Pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
Given that
Let z* be the common (finite) optimal value of P and D.
Suppose that I is a basic infeasible solution to P whose complementary dual basic solution is feasible.
Here, for linear program, we have to
Minimize {x1 : 2x1 - x2 [tex]\geq[/tex] 0, -2x1 + 3x2 [tex]\geq[/tex] - 6}, x1 [tex]\geq[/tex] 0
Stimulate equation 1 and equation 2:
[tex]2x_1 - x_2 = 0\\\\-2x_1 + 3x_2 = -6[/tex]
Canceling [tex]-2x_2[/tex] from both the equations, we get
[tex]2x_2[/tex] = -6
= [tex]x_2[/tex] = -3
So now,
[tex]2x_1 + 3 + S_1 = 0\\\\x_1 = -3-S_1/2[/tex]
Hence the answer is pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
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a couple has three children. assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? a. 1 b. .125 c. .5 d. .875
Answer:
d. 0.875
Step-by-step explanation:
Having at least 1 girl out of 3 children means that there can be 1, 2 or 3 girls out of the 3 children.
So having at lest 1 girl out of 3 children is the same as saying that all 3 children are not boys.
The probability that all 3 children are boys would be
chance that child 1 is a boy * chance that child 2 is a boy * chance that child 3 is a boy = 0.5 * 0.5 * 0.5 = 0.125
And the probability that NOT all 3 children are boys would be
100% - probability that all 3 children are boys = 1 - 0.125 = 0.875
an undirected graph is defined to be biconnected if it is connected and has no articulation points. describe a test for biconnectedness that uses dfs. could you also use bfs to answer this question
Depth first search (DFS) is an algorithm for reversing traversing or searching tree or graph data structures.
If there are two vertex-disjoint paths connecting any two vertices, the graph is biconnected .A straightforward cycle passes through any two vertices in a biconnected graph.
If a connected graph is connected but does not have any Articulation Points, it is Biconnected .In a graph, we mostly need to check two things.
1.The chart is associated.
2.There isn't enunciation point in diagram.
DFS traversal commences at any vertex. We check to see if there is an articulation point during DFS traversal .
The graph is biconnected if no articulation points are found. Lastly, we must determine whether DFS was able to reach all vertices. The graph would not even be connected if none of its vertices could be reached.
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One day the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. How far did the water level drop during the week?
If the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. The water level drop during the week is 23 cm.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that one day the latter's water level was 35 cm above the mark. It was 12 cm below the mark one week later.
We have to apply the subtraction operation for the given operation,
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
=35 - 12
=23 cm
Thus, if the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. The water level drop during the week is 23 cm.
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please help
It's really important
How to answer: You divide the first number by the second number
a) 85.50/7=12.21
b) 76.00/6=12.67 or 12.6 repeating
c) 120/10= 12
d) 30/0.5= 60
e) 6/2.40= 2.5
f) 399/3= 133
g) 3/2.25= 1.33 or 1.3 repeating
h) 400/5= 80
i) 43.80/5.5=7.7182 or 7.718 (the 18 repeating)
I hope this helped
Wo familie viited an amuement park. The firt family bought 4 hot dog and 6 bottle of water, which totaled $22. The econd family bought 8 hot dog and 3 bottle of water, which totaled $35. How much did one hot dog cot?
The cost of one hot dog would be $4 and the cost of one water bottle would be $1.
What are the linear equations in two variables?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.
Let the cost of one hot dog be 'x' dollars and the cost of one water bottle be 'y' dollars.
By using the given data, we can prepare the equations
4x + 6y = 22 ------(I)
8x + 3y = 35------(II)
Multiplying equation(I) and taking subtraction, we get
9y = 9
y = 9/9
y = 1
Put y = 1 in equation (I), and we get
4x + 6 = 22
4x = 22 - 6
4x = 16
x = 4
Hence, the cost of one hot dog would be $4 and the cost of one water bottle would be $1.
