A farmer needs to enclose three sides of a plot with a fence (the fourth side is a river). The farmer has 54 yards of fence and wants the plot to have an area of 360 sq-yards. What should the dimensions of the plot be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)

length = yards
width = yards

Enter your answers as numbers. If necessary, round to the nearest hundredths.

The monthly cost for 17 hundred of cubic feet is $52.13.

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the bill paid for x HCF of water.

The slope is 1.45, hence m = 1.45.

The monthly cost for 13 HCF is $46.33, hence:

46.33 = 1.45(13) + b

b = 27.48

y = 1.45x + 27.48

For 17 HCF:

y = 1.45(17) + 27.48 = 52.13

The monthly cost for 17 hundred of cubic feet is $52.13.

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Answer:

Mary climbed higher

Step-by-step explanation:

think of it like this a wall is four feet and you climb 3 feet up. You are closer to the top than if you climbed 3 feet up a 8 wall.

You should know that

p ⇒ q ≡ ¬p ∨ q

so that

p ⇒ (q ∧ r) ≡ ¬p ∨ (q ∧ r)

Then making the truth table is simple:

[tex]\begin{array}{cccccc} p & q & r & \neg p & q \land r & p \implies (q\land r) \\ T & T & T & F & T & T \\ T & T & F & F & F & F \\ T & F & T & F & F & F \\ T & F & F & F & F & F \\ F & T & T & T &  T & T \\ F & T & F & T & F &  T \\ F & F & T & T & F & T \\ F & F & F & T & F & T \end{array}[/tex]

Answer:

aₙ = a₁ * 2ⁿ⁺¹

Step-by-step explanation:

a₁ = 6

a₂ = 12

a₃ = 24

Note a₂/a₁ = 2 = a₃/a₂

So it is a geometric sequence with common ratio of 2

a₂ = a₁ * 2 = a₁ * 2¹ = a₁ * 2²⁺¹

a₃ = a₂ * 2 = a₁ * 2 * 2 = a₁ * 2² = a₁ * 2³⁺¹

Then

aₙ = a₁ * 2ⁿ⁺¹

Answer:

Good morning! Number of trials are 250.

Step-by-step explanation:

A researcher finds 50% of all commuters in a metropolitan area take the train to work.

The researcher polls 250 people in the area to ask them whether they take the train to work or not.

We have tell the number of trials for this binomial experiment.

Researcher will do 250 trials to confirm whether they take the train work and this irrespective of their response.

_AnnieTheDreamGirl, 3/8/2022

Answer:

28

Step-by-step explanation:

2*28 = 56

3*28 = 84 -10 = 74

74+56+50 = 180

180 degrees in a triangle

Answer:

# of reserved seats = R;  # of general admission seats = G

                                                    G - R = 85

                                         $18R + $9G =$3600

Multiply 1st equation by 18:  18G - 18R = 1530

Rearrange 2nd equation:   $9G + $18R =$3600

Combine the equations:               27 G  =   5130

                                                       G  =  190

                                                       R  =  105

Step-by-step explanation:

Answer:

X=48

Step-by-step explanation:

100 = 2x+4

100-4 = 2x

96 = 2x

96/2 = x

x = 48

Answer:

21,400

Solving steps:

Since, Marie has $60,000 in a savings account that earns 7% interest per year.

Find: How much will she have in 4 months.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: solution[/tex]

Step 1: Find the money for the 7% rate

=> [tex] 60000 \times \frac{7}{100} [/tex]

=> [tex] \frac{60000}{1} \times \frac{7}{100} [/tex]

cancel the two zeros of 60,000 and 100

=> 600 × 7

=> 4,200

Add 4,200 to 60,000

=> 64,200

per year = 64,200

Now, divide 64,200 by 12

since 12 months to make one year

=> 64,200 ÷ 12

=> 5,350

now multiply it by 4 months she gets 5350 per month

=> 21,400

Answer:

You started with 32.00

Step-by-step explanation:

47 minus 15 is 32

The distance from building A to building C is 433m

Therefore,

sin 60° = opposite / hypotenuse

sin 60° = b / 500

cross multiply

b = 500 sin 60°

b = 500 × 0.86602540378

b = 433.0127

b = 433 meters

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Answer:

93/100

Step-by-step explanation:

You have to make the denominator the same so

7x10=70 and 10x10=100. Then you add 23+70 which is 93 so the answer is 93/100

Answer:

this expression is true for all values of a.

