The reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.
To reformulate the given linear programming problem using the big-M method, we introduce additional binary variables and big-M constants. The reformulated problem is as follows:
maximize 2x₁ + x₂ + x₃
subject to:
x₂ + x₃ + s₁ = 5
x₁ - x₂ + s₂ = 1
x₁ + x₂ + 3x₃ + s₃ = 25
x₁, x₂, x₃, s₁, s₂, s₃ ≥ 0
where s₁, s₂, and s₃ are slack variables, and we choose a large positive constant M to represent infinity.
Introducing slack variable s₁ for the inequality constraint x₂ + x₃ ≥ 5:
We add s₁ to the left-hand side of the inequality to transform it into an equation: x₂ + x₃ + s₁ = 5.
Introducing slack variable s₂ for the inequality constraint x₁ - x₂ ≥ 1:
We subtract s₂ from both sides of the inequality to transform it into an equation: x₁ - x₂ + s₂ = 1.
Introducing slack variable s₃ for the inequality constraint x₁ + x₂ + 3x₃ ≤ 25: We subtract s₃ from the left-hand side of the inequality to transform it into an equation: x₁ + x₂ + 3x₃ + s₃ = 25.
Since all variables in the original problem are non-negative (x₁, x₂, x₃ ≥ 0), we explicitly state this in the reformulation.
Therefore, the reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.
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Incomplete question:
Reformulate the following LP by the big-M method (only the reformulation is required, no need to solve the LP).
maxₓ 2x₁ + x₂ + x₃
s.t.
x₂+x₃ ≥ 5
x₁ - x₂ ≥ 1
x₁ + x₂+ 3x₃ ≤ 25
x₁, x₂, x₃ ≥0
help with questions 10-13 plz!!
Answer:
._. ;
._. ;
._. ;
A medical team randomly selects people in an area, until he finds a person who has a corona virus, Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus?
Answer : i) The probability of finding the first case in 4 trials is 0.1024 ii) The probability that the team must select more than 6 people before finding one who has a corona virus is 0.4095.
Explanation : Given information:Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success.
(i) What is the probability that the team must select 4 people until he finds one who has a corona virus?
The number of trials required until the first success follows geometric distribution.
The probability of finding the first case in 4 trials is: P(X = 4) = q^3p, where q = 1 - p. We have p = 0.2 and q = 0.8. So, P(X = 4) = 0.8^3 × 0.2 = 0.1024
(ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus? P(X > 6) = 1 - P(X ≤ 6) The probability of finding the first case in the first 6 trials is:P(X ≤ 6) = 1 - q^6p= 1 - 0.8^6 × 0.2= 0.59049P(X > 6) = 1 - P(X ≤ 6)= 1 - 0.59049= 0.4095 Therefore, the probability that the team must select more than 6 people before finding one who has a corona virus is 0.4095.
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Which golf ball went higher, and how many feet? (Desmos!)
Answer:
1. 36
2. Second
Step-by-step explanation:
- For the first ball, we can see the given function:
[tex]f(x)=-16(t^{2}-3t )[/tex]
[tex]=-16[t^{2} -3t+(3/2)^{2}-(3/2)^{2} ][/tex]
[tex]=-16(t-\frac{3}{2} )^{2} +(-\frac{3}{2} )^{2} *(-16)[/tex]
[tex]-16(t-\frac{3}{2} )^{2} +36[/tex]
So the vertex is ([tex]\frac{3}{2}[/tex], 36), it means when the ball was hit by the [tex]\frac{3}{2}[/tex] seconds, it arrived at the highest height of 36 feet.
- For the second ball, we can see the given graph: the vertex is (2,64), it means when the ball was hit by the 2 seconds, it arrived at the highest height of 64 feet.
- Compare to the two heights, 36 (first ball) is less than 64 (second ball), so the second ball went higher.
who are these bots giving us links i’m literally gonna fail now
Answer:
Fr. It’s annoying. My mom yells at me for not passing lolz.
Step-by-step explanation:
Answer:
Ignore them and re-upload the questions. The links are very bad.