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In an experiment involving single-cell RNA sequencing (scRNA-seq), researchers looked at the expression levels of a particular gene measured by the amount of mRNA from that gene present in tissue samples from mice with diabetes and mice without diabetes. The data for 14 cells in each category are here: Mice with diabetes: 0.099.0.093.0.106, 0.106, 0.102, 0.107.0.103, 0.153, 0.144, 0.153, 0.155.0.152.0.152, 0.155 Mice without diabetes: 0.127,0.120, 0.118, 0.125, 0.123, 0.130.0.115,0.178, 0.175, 0.171, 0.173.0.172, 0.164, 0.170 Use R to make two normal QQ plots, one for each sample. Is it plausible the two population distributions are normal?
The population difference within the pair is normal.
The population distribution of mice with and without diabetes are identical.
mRNA population distribution for mice with diabetes is shifted relative to the population distribution for mice without diabetes.
Conclusion,
the two population has same shape , the two samples are independent simple random samples and the two samples are paired , the population means are the same .
Hence, each of the two population distribution is normal.
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Explain why, when solving absolute value equations, you must set up both the positive and the negative equations.
Both the positive and the negative equations are set up to check the same distance from zero.
Absolute value refers to the distance of a number from zero regardless of the direction, which is indicated by the signs (positive if to the right of zero, and negative if to its left).
When solving absolute value equations, we must provide all possible answers that are of the same distance from zero. That means solving for the positive equation, which gives us the number to the right of zero, as well as solving for the negative equation, which gives us the number to the left of zero with the given distance (absolute value).
Therefore, both the positive and the negative equations are set up to check the same distance from zero.
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What is the constant variation of Y 8 when X 16?.
The constant variation of Y 8 when X 16 is 2.
What is Direct Proportion?
"When the relationship between two quantities is such that if we increase one, the other will also rise, and if we decrease one, the other quantity will also drop, then the two quantities are in a direct proportion," according to the definition of direct proportion. For instance, suppose there are two numbers, x and y, where x is the number of candies and y is the total amount of money spent. If we purchase more candy, we will be required to pay more, and if we purchase fewer candies, we will be required to pay less. This means that x and y are directly proportional to one another in this situation. The symbol for it is x y. Direct variation is another name for direct proportion.
So,
In the given question, we have:
y as 8 and x as 16;
So,
In order to find the proportional value, we have to divide the x quantity by the y quantity.
So, after dividing we get:
[tex]\frac{X}{Y} = \frac{16}{8}[/tex]
[tex]\frac{X}{Y} = 2[/tex]
So,
The constant proportion will be 2.
Hence,
The constant proportion will be 2.
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[tex]2x + 3x=-3/4-1/5[/tex]
The value of variable x in the equation is as follows;
x = - 19 / 100
How to solve equations?An equation is a mathematical statement that shows that two mathematical expressions are equal.
In other words, equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's solve the equation for variable x.
Variables are numbers represented with letters in an equation.
Therefore,
[tex]2x+3x = -\frac{3}{4}-\frac{1}{5}[/tex]
[tex]5x = \frac{-15-4}{20}[/tex]
cross multiply
20(5x) = - 19
100x = -19
divide both sides by 100
Hence,
x = - 19 / 100
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Which is the range of the function?.
The Range of the function f(x) = x² is [0,∞) .
Range of the function f(x) is defined as the set of all output values of the function.
In the question,
the function is given as f(x) = x² ,
we have to find the Range of it .
So , f(x) = x² ,
on substituting the x [tex]=[/tex] -1 , we get the value of f(-1) is = 1 ,
on substituting x = 0 , we get f(0) = 0 ,
on substituting x = 1 , we get f(1) = 1.
we see that Substituting positive values as well as negative values , the result is positive .
So , the Range of the function f(x) is [0,∞) .
Therefore , the Range of x² is [0,∞) .
The given question is incomplete , the complete question is
What is the range of the function f(x) = x² ?
