Consider the following linear program: Max5A+2B s.t. 1A−2B≤4302A+3B≤6106A−1B≤125A,​B≥0​ Write the linear program in standard form. Max5A+2B+()S1​+(S2​+(S3​s.t. 1A−2B+ =430 2A+3B +=610 6A−1B +=125 A,B,S1​,S2​,S3​0

Answer:

It would be the first one

Step-by-step explanation:

Start at 0 and the end shows 2.5

In  cases (a), (b), and (d), the firm produces zero units regardless of the price, while in case (c), there is no supply curve.

To determine the short-run supply function for each case, we need to find the quantity (qi) at which the firm's cost is minimized and compare it to the given production conditions.

a) Case: P = 35 - 15q + 3q^2 (if P ≥ $52, otherwise zero units)

To find the short-run supply function, we need to determine the quantity at which the firm's cost is minimized. The cost function is given as C(qi) = 160 - 58qi + 6qi^2 - qi^3.

First, take the derivative of the cost function with respect to qi and set it equal to zero to find the minimum:

C'(qi) = -58 + 12qi - 3qi^2 = 0

Simplifying the equation:

3qi^2 - 12qi + 58 = 0

Using the quadratic formula, we can find the value of qi that minimizes the cost:

qi = (-(-12) ± √((-12)^2 - 4(3)(58))) / (2(3))

qi = (12 ± √(144 - 696)) / 6

qi = (12 ± √(-552)) / 6

Since the discriminant is negative, there are no real solutions. Hence, there is no positive quantity at which the firm's cost is minimized. As a result, the firm produces zero units regardless of the price.

b) Case: P = 40 - 8q + 2q^2 (if P ≥ $55, otherwise zero units)

Following the same steps as in case (a), we find:

qi = (8 ± √(8^2 - 4(2)(40))) / (2(2))

qi = (8 ± √(-96)) / 4

Again, the discriminant is negative, indicating no real solutions. Therefore, the firm produces zero units regardless of the price.

c) Case: No supply curve

In this case, the firm does not have a supply curve. There is no relationship between the price and the quantity produced.

d) Case: P = 58 - 12q + 3q^2 (if P ≥ $49, otherwise zero units)

Following the same steps as before, we find:

qi = (12 ± √(12^2 - 4(3)(58))) / (2(3))

qi = (12 ± √(144 - 696)) / 6

qi = (12 ± √(-552)) / 6

Once again, the discriminant is negative, indicating no real solutions. Therefore, the firm produces zero units regardless of the price.

In summary, in cases (a), (b), and (d), the firm produces zero units regardless of the price, while in case (c), there is no supply curve.

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Chelsea made 53.57% of the recipes she downloaded from the Internet.

What is Equation ?

In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. It consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). The expressions on both sides of the equal sign can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

The equation that can be used to answer the question is:

15÷28 = x÷100

where x represents the percent of recipes Chelsea made.

To solve for x, you can cross-multiply and simplify:

15 * 100 = 28 * x

1500 = 28x

x = 1500÷28

x ≈ 53.57%

Therefore, Chelsea made 53.57% of the recipes she downloaded from the Internet.

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Chelsea made approximately 53.57% of the recipes she downloaded from the internet.

A number or quantity can be expressed as a fraction of 100 by using a percentage. The symbol for percentage is "%". It is often used to compare quantities or to express how much of something is present in relation to the whole.

To calculate a percentage, you first need to express the number you want to convert as a fraction of the whole, and then multiply that fraction by 100.

The equation that represents the percentage of the recipes did Chelsea make if she made 15 out of 28 downloaded recipes is:

15/28 = x/100

where x is the percentage of the recipes she made.

To solve for x, we can cross-multiply:

15 x 100 = 28x

1500 = 28x

x = 1500/28

x ≈ 53.57

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Answer:

16

Step-by-step explanation:

f(x) = 2x + 4

f(6) = 2(6) + 4

=> f(6) = 12 + 4

=> f(6) = 16

The job with the longest process time is scheduled first, followed by the next longest, and so on.

Using the LPT (Longest Processing Time) priority, the sequence for jobs a, b, c, and d with process times 4, 6, 5, and 2 respectively would be:

1. Job b (6 units)
2. Job c (5 units)
3. Job a (4 units)
4. Job d (2 units)

The LPT priority rule arranges the jobs in decreasing order of their process times. So, the job with the longest process time is scheduled first, followed by the next longest, and so on.

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Answer:

4 yards

Step-by-step explanation:

they gained 12 yards and then lost 8

that can be expressed as 12-8=4

Answer:

12+(−8)

Step-by-step explanation:

Answer:

x=42

y=12

Step-by-step explanation:

The given options, the equivalent ratio is:

6 to 15.24

Therefore, the answer is option "6 to 15.24."

