Answer:
36 attempts
Step-by-step explanation:
Find the exact value of cos J in simplest form.
√29
14
15
H
The cosine of angle J is given as follows:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:
Sine = length of opposite side/length of hypotenuse.Cosine = length of adjacent side/length of hypotenuse.Tangent = length of opposite side/length of adjacent side = sine/cosine.For the angle J in this problem, we have that:
4 is the adjacent side.\(\sqrt{98}\) is the hypotenuse.Hence the cosine of angle J is given as follows:
\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)
\(\cos{J} = \frac{4\sqrt{98}}{98}\)
\(\cos{J} = \frac{2\sqrt{98}}{49}\)
As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:
\(\cos{J} = \frac{14\sqrt{2}}{49}\)
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129 divided 50 pls hurry
Answer:
2.58
Step-by-step explanation:
129/50 = 2.58
Number equivalent to 129 /50 is 2.58 .
Given,
129 divided 50
Using division property,
The rules for division are:
(1) positive × or ÷ positive = positive
(2) positive × or ÷ negative = negative
(3) negative × or ÷ negative = positive
Rule for long division method,
Divide the tens column dividend by the divisor.
Multiply the divisor by the quotient in the tens place column.
Subtract the product from the divisor.
Bring down the dividend in the ones column and repeat.
Therefore,
divide, multiply, subtract, bring down and repeat or find the remainder.
Here the required value is of :
129/50
= 2.58
Hence the answer is2.58
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Rewrite 3 + 7 = 10 using the Commutative Law of Addition.
A. (3+7)= 10
B. 7+3= 10
C. 3=7+10
D. 10-7 = 3
Answer:
Step-by-step explanation:
It's B
7 + 3 = 10
what is t he chance that a randomly selected indivudal found to have a positive result actuall yhas the disease
The chance that a randomly selected individual found to have a positive result actually has the disease is called the Positive Predictive Value (PPV). What is the chance that a randomly selected individual found to have a positive result actually has the disease?
The probability that a randomly chosen individual with a positive test result really has the disease is referred to as the Positive Predictive Value (PPV). It reflects how well the test can detect disease in those who have it. In statistics, the PPV is calculated as follows:
PPV = True Positives / (True Positives + False Positives) x 100
In addition, the PPV is influenced by a variety of factors, including the disease's prevalence, the sensitivity and specificity of the test, and the prevalence of the disease in the population.
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The derivative of a function f at a number a denoted by f'(a), is f(a) lima+h)- f(a) = h h 0 if this limit exists Sketch f(x) and draw a representation that shows the relationship between f'(a), f(a+h) and f(a). Explain how your illustration represents the definition of the derivative a function at a number a.
The derivative of a function at a point can be shown as the slope of the tangent line to the graph of the function at that point [a,f(a)]. This slope is found by taking the limit of the difference quotient [f(a+h) - f(a)]/h as h approaches 0.
The derivative of a function f at a number a, denoted by f'(a), can be represented graphically as the slope of the tangent line to the graph of f at the point [a,f(a)].
To illustrate this, we can sketch the graph of f(x) and draw a secant line passing through the points [a,f(a)] and [a+h, f(a+h)], where h is a small positive number. As h approaches 0, the secant line becomes closer and closer to the tangent line at the point [a,f(a)].
The slope of the secant line is given by the difference quotient [f(a+h) - f(a)]/h, and the slope of the tangent line is given by the limit of this difference quotient as h approaches 0. This limit is f'(a), the derivative of f at a.
In summary, the definition of the derivative of a function at a point a can be represented graphically as the slope of the tangent line to the graph of the function at the point [a,f(a)]. This slope is found by taking the limit of the difference quotient [f(a+h) - f(a)]/h as h approaches 0.
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can someone find the area please?
Answer:
16
Step-by-step explanation:
i think
Answer:
7.348469228
Step-by-step explanation:
34+24+50=108
108/2=54
then you take 54 and minus each side like 54-34,54-24 and 54-50 then square root the final solution.
hope this help:)
which sample proportion will require the largest number of work sampling observations for a given confidence level and allowable error? multiple choice .95 .05 .25 .50 .75
0.50 sample proportion will require the largest number of work sampling observations for a given confidence level and allowable error as the variability is largest at 0.50.