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Find the arc length of the partial circle.
The arc length of the partial circle is 12,56 units.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 90 degrees
r = 8 units
length of an arc = 90 / 360 × 2 × 3.14 × 8
length of an arc = 4521.6 / 360
length of an arc = 12.56 units.
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How do you know if a graph will cross or bounce?.
We know that the graph of a polynomial function will intersect the x-axis at its root values, and we know that if the multiplicity of that root is even, the graph will "bounce off"
If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.
If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity.
If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.
The sum of the multiplicities is n.
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indicate whether the statements are true or false. a. adverse selection occurs because of asymmetric information. true false
The given statement that Adverse selection occurs because of asymmetric information is true . Because it happens when one party have no idea about other party .
Adverse Selection:
Adverse selection generally refers to the situation in which the seller has information that the buyer does not have or, conversely, knows about aspects of the product's quality. In other words, it is a case of misusing asymmetric information. Information asymmetry, also known as information impairment, occurs when one party to a transaction has more important knowledge than the other party.
For example, corporate managers may be more willing to issue stock if they know that the stock is overvalued relative to its true value. Buyers may suffer losses by purchasing overvalued stocks. In the used car market, sellers can learn about vehicle defects and charge buyers extra fees without disclosing the problem.
A common consequence of negative selection is that consumers lack information from sellers and manufacturers, increasing costs and creating market asymmetries.
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The cost to manufacture a hair clip is $0. 50. With a markup of 200 percent, what is the selling price of this hair clip?.
Selling price of the hair clip with markup 200 percent and cost of $0.50 is $1.50.
As given in the question,
Cost to manufacture a hair clip is equal to $0.50
Markup percent = 200%
Let 'x' be the selling price of the hair clip.
Formula used for markup percent is:
Markup percent =( Selling price - cost ) / cost
Substitute the value we get,
⇒ 200% =( x- 0.50) / 0.50
⇒ 200/100 =( x- 0.50) / 0.50
⇒ x - 0.50 =2 × 0.50
⇒ x = $1.50
Therefore, the selling price of the hair clip with given markup percent and cost is $1.50.
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Which ordered pair makes the inequality true?.
The ordered pairs (-2,3) and (5,1) make the inequality true.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
(-2,3)
x= -2 , y= 3
-2+3(3) < 9
7< 9
true
(5,1)
x= 5 , y= 1
5+3(1) < 9
8< 9
true
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Question:
Which ordered pairs make the inequality true?
x + 3y < 9
Choose all answers that are correct.
(Points : 1)
(–2, 3)
(–1, 4)
(1, 3)
(5, 1)
How many positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits? leading 0’s are also not allowed.
The number of 5 or fewer digits that are even or divisible by 5 and do not contain any repeated digits is 2500.
What are digits?In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.
A digit is a part of a set that, when combined, makes up a numeration system.
For example 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits.
The number of even digits 5 is 0,2,4,6,8.
Number of ways we can choose the first digit = 2,4,6,8 (0 cannot be taken in first)
Number of ways we can choose second, third, fourth, and fifth digits = 5
Number of ways or combinations,
4 × 5 × 5 × 5 × 5 = 2500
Hence "The number of 5 or fewer digits that are even or divisible by 5 and do not contain any repeated digits is 2500".
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An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, _____ the quantity demanded of the asset.
A) increases
B) decreases
C) has no effect on
D) erases
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
Given,
Asset's expected return;-
The weight of each asset is multiplied by its projected return to determine the expected return. The total predicted return for your portfolio may then be calculated by adding the figures for each investment. Hence, the equation Asset 1 Weight x Expected Return = Expected Portfolio Return Plus (Asset 2 Weight x Expected Return)
Hence,
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
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Present age of nick is 8 years and Jonas age is 14 years. What fraction of Jonas age represent the age of nick after 6 years?
