in increments of 2. The y-axis is extended from negative 4 to 4, in increments of 2. The function passes through points at ordered pair negative 1 comma negative 2 and ordered pair 2 comma 4.
Answer:
the graph of f represents a direct variation
Step-by-step explanation:
All direct variations are going to be linear functions, thus the graph of f represents a direct variation. However, I will give you a longer way to solve this problem, a more visual one, that will help understand this concept in an easier manner.
the basic formula for a direct variation is "y = k·x" and the basic formula for an inverse variation is "y = [tex]\frac{k}{x}[/tex]" (with k representing any costant)
we can solve this question by using the basic formulas to write inverse and direct variations, graph them, and see which one is the most similar to the one given in the question.
Since line f has a slope of 2, I decided to use 2 as the constant for both functions. Now we just substitute k for 2 in each function and graph it.
direct variation: y = 2x
inverse variation: y = [tex]\frac{2}{x}[/tex]
After re-writting the functions, I graphed them on desmos to see what they would look like. After comparing the original graph to the ones I created on Desmos, it can be seen that the red line graph (direct variation) is identical to the original one. Thus, the graph of f represents a direct variation.
p.s.: be familiar with teh formulas for direct and indirect variation, as they will be used a lot in the years to come (regaring math classes), even in AP Calculus
hope this helps! :)
Write the equation of a parabola with x-intercept at (3,0) and (9,0) the passes through the point (10,-7)
Answer:
[tex]y=-x^2+12x-27[/tex]
Step-by-step explanation:
The general equation of the parabola is [tex]y=ax^2+bx+c[/tex]
As the parabola passes through [tex](3,0),(9,0)[/tex]
[tex]0=9a+3b+c\,\,\,...(i)\\0=81a+9b+c\,\,\,...(ii)[/tex]
Subtract (i) from (ii)
[tex](81a+9b+c)-(9a+3b+c)=0\\72a+6b=0\\12a+b=0\\b=-12a[/tex]
Also, the parabola passes through [tex](10,-7)[/tex],
[tex]-7=100a+10b+c\,\,\,...(iii)[/tex]
Subtract (i) from (iii)
[tex](100a+10b+c)-(9a+3b+c)=-7-0\\91a+7b=-7[/tex]
Put [tex]b=-12a[/tex]
[tex]91a+7(-12a)=-7\\91a-84a=-7\\7a=-7\\a=-1[/tex]
Put [tex]a=-1[/tex] in [tex]b=-12a[/tex]
[tex]b=-12(-1)=12[/tex]
Put [tex]a=-1,b=12[/tex] in (i)
[tex]0=9a+3b+c\\0=-9+36+c\\0=27+c\\c=-27[/tex]
So, equation is [tex]y=-x^2+12x-27[/tex]
The equation of the parabola is y = -x² + 12x - 27
Parabola is the locus of a point such that the same distance from a fixed line, called the directrix, and a fixed point (the focus) is the same.
The equation of a parabola is in quadratic form. Hence it is given as:
y = ax² + bx + c
At point (3, 0):
0 = a(3²) + b(3) + c
9a + 3b + c = 0 (1)
At point (9, 0):
0 = a(9²) + b(9) + c
81a + 9b + c = 0 (2)
At point (10, -7):
-7 = a(10²) + b(10) + c
100a + 10b + c = -7 (3)
Solving equations 1, 2, 3 gives: a = -1, b = 12, c = -27
The equation of the parabola is hence y = -x² + 12x - 27
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Consider a variant of the Longest Increasing Subsequence (MIS) problem, the heaviest LIS problem. In the heaviest LIS problem, you are given a sequence a1,..., an, where each a, is a positive integer, the goal is find an increasing subsequence such that its sum is maximized. Give a O(n) algorithm for computing a heaviest LIS.
To compute a heaviest Longest Increasing Subsequence (LIS) in a given sequence efficiently with a time complexity of O(n), we can use the concept of dynamic programming.
The algorithm follows these steps: 1. Initialize two arrays, "lis" and "sum," both of size n, where n is the length of the sequence. The "lis" array will store the length of the LIS ending at each element, and the "sum" array will store the maximum sum of the LIS ending at each element.
2. Initialize the "lis" and "sum" arrays with values of 1 and the corresponding element values of the sequence, respectively.
3. Traverse the sequence from left to right. For each element, compare it with all previous elements. If the current element is greater than the previous element and the sum of the LIS ending at the previous element plus the current element is greater than the sum at the current element, update the "lis" and "sum" arrays accordingly.
4. Finally, find the element in the "sum" array with the maximum value and trace back the LIS by following the indices stored in the "lis" array.
By following these steps, we can compute a heaviest LIS in linear time, O(n), where n is the length of the input sequence. The dynamic programming approach allows us to efficiently update and store the necessary information for calculating the maximum sum.
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