Step-by-step explanation:

So if the expression is:

a - 5 = 5 - a

For this reason:

2a = 10

a = 5

a - 5 = -5 + a

0 = 0

Answer:

x = 110

y = 102

z = 82

Step-by-step explanation:

Angles that create a line are equal to 180

x + 70 = 180

x = 110

y + 78 = 180

y = 102

A quadrilateral's angles add up to 360

110 + 78 + 90 + z = 360

278 + z = 360

z = 82

Answer:

a cube that is 1 yard long, 1 yard wide, and 1 yard high

Step-by-step explanation:

The dimensions for a unit cube are:

[tex]1\times1\times1[/tex]

Please note that the units for each side MUST be the same (or if they're different, then the lengths have to be equivalent).

Looking at the answer choices, we can see that the last answer choice is a 1 yd by 1 yd by 1 yd cube, therefore it is a unit cube.

Answer:

I guess 4, because it has only 1 unit in it, and not 9 inches^3.

Step-by-step explanation:

Hope this helps.

Answer:

x = 2•sqroot(5)

x ~= 4.47

Step-by-step explanation:

Draw a line to make the "top" part be a

4 × 3 rectangle. see image.

Then you will have a right triangle on the bottom. It has legs 2 and 4 units long. Use the Pythagorean theorem to solve for x. see image.

Answer:

4.5

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] of the water takes [tex]\frac{1}{2}[/tex] of the fuel and empty tank takes [tex]\frac{1}{6}[/tex] of the fuel, the

fraction that would will be spent if there was no leak is [tex]\underline{\dfrac{11}{18}}[/tex] of the fuel

The given parameters are;

The volume of oil consumed = [tex]\mathbf{\dfrac{1}{2}}[/tex] of the fuel tank

Volume consumed if the water tank was empty = [tex]\dfrac{1}{6}[/tex] of the fuel tank

Let w represent the weight of the water that fills the tank.

Therefore;

[tex]The \ average \ weight \ carried \ by \ oil = \dfrac{w + \dfrac{w}{2} }{2} = \mathbf{\dfrac{3 \cdot w}{4}}[/tex]

The amount of fuel consumed by the water that leaked = [tex]\dfrac{1}{2} - \dfrac{1}{6} = \dfrac{1}{3}[/tex]

Let x represent the amount of oil used to carry only the water if there

was no leak, therefore;

[tex]\mathbf{\dfrac{\frac{3 \cdot w}{4} }{w} }= \dfrac{\frac{1}{3} }{x}[/tex]

Which gives;

[tex]\mathbf{\dfrac{3 \cdot w}{4} \times x}} = \dfrac{1}{3} \times w }[/tex]

[tex]x = \dfrac{4}{3 \times 3} = \dfrac{4}{9}[/tex]

The total amount of fuel that will be consumed without leakage is

therefore;

[tex]Total \ amount \ of \ fuel = \dfrac{4}{9} + \dfrac{1}{6} = \mathbf{ \dfrac{11}{18}}[/tex]

The amount of oil consumed if there was no leakage is therefore;

Learn more about averages here;

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Answer:

the answer is A

Step-by-step explanation: it is A because 45 percent of $166 is $47.7 and if you subtract it from 166 it turns out to be $118.3

Answer:

1, 4, 3, 5, 6

Step-by-step explanation:

5(5x² - 9x) = 45x + 40 ← distribute parenthesis on left side

25x² - 45x = 45x + 40 ← subtract 45x + 40 from both sides

25x² - 90x - 40 = 0 ← factor out 5 from each term

5(5x² - 18x - 8) = 0

5(x(5x + 2) - 4(5x + 2))

5(x - 4)(5x + 2)

Answer:

The order is: 1, 4, 3, 5, 6

Step-by-step explanation:

5(5x² - 9x) = 45x + 40

25x² - 45x = 45x + 40

25x² - 90x - 40 = 0

5(5x² - 18x - 8) = 0

5(x(5x + 2) - 4(5x + 2)

5(x - 4)(5x + 2)

The order is: 1, 4, 3, 5, 6

The significance level shows that z approximately equals 1.41 for a p-value of 0.078642.

Based on the complete question, the sample proportion for city A will be:

= 54/90 = 0.60

The sample proportion for city B will be:

= 63/90 = 0.70

Using the table given, it can be deduced that the test statistic value will be 1.41. Therefore, the p-value will be 0.078652 in the Excel function.