Given that a ratio 1:2.54, we need to find an equivalent ratio for the given ratio,

To determine the equivalent ratio, we need to convert the given inches to centimeters using the conversion factor of 1 inch = 2.54 centimeters. Let's calculate the corresponding centimeters for each option:

3.5 inches = 3.5 x 2.54 = 8.89 centimeters

4 inches = 4 x 2.54 = 10.16 centimeters

5 inches = 5 x 2.54 = 12.7 centimeters

6 inches = 6 x 2.54 = 15.24 centimeters

Among the given options, the equivalent ratio is:

6 to 15.24

Therefore, the answer is option "6 to 15.24."

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Answer:

9.6

Step-by-step explanation:

What is the mean of the following data set 4 8 11 12 13?

Mean: is the average of values so:

(4 + 8 + 11 + 12 + 13) / 5 = 9.6

Answer:

David is saving up money to buy a new car. He had $1,350 saved up 4 months ago, and now has $2,150. He adds the same amount of money each month

Step-by-step explanation:

I'm not clear on your actual question, but I'm guessing you want to know how much money he has saved each of the last four months.

2150 - 1350 = $800 saved over the past four months

$800 / 4 months = $200 saved per month

Answer:

l + w = 25 and lw = 136

w(25 - w) = 136

25w - w² = 36

w² - 25w - 136 = 0

(w - 17)(w - 8) = 0

w = 8, so l = 17

The dimensions of the bookmark are 8 cm by 17 cm.

Answer:

1. x = 10 , y = 2

Step-by-step explanation:

hope it helps ☺️

The probability of Dhruv selecting a compact car, P(compact car), is 4/25, or approximately 0.16 when rounded to 2 decimal places.

We want to find the probability of Dhruv selecting a compact car (P(compact car)) when there are 13 trucks, 8 vans, and 4 compact cars at the dealership.

To find P(compact car), follow these steps:

1. Calculate the total number of vehicles:

13 trucks + 8 vans + 4 compact cars = 25 vehicles.

2. Determine the number of compact cars: 4 compact cars.

3. Calculate the probability: P(compact car) = (Number of compact cars) / (Total number of vehicles) = 4 / 25.

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Answer:

8a = 103 - 11b

Step-by-step explanation:

Given that:

Number of barrels = 12

Pounds of barrel = 103 pounds

Available barrel options

a = 8 pound barrel

b = 11 pound barrel

Number constaint;

a + b = 12

Pounds of barrel constraint ;to mazimize barrel load ;

(8*a) + (11*b) = 103

8a + 11b = 103

8a = 103 - 11b ; 11b = 103 - 8a

To solve the inequalities -2x + 4 < 8 and 3x + 4 ≤ -5, we will solve them individually and then represent the solutions on a number line.

For the first inequality, -2x + 4 < 8, we will isolate x:

-2x + 4 - 4 < 8 - 4

-2x < 4

Dividing both sides by -2 (remembering to reverse the inequality when multiplying/dividing by a negative number):

x > -2

For the second inequality, 3x + 4 ≤ -5, we isolate x:

3x + 4 - 4 ≤ -5 - 4

3x ≤ -9

Dividing both sides by 3:

x ≤ -3

Now we represent the solutions on a number line. We mark -2 with an open circle (since x > -2), and -3 with a closed circle (since x can be equal to -3). Then we shade the region to the right of -2 and include -3 to represent the solutions.

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Answer:4log5=4log5

Step-by-step explanation:

Take the log of both sides

log5^4 =log 625

By log log a^b=b loga

4log 5=log5^4

4log5 =4log 5

Expressions and equations can be written in logarithmic forms.

The logarithmic form of \(5^4 = 625\) is \(\log_5(625) = 4\)

The equation is given as:

\(5^4 = 625\)

Take the logarithm of both sides of the equation

\(\log(5^4) = \log(625)\)

Apply law of logarithm

\(4\log(5) = \log(625)\)

Divide both sides of the equation by log(5)

\(4 = \frac{\log(625)}{\log(5)}\)

Apply change of base law of logarithm

\(4 = \log_5(625)\)

Rewrite the equation as follows:

\(\log_5(625) = 4\)

Hence, the logarithmic form of \(5^4 = 625\) is \(\log_5(625) = 4\)

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Answer: 78

Step-by-step explanation:

The mode is the number that appears the most number of times. In this case the number 78 appears twice unlike the other numbers that only appear once. Hence, 78 is the mode :)

Answer:

78

Step-by-step explanation:

The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

When each ticket costs $2, and the prize for the winner is $50 then the cheerleading squad needs to sell at least 88 tickets to raise $175.

The cheerleading squad wants to raise $175 through their raffle ticket sales.

Each ticket costs $2, and the prize for the winner is $50. We need to determine how many tickets the team needs to sell to reach their fundraising goal.

