75th Percentile = 45 means that 75% of the observations are values less than or equal to 45.
To calculate the 75th percentile, we arrange the observations in ascending order and find the value at which 75% of the data falls below. In this case, the 75th percentile is 45, indicating that 75% of the observations have values less than or equal to 45.
In other words, if we have a dataset with 100 observations, the 75th percentile value would be the value that separates the top 25% (from observation 76 to 100) from the bottom 75% (from observation 1 to 75), and that value is 45.
the statement "75th Percentile = 45" means that 75% of the observations in the dataset have values less than or equal to 45.
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I NEED HELP ASAP IN ON TIMER!!!!
What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2 ?
A. square the binomial (x + 3), distribute the negative to the binomial (x2 + 9), simplify the dividend, and then divide divide,
B. square the binomial (x + 3), distribute the negative to the binomial (x2 + 9), and then simplify the dividend
C. square the binomial (x + 3), divide, distribute the negative to the binomial (x2 + 9), and then simplify the dividend
D. square the binomial (x + 3), distribute the negative to the binomial (x2 + 9), divide, and then simplify the dividen
Answer:
A: square the binomial (x + 3), distribute the negative to the binomial (x2 + 9), simplify the dividend, and then divide
Step-by-step explanation:
I just took the test
Answer:
A. square the binomial (x + 3), distribute the negative to the binomial (x2 + 9), simplify the dividend, and then divide
Step-by-step explanation:
I got 100%
Two numbers are each a distance of 3 units away from another number. The other number is 5. Write an absolute value equation to represent the two numbers
Answer:
I
Step-by-step explanation:
I am not sure but I will tell if u would like me to say
Problem 775702: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming season. Zed and Adrian estimate that the demand for bicycles this season will be 20,30,40, or 50 bicycles with probabilities of 0.2,0.4,0.3, and 0.1 respectively. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20,$60 if they order 40,$52 if they order 60 . The bicycles will be sold for $76 each if they are not on sale. Any bicycles left over at the end of the season will go on sale and will be sold at $46 each. Create a payoff table that helps Z to A Bicycle decide how many bicycles (20,40, or 60) to order. Complete the Following Payoff Table:
To create the payoff table, we need to consider the different combinations of order quantities and demand scenarios and calculate the corresponding profits or losses. The table will have rows representing the order quantities (20, 40, and 60) and columns representing the demand scenarios (20, 30, 40, and 50).
For each combination, we calculate the profit or loss based on the given costs and selling prices. If the order quantity is greater than the demand, the excess bicycles will be sold at the sale price. If the order quantity is less than the demand, there will be unmet demand In the table, the numbers represent the profit or loss in dollars. Negative numbers indicate losses, and positive numbers indicate profits. The values are calculated by multiplying the difference between the selling price and the cost per bicycle by the demand probability for each scenario. By analyzing the payoff table, Zed and Adrian can determine the order quantity that maximizes their expected profit or minimizes their expected loss based on the probabilities and associated payoffs.
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simplify the expression:
2 (3 + m) =
Answer:
6 + 2m
Step-by-step explanation:
You need to use the distributive property - multiply the outside number by each inside value or variable
So: 2 times 3 = 6 and 2 times m = 2m
Put it all back together: 6 + 2m
Answer:
6m
Step-by-step explanation:
#15
Hi there,
I would really appreciate it if someone could help me solve
these . PLEASE SHOW YOUR WORK, so I can understand much
better.
thank you, advance
Find the volume of the figure, where x = 30 cm and h = 27 cm. Give the exact answer and an approximation to the nearest hundredth. cm³ cm3 X Right regular triangular pyramid ≈
The radius of a circle with an area of 289 cm² can be found by taking the square root of the area divided by π.
The area of a circle is given by the formula A = πr², where A represents the area and r represents the radius of the circle. In this case, the area is given as 289 cm². To find the radius, we rearrange the formula to solve for r.
We start by dividing both sides of the equation by π, which gives us A/π = r². Substituting the given area of 289 cm², we have 289/π = r².
To find the radius, we take the square root of both sides of the equation, which gives us √(289/π) = r.