Step-by-step explanation:
[tex]\left \{ {{x=3} \atop {y+1=0}} \right.[/tex] solve graphically this linear system of equations
Answer:
The solution is the point (3, -1)
Step-by-step explanation:
We have the system of equations:
x = 3
y + 1 = 0
To solve this graphically, we need to graph these two lines and see in which point the lines intersect.
To graph the line x = 3, we need to draw a vertical line that passes through x = 3.
To graph y + 1 = 0
First we should isolate y.
y = -1
This is graphed as a horizontal line that passes through y = -1
The graph of these two lines can be seen in the image below.
Where the green line is x = 3, and the blue line is y = -1
Now, looking at the graph we can see that the lines do intersect in the point (3, -1)
Then the solution of the system is the point (3, -1)
NOLINKS ..................
Answer:
The answer is in the link
Step-by-step explanation:
quntyfcjb/crown!.com :))))
A bakery produces five types of bagels, two of which are chocolate chip and cinnamon raisin.
(a) If there are at least 10 bagels of each type, how many different selections of 10 bagels are there?
(b) Suppose there are only 3 chocolate chip and 2 cinnamon raisin bagels, but at least 10 of the other three types. How many different selections of 10 bagels are there?
a) If there are at least 10 bagels of each type, we can calculate the number of different selections of 10 bagels by using the concept of combinations. Since there are 5 types of bagels and we need to select 10 bagels, the calculation can be done as follows:
[tex]\(\binom{10+5-1}{10} = \binom{14}{10}\)[/tex]
b) If there are 3 chocolate chip and 2 cinnamon raisin bagels, and at least 10 of the other three types, we can calculate the number of different selections of 10 bagels using the same concept of combinations. In this case, we have 3 types of bagels (excluding chocolate chip and cinnamon raisin) with at least 10 bagels each. So the calculation becomes:
[tex]\(\binom{10+3-1}{10} = \binom{12}{10}\)[/tex]
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2.1. let a be the event that 2 consecutive flips both yield heads and let b be the event that the first or last flip yields tails. prove or disprove that events a and b are independent.
The events A and B are not independent. The occurrence of event B affects the probability of event A.
To determine whether events A and B are independent,
we need to check if the probability of event A occurring is affected by the occurrence of event B, and vice versa.
Probability of event A: Since we are flipping two coins,
the probability of getting heads on each flip is 1/2.
Therefore, the probability of getting two consecutive heads is
[tex](1/2) \times (1/2) = 1/4[/tex]
Probability of event B: The first or last flip yielding tails means there are two possibilities:
either the first flip is tails and the second flip is any outcome,
or the first flip is any outcome and the second flip is tails.
Each of these individual possibilities has a probability of
[tex](1/2) \times (1/2) = 1/4[/tex]
Hence, theprobability of event B is 1/4 + 1/4 = 1/2.
Since the probability of event A is 1/4 and the probability of event B is 1/2, and 1/4 ≠ 1/2,
we can conclude that events A and B are not independent.
The occurrence of event B (first or last flip yielding tails) affects the probability of event A (two consecutive flips yielding heads).
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Suppose that 5 people should be randomly selected from a group of 20 forming couples by 10. What is the probability that the 5 unrelated chosen from related persons (that is, no chosen person be a couple)?
The probability that none of the 5 randomly selected individuals are part of a couple is 0.016.
What is the probability that none of the 5 randomly selected individuals are part of a couple?A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.
We will know total number of possible outcomes when selecting 5 individuals from a group of 20. This can be calculated using the combination formula:
C(20, 5) = 20! / (5! * (20 - 5)!)
C(20, 5) = 15,504
We know that when we select an individual, we are removing their corresponding partner from the pool of available choices. This means that for each individual we choose, the number of available choices decreases by 1.
The number of favorable outcomes can be calculated as follows:
= 20 * 18 * 16 * 14 * 12
= 967,680
The probability will be:
= Outcomes / Favorable outcomes
= 15,504 / 967,680
= 0.01602182539
= 0.016.
