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A new homeowner needs to put up a fence to make his yard secure. the house itself forms the south boundary and the garage forms the west boundary of the property, so he needs to fence only 2 sides. the area of the yard is 4000 sq ft. he has enough material for 160 ft of fence. find the length and width of the yard.

Answers

Answer 1
Answer:

Let the width = x feet, then the length = 160 - x  feet.

The area =  x * (160 - x) = 4000

160x - x^2 = 4000

x^2 - 160x + 4000 = 0

x =  [- (-160) +/-  sqrt (160^2 - 3 * 1 * 4000)] / 2

x =   128.98 or 31.01

answer is length = 129 feet and width = 31 feet   ( to nearest foot).

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Which is an example of a situation that is in equilibrium?A. The amount of air in a room increases quickly when the door is
opened.
B. The amount of money in a bank account never changes
C. The amount of water in a cup decreases as it evaporates
D. A flower slowly grows taller​

Answers

Answer:B the amount of money in a bank account never changes.

Step-by-step explanation:

Answer:

B. The amount of money in a bank account never changes.

Step-by-step explanation:

Equilibrium is achieved when the state of a reversible reaction of opposing forces cancel each other out. While in a state of equilibrium, the competing influences are balanced out. Imagine a cup with a hole in it being filled with water from a tap. The level of water in this cup would stay the same if the rate at which the water that flows inside is the same as the water that flows outside. Option B will be the correct answer because the amount of money going into the account is at the same rate of money coming out of the account.

Will mark brainliest, 60 points

Answers

Answer:

\boxed{ \bold{ \sf{ \: 1. \: \: \: \: \: 198}}}

\boxed{ \bold{ \sf{2. \: \: \: \: \: - 8}}}

\boxed{ \bold{ \sf{ 3. \: \: \: \: \: (64)/(343) }}}

Step-by-step explanation:

1. Given, u = 20 , x = 4 , y = 7 , z = 10

\sf{ (u)/(z) + x {y}^(2) }

⇒\sf{ (20)/(10) + 4 * {7}^(2) }

⇒\sf{ (20)/(10) + 4 * 49}

⇒\sf{ (20)/(10) + 196}

⇒\sf{ (20 + 196 * 10)/(10) }

⇒\sf{ (20 + 1960)/(10) }

⇒\sf{ (1980)/(10) }

⇒\sf{198}

2. \sf{4( - 2)}

Multiplying or dividing a positive integer by any negative integer gives a negative integer

= -8

3. \sf{( (4)/(7) ) ^(3) }

⇒\sf{( \frac{ {4}^(3) }{ {7}^(3) } })

⇒\sf{ (4 * 4 * 4 )/(7 * 7 * 7)}

⇒\sf{ (64)/(343) }

Hope I helped!

Best regards! :D

Answer:

\Huge \boxed{\mathrm{18. \ \ \ 198}} \n\n\n \Huge \boxed{\mathrm{19. \ \ \ -8}} \n\n\n \Huge \boxed{\mathrm{20. \ \ \ (64)/(343) }}

\rule[225]{225}{2}

Step-by-step explanation:

18.

\displaystyle (u)/(z) +xy^2

u = 20, x = 4, y = 7, and z = 10.

\Rightarrow \displaystyle (20)/(10) +(4)(7)^2

\Rightarrow \displaystyle 2+(4)(49)

\Rightarrow 2+196

\Rightarrow 198

19.

4(-2)

Rewriting.

\Rightarrow -(4*2)

Multiplying.

\Rightarrow -8

20.

\displaystyle ( (4)/(7) )^3

Distributing the cube sign to the numerator and the denominator.

\Rightarrow \displaystyle (4^3 )/(7^3 )

\Rightarrow \displaystyle (64)/(343)

\rule[225]{225}{2}

You need to borrow $15,000 to buy a car, and you determine that you can afford monthly payments of $325. The bank offers three choices: a 3-yearloan at 7% APR, a 4-year loan at 7.5% APR, or a 5-year loan a 8% APR. Which loan best meets your needs? Show your work and explain your reasoning.

Answers

The 4-year loan at 7.5% APR seems to be the best choice as it strikes a balance between a reasonable monthly payment and minimizing the total interest paid.

To determine which loan option best meets your needs, you should consider both the monthly payment amount and the total cost of the loan. Here's how you can calculate and compare the three options:

1. 3-year loan at 7% APR:

  - Monthly payment: $325

  - Total payments over the loan term: $325 * 12 months/year * 3 years = $11,700

  - Total interest paid: $11,700 - $15,000 = $3,300

2. 4-year loan at 7.5% APR:

  - Monthly payment: $325

  - Total payments over the loan term: $325 * 12 months/year * 4 years = $15,600

  - Total interest paid: $15,600 - $15,000 = $600

3. 5-year loan at 8% APR:

  - Monthly payment: $325

  - Total payments over the loan term: $325 * 12 months/year * 5 years = $19,500

  - Total interest paid: $19,500 - $15,000 = $4,500

Now, let's analyze the options:

- The 4-year loan at 7.5% APR has the highest monthly payment but the lowest total interest cost, making it the most cost-effective option. However, you should ensure that the higher monthly payment fits comfortably within your budget.

