Help I’m being timed!!!!

(i) To analyze the linear programming problem using the two-phase simplex method, we need to convert the problem into standard form by introducing slack variables. The problem can be expressed as:

Minimize z = x1 + x2

subject to:

3x1 + x2 + x3 = 1

7x1 + 3x2 - x4 = 4

x1, x2, x3, x4 ≥ 0

The two-phase simplex method involves two phases: the first phase identifies an initial feasible solution, and the second phase optimizes the objective function.

In this case, we start with the artificial variables x3 and x4. In the first phase, we maximize the sum of artificial variables while minimizing the objective function. After the first phase, we check if the optimal solution is feasible (i.e., if the value of the objective function is zero).

Once a feasible solution is obtained, we move to the second phase and proceed with the standard simplex method to optimize the objective function. The optimal solution will be obtained when all artificial variables are eliminated, and the objective function reaches its minimum value.

(ii) Yes, this problem can be solved using the dual simplex method. The dual simplex method is used to solve linear programming problems by analyzing the dual problem. However, to apply the dual simplex method, the problem must satisfy certain conditions, such as having a feasible solution and a bounded feasible region.

In this case, since the problem is a minimization problem and has a feasible solution, the dual simplex method can be applied. It involves analyzing the dual problem, constructing a dual tableau, and performing iterations to improve the objective function value.

By applying the dual simplex method, we can find the optimal solution and determine if any additional iterations are required to reach the minimum value of the objective function while satisfying the constraints.

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The interest on the loan is: $375.44

The maturity value is: $4,775.44.

Maturity value and interest on a loan can be calculated as follows:

Maturity value: it is the amount of the loan plus the interest charged on it. It can be calculated using the formula:

MV = P + I

where MV is the maturity value, P is the principal (original loan amount), and I is the interest charged on the loan.

Interest: it is the amount charged by the lender for the use of their money. It can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the term of the loan (in years or days).

Therefore:

Exact interest: 4,400 * 6% * 172/365 = $375.44

Maturity value: 4,400 + 375.44 = $4,775.44

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Answer:

4

Step-by-step explanation:

Because 8 + 8 is 16. 16 / 4 is 4. Or 4 x 4 is 16.

Hope this helps! <3

Answer: She gave away 7 pieces and was left with 9 pieces

Step-by-step explanation: Because 8+8+16 the next smallest square you can end up with is 3x3, or 9.

Step 1

Boiling point of mercury = 357℃

Let the boiling point of the lead be x

41/200 x=357

Step 2

41/200 x=357

41/200 x times 200/41 =357 times 200/41

x=1741.46

Step 3

The boiling point of lead is 1741.46

Result

41/200x=357

The boiling point of lead is 1741.46

Hope this helped

Answer: The boiling point of lead is 1741.46°C

Step-by-step explanation: Explanation:

The boiling point of mercury = 357°C

The boiling point of lead is x

41/200 x = 357

x = 357 x (200/41)

x = 1741.46

The boiling point of lead is 1741.46°C

The volume of a tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (2,0,0), (0,1,0), and (0,0,4) using integration, with the order of integration dzdydx i.e. V = ∫[0 to 2] ∫[0 to 1 - x/2] ∫[0 to 4] dz dy dx.

To find the volume of the tetrahedron, we can set up a triple integral using the given order of integration dzdydx. The limits of integration will correspond to the bounds of the region within the tetrahedron. Since the tetrahedron is bounded by the coordinate planes and the plane passing through (2,0,0), (0,1,0), and (0,0,4), the limits of integration will be:

For z: 0 to 4

For y: 0 to 1 - x/2

For x: 0 to 2

Setting up the integral, we have:

V = ∫∫∫ dzdydx

V = ∫[0 to 2] ∫[0 to 1 - x/2] ∫[0 to 4] dz dy dx

Evaluating this triple integral will give us the volume of the tetrahedron in the first octant.