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can i get an owa owa ?????
owa owa???
owa owa??
OWA OWA??
OWA OWA??
OWA OWA?The volume of this cylinder is 4,939.22 cubic millimeters. What is the height? Use a 3.14 and round your answer to the nearest hundredth.
Answer:
13 mm
Step-by-step explanation:
V = πr²h
4,939.22 mm³ = 3.14 × (11 mm)²h
4,939.22 mm³ = 3.14 × (11 mm)²h
h = 13 mm
Answer: 13 mm
How many permutations of S9, have cycle strucrure 3^3?
There is only 1 permutation in S9 with a cycle structure of [tex]3^3[/tex].
To find the number of permutations of S9 with a cycle structure of [tex]3^3[/tex], we can use the concept of cycle index.
In a permutation with a cycle structure of[tex]3^3[/tex], we have three cycles of length 3. The cycle index of S9 with respect to cycles of length 3 can be determined using the Polya enumeration theorem.
The cycle index of S9 with respect to cycles of length 3 is given by:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3[/tex]
Expanding this expression, we get:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3\\\= (t1^9 + 3t1^6t3^3 + 3t1^3t3^6 + t3^9)[/tex]
To count the number of permutations with the desired cycle structure, we need to find the coefficient of the term [tex]t1^9t3^9[/tex].
From the expanded form, we see that the coefficient [tex]t1^9t3^9[/tex] is 1.
Therefore, there is only one permutation in S9 with a cycle structure of [tex]3^3[/tex]
In summary, there is 1 permutation of S9 that has a cycle structure of [tex]3^3[/tex].
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A solid object has the right triangle with vertices (0, 0), (3, 0), and (0, 4) as its base.
a) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x-axis, is a square. Find the volume of the solid.
b) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x -axis, is a smi-circle. Find the volume of the solid.
a. The volume of the solid is 24 cubic units.
b. The volume of the solid is 4π cubic units.
How to calculate tie valuea. Volume = Area of Base * Height
The base is a right triangle with base length of 3 units and height of 4 units. The area of the base can be calculated as:
Area of Base = (1/2) * base * height
= (1/2) * 3 * 4
= 6 square units
The height of the solid is 4 units.
Volume = Area of Base * Height
= 6 * 4
= 24 cubic units
b) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x-axis, is a semicircle.
Volume = (1/2) * π * radius² × height
Volume = (1/2) * (1/2) * π * 2² * 4
= (1/4) * π * 4 * 4
= π * 4
Therefore, the volume of the solid is 4π cubic units.
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Could someone please help me with this !
And also show work
Answer: C. K= 2.5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
[tex]\Huge\boxed{k=2.5}[/tex]
Step-by-step explanation:
Given -2.1k + 13 + 6.5k = 24 we need to isolate the variable using inverse operations
step 1 combine any like terms
sometimes there are not like terms but in this case there are. When there are like terms (must be on the same side of the = ) you add them together
-2.1k + 6.5k = 4.4k
now we have
4.4k + 13 = 24
Now we want to get rid of the 13
To do so we subtract 13 from each side
13 - 13 cancels out
24 - 13 = 11
now we have 4.4k=11
now we want to get rid of the 4.4
To do so we divide each side by 4.4
4.4k/4=k
11/4.4=2.5
we're left with k - 2.5
Find all possible trigonometric ratios given the following:
tan θ = -7/24 and cos θ > 0
The given information allows us to find the values of trigonometric ratios involving angle θ. Given that tan θ = -7/24 and cos θ > 0, we can determine the following trigonometric ratios: sin θ, csc θ, sec θ, and cot θ
We are given that tan θ = -7/24. Using this information, we can determine the values of sin θ and csc θ.
Since tan θ = sin θ / cos θ, we can write -7/24 = sin θ / cos θ. Rearranging the equation, sin θ = -7 and cos θ = 24.
Now, we can find the values of csc θ, sec θ, and cot θ.
csc θ is the reciprocal of sin θ, so csc θ = 1 / sin θ = 1 / (-7) = -1/7.
