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Answer: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)

a) Formulate this problem in terms of an objective function and constraint(s).

b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.

c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2

d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?

e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?

Step-by-step explanation: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)

a) Formulate this problem in terms of an objective function and constraint(s).

b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.

c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2

d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?

e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?

Answer:

The student must pay 4247.5 - 4000 = 247.50 dollars in interest

Step-by-step explanation:

Answer:

A 3.00/12=.25 ea

B 7.50/3=2.50/1lb

C 2.00/4=.50ea

S 3.50/10=.35/ea

Here you go! Hope it helps.

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Thank you -= Miss Hawaii

First, find the tax rate for a person whose taxable income is $130,000. By looking at the table, you can see the tax rate is 33%. To find the total tax, multiply 33% by $130,000.

[tex]0.33 \times 130000 = 42900[/tex]

Thus, the tax this person has to pay is $42,900.

Answer:

it's an scalene triangle

having all the sides and angels different from each other

Step-by-step explanation:

brainliest plz

Answer:

$300

Step-by-step explanation:

Diane's interest rate on the loan is approximately 8.43%.

Let's determine Diane's interest rate step by step.

1. First, we need to understand the formula for simple interest:

  Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

  where:

  P = Principal amount (initial loan amount)

  R = Interest rate (unknown, what we want to find)

  T = Time period in years

2. We have the following information from the problem:

  P = $3000 (Principal amount)

  SI = $253 (Total interest paid)

  T = 11 months

3. However, to use the formula, we need to convert the time from months to years. Since 1 year has 12 months, we can write:

  T = 11 months ÷ 12 months/year

     ≈ 0.917 years

4. Now, let's rearrange the formula to solve for the interest rate (R):

  R = SI / (P × T)

  Substituting the given values:

  R = $253 / ($3000 × 0.917) ≈ 0.0925

5. Finally, we need to convert the interest rate from a decimal to a percentage:

  R = 0.0925 × 100 ≈ 8.43%

So, Diane's interest rate on the loan is approximately 8.43%.

In summary, to find the interest rate, we used the simple interest formula and rearranged it to solve for the rate. We converted the time from months to years before calculating the interest rate. The result is approximately 8.43% interest rate, indicating the percentage of the principal that Diane had to pay as interest over 11 months.

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The amount that will be gotten by each nephew when Virgie will equally give P 742.60 among her 4 nephews will be $185.65.

Since Virgie will equally give P 742.60 among her 4 nephews, the amount that each nephew gets will be:

= 742.60 / 4

= $185.65

If Php 5876 are distributed equally among 26 men, the amount that each person gets will be:

= Php 5876 / 26

= Php 226

If Bernard wants to cut a straight board into 4 equal pieces and the board is 112.12 cm, the length of each piece will be:

= 112.12cm / 4

= 28.03cm

The number of 25cents coins that are equal to P 5.00 will be:

= 5/0.25

= 20

There will be 20 25 cents coins on P5.00.

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Answer:

im pretty sure its 1/44 plz make me branliest

Step-by-step explanation:

Answer:

I'm not sure what this is asking but footaction is cheaper

Step-by-step explanation:

footlocker the shoes (single pair) is 69.98/2 or 34.99

footaction is 99.99/3 or 33.33

Answer:

21.6 magazines

Step-by-step explanation:

260/12=21.6

Answer: 25

Step-by-step explanation:

To find the greatest common factor of an number, you start by listing the factors of each number. The factor that appears the greatest amount of times is the greatest common factor.

175: 1,5,7,25,35,175.

75: 1,3,5,15,25,75.

25:1,5,25.

The number 25 in this case appears the most frequently, therefore the answer is 25.

The greatest common factor (GCF), of the given numbers 50, 75, and 150 is 25.

To find the GCF, we identify the common factors of the given numbers and then select the largest one. The common factors of 50, 75, and 150 are the numbers that divide each of them without leaving a remainder.

In this case, 25 is the largest number that divides all three numbers evenly.

50 = 2 × 5 × 5

75 = 3 × 5 × 5

150 = 2 × 3 × 5 × 5

Since 25 is present as a factor in all three numbers, it's the greatest common factor.

Therefore, The GCF of 50, 75, and 150 is 25.

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Step-by-step explanation:

gcvnjgcnhkk xdhvchjjudvhtuk xecn9

1. The equivalent rational expression with the lowest common denominator of   [tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex]   is [tex]\frac{2}{(d+5)(3d-1)}[/tex]

2. The equivalent rational expression with the lowest common denominator of [tex]\frac{3d}{3d^{2} - 22d + 7}[/tex]  is [tex]\frac{3d}{(d-7)(3d-1)}[/tex]

1.

  [tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex]

Let factorise the denominator below

3d² + 14d - 5

-15 and 14

Two numbers we can multiply to get -15 and add to get 14 are 15 and -1.