What is proportion?A part, share, or quantity is a percentage when it is compared to the total. It can be any number between 0 and 1, 0, or 1. A number or percentage can be used to represent it. The percentage of Canadians who reside in a certain province is one illustration from official statistics. A special class of ratio called a proportion has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women.
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This is the second to last question I have to do
Answer:
aunt clares cup of tea was darker because the extra milk in megs made it lighter than aunt clares
Step-by-step explanation:
if y=4x^2 −3 , what is the minimum value of the product xy ?
a. -1
b. 1
c. -12
d. -2
The minimum value of the product xy is -2. The correct option is d.
To find the minimum value of the product xy, we need to find the minimum value of y and then multiply it by the corresponding x value. In this case, the given equation is y = 4x² - 3.
To determine the minimum value of y, we observe that the coefficient of the x² term is positive (4), indicating a U-shaped parabola that opens upward. Since the parabola opens upward, the vertex of the parabola represents the minimum point.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a and b are the coefficients of the x² and x terms, respectively. In this equation, a = 4 and b = 0. Plugging these values into the formula, we get x = -0 / (2 * 4) = 0.
To find the corresponding y-coordinate, we substitute the value of x = 0 into the equation: y = 4(0)² - 3 = -3.
Therefore, the minimum value of y is -3. Multiplying this minimum y value by the corresponding x value, we get xy = 0 * (-3) = 0.
Therefore the correct option is d.
However, none of the answer options provided includes 0 as a choice. Instead, the closest option is -2 (option d). Although -2 is not the minimum value, it is the closest available option in the given choices.
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Answer, please Please
Answer:
18
Step-by-step explanation:
9+(-15)+4+20
9-15+4+20
18 ans
please help teach might of made a mistake
Answer:
its d
Explanation:
bc it ask for the lowest Price for the yacht
3. determine using any method you like whether the functions 1 x, 1-x^2, and 1-3x
The functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x=0, but they are dependent at x=0.
How to find functions that are linearly independent?To determine whether the functions 1/x, 1-x², and 1-3x are linearly independent, we can use the Wronskian method. The Wronskian of a set of functions f1(x), f2(x), ..., fn(x) is defined as:
W(f1, f2, ..., fn) = det | f1 f2 ... fn |
| f1' f2' ... fn' |
where f1', f2', ..., fn' are the derivatives of the functions with respect to x.
If the Wronskian is nonzero for all values of x in a given interval, then the functions are linearly independent on that interval. If the Wronskian is zero for at least one value of x in the interval, then the functions are linearly dependent on that interval.
For the functions 1/x, 1-x², and 1-3x, we have:
W(1/x, 1-x², 1-3x) = det | 1/x 1-x² 1-3x |
| -1/x² -2x -3 |
| 0 -2x 0 |
Expanding the determinant, we get:
W(1/x, 1-x², 1-3x) = -6/\(x^3\)
Since the Wronskian is nonzero for all values of x except x = 0, the functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x = 0.
Therefore, the functions are linearly independent except at x = 0.
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can you guys answer these sequences?
Which inequality does this graph show? A. y > 0 B. y < 0 C. D.
Answer: The answer is B) y < 0
Answer: B
Step-by-step explanation:
r to the nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?
14) Bill enlarged the size of a photo to a
height of 6 cm. What is the new width if
it was originally 2 cm tall and 4 cm wide?
The nearest whole number to which the new height of the image is enlarged is 9cm.
What is meant by height?
Height is a mathematical term that refers to the vertical distance between an object's top and base.On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.Below are a few mathematical illustrations of height.Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).For instance, "That building is 50 meters high," or "An airplane flies around 10,000 meters high."the height of something above the ground or another level of your choice. At a height of 15,000 meters, we flew.To learn more about height refer to
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12) The new height is 9cm it was originally 4cm wide and 3cm tall, scale factor is 3.
14) The new width is 12cm it was originally 2cm tall and 4cm wide, scale factor is 3.