To find sec θ, we use the fact that sec θ = 1 / cos θ. So, sec θ = 1 / (24) = 1/24.
Lastly, to calculate cot θ, we know that cot θ = 1 / tan θ. Thus, cot θ = 1 / (-7/24) = -24/7.
In summary, given tan θ = -7/24 and cos θ > 0, we have sin θ = -7, csc θ = -1/7, sec θ = 1/24, and cot θ = -24/7.
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Select all the figures that are shaded to represent 60% of the whole. Whoever answers correctly and first will be marked as brainliest!!!!
Answer:
the first one
Step-by-step explanation:
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps. 7. What is the radius? 8. What is the circumference? 9. What is the area?
Answer:
7. 13.25mm
8. 83.25 mm
9. 551.55 mm²
Step-by-step explanation:
The shape of a coin is circular.
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps.
7. What is the radius?
The formula for radius = Diameter/2
= 26.5 mm/2
= 13.25 mm
8. What is the circumference?
The formula for the circumference of a circle = 2πr
= 2× π × 13.25mm
= 83.25220532 mm
Approximately to the nearest hundredth = 83.25 mm
9. What is the area?
The formula for the area of a circle = πr²
= π × (13.25mm)²
= 551.54586025 mm²
Approximately to the nearest hundredth = 551.55 mm²
select the correct answer. which expression is equivalent to x 3x2−2x−3÷x2 2x−3x 1 if no denominator equals zero? a. 1x2−2x−3 b. 1x2−4x 3 c. 1x2 2x−3 d. x 3x 1
The correct answer is option c. 1/(x² + 2x - 3). To determine which expression is equivalent to the given expression, let's simplify it step by step:
The given expression is (x³ - 2x - 3) ÷ (x² + 2x - 3).
Option a. 1/(x² - 2x - 3):
This option is not equivalent to the given expression because it represents the reciprocal of the quadratic denominator, which is different from the given expression.
Option b. 1/(x² - 4x + 3):
This option is not equivalent to the given expression because the signs of the quadratic terms are different. The given expression has a positive quadratic term, while this option has a negative quadratic term.
Option c. 1/(x² + 2x - 3):
This option is equivalent to the given expression because it represents the reciprocal of the quadratic denominator with the same signs for the quadratic terms.
Option d. x/(3x - 1):
This option is not equivalent to the given expression because it lacks the term x³ in the numerator.
Therefore, the correct answer is option c. 1/(x² + 2x - 3).
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ms.Rivera went to dinner for new year's eve the meal and sodas cost a total of $138 the sales tax in new york state is about 8% and ms Rivera wanted to leave a 20% tip because the service was good. What was the total cost of the meal
Answer:
138 + 27.6 = 165.6
Step-by-step explanation:
Please give brainliest
PLEASE HELP ME!!!! I WILL MARK!!!
Answer:
6(x - 3 ) = 6x - 18
2(3x - 3) = 6x - 6
Step-by-step explanation:
What is the lyrics for its good to be alive by among us?
Answer:
HEHEHEHEHEH
I've been waiting for this moment
Feels good to be alive right about now
Good, good, good, good to be alive right about now
Good, good, good, good to be alive right about now
Hallelujah, let that bass line move ya, say hey
Step-by-step explanation:
Have fun
I need help on the circled problem please
Answer:
There would be infinite solutions because the equations are exactly the same.
I hope this answered your question
2. Find the area of a circle with a diameter of 10
feet.
Step-by-step explanation:
d=2r
πr^2
10/2=r
5=r
5^2π
25π=78.5398
Hope that helps :)
IM GIVING BRAINLIEST!!PLEASE HELP!!
Answer: c
Step-by-step explanation:
Find the surface area of the prism.
7 cm
13 cm
5 cm
12 cm
The surface area is
Answer:
please give more information
Step-by-step explanation:
please someone answer fast!!! I'm so confused and this is due today
Answer:
From greatest to least it would be 3.66666,[tex]\sqrt{11}[/tex],2(1/4),-2.5,-3.97621
Step-by-step explanation:
Just type in a calc
Answer:
[tex]\sqrt{11}=3.31[/tex], -2.5, [tex]2\frac{1}{2}= 2.25[/tex], 3.6, -3.97621...