Let's assume the number of tickets the team needs to sell is 'x'.

Since each ticket costs $2, the total revenue generated from ticket sales can be calculated as 2 * x.

To reach their fundraising goal of $175, the total revenue from ticket sales should be equal to $175.

Therefore, we can set up the equation:

2 * x = 175

Solving for 'x', we divide both sides of the equation by 2:

x = 175 / 2

Simplifying further, we get:

x = 87.5

Since we cannot sell a fractional number of tickets, we round up the value to the nearest whole number.

Therefore, the cheerleading squad needs to sell at least 88 tickets to raise $175.

It's worth noting that selling exactly 87 tickets would only generate $174 in revenue, which is less than the fundraising goal.

Hence, they need to sell a minimum of 88 tickets to reach or exceed their target of $175.

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The equation of the line passing through (2,1) and (4,2) is x - 2y = 0.

To identify the equation of a line that passes through points (2,1) and (4,2), we can use the point-slope form of the equation of a line. This form is given by:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points, and m is the slope of the line. To identify m, we use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two given points.

Substituting the given values, we have:m = (2 - 1) / (4 - 2) = 1 / 2So, the slope of the line is 1/2. Now, let's use the point-slope form of the equation of a line to identify the equation of the line passing through (2,1) and (4,2). By choosing (2,1) as the point, we have:

y - 1 = (1/2)(x - 2)

Multiplying both sides by 2, we get:

2y - 2 = x - 2

Simplifying, we get:

x - 2y = 0

This is the equation of the line passing through (2,1) and (4,2).

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Answer:

idkkk im trying to figure it out as quick as i cannn

Step-by-step explanation:

Probability is the likelihood or chance of an event occurring.

In the given grid, there are 4 black points out of a total of 9 points.

Therefore, the probability of selecting a black point randomly is:

P(black) = Number of black points / Total number of points

= 4 / 9

= 0.444 or 44.4% (rounded to one decimal place)

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Answer:

4/5

Step-by-step explanation:

If two lines are parallel, then they have the same slope. So, we first need to put the equation in slope intercept form (y = kx + b)

8x - 10y = -60

-10y = -8x - 60

y = 4/5x + 6

So the slope is 4/5.

Answer:

In slope intercept form -5y = -4 - 30

Step-by-step explanation:

Slope intercept form is y=mx + b

Rewrite your equation in this form

-10y = -8x - 60

Find GCF (Greatest Common Factor) in this case it is 2

Divide all by 2

-5y = -4x - 30

Answer:

17 in.

Step-by-step explanation:

There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.

Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

\(mass(t) = mass(0)*e^{-\lambda*t}\)

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

\(\frac{mass(0)}{2} = mass(0)*e^{-\lambda*12}\)

\(\frac{1}{2} = e^{-\lambda*12}\)

\(ln(\frac{1}{2}) = -12*\lambda\\\lambda = -\frac{ln(0.5)}{12} =0.0577623\)

Therefore the mass of the element is given by:

\(mass(t) = mass(0)*e^{-0.0577623*t}\)

If the initial mass is 760 g and the final mass is 15 g, we have:

\(mass(t) = mass(0)*e^{-0.0577623*t}\\\\15 = 760*e^{-0.0577623*t}\\\\e^{-0.0577623*t} = \frac{15}{760}\\\\ln(e^{-0.0577623*t}) = ln(\frac{15}{760})\\\\-0.0577623*t = ln(\frac{15}{760})\\\\t = \frac{ln(\frac{15}{760})}{-0.0577623}\\\\t = 67.9555\)

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Answer:

$2400

Step-by-step explanation:

15*24=360

1 yd=3 ft, so, 360/3=120

120*20=2400

Answer and Step-by-step explanation:

Differences:

Interval notation is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example set of all real numbers can be described in interval notation as 0 ≤ x ≤1.  Interval notation press the solution set to equality, and it is important to express solution sets in calculus. Set builder notation is a mathematical notation for describing a set by its elements, and their member satisfies' properties.It describes the elements of a set instead of listing the element. For example the set {1, 2, 3, 4, 5, 6, 7, 8, 9} is written in builder notation will be {x/x is a counting number less than 10}.Inequality notation is a relation that makes a non equal comparison between two numbers. Set are also defined by using some inequalities like >, <, ≤, ≥. These are called inequality notations.

Similarities:

The purpose of inequality notation, set builder notation, and interval notation is the same because these notations used to describe a set and the characteristics of each element of a set. When a set is representing in set builder notation, it defines characteristics of elements.  If the set is represented in interval notation, we need to know the upper and lower bound set. In inequality notation, the set is described by the graph on a number line.

Answer:

21

Step-by-step explanation:

Steps to solve:

-6^2

-6 * -6

6 * 6

36

Best of Luck!