A garden bed is 4’ by 3’ and a 6’ layer of soil will be spread over the garden. A bag of soil contains 2ft3 of soil how many bags r needed

The median price from the given data is 648,303.

To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.

Let's arrange the data in ascending order:

181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954

There are a total of 13 data points, which is an odd number. So, the median price is the middle value.

The middle value is the 7th value:

Median Price = 648,303

Therefore, the median price from the given data is 648,303.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Answer:

1. The amount of ice needed for the sculpture is 18 m³

2. The amount of fabric needed to manufacture the umbrella is 0.757 m²

3. The height of the cone is 37.5 cm

4. The largest possible storage area which is obtained by attaching the storage area to the back of the building is 87.11 m²

Step-by-step explanation:

1. The volume, V, of a rectangular pyramid = \(\dfrac{1}{3} \cdot B \cdot h\)

Where:

B = Base area = Length, L  × Width, W

h = Height of the pyramid = 3.6 m

L = 5 m

W = 3 m

The volume = 1/3 × 5 × 3 × 3.6 = 18 m³

The amount of ice needed for the sculpture is 18 m³

2) The surface area of a cone = π·r·s

s = Slant height

r = Radius of the cone's base = 0.4 m

h = The height of the cone = 0.45m

s = √(0.4² + 0.45²) = (√145)/20

The surface area of the cone = π × 0.4 × (√145)/20 = 0.757 m²

The amount of fabric needed to manufacture the umbrella is 0.757 m²

3) The volume, V of the cone = 150 cm³

The base area, \(A_b\), of the cone = 12 cm²

The height of the cone = h

We note that the volume of a cone = \(\dfrac{1}{3} \cdot A_b \cdot h\)

Therefore;

\(\dfrac{1}{3} \times 12 \times h = 150\)

4·h = 150

h = 150/4 = 37.5 cm

The height of the cone = 37.5 cm

4) The storage area at the back corner  with four sides = 100 m²

The storage area at the back of the building with three sides = 98 m²

Given that the available riling = 28 m, we have;

For maximum area the four sides should be equal, hence dimension of each side = 28/4 = 7

The area of storage space that can be fenced on four sides at the back corner = 7 × 7 = 49 m²

At the back of the building only three sides need fencing, we therefore have;

The side length = 28/3 = \(9\frac{1}{3}\)

The area fenced = \(\left 9\frac{1}{3} \right \times 9\frac{1}{3} = 87\frac{1}{9} \ m^2\) = 87.11 m²

Therefore, the largest possible storage area, 87.11 m², is obtained by attaching the storage area to the back of the building.

Answer:

6-16=10x here is you answer

The answer to this question is B: the original optimal solution will remain the same

If one of the coefficients of the objective function is changed to a value inside of its respective sensitivity range (lower than the upper limit or greater than the lower limit), the original optimal solution will remain the same. Sensitivity analysis is the examination of the way a change in an objective function's coefficient changes the optimal solution's value.

This analysis is also known as "What-If" Analysis.The sensitivity range is the range of possible values for the objective function coefficients within which the existing optimal solution remains optimal. The optimal solution's coefficients or values are considered sensitive within the sensitivity range.

If any of the coefficients in the optimal solution changes inside the sensitivity range, the original optimal solution will remain optimal.

Shadow Price:In linear programming, the shadow price is the increase in the objective function's value when a constraint's right-hand side is increased by one unit, while all other variables remain constant. The shadow price for the decision variables can be used to identify how much each additional unit of a limited resource is worth.

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Answer:

Black: 1/2 * 12 = 6

Silver: 12 * 1/6 = 2

Other: 12 - 6 - 2 = 4

Set linear equations for both amounts:

Since the amounts are same, set them equal:

After 3 weeks.

After 3 weeks they will have:

The amount saved is $7.

The intersection of two lines has coordinates of (3, 7) which indicate the number of weeks and saved amount.

Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Using the linear model Y = 1.09X + 18.77, we can estimate the profit for the year 1977. The estimated profit for 1977 is $20.95.

To estimate the profit for the year 1977, we substitute X = 2 (representing 1977 - 1975 = 2) into the linear model Y = 1.09X + 18.77.

Y = 1.09 * 2 + 18.77

Y ≈ 20.95

Therefore, the estimated profit for the year 1977 is approximately $20.95.

To estimate the profit in 1977 using the linear model Y = 1.09X + 18.77, we need to determine the value of X for the year 1977. In this case, X represents the number of years after 1975. So, to find the value of X for 1977, we subtract 1975 from the year 1977:

X = 1977 - 1975 = 2

Now, we can substitute this value into the equation to estimate the profit in 1977:

Y = 1.09 * X + 18.77

Y = 1.09 * 2 + 18.77

Y = 2.18 + 18.77

Y ≈ 20.95

Therefore, the estimated profit for the company in 1977, based on the linear model, is approximately 20.95.