What is scale factor?In mathematics, a scale factor is the proportion between corresponding measurements of an object and a representation of that object. The copy will be bigger if the scale factor is a whole number. A fraction scale factor means that the copy will be smaller.
To increase an object by a scale factor, measure each side of the object and multiply the result by the scale factor. A 2x2 cm square is presented to you.
Increase the square by a scale factor of 2.
To do this, multiply each side by 2.
The result is a 4x4cm square.
12) scale factor = 12/4
scale factor = 3
14) scale factor = 6/2
scale factor = 3
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Please help me asap I will give brainliest
Answer:
I think The answer is A
Step-by-step explanation:
Gavin combines Thirty-two and two-fifths ounces of water and 7.15 ounces of lemon juice in a pitcher to make lemonade. Which is the most reasonable estimate for the amount of liquid in the pitcher? 39 ounces 42 ounces 45 ounces 47 ounces
Answer:
OPTION A is correct
39 ounces
Step-by-step explanation:
Given:
The amount of water in the pitcher= 32 ounces
The amount of lemon juice in the pitcher = 7.15 ounces
We were to calculate the most reasonable estimate for the amount of liquid in the pitcher
To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is
32 ounces + 7.15 ounces
=39.15 ounces
Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces
Pedro owns a shrimp truck near the beach. he sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate. each day pedro stocks enough shrimp to sell at most 120 plates total, but he would like to earn at least $800. which combination of garlic shrimp plates and spicy shrimp plates can pedro sell to meet his goal?
Pedro can sell enough by combining the sales of 40 plates of garlic shrimp and 80 dishes of spicy shrimp to reach his objective.
As a resultNear the shore, Pedro runs a shrimp delivery business.
He offers spicy shrimp for $6 a plate and garlic shrimp for $8 per plate.
Pedro wants to make at least $800 per day but only stocks enough shrimp to sell a maximum of 120 plates.
We need to ascertain,
Which dish combining hot shrimp and garlicky shrimp can Pedro sell to reach his objective?
In response to the query,
Let's sell the x dishes of garlic shrimp.
And plates of hot shrimp were sold.
Pedro has 120 dishes' worth of shrimp in stock each day.
Then,
Shrimp sold daily total is equal to the sum of plates of garlic shrimp and spicy shrimp.
X + Y = 120
Furthermore, He offers $6spicy and $8garlic shrimp, per plate.
To make at least $800 is what he wants to do.
Then,
the sum of the price of the spicy shrimp per plate and the price of the garlic shrimp per plate,
8X + 6Y = 800
When the two equations are solved,
X + Y = 120
8X + 6Y = 800
From equation 1,
Y = 120 - X
In equation 2, replace x with its value.
8X + 6Y = 800
8(120 - Y) + 6Y = 800
960 - 8Y + 6Y = 800
- 2Y = - 160
Y = 160/2
Y = 80
In equation 1, replace y with its value.
X + Y = 120
X + 80 = 120
X = 120 - 80
X = 40
In order to achieve his objective, Pedro sold a combination of 40 plates of garlic shrimp and 80 dishes of spicy shrimp.
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Answer:
Step-by-step explanation:
Make equations
8x+6y≥800
x+y≤120
Graph the system of equations and see which answer falls in the shaded area
Answer: 90 Garlic, 25 Spicy
14. PLEASE HELP ME
Which of the quadratic functions has the narrowest graph?
A. y= 1/8x2
B. y= 1/6x2
C. y= -x2
D. y= 2x2
Answer:
D. y= 2x2
Step-by-step explanation:
y = ax^2
If the absolute value of a is <1 the graph is wider than when a = 1
If the absolute value of a is >1 the graph is narrow than when a = 1
The only function that fits that description is
y = 2x^2
B <<< answer.
Given: We are given equation of parabola ans to choose narrowest graph.
Parabola form narrowest and widest.
Larger value of a most narrowest graph.
Smaller value of a most widest graph.
Now, we will see the coefficient of x²
Now, we arrange the value of a in descending order.
2 is largest value of these.