Answer:
70%
Step-by-step explanation:
Nick now: 8
Jonas now: 14
Nick in 6 years: 8 + 6 = 14
Jonas in 6 years: 14 + 6 = 20
percent = part/whole × 100%
percent = 14/20 × 100%
percent = 0.7 × 100%
percent = 70%
the sugar-sweet company will choose from two companies to transport its sugar to the market.
the first company charges $5495 to rent trucks plus an additialfee of $200.75 for each ton of sugar. The second company charged $7500 to rent trucks plus an additional fee of $100.50for ech ton of sugar. For what mount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
The two companies will charge the same for 20 tons of sugar and the cost when the two companies charge the same is calculated to be $9510
The amount of sugar for which the charge will be equal can be determined by using an algebraic expression as follows;
5495 + 200.75x = 7500 + 100.50x
Here x represents tons of sugar
200.75x - 100.50x = 7500 - 5495
100.25x = 2005
x = 2005 ÷ 100.25
x = 20
Hence for 20 tons of sugar, the two companies will charge the same. Now by substituting the value of x = 20, the cost when the two companies charge the same can be determined as follows;
5495 + 200.75x = 5495 + 200.75 (20) = 5495 + 4015 = $9510
Hence $9510 is the cost when the two companies charge the same.
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Solve for f.
–(f + –8) = –1
Answer:
[tex]\huge\boxed{\sf f = 9}[/tex]
Step-by-step explanation:
Given Equation:-(f + -8) = -1
Distribute
-f + 8 = -1
Subtract 8 to both sides
-f = -1-8
-f = -9
Divide -1 to both sides
f = 9[tex]\rule[225]{225}{2}[/tex]
Two places X and Y on the equator are on the longitude 67°E and 123°E respectively
a) What is the distance between them along the equator?
b)How far is X from the North Pole
(take π to be 22/7 and Earth to be 6400km).
i) Distance between X and Y along the equator ≊ 6258 km
ii) Distance of X from the North pole ≊ 10057 km
What is the equator ?
The Equator is a fictitious line that circles the globe's center. The line that separates the Northern Hemisphere from the Southern Hemisphere is located halfway between the North and South Poles.
The Longitude difference = 123° - 67° = 56°
(i) Distance between X and Y along the equator
= (56/360)×2×(22/7)×6400cos(0)
= (56/360)×2×(22/7)×6400
= 6257.78 km
≊ 6258 km
(ii) Latitude difference = 90°
Distance from the North pole
= (90/360)×2×(22/7)×6400
= 10057.14 km
≊10057 km
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How do you replace an equation with another?.
The algebraic approach to solving simultaneous linear equations is known as substitution method.
The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve. The steps shown below can be used to find the solution to the system of two equations with two unknown values. Here, the procedure for resolving the linear equation is listed. Those are Expand the parenthesis to simplify the given equation. Either x or y must be solved for in one of the equations. Replace the step 2 solution with the other equation, then use basic arithmetic operations to solve the newly obtained problem. Finally, obtain the second value by solving the equation.
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What is the value of log 1 by 3?.
-0.477 is the value of log 1 by 3 .
A logarithm is defined simply?
The logarithm represents the power to which a number must be raised to obtain another number (see Section 3 of this Math Review for more about exponents).
For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.
log (1/3)
= log1 - log3
= 0 - 0.477
= -0.477
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the sum of two numbers is 30. when is the product of the first number multiplied by the square of the second number maximum
The two numbers required to solve the following problem are, 13.3 and 6.7
What is Derivative?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
Solution:
Let the ture positive numbers be x,(x,y>0)
x + y = 20 -------- Given
We need to maximise [tex]xy^{2}[/tex]
x = 20 - y
f(y) = (20 - y)*[tex]y^{2}[/tex]
f(y) = 20[tex]y^{2}[/tex] - [tex]y^{3}[/tex]
f'(y) = 0
On differentiating:
f'(y) = 40y - 3[tex]y^{2}[/tex]
0 = 40 - 3y
y = 13.3
x = 6.7
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Help me with this one?