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Based on the fact that in the simple random variable, 5 is the sample mean, then it is a d. point estimate.

A point estimate refers to a specific value in a random group of variables that tell us more about the variables.

The mean is therefore a point estimate as it tells us the average value amounts the random sample of 31 observations.

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Rectangle pqrs is folded along the line pr. The ratio of the area of rectangle pqrs to the new area of the figure is 11:7, the area of rectangle pqrs is 106.8 cm².

Let the area of the rectangle be x

therefore, we already know that x/68 = 11/7 as the area of the shaded part is 68cm and the ratio of the area of rectangle pqrs to the new area of the figure is 11:7.

x = 11/7 × 68

x = 11 × 9.71428

x = 11 × 9.71

x = 106.81 cm² or we can round it off as 106.8 cm²

Rectangle pqrs is folded along the line pr. The ratio of the area of rectangle pqrs to the new area of the figure is 11:7. The area of the shaded part is 68cm, the area of rectangle pqrs is 106.8 cm².

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Step-by-step explanation:

so so first you have to use that common sense and see what y is equal to and what x is equal to

The maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).

Let's analyze the pricing structure to determine the maximum number of items that can be purchased together for a total price that is less than a given amount.

The first item is priced at $3, and each additional item is priced at $1. This implies that the price increases by $1 for each additional item.

To find the maximum number of items, we need to consider the total price and the number of additional items beyond the first item. Let's denote the total price as P and the number of additional items as n.

The total price can be expressed as follows:

P = $3 + $1 * n

To determine the maximum number of items, we need to find the highest value of n that satisfies the condition P < T, where T is the given amount that the total price should be less than.

Substituting the expression for P, we have:

$3 + $1 * n < T

Simplifying the inequality:

$1 * n < T - $3

n < T - $3

Since the number of items must be a whole number, the maximum value of n would be the largest integer that satisfies the inequality n < T - $3.

Therefore, the maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).

For example, if T is $10, the maximum number of items would be the integer part of (10 - 3) = 7.

It's important to note that the maximum number of items calculated using this pricing structure assumes that customers can purchase fractional amounts of items. In practice, stores may have policies that limit the number of items to whole numbers or impose other restrictions.

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Answer:

y = x - 3

Explanation:

take two points: (1, -2), (2, -1)

Find slope:

\(\boxed{\sf \frac{y_2 - y_1}{x_2 - x_1} }\) where (x1, y1), (x2, y2)

\(\sf \rightarrow \dfrac{-1-(-2)}{2-1}\)

\(\sf \rightarrow 1\)

Equation:

y - y1 = m(x -x1)

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

y + 2 = x - 1

y = x - 3

Answer:

\(\huge \boxed{\bf{y = x - 3}}\)

Step-by-step explanation:

Given:-

Take two point:

To find:-

Ans:-

~Find slope in two point:

\(\sf \to m = \frac{y_2 - y_1}{x_2 - x_1} \)

\(\sf \to m = \frac{-1 - (-2)}{2 - 1} \)

\(\sf \to m = \frac{1}{1} \)

\(\sf \to m = 1 \)

\( \: \)

~Find equation:

\( \sf \to y - y_1 = m(x - x_1) \)

\( \sf \to y - (-2) = 1(x - 1) \)

\( \sf \to y + 2 = x - 1 \)

\( \sf \to y = x - 1 - 2 \)

\( \sf \to y = x - 3 \)

\( \: \)

\( \huge\colorbox{blue}{BlackPain} \)

The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday. Therefore, option B is the correct answer.

We can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.

On Thursday, 13 non-fiction books and 19 arts and crafts books were sold. If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)×2.5 = 23.75, which is not a whole number. Therefore, this prediction is not supported by the data.

Therefore, option B is the correct answer.

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The angles and length of the right triangle are as follows:

WX = 10√141 units

m∠X  = 30°

m∠V = 60°

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.

Trigonometric ratios can be used to find the side and angles of the right triangle as follows;

Therefore,

Using Pythagoras's theorem,

WX² = (20√47)² - (10√47)²

WX² = 400(47) - 100(47)

WX² = 18800 - 4700

WX = √14100

WX = 10√141

Let's find the angles

sin m∠X  = opposite / hypotenuse

sin m∠X  = 10√47 / 20√47

sin m∠X  = 1 / 2

m∠X  = sin⁻¹ 0.5

m∠X  = 30 degrees

Therefore,

m∠V = 180 - 90 - 30

m∠V = 60 degrees

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Answer:

p= -3

Step-by-step explanation:

4p+(10=5p)=7

_4p        -4p

10+p=7

-10  -10

P= -3

Answer:

-1/3

Step-by-step explanation:

First off, you need to add the common variables like 4p and 5p which is 9p.

Now we have,

9p + 10 = 7

      -10   -10

9p = -3

Here were going to have to isolate the variable, the variable really hates that 9 so let's divide them.

9p/9 = p so now "p" is single. That was our goal but what's it's value?