Therefore,

3d²- d + 15d - 5

d(3d - 1) + 5(3d - 1)

(d+5)(3d-1)

Therefore, the equivalent rational expression with the lowest common denominator will be

[tex]\frac{2}{(d+5)(3d-1)}[/tex]

2.

[tex]\frac{3d}{3d^{2} - 22d + 7}[/tex]

Factorise the denominator

3d²- 22d+7

3d²- d - 21d + 7

d(3d - 1) - 7(3d - 1)

(d - 7)(3d - 1)

Therefore, the equivalent rational expression with the lowest common denominator will be

[tex]\frac{3d}{(d-7)(3d-1)}[/tex]

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Answer:

356

Step-by-step explanation:

She will earn a total of $296.

We have - Alani who has a summer job as a lifeguard. She makes $8/h for up to 40 h each week. If she works more than 40 h, she makes 1.5 times her hourly pay, or $12/h for each hour over 40 h. How much will Alani earn if she works: a. 37 hours.

We have to determine - How much will Alani earn if she works for 37 hours.

The amount of money you will earn will be = $30[tex]x[/tex].

According to question, we have -

Pay per hour = $8

Number of hours she work in a week = 40 hours

For working 37 hours, which is less than 40, she will receive an hourly wage of $8 only. Therefore -

$8 x 37 = $296

Hence, she will earn a total of $296.

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Answer:

- 4

Step-by-step explanation:

(2x + 4)² + 1 = 5 ← expand left side using FOIL and simplify

4x² + 16x + 16 + 1 = 5

4x² + 16x + 17 = 5 ( subtract 5 from both sides )

4x² + 16x + 12 = 0 ( divide terms by common factor 4 )

x² + 4x + 3 = 0 ← in standard form

(x + 3)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 1 = 0 ⇒ x = - 1

Summation of solutions = - 3 + (- 1) = - 3 - 1 = - 4

Answer:

[tex]x = \frac{ - 24 \pm \sqrt{ - 288} }{4} \\ = \frac{ - 24 \pm \sqrt{ ( - 1) {(12)}^{2} (2)} }{4} \\ = \frac{ - 24 \pm \sqrt{ - 1} \sqrt{ {12}^{2} } \sqrt{2} }{4} \\ = \frac{ - 24 \pm i 12\sqrt{2} }{4} \\ =-\frac{24}{4}\pm \frac{i12\sqrt{2}}{4}\\= - 6 \pm \: i3 \sqrt{2} [/tex]

Answer:

7.5 < 7.5061 < 7.56 < 9.213

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

500 = 400 + 50s. Therefore, Bart can buy 2 pairs of shoes.

=============================================================

Explanation:

s = number of pairs of shoes

50s = amount spent on shoes ($50 per pair)

50s+400 = total amount spent on shoes and uniforms

That expression is the same as 400+50s because we can add numbers in any order we want. Set this equal to the $500 he started with to get the equation 500 = 400 + 50s

We have enough info to determine the answer must be choice B

We can stop here if you wanted.

----------

Let's solve that equation for s

500 = 400 + 50s

400 + 50s = 500

50s = 500-400 .... subtract 400 from both sides

50s = 100

s = 100/50 .... divide both sides by 50

s = 2

This means he can buy 2 pairs of shoes.

Buying the shoes only will cost 50s = 50*2 = 100 dollars, which on top of the $400 for the uniforms, leads to a grand total of 400+50s = 400+100 = 500 dollars. This helps confirm we have the correct value for s.

Answer:  $1.40

Work Shown:

x = cost before markup

1.45x = cost after the 45% markup

1.45x = 2.03

x = (2.03)/(1.45)

x = 1.40

Answer:

A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b

Step-by-step explanation:

First: Find out their decimal form.

- 2 1/6 as a decimal is 2.16

7/3 as a decimal

To get 7/3 converted to decimal, you simply divide 7 by 3. Don't worry. You don't need to get the calculator out, because we did this for you.

7/3 as a decimal is:

2.333333333

Answer:

[tex]{ \rm{ {5b}^{4} \times {4b}^{3} }}[/tex]

• from laws of indices:

[tex] \hookrightarrow \: { \boxed{ \rm{ {rx}^{n} + {px}^{m} = (r \times p) {x}^{(n + m)} }}} \\ [/tex]

• substitute:

[tex]{ \rm{ {5b}^{4} \times {4b}^{3} = (5 \times 4) {b}^{(4 + 3)} }} \\ \\ = { \boxed{ \boxed{ \rm{ \: 20 {b}^{7} \: \: }}}}[/tex]

Answer:

17.49955

Step-by-step explanation:

Hope this helps

Answer:

The profit will be 7.7 million in 2007

Step-by-step explanation:

6x(1+ 0.13)^2

6x1.13^2

6x1.2769

Answer:8

Step-by-step explanation:

Answer:

not sure about it this one is tuff