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Step-by-step explanation:

AC = AC by reflexive

∆ABC = ∆CDA by SSS

Angle CAD = angle ACB by CPCTC

Since alt interior angles are congruent, BC //AD

Repeat the same process to show AB//CD

Answer:

22 more minutes.

Step-by-step explanation:

4x + 12 = 100

4x = 100 - 12

4x = 88

x = 88/4

x = 22

Kerry can play for 22 more minutes

Answer:

I'm pretty sure the answer is 22 more minutes

The number of cows and ducks in the garden are 3 and 4 respectively.

Let the numbers of cows be x and the number of ducks is y.

Total number of legs=20

Total number of eyes=14

Linear equation for the total number of legs in the garden,

4x+2y=20 -(1)

Linear equation for the total number of eyes in the garden,

2x+2y=14 -(2)

Solve the system of the two linear equations to find the values of x and y.

Subtract equation (1) from equation (2), and we get,

2x=6

\(x=\frac{6}{2}\\\)

x=3

Substitute the value of x in equation (1), and we get,

4(3)+2y=20

12+2y=20

2y=20-12

2y=8

\(y=\frac{8}{2}\\\)

y=4

Number of cows=3

Number of ducks=4

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Answer:

60 • 15 = $900

Step-by-step explanation:

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Answer:

Step-by-step explanation:

the answer is 4

Answer:

87.5 ml tube of toothpaste slightly offers the better value of money.

Step-by-step explanation:

In order to know the better value of money, we need to find the volume of each toothpaste for 1p.

For first tube of toothpaste:

87.5 ml costs 49p

Therefore, for 1 p = 87.5/49 = 1.78571429 = 1.8 ml

For second tube of toothpaste:

125 ml costs 72 p

Therefore, for 1 p = 125/72 = 1.73611111 = 1.7 ml

Since, 1.8 ml > 1.7 ml

So, 87.5 ml tube of toothpaste slightly offers the better value of money.

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

No because 21 is close to it.

Step-by-step explanation:

To be considered an outlier, it would need to be a farther distance such as the distance from 28 to 21.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

No. it's close to 21.

Step-by-step explanation:

There's a formula for fidning out if something is an outlier or not but i forgot, pff, look it up :P

When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it

The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.

These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.

Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.

For this reason, the correct choice is get closer and closer to the x-axis but never touches it.

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An equation for the fish population, after years is P(t) ≈ 8000e-0.664t ± 0.00005

The equation for the fish population in a stocked lake can be determined using exponential growth.

The formula for exponential growth is

P(t) = \(P_0\)ert

where P(t) is the population after time t,

\(P_0\) is the initial population,

r is the rate of growth, and

e is the mathematical constant approximately equal to 2.71828.

The carrying capacity, K, is the maximum population that can be supported by the environment, and it is a limiting factor for population growth. When the population reaches K, the growth rate slows down until it reaches a point of equilibrium.

The carrying capacity can be estimated using a variety of methods, including the logistic model, which incorporates the carrying capacity into the equation for population growth.

However, for this problem, we are given an estimate of the carrying capacity, which we will use in the exponential growth equation.

We are also given the initial population,

\(P_0\) = 1100, and we are asked to find an equation for the fish population, P(t), after t years.

The rate of growth, r, can be determined using the following formula:

r = ln(P/K) / t

where ln is the natural logarithm, and t is the time it takes to reach the carrying capacity, K.

Since we don't have an exact value for K, we will use the estimated value of 8000.

Thus,

r = ln(1100/8000) / 1

r ≈ -0.664

The negative sign indicates that the population is decreasing, since the growth rate is negative.

Therefore, the equation for the fish population after t years is:

P(t) = 8000e-0.664t

To round to 4 decimal places, we can use the formula:

P(t) ≈ 8000e-0.664t ± 0.00005

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Answer:

v=Bh

12*8= 96. <---B

2 <----h

v=192

Step-by-step explanation:

I hope that helps

Answer:

Answer Graph C

Step-by-step explanation:

Plugged the equation into a graphing calculator.