Hence, The narrowest graph is
there are 2 more pictures i have to upload but it won't let me
ILL GIVE U BRAINLIST PLS HELP
Answer:
A. Right a multiple of 2 and up a multiple of 1.
B. (2, 1)
C. the same
Step-by-step explanation:
A. The original point was (2, 1), so if Larissa moves right a multiple of 2 and up a multiple of 1, she'll stay within the ratio.
B. We already know this is proportional, since it goes through the origin; the line just has to pass through the right point: (2,1)
C. The line will be proportional, so as long x is twice as much as y, Larissa will have the same shade of green paint every time.
The ______ variable in a study, also known as the response variable, is affected by the ______ variables.
The dependent variable in a study, also known as the response variable, is affected by the independent variables.
What is a variable?
A variable is a sign and placeholder for any mathematical object (from the Latin variabilis, "changeable") in mathematics. A variable can, for example, represent a number, a vector, a matrix, a function, the argument of a function, a set, or a set's component.
Numerous issues are resolved in a single computation by using variables in algebraic calculations as if they were explicit integers. For instance, by exchanging the variables that represent them in the quadratic formula with the numerical values of the coefficients in any given quadratic equation, the quadratic formula may solve any quadratic equation. A variable in mathematical logic is either a symbol for an undefined term in the theory or an undefined phrase itself (a meta-variable).
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an agricultural field test compares two varieties of corn, silver queen and country gentlemen. the researches takes 10 plots and divides each of these plots in half. each plot has a similar amount of sun light, shade, quality of soil and irrigation. the variety of corn is randomly chosen for each half of a plot. after the harvest, the yield of corn is measured for each half plot at each location. the yield from silver queen was compared to the yield of country gentlemen. note: differences were taken by taking silver queen - country gentlemen the 95% confidence interval for the mean is (-0.223, 0.988). what can we expect will be the p-value for a two sided test using this data?
The solution to this problem is the p-value must be higher than 0.05.
Confidence interval definition:A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.
Here ,
In this given problem we can see confidence interval has 0 in it.
So,
Since the confidence interval comprises 0, the null hypothesis should be rejected.
When the p-value exceeds the level of significance, the null hypothesis is only rejected.
Since alpha=0.05 in this case, the p-value must be higher than 0.05.
Thus, the p-value must be higher than 0.05.
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.
There are 25 questions in a quiz.
Each correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
vach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
vach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
Step-by-step explanation:
ach correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Answer:
2h
Step-by-step explanation:
Question
.
There are 25 questions in a quiz.
Each correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0
It is possible to finish the quiz with a negative score.
1) If 75 is the maximum score you can get, what is the minimum score on the quiz?
2) A student answers 21 questions. 6 are correct. How many points does she score?
Two initial centroids (12.0, 12.5), (15.0, 15.5). please find the next two centroids after one iteration using k-means with k = 2 and euclidean distance.
The next two centroids after one iteration using k-means with k = 2 and euclidean distance are (14.5, 12.75) and (15.5, 15.5).
1. Assign each point to its closest centroid:
- For (12.0, 12.5):
- Calculate the distance to (12.0, 12.5) and (15.0, 15.5).
- Assume the distance to (12.0, 12.5) is closer, so assign the point to that centroid.
- For (15.0, 16.0):
- Calculate the distance to (12.0, 12.5) and (15.0, 15.5).
- Assume the distance to (15.0, 15.5) is closer, so assign the point to that centroid.
- For (16.0, 15.0):
- Calculate the distance to (12.0, 12.5) and (15.0, 15.5).
- Assume the distance to (15.0, 15.5) is closer, so assign the point to that centroid.
- For (17.0, 13.0):
- Calculate the distance to (12.0, 12.5) and (15.0, 15.5).
- Assume the distance to (12.0, 12.5) is closer, so assign the point to that centroid.