Since the p-value is greater than 0.05, then we fail to reject the null hypothesis that there is no difference in the commute time.

Learn more about significance level on:

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Answer:

4 1/4 in.

Step-by-step explanation:

Highest record: 24 ft. 6 3/4 in.

John's best long jump: 24 ft. 2 1/2 in.

convert 1/2 to have denominator of 4...

1/2 x 2/2=2/4

subtract from highest record...

3/4-2/4=1/4

add to whole numbers...

6-2=4

4+1/4= 4 1/4

Answer:

this is just division

6/4=1/2

each book weighs 1/2

Hope This Helps!!!

Answer:

the answer is 1.5 pounds

Step-by-step explanation:

just took the the test

Answer:

The axis of symmetry of this parabola will be the line x=−b2a .

Step-by-step explanation:

Graph the parabola y=x2−7x+2 .

Compare the equation with y=ax2+bx+c to find the values of a , b , and c .

Here, a=1,b=−7 and c=2 .

Use the values of the coefficients to write the equation of axis of symmetry .

The graph of a quadratic equation in the form   y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .

Substitute x=72 in the equation to find the y -coordinate of the vertex.

y=(72)2−7(72)+2    =494−492+2    =49 − 98 + 84     =−414

Therefore, the coordinates of the vertex are (72,−414) .

Answer:

2

Step-by-step explanation:

Answer:

  B. X=0.02

Step-by-step explanation:

The solution to the natural log equation is found by taking antilogs.

  ln(x) = -4 . . . . . . . given equation

  x = e^-4 . . . . . . . take antilogs

  x ≈ 0.0183156

  x ≈ 0.02 . . . . rounded to 2 decimal places

_____

Additional comment

Essentially, we use each side of the equation as a power of e.

  e^ln(x) = e^(-4)

  x = e^-4 . . . . . . . simplified

Choices C and D can be eliminated by the fact that ln(x) for x < 0 is undefined. x cannot be negative.

Answer:

a. -1

Subtracting 6-7 would give you -1. Negative 1 is 7 units from the number 6.

b. -5 and 15

Adding and subtracting 10 from 5 would give you -5 and 15.

c. -3

Starting at -7, and going to the right 4 means that Darcy moved +4. -7+4 would give you negative 3.

Answer:

[A] - 1

[B] - 5

[C] -3

Step-by-step explanation:

[A] The number 6 is 7 units away from 13 on a number line. Which other integer is 7 units away from 6 on a number line?

Solve:

6+7=13

6-7=-1

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[B] which integers are 10 units away from 5 on a number line?

Solve:

5-10=-5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[C] Starting at -7 on a number line,Darcy moved 4 units to the right. What integer did Darcy land on?

Solve:

-7+4=-3

Negative + Positive =[ Negative]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

Answer:

Percentage of Money Zack receives =

[tex]\bold{\frac{the \:share \:he\: gets \:in\: ratio \:form}{Total \:share \:in\: ratio \:form} \times 100}\\[/tex]

[tex] \bold{\frac{9}{11 + 9} \times 100} \\ \\\bold{ ⇢ \frac{9}{\cancel{20}} \times\cancel{ 100} }\\ \\ \bold\blue{ ⇢ 45\%}[/tex]

hope helpful~

Answer:

-1 I apologize if I'm wrong

Answer:

-5 steps away

explanation:

Add the x and y axis and then count how many it resulted in.

I'm not sure where the gift shop was, but since that wasn't included I had to assume it was at (0, 0). Let me know so I can change this if I need to. Thank you.

Step-by-step explanation:

we want to find the hypotenuse

soh cah toa

he have hypotenuse and opposite

soh

sin 20 = H/4

can u do the rest and put answer in comments please mark brainest

Step-by-step explanation:

it's a right triangle

Pythagorean theorem

the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

x² = 9² - 2²

x² = 81 - 4

x² = 77

x = √77

or

x = 8.77

---------------------

Answer:

(x - 2)² + (y - 2)² = 4

Step-by-step explanation:

The circle is tangent to both axes, so the radius = x = y

Center is on 2x + 3y = 0, so 2x + 3x = 1-

x = 2 = y

center: (2, 2)

radius = 2

equation: (x - 2)² + (y - 2)² = 2²

(x - 2)² + (y - 2)² = 4