We're going to need to divide -3/9 to get a really long decimal so we can just simplify it to -1/3. And that's why -1/3 is the answer.

Hope that helps and have a great day!

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

Answer:

Step-by-step explanation:

60+20=80

Answer:

Step-by-step explanation:

sorry but i,m not sure

Answer:

A sector of a circle is simply a part of a circle that is enclosed by two radii and a part of the circle's circumference (arc). If the arc makes an angle θ at the center of the circle, then the area of the sector is equal to A=θ360πr2 A = θ 360 π r 2 .

Step-by-step explanation:

The difference of the expression is as follows:

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4) = x - 19

The difference of the expression can be found when we combine the like terms.

Therefore,

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)

6y⁴ + 3y² - 7  - 12y⁴ + y² - 5

6y⁴ - 12y⁴ + 3y² + y² - 7 - 5

- 6y⁴ + 4y² - 12

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

3x - 15 - 2x - 4

3x - 2x - 15 - 4

x - 19

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Answer:

(-2, -36)

Step-by-step explanation:

This is written in Standard Form

\(f(x)=5x^{2} +20x-16\)

\(ax^{2} +bx+c\)

Convert to vertex form.

\(f(x)=a(x-h)^{2}+k\)

\(f(x)=5(x+2)^{2}-36\)

Answer:

Below in bold.

Step-by-step explanation:

10,16,22,28

16-10 = 6, 22-16 = 6 and 28-22 = 6

This is an arithmetic sequence with first term a1 = 10 and common difference d = 6

General (nth) term = a1 + d(n - 1)

10th term =  10 + 6(9 -1)

                 =  10 + 48

                 = 58.

Answer: a)  Unimodal and symmetric

b) 0.26

c) 0.038

Step-by-step explanation:

Given: Sample size of investors (n)= 131

True proportion of smartphone users(p)  =26%

a) Since sampling distribution for the sample proportion is approximately normal when n is larger.

Normal distribution is Unimodal and symmetric.

So correct option : Unimodal and symmetric

b)  mean of this sampling​ distribution = p = 0.26

c)  standard deviation of the sampling​distribution = \(\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26\times (1-0.26)}{131}}=\sqrt{0.00146870229008}\)

\(=0.0383236518364\approx0.038\)

The triangles that are given above that matches the correct descriptions would be listed below as follows:

First triangle = Scalene right

Second triangle = Isosceles right

Third triangle = Scalene obtuse

A triangle is defined as the type of polygon that is always made up of three edges and three vertices. There are different types of triangle which are based on the length of their sides and the range of the interior angles.

Scalene right triangle is defined as the type of triangle that all three sides are different in length and one angle is equal to 90 degree. This is seen in the first triangle.

Isosceles right is defined as the type of triangle that has two side lengths that are equal. This is seen in the second triangle.

Scalene obtuse is defined as the type of triangle that one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. This is seen in the third triangle.

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It would take approximately 6 minutes to travel through the thickest oceanic crust at a speed of 100 km/hr.

To determine the time it would take to travel through the thickest oceanic crust at a speed of 100 km/hr, we need to know the thickness of the oceanic crust.

The oceanic crust is the outermost layer of the ocean floor and is generally thinner than the continental crust. On average, the thickness of the oceanic crust ranges from 5 to 10 kilometers (km). However, the thickness can vary depending on the specific location and geological factors.

Assuming we consider the thickest part of the oceanic crust, which could be up to 10 km thick, we can calculate the time it would take to travel through it at a speed of 100 km/hr.

Using the formula Time = Distance / Speed, we can determine the time as follows:

Time = (Thickness of Oceanic Crust) / (Speed)

Time = 10 km / 100 km/hr = 0.1 hr

Converting 0.1 hour to minutes, we have:

Time = 0.1 hr * 60 min/hr = 6 minutes

The correct answer is D. 6 minutes. This calculation is based on the assumption that we are considering the thickest part of the oceanic crust, which is approximately 10 km thick. It's important to note that the actual thickness of the oceanic crust can vary, and the time required would depend on the specific thickness encountered during the journey.

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The three consecutive integers are 10, 11, and 12.

To find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest, follow these steps:

1. Let the smallest integer be x. Then, the other two consecutive integers are x + 1 and x + 2.

2. The sum of their squares is x^2 + (x + 1)^2 + (x + 2)^2.

3. The given condition is that this sum is 65 more than three times the square of the smallest integer: x^2 + (x + 1)^2 + (x + 2)^2 = 3x^2 + 65.

4. Simplify the equation:
  x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 3x^2 + 65

5. Combine like terms:
  3x^2 + 6x + 5 = 3x^2 + 65

6. Subtract 3x^2 from both sides to eliminate the x^2 terms:
  6x + 5 = 65

7. Subtract 5 from both sides:
  6x = 60

8. Divide by 6:
  x = 10

So, the three consecutive integers are 10, 11, and 12.

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