Calculating the square root of 289 gives us 17, and the square root of π is an irrational number, approximately 1.7725. Thus, the radius of the circle is approximately 17/1.7725 = 9.59 cm.
Therefore, the radius of the circle with an area of 289 cm² is approximately 9.59 cm.
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Find the radius of a circle that has an area of 289 cm². 10 x cm
Please help I’ll give brainiest!
Make sure to tell me steps by steps!:D
Answer:
see below
Step-by-step explanation:
h(x) = 2x-10
Let x=3
h(3) = 2*3 -10
= 6-10
=4
Let x=-3
h(-3) = 2*-3 -10
= -6-10
=-16
Sarah was 50 1/4 inches tall when she was 12 years old. she was 48 1/2 inches tall when she was 11. how much did she grow during the year?
Solve the following LP problem using the simplex method. Minimize z=4x 1−x 2 Subject to
2x 1 +x 2 ≤8
x 2 ≤5
x 1 −2x 2 ≤4
x 1 ,x 2 ≥0
The minimum value of z is 17, and the optimal values of x1 and x2 are 5 and 3, respectively.
To solve the given linear programming problem using the simplex method, let's set up the initial tableau:
Cj 4 -1 0
-----------------
|
2 | 1 1 <= 8
1 | 0 1 <= 5
0 | 1 -2 <= 4
Here, Cj represents the coefficients of the objective function z, and the bottom row represents the right-hand side (RHS) values of the constraints.
Step 1: Select the most negative coefficient in the bottom row as the pivot column. In this case, it is -2.
Step 2: Determine the pivot row by selecting the smallest non-negative ratio from the RHS values divided by the corresponding entries in the pivot column. In this case, the smallest ratio is 4/(-2) = -2.
Step 3: Perform the pivot operation to make the pivot element (in this case, -2) equal to 1 and eliminate all other elements in the pivot column. The pivot row becomes the new row with the pivot element.
Pivot column: x2
|
2 | 1 1 <= 8
1 | 0 1 <= 5
0 | 1 -2 <= 4
Pivot row: R2
|
2 | 1 1 <= 8
0 | 0 1 <= 3
0 | 1 -2 <= 4
Step 4: Update the tableau by performing elementary row operations to eliminate other elements in the pivot column.
|
2 | 1 1 <= 8
0 | 0 1 <= 3
0 | 1 -2 <= 4
R1 = R1 - R2
|
2 | 1 0 <= 5
0 | 0 1 <= 3
0 | 1 -2 <= 4
Step 5: Check if the current solution is optimal. If there are no negative coefficients in the top row (except for z = 0), the solution is optimal. In this case, the solution is optimal since all coefficients are non-negative.
Step 6: Read the optimal solution from the tableau. The values of x1 and x2 can be found in the right-most column of the variables' columns.
Optimal solution:
x1 = 5
x2 = 3
Step 7: Calculate the value of the objective function z using the optimal solution.
z = 4x1 - x2
z = 4(5) - 3
z = 20 - 3
z = 17
Therefore, the minimum value of z is 17, and the optimal values of x1 and x2 are 5 and 3, respectively.
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Can someone please solve these brain teasers?
Answer:
more info
Step-by-step explanation:
we need more info for these questions or we will just get confused
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
Q2/The following data for an IC engine:-mrod= 1.3 kg.Lord =200 mm.Cg of rod at 60 mm from crank pin centre.Mp=0.96kg.λ=0.25lf the piston area Ap =4x10-3 m2, engine speed 3000 RPM, the gas pressure given by the indicator diagram as shown in the following table 0 0 350 630 720 5 points P • 2 -0.25 C 1 ° the torque of the engine at TDC 157 N.m zero N zero N.m 157 N
The given data provides information about an IC engine, including the mass of the connecting rod (mrod), length of the connecting rod (Lord), center of gravity of the rod (Cg), mass of the piston (Mp), piston area (Ap), engine speed (3000 RPM), and gas pressure at various points in the indicator diagram. We are asked to determine the torque of the engine at top dead center (TDC).
