Use the following word problem to answer the following questions.
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
1. Provide the mathematical model specific to the word problem(table of values, graph, statement)
2.explain why you chose that type of model
3. what is the answer to the word problem

Answer:

500=D 100=M

Step-by-step explanation:

I hope that helps :D

Answer:

Buying 5 packs of bread rolls and 3 packs of burger meat

Step-by-step explanation:

Sara needs to find the least common multiple between 6 bread rolls and 10  pieces of burger meat:

\(LCM:\\10\ 6\ |2\\5\ \ 3\ |3\\5\ \ 1\ |5\\1\ \ 1\ |1\\\\LCM = 2*3*5=30\)

Sara will get the same amount of burger to bread rolls when she buys 30 units of each. The numbers of packs of each product that she must buy are:

\(B=\frac{30}{6}=5\ packs\\ M=\frac{30}{10}=3\ packs\)

Sara should buy 5 packs of bread rolls and 3 packs of burger meat.

Answer:

it is a trapezoid and a quadrilateral

Explaination -

Square is a quadrilateral of 4 equal side and 4 equal angles so it is not square as all sides are unequal and all angles are also unequal

rhombus is a quadrilateral which has equal sides 4 equal angles and it's diagonal bisects each other.

rectangle has two opposite sides equal and parallel and each Ange equal as 90°

parallelogram is a quadrilateral in which a pair of opposite sides are parallel and equal and the remaining sides are unequal

The equation for the line of best fit is approximately y = 0.06x + 2.70.

We have,

To find the line of best fit in the form of y = mx + b, where x represents the years since 2000 and y represents the average cost, we need to determine the values of m and b.

We can use linear regression to estimate these values based on the given data points.

Using the given data, we have:

x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

y: 2.59, 2.81, 2.65, 2.67, 2.88, 2.70, 2.85, 2.88, 3.17, 3.24

To calculate the line of best fit, we can use statistical software or a spreadsheet program.

Once the calculations are done, we obtain the following results:

m ≈ 0.0569

b ≈ 2.704

Rounding these values to the nearest hundredths, we get:

m ≈ 0.06

b ≈ 2.70

Therefore,

The line of best fit is approximately y = 0.06x + 2.70.

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An inequality that shows all of the ways that Nita will win if Erik chooses 17 is

This refers to the relation in mathematics that makes an unequal comparison between two numbers or expressions.

Therefore, according to the rules of the game, they would have to make random selections from 0 to 20 and if the difference between their two numbers is less than 10, then Erik wins, the inequality that would show all of the ways that Nita will win if Erik chooses 17 are listed above.

Hence, we can see that the complete question goes thus:

"Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins.

Use what you know about inequalities and absolute values to better understand the game."

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Step-by-step explanation:

An + c = d

an=d-c

a=(d-c)/n is your answer

The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.

This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:

y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.

Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.

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Answer:

No

Step-by-step explanation:

if both equations begin with 'y=' then we can set the expressions equal to each other:

-x+1 = -x+5

1 ≠ 5 ∴ there are no solution to this system of equations

The intensity will be 304R, the correct option is d. 304R

An attribute of being intense or the quantifiable amount of a property, such as force, brightness, or a magnetic field, are both considered to be intensities.

The intensity of a source follows the inverse square law, which states that the intensity is inversely proportional to the square of the distance from the source.

Let's denote the initial distance as d1 (15 inches) and the initial intensity as I1 (10R). Let d2 (45 inches) be the new distance, and we need to find the new intensity, denoted as I2.

According to the inverse square law:

I1 / I2 = (d2 / d1)²

Plugging in the values:

10R / I2 = (45 inches / 15 inches)²

Simplifying:

10R / I2 = 3²

10R / I2 = 9

Now, solve for I2:

I2 = 10R / 9

So, the intensity at 45 inches (I2) will be 10R divided by 9.

Therefore, the answer is:

d. 304R

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Answer: 20/3 mph or 6.667 mph.

Step-by-step explanation:

Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.

The matrix I - A(A^T) is the projection matrix that projects vectors onto the orthogonal complement of the range of matrix A, effectively removing any components lying within the range of A.

To prove this, let's consider a vector x in the column space (range) of matrix A. Then there exists a vector y such that Ax = Ay. The projection matrix onto the orthogonal complement of the range of A, denoted Pᵤ, is defined as Pᵤ = I - A(A^T).

Now, let's apply the projection matrix Pᵤ to vector x. We have Pᵤx = (I - A(A^T))x. Using matrix multiplication, this simplifies to Pᵤx = x - A(A^T)x.