This gives us two clusters of points assigned to each centroid:
- Cluster 1: (12.0, 12.5), (17.0, 13.0)
- Cluster 2: (15.0, 16.0), (16.0, 15.0)
2. Calculate the mean of the points assigned to each centroid to get the new centroid location:
- For Cluster 1:
- Mean of (12.0, 12.5) and (17.0, 13.0) = \((\frac{12.0+17.0}{2},\frac{12.5+13.0}{2})\) = (14.5, 12.75)
- For Cluster 2:
- Mean of (15.0, 16.0) and (16.0, 15.0) = \((\frac{15.0+16.0}{2},\frac{16.0+15.0}{2})\) = (15.5, 15.5)
Therefore, the next two centroids after one iteration using k-means with k = 2 and euclidean distance are (14.5, 12.75) and (15.5, 15.5).
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To stock your school store, you buy a total of 25 sweatshirts and hats for $172.50. You pay $8.00 per sweatshirt and $2.50 per hat. How many of each item do you buy?
Answer:
the answer is 20 and 5
Step-by-step explanation:
Number of hats is 5 and the number of sweatshirts is 20
The total number of items bought is 25
The total amount is $172.50
Let a represent the number of sweatshirts
Number of hats is 25-a
Cost of sweatshirt= 8x
Cost of hat= 2.50×(25-x)
= 62.50-2.5x
8x + 62.50 - 2.5x-172.50
8x-2.5x+62.50-172.50
5.5x -110
5.5x= 110
x= 110/5.5
= 20
Number of hats= 25-20, = 5
Number of sweatshirts= 20
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PLSSSSS HELP 20 POINTS!!!!! NEEDE BY NOV 19 2022The length of the side of a rhombus is 14 in. The measure of each obtuse angle is 160°. Find the length of the longer diagonal of the rhombus.
Answer:
27.57 in
Step-by-step explanation:
You want the length of the longer diagonal of a rhombus with side lengths 14 inches and obtuse angle 160°.
Law of CosinesThe law of cosines can be used to find the diagonal length. The length of the third side (c) is given by ...
c² = a² +b² -2ab·cos(C)
where a and b are the other two sides, enclosing angle C.
Applicationc² = 14² +14² -2·14·14·cos(160°)
c² = 392 -392·cos(160°) ≈ 760.35951
c ≈ 27.5746
The longer diagonal is about 27.57 inches long.
Answer:
Step-by-step explanation:
fars
Albert wants to buy two pomegranates and some peaches • The price of one pomegranate is $1.59. • The price of peaches is $1.19 per pound. Albert wants to no more than $10.00. Which graph represents the number of whole pounds of peaches Albert can buy?
Answer:
He can buy 5 pounds of peaches.
Step-by-step explanation:
2 pomegranates cost $3.18 so, subtract that from $10.00 and you get $6.82. Multiply the different number of pounds with the cost per pound until you go over $6.82. Then go back a pound and multiply. 5 pounds times $1.19 equals $5.95.
f(x) = x² + 7
X(-2) =
Answer:
hope it will help you
Step-by-step explanation:
f(x)=x²+7
X(-2)=?
therefore X(-2)=(-2)²+7
=4+7
=11
By what number must you multiply each side of the equation 45x=8 to produce the equivalent equation x = 10?.
Answer:
5
Step-by-step explanation:
For this case, we have the following equation:
4/5x = 8
We must find a number that when multiplied on both sides of the equation, as a result:
x = 10x
So, if we multiply 8 * 5 = 40
Now, the left side must also be multiplied by 5 to not alter the equation:
(4/5)x*5=4x
x∗5=4x
Finally we have 4x=40
Clearing "x":
\begin{gathered}x = 40/4
x=10
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please hand solve and show steps
(a) Find the dual of the LP .
(b) Find the standard form of the LP and dual.
(c)Optimal solution for the primal problem is: x ∗ 1 = 20, x∗ 2
= 60, s∗ 1 = 0, s∗
objective m constraints n decision variables Consider the following LP. Primal and Dual pair min b₁y₁+ max C₁x₁++GX+ CnXn 8/1X1 +2X2 + + ax ≤ bi ax1 + a2x2 + +anxn bi a/1X1 + a2x2 + +anxn 2
(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)
Let us find the dual of the above primal problem.
Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)
and\($y_1, y_2, ..., y_m \geq 0$\)
(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)
Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)
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