To calculate the torque of the engine at TDC, we need to consider the forces acting on the connecting rod and the piston. The torque can be determined using the equation:
Torque = Force × distance
First, we calculate the force acting on the connecting rod. The force can be obtained using the equation:
Force = Mass × acceleration
The acceleration can be determined using the equation:
Acceleration = (Change in velocity) / time
Since the engine speed is given as 3000 RPM, we convert it to radians per second:
Angular Velocity = (3000 RPM) × (2π radians / 1 minute) × (1 minute / 60 seconds) = 100π radians/second
We can calculate the change in velocity by subtracting the velocity at TDC from the velocity at the given point on the indicator diagram. Then we divide the change in velocity by the time period.
Next, we can determine the distance from the center of the crankshaft to the center of the connecting rod (crank radius) using the given length of the connecting rod and the position of the center of gravity of the rod.
Finally, we can calculate the torque at TDC by multiplying the force acting on the connecting rod by the crank radius.
By following these calculations, we can determine the torque of the engine at top dead center (TDC) based on the given data.
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Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
P
50⁰
5 R
A. SAS theorem
50°
B. Similarity cannot be determined.
OC. AA postulate
D. SSS theorem
15
Zo
The similarity theorem used for this problem is given as follows:
A. SAS theorem.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
The sides forming a proportional relationship are given as follows:
3 and 9.5 and 15.The angle of 50º between these two sides also forms a proportional relationship, hence the SAS theorem can be used.
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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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Solve the applied problem.
A radiator contains 8 quarts of fluid, 40% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze?
Answer:
8(.4) + .4a - a = .6(8)
3.2 - .6a = 4.8
.6a = 1.6, so a = 2 2/3 quarts
Find the midpoint of the segment with endpoints of
(1,0), (-2,-4)
Answer:
The midpoint is ( -1/2, -2)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( 1+-2)/2 = -1/2
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
( 0+-4)/2 = -4/2=-2
The midpoint is ( -1/2, -2)
Given sin(theta) = -3/7 and tan(theta) > 0, what are all 6 exact trig values and what is the corresponding quadrant and point on the circle?
Given[tex]sin(theta) = -3/7 and tan(theta) > 0[/tex].The value of sin(theta) is negative and the value of tan(theta) is positive. We know that sin(theta) = opposite/hypotenuse and tan(theta) = opposite/adjacent.
In this case, we can use the Pythagorean theorem to find the value of the adjacent side of the triangle formed.Using the Pythagorean theorem, we can find the value of the adjacent side:
[tex]7² - 3² = 40Adjacent = √40 = 2√10[/tex]
The six trigonometric values are:
[tex]sin(theta) = -3/7, \\cos(theta) = 2√10/7,\\ tan(theta) = -3/2√10, \\csc(theta) = -7/3, \\sec(theta) = 7/2√10, \\cot(theta) = -2√10/3[/tex]
The value of sin(theta) is negative, which means that the angle is in the third or fourth quadrant. Since the value of tan(theta) is positive, the angle must be in the fourth quadrant. Using the coordinates on the unit circle, we can find the corresponding point.
We know that sin(theta) = y and cos(theta) = x. Plugging in the values we get:
[tex]sin(theta) = -3/7 and cos(theta) = 2√10/7[/tex]
The corresponding point on the unit circle is (2√10/7, -3/7)
Therefore, the six exact trigonometric values are:
sin(theta) = -3/7, cos(theta) = 2√10/7, tan(theta) = -3/2√10, csc(theta) = -7/3, sec(theta) = 7/2√10, cot(theta) = -2√10/3.
The angle is in the fourth quadrant and the corresponding point on the circle is (2√10/7, -3/7).
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PLEASE HELP I WILL MARK YOU BRAINLIEST PLEASE
Answer: 2286 ^2 ft
Step-by-step explanation:
Answer:
the answer is 3182540.hope this helps
pls help its rq ill give u brainliest
Answer:
Option 2
Step-by-step explanation:
Joshua is designing a rectangular mirror. He let w = the width, in inches, of the mirror. The length of the mirror will be 6 inches more than the width. The perimeter of the mirror will be less than 96 inches and greater than 76 inches. Which of the following inequalities shows the possible widths, in inches, of the mirror?