- The 3-year loan at 7% APR has a lower interest cost than the 5-year loan but a higher monthly payment. It's a good middle-ground choice if you can afford the monthly payments.

- The 5-year loan at 8% APR offers the lowest monthly payment but results in the highest total interest cost. It's the least cost-effective option, and you would end up paying significantly more over the loan term.

Ultimately, the 4-year loan at 7.5% APR seems to be the best choice as it strikes a balance between a reasonable monthly payment and minimizing the total interest paid. However, ensure that the monthly payment aligns with your financial situation before making a decision.

For more such questions on monthly payment:

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Answer:

the 5yr/ $270mth

Step-by-step explanation:

$15k × 8% = $1200 interest

$15k + $1200 = $16,200.00

$16500 ÷ 60months (5years) = $270/mth pymt

Three times a number is less than 96.

Answers

Answer:

x is greater than sign then 32

Step-by-step explanation:

Please help

determine all the unknown values of the figure below.

Answers

Answer:

F=12.76

S=27.18

X=62 degrees

Step-by-step explanation:

hope this helps

mark brianliest ;)

Based on the right-angled triangle shown above, all the unknown values are;

S = 27.18 units

F = 12.76 units

x = 62°.

How to determine the measure of the missing side lengths and angle?

In order to determine the measure of the missing side length, we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side (24) of a right-angled triangle;

cos(θ) = Adj/Hyp

Where:

  • Adj represent the adjacent side of a right-angled triangle.
  • Hyp represent the hypotenuse of a right-angled triangle.
  • θ represent the angle.

For the cosine trigonometric function ratio, we have the following:

cos(28) = 24/S

S = 24/cos(28)

S = 27.18 units

From tangent trigonometric function ratio, we have the following:

tan(28) = F/24

F = 24tan(28)

F = 12.76 units

Since the angles formed by a right-angled triangle are acute complementary angles;

x + 28 = 90

x = 90 - 28

x = 62°.

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The U.S. Department of Agriculture guarantees dairy producers that they will receive at least $1.00 per pound of butter they supply to the market. Below is the current monthly demand and supply schedule for wholesale butter (in millions of pounds per month). Wholesale Butter Market Price (dollars per pound) Quantity of Butter Demanded Quantity of Butter Supplied
(millions of pounds) (millions of pounds)
$0.80 107 63 0
.90 104 71
1.00 101 79
1.10 98 87
1.20 95 95
1.30 92 103
1.40 89 111
1.50 86 119
1.60 83 127
1.70 80 135
1.80 77 143
a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.
b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program? 22 million pounds 79 million pounds Zero 11 million pounds Suppose that a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price.

Answers

Answer:

a. In the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.

b. The correct option is zero.

c. See the attached excel file for the new supply schedule.

d. The monthly surplus created by the price support program is 18 million pounds given the new supply of butter.

Step-by-step explanation:

Note: This question is not complete. A complete question is therefore provided in the attached Microsoft word file.

a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.

At equilibrium, quantity demanded must be equal with the quantity supplied.

In this question, equilibrium occurs at the price of $1.20 per pound and quantity of 95 million pounds.

Therefore, in the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.

b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program?

Price floor refers to a government price control on the lowest price that can be charged for a commodity.

It should be noted that for a price floor to be binding, it has to be fixed above the equilibrium price.

Since the price floor of $1 per pound is lower than the equilibrium price of $1.2 per pound, the price floor will therefore not be binding. As a result, the market will still be at the equilibrium point and the monthly surplus created in the wholesale butter market due to the price support (price floor) program will be zero.

Therefore, the correct option is zero.

c. Fill in the new supply schedule given the change in the cost of feeding cows.

Since a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price, this implies that there will be an increase in supply by 40 million at each price.

Note: Find attached the excel file for the new supply schedule.

d. Given the new supply of butter, what is the monthly surplus of butter created by the price support program?

Since the price floor has been fixed at $1 per pound by the price support program, we can observe that the quantity demanded is 101 million pounds and quantity supplied is 119 million pounds at this price floor of $1. The surplus created is then the difference between the quantity demanded and quantity supplied as follows:

Surplus created = Quantity supplied - Quantity demanded = 119 - 101 = 18 million pounds

Therefore, the monthly surplus created by the price support program is 18 million pounds given the new supply of butter.

Final answer:

In the wholesale butter market, the equilibrium quantity is 95 million pounds and price is $1.20 a pound. The monthly surplus with price support is -22 million pounds showing a shortage. The decrease in cost of feeding cows shifts the supply to right, creating a potential surplus.

Explanation:

The equilibrium quantity and price in the wholesale butter market are determined by where the quantity demanded equals the quantity supplied. From the given schedule, we can see that this occur when the price is $1.20 per pound and the quantity is 95 million pounds.

The monthly surplus created due to the price support is calculated by subtracting the quantity demanded from the quantity supplied at the price floor of $1.00. This gives us a surplus of 79 million pounds - 101 million pounds = -22 million pounds, indicating a shortage rather than a surplus.

If the cost of feeding cows decreases, shifting the supply schedule to the right by 40 million pounds, the new equilibrium will need to be found again where quantity demanded equals quantity supplied. This shift would increase the quantity supplied at every price point, resulting in a potential surplus if demand conditions remain unchanged.

Learn more about Price Support and Market Equilibrium here:

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