The standards that use 2.4 GHz are:

A wifi standard defines two characteristics of the wi-fi network, which are speed and frequency.

Such that there are two common frequencies, 2.4 GHz (usually with larger speed) and 5 GHz (usually with lower speed)

The standards that use 2.4 GHz are:

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Given:

The expression is

\(\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=\)

To find:

The simplified form of the expression.

Solution:

We have,

\(\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=\)

The expression \(\sqrt[3]{48}\) can be written as

\(\sqrt[3]{48}=\sqrt[3]{8\cdot 6}\)

\(\sqrt[3]{48}=\sqrt[3]{8}\cdot \sqrt[3]{6}\)       \([\because \sqrt[3]{ab}=\sqrt[3]{a}\sqrt[3]{b}]\)

\(\sqrt[3]{48}=2\cdot \sqrt[3]{6}\)

\(\sqrt[3]{48}=2\sqrt[3]{6}\)

Therefore, \(\sqrt[3]{48}=\sqrt[3]{8\cdot 6}=2\sqrt[3]{6}\).

Answer:

\(150( {1.01}^{12} ) - 150 = 19.02\)

The account will earn $19.02 interest in 12 months.

Answer:

Step-by-step explanation:

To determine the future value of the savings account after 12 months, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the account

P = the principal or initial value of the account (in this case, $150)

r = the annual interest rate (1% per month or 0.01)

n = the number of times the interest is compounded per year (12)

t = the time period in years (1)

Plugging in these values, we get:

A = 150(1 + 0.01/12)^(12*1)

A = 150(1.0075)^12

A = $162.89

Therefore, the savings account will be worth approximately $162.89 after 12 months with 1% monthly interest. It is important to note that this is only an estimate, as the actual amount could vary depending on any additional deposits or withdrawals made during the year, and the interest rate could also change.

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Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is  

that the student has blonde hair, it is  

that the student has brown hair, it is  

that the student has black hair, and it is  

that the student has red hair.

Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is

unlikely

that the student has blonde hair, it is

neither likely nor unlikely

that the student has brown hair, it is

unlikely

that the student has black hair, and it is

unlikely

that the student has red hair.

Step-by-step explanation:

Answer:

by x:

Answer:

\( \sf \: 56ef \)

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

Forming the expression,

→ 7 × e × f × 8

Let's simplify the expression,

→ 7 × e × f × 8

→ (7 × 8) × (e × f)

→ (56) × (ef)

→ 56 × ef

→ 56ef

Hence, the answer is 56ef.

Answer:

Answer is 0.375 :)

Step-by-step explanation:

The probability of the spinner landing only once on yellow in two spins is 0.375.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

As per the given data:

We are given the sample space of possible outcomes for a fair spinner.

Also, we are given a table which denotes the frequency of the color yellow appearing on the spinner.

For finding out the probability of the spinner landing only once on yellow in two spins.

= Favorable outcomes / Total number of outcomes

From the given table:

Favorable outcomes = 6

= Favorable outcomes / Total number of outcomes = 6 / 16

= 0.375

The probability of the spinner landing only once on yellow in two spins is 0.375.

Hence, The probability of the spinner landing only once on yellow in two spins is 0.375.

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Answer:1.6

Step-by-step explanation:

25/5=5

8/5=1.6

Answer:

Step-by-step explanation:

if 5miles = 25 minutes

then, 8 miles = X

hence X minutes

\(x = \frac{25minutes}{5miles} \times 8miles\)

Answer:

-2m -5n = 7m - 3n

<=> -5n + 3n = 7m + 2m

<=> -2n = 9m

<=> m = \(\frac{-2}{9}n\)

Step-by-step explanation:

Answer:

n = -9/2m

Step-by-step explanation:

I got this answer from Khan Academy.

Hope this helps! :)

Answer:

7/8 is less than 1, sure it is close to one but not 1.

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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