Answer:
16 < w < 21
Step-by-step explanation:
Given that :
Width if mirror = w
Length of mirror = l
L = 6 + w
Perimeter of mirror < 96 and > 76
Possible width of the mirror
Perimeter of a rectangle :
2(l + w)
2(6 + w + w)
= 2(6 + 2w)
= 12 + 4w
Hence,
76 < perimeter < 96
76 < 12 + 4w < 96
76 - 12 < 4w < 96 - 12
64 < 4w < 84
16 < w < 21
scores on a test are normally distributed with a mean of 109 and a standard deviation of 15. what percentage of scores are greater than 154?
The percentage of scores that are greater than 154 on the test is approximately 0.13%.
To find the percentage of scores that are greater than 154 on a test with a normal distribution, we can use the properties of the standard normal distribution.
First, we need to standardize the value of 154 by converting it into a z-score. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
In this case, x = 154, μ = 109, and σ = 15.
Calculating the z-score:
z = (154 - 109) / 15
z = 45 / 15
z = 3
Now that we have the z-score, we can use a standard normal distribution table or a calculator to find the percentage of scores greater than 154.
Looking up the z-score of 3 in the standard normal distribution table, we find that the area to the left of z = 3 is approximately 0.9987.
Since we want to find the percentage of scores greater than 154, we subtract the area to the left from 1 to get the area to the right.
Area to the right = 1 - 0.9987 = 0.0013
Converting this to a percentage:
Percentage = 0.0013 * 100 = 0.13%
Therefore, approximately 0.13% of scores are greater than 154 on this test.
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PLEASE HURRY
Given the logical argument:
If the cat eats guacamole, then he will be happy.
The cat ate guacamole.
Therefore, the cat is happy.
The conclusion of this argument was formed using the Law of...
Syllogism
Contrapositive
Detachment
Answer:
I believe it's Syllogism
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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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:
Which statement below explains why the graph below is not a function?
A. The input of X=1 has to outputs Y=1 and y=2 so it is not a function.
_____________________
B. Each input has exactly 1 output so it is not a function.
____________________
C.The output y=1 occurs twice so it is not a function.
_____________________
D.Trick question- it is a function.
Answer:
the answer is a
Step-by-step explanation:
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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( Will give Brainliest) please Helpp
Answer:
See explanation
Step-by-step explanation:
Step 1: Write equation
n - 4 = -15
Step 2: Solve for n
n = -11
3)
Convert 8 quarts into liters. Round your answer to the nearest tenth
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (mL)
Answer:
7.6 liters
Step-by-step explanation:
The required converted value is 7.6 liters, which is 8 quarts into liters.
To convert 8 quarts into liters, we can use the following conversion factors:
1 quart (qt) = 4 cups (cups)
1 cup (cup) = 8 fluid ounces (fl oz)
1 fluid ounce (fl oz) = 29.574 milliliters (mL)
1 liter (L) = 1000 milliliters (mL)
First, let's convert quarts to cups:
8 quarts x 4 cups/quart = 32 cups
Next, convert cups to fluid ounces:
32 cups x 8 fl oz/cup = 256 fl oz
Now, convert fluid ounces to milliliters:
256 fl oz x 29.574 mL/fl oz = 7570.94 mL
Finally, convert milliliters to liters:
7570.94 mL / 1000 mL/L = 7.57094 L
Rounded to the nearest tenth, 8 quarts is approximately 7.6 liters.
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The complete question is as follows:
Convert 8 quarts into liters. Round your answer to the nearest tenth
*Note: you must use these exact conversion factors to get this question right.
1 cup (cup) = 8 fluid ounces (fl oz)
1 liter (L) 1000 milliliters (mL)
1 pint (pt) = 2 cups (cups)
1 cubic meter (m³) = 1000 liters (L)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)
1 cubic foot (ft³) = 7.481 gallons (gal)
Which of the following is the solution to the inequality below? -6/5(4-x)<-4(x+1/2)
Answer:
x < 7 /13
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Wendy has taken two tests with scores of 77 and
80. To get an 82 average, what must her grade be
on the third test?
Answer:
Her grade must be an 89 or better
Step-by-step explanation:
to find the average you add all the numbers than divide but the total numbers of numbers so when she had the first two test her average was an 78.5 if she has an 85 it is close to the 80's but still less than but if she has a 90 she is averaged to be about 85 so if she gets an 89 she has an exact average of 82
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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