Step-by-step explanation:
Greatest to least would be:
3.6, [tex]\sqrt{11}[/tex], [tex]2\frac{1}{4}[/tex], -2.5, -3.97621...
Least to greatest would be:
-3.97621, -2.5, [tex]2\frac{1}{4}[/tex], [tex]\sqrt{11}[/tex], 3.6
Hopefully, that helps.
Find the flux of the given vector field F across the upper hemisphere x^2 + y^2 + z^2 = a^2, z >= 0. Orient the hemisphere with an upward-pointing normal.
19. F= yj
20. F = yi - xj
21. F= -yi+xj-k
22. F = x^2i + xyj+xzk
6πa² is the flux of F across the upper hemisphere.
The problem requires us to compute the flux of the given vector field F across the upper hemisphere x² + y² + z² = a², z ≥ 0. We are to orient the hemisphere with an upward-pointing normal. The four vector fields are:
F = yj
F = yi - xj
F = -yi + xj - kz
F = x²i + xyj + xzk
To begin with, we'll make use of the Divergence Theorem, which states that the flux of a vector field F across a closed surface S is equivalent to the volume integral of the divergence of the vector field over the region enclosed by the surface, V, that is:
F · n dS = ∭V (div F) dV
where n is the outward pointing normal unit vector at each point of the surface S, and div F is the divergence of F.
We'll need to write the vector fields in terms of i, j, and k before we can compute their divergence. Let's start with the first vector field:
F = yj
We can rewrite this as:
F = 0i + yj + 0k
Then, we compute the divergence of F:
div F = d/dx (0) + d/dy (y) + d/dz (0)
= 0 + 0 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Now, let's move onto the second vector field:
F = yi - xj
We can rewrite this as:
F = xi + (-xj) + 0k
Then, we compute the divergence of F:
div F = d/dx (x) + d/dy (-x) + d/dz (0)
= 1 - 1 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Let's move onto the third vector field:
F = -yi + xj - kz
We can rewrite this as:
F = xi + y(-1j) + (-1)k
Then, we compute the divergence of F:
div F = d/dx (x) + d/dy (y(-1)) + d/dz (-1)
= 1 - 1 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Lastly, let's consider the fourth vector field:
F = x²i + xyj + xzk
We can compute the divergence of F directly:
div F = d/dx (x²) + d/dy (xy) + d/dz (xz)
= 2x + x + 0 = 3x
Then, we express the surface as a function of spherical coordinates:
r = a, 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π/2
Note that the upper hemisphere corresponds to 0 ≤ φ ≤ π/2.
We can compute the flux of F over the hemisphere by computing the volume integral of the divergence of F over the region V that is enclosed by the surface:
r² sin φ dr dφ dθ
= ∫[0,2π] ∫[0,π/2] ∫[0,a] 3r cos φ dr dφ dθ
= ∫[0,2π] ∫[0,π/2] (3a²/2) sin φ dφ dθ
= (3a²/2) ∫[0,2π] ∫[0,π/2] sin φ dφ dθ
= (3a²/2) [2π] [2] = 6πa²
Therefore, the flux of F across the upper hemisphere is 6πa².
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A triangle has three angles that measure 15 degrees, 85 degrees and (4x - 20). What is the value of x?
1. Identify the Parent function related to the given function. Choose the correct answer from the choices below:
f(x)=1/2x-9 4/5
Linear Function
Not a Function
Absolute Value Function
Quadratic Function
This equation shows how the amount of time that a receptionist named Terrence spends on the phone is related to the number of phone calls he routes to employees.
t = p + 17
The variable p represents the number phone calls he routes, and the variable t represents the number of minutes he is on the phone. In all, how many phone calls does Terrence have to route to spend a total of 20 minutes on the phone?
phone calls
hmmm I dunno sorry ......