Just write out the statements and reasons. thank u
Answer:
because these angles are equal to right angle triangle
match each expression to the correct point.
help please? :,)
The correct matching of a, b, and c with -6.283, -5.667, and -4.243, respectively.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The numbers are given below.
-17/3, -2π, and -√18
Convert each number into a decimal number. Then we have
-17/3, -2π, and -√18
-5.667, -6.283, and -4.243
Then the correct matching of a, b, and c with -6.283, -5.667, and -4.243, respectively.
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a poker hand consists of 5 cards dealth from a deck of 52 cards. let x and y be the number of aces and kings in a poker hand. find the joint distribution of x and uy
Joint Distribution of x and y is 25.
Joint Distribution is based on joint probability, which can be simply defined as the probability of two events happening together.
We know the formula for joint distribution
F(x,y) = P(X ≤ x and Y ≤ y) = ∑∑p(xi,yi)
Here x is the number of aces and y is the number of kings in a poker hand.
That means x can take values from 0 to 4 and y can take values from 0 to 4.
∴ F(x,y) = P(X ≤ 4 and Y ≤ 4)
⇒ F(x,y) = p(0,0) + p(0,1) + p(0,2) + p(0,3) + p(0,4) + p(1,0) + p(1,1) + p(1,2) + p(1,3) + p(1,4) + p(2,0) + p(2,1) + p(2,2) + p(2,3) + p(2,4) + p(3,0) + p(3,1) + p(3,2) + p(3,3) + p(3,4) + p(4,0) + p(4,1) + p(4,2) + p(4,3) + p(4,4).
To find all these values we will construct a table as follows;
P(x,y) Y=0 Y=1 Y=2 Y=3 Y=4
X=0 0 1/4 1/2 3/4 1
X=1 1/4 1/2 3/4 1 5/4
X=2 1/2 3/4 1 5/4 3/2
X=3 3/4 1 5/4 3/2 7/4
X=4 1 5/4 3/2 7/4 2
Now the joint distribution will become,
F(x,y) = 0 + 1/4 + 1/2 + 3/4 + 1 + 1/4 + 1/2 + 3/4 +1 + 5/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2 + 3/4 + 1 + 5/4 + 3/2 + 7/4 + 1 + 5/4 + 3/2 + 7/4 + 2
F(x,y) = 25
Therefore the joint distribution of x and y is 25.
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the compounding periods and the payment periods are the same for an annuity and for an amortization. determine the present value of the annuity that will pay the given periodic payments. (round your final answer to two decimal places.) monthly payments of $430.80 for 6 years at 4.3% interest.
The present value of the annuity that will pay the given periodic payments is $ 332.99
since we are given a monthly payment of $430.80 for the period of 6 years with an interest of 4.3%, and it is said that the compounding periods and the payment periods are the same for an annuity and for an amortization.The formula for calculating the present value of the annuity is : FV= PV(1+i/12)¹²ⁿ, where F Vis the future value, PV is the present value, i is the interest and n is the period of time.So substituting the know values in the above formula, we get the present value to be: $ 332.99
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Which is true of the measures of the sides of the original square? each side of the original square is one-fourth the length of each side of the scale model. Each side of the original square is 4 times the length of each side of the scale model. Each side of the original square is the same length as each side of the scale model. Each side of the original square is 4 feet less than the scale model.
For the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
It is known to us that -
The value of the scale factor = 4
We also know that -
Each side of the scale model = Scale factor * Side of the original square
=> Each side of the scale model = 4 * Side of the original square
=> Side of the original square = (1/4) * Each side of the scale model
Thus, for the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
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Which function has no solution?.
Modulus function has no solution.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Nothing can ever be 0 in an expression of an absolute value. That is a phrase for an absolute value that has been entirely lowered and must be larger than or equal to zero.
There are no solutions to an absolute value expression if, after simplifying it, the value on the opposite side is a negative number or has a negative sign.
Hence, the Modulus function has no solution.
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