Since Ax = Ay, we can substitute Ay for Ax in the equation above, resulting in Pᵤx = x - Ay. Rearranging, we have Pᵤx = x - Ax, which is the definition of the orthogonal complement.

Therefore, Pᵤx is equal to the projection of vector x onto the orthogonal complement of the range of A, proving that I - A(A^T) is the projection matrix onto the orthogonal complement of range A.

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The value of the function f(2) is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x - 1

Also, we have

x  = 2

Substitute the known values in the above equation, so, we have the following representation

f(2) = 2 * 2 - 1

Evaluate

f(2) = 3

Hence, the solution is 3

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Complete question

Consider the function,f(x) = 2x - 1

Calculate f(x) when x = 2

Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).

To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.

The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.

Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.

The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).

The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).

The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).

The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).

Therefore, the total number of ways the lights can be arranged on the string is:

14! / (2! * 4! * 5! * 2!)

You can calculate this expression to find the specific number of arrangements.

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Answer: i think hope this helps

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

There you go bro oh yeah you're welcome

The group that worked with men between the ages of 16 and 25, providing them with job training as well as with part-time work was the Civilian Conservation Corps (CCC).The Civilian Conservation Corps (CCC) was a New Deal program established by President Franklin D.

Roosevelt in 1933 in response to the Great Depression. It was a public work relief program that operated from 1933 to 1942 in the United States for unemployed and unmarried men between the ages of 16 and 25.The CCC provided jobs for millions of unemployed young men, particularly in rural areas. It was designed to conserve natural resources in rural areas through conservation and development activities, including soil conservation, forestry, and state and national parks development. In addition, it provided valuable training and education opportunities for young men who had little or no education.

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Formula :

Volume = length × width × height

Given :

Length = 13 cm

Width = 5 cm

Height = 5 cm

Lets , find the volume of the rectangular prism :

Volume = length x width x height

→ Volume = 13cm × 5cm × 5cm

→ Volume = 325 cm²

Answer:

-9x^2+x-10

Step-by-step explanation:

the ones with the higher squares come first then the coefficent than the constant

The solution to the system of equations is x = -3 and y = 2. The y-value of the solution is 2

To find the y-value of the solution to the system of equations, we can solve the system using any suitable method such as substitution or elimination.

Given system of equations:

3x + 5y = 1

7x + 4y = -13

Let's use the method of elimination to solve the system:

Multiply equation 1 by 4 and equation 2 by 5 to make the coefficients of y in both equations equal:

4(3x + 5y) = 4(1) --> 12x + 20y = 4

5(7x + 4y) = 5(-13) --> 35x + 20y = -65

Now, subtract equation 1 from equation 2 to eliminate the y term:

(35x + 20y) - (12x + 20y) = -65 - 4

35x - 12x = -69

23x = -69

x = -69/23

x = -3

Substitute the value of x into equation 1 to find y:

3(-3) + 5y = 1

-9 + 5y = 1

5y = 1 + 9

5y = 10

y = 10/5

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2. The y-value of the solution is 2.

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The rug will fit on the floor of Lanie's room. The height of the parallelogram is 12 feet.

To determine if the rug will fit in Lanie's room, we need to compare the dimensions of the rug and the room. The room is a parallelogram with a base of 9 feet, and the area is 108 square feet. To find the height, use the formula for the area of a parallelogram: Area = base × height. For Lanie's room, 108 = 9 × h. Divide both sides by 9 to find the height, h = 12 feet. Now, compare the dimensions of the rug (6 feet wide, 10 feet long) with the dimensions of the room (9 feet base, 12 feet height). The length of the rug (10) is less than the height of the parallelogram (12), and the width of the rug (6) is less than the base of the parallelogram (9). Therefore, the rug will fit on the floor of Lanie's room.

Calculation steps:
1. Area of the parallelogram = base × height
2. 108 = 9 × h
3. h = 108 / 9
4. h = 12 feet
5. Compare dimensions: rug (6 feet wide, 10 feet long) vs room (9 feet base, 12 feet height)

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The government needs to raise spending by $3300 to bring the economy to full employment.

The formula for the GDP of a closed economy is given by the following:

Y = C + I

whereY = Aggregate Income

C = Aggregate Consumption

I = Investment

Therefore,Y = C + I250 + 0.75

Y = 100 + Y

Where Y is the full-employment GDP, we have to solve for Y in order to find out the output level that corresponds to full employment.

To do so, let's subtract 0.75Y from both sides of the equation: 250 + 0.25Y = 100

Adding -250 to both sides of the equation: 0.25Y = -150

Dividing both sides of the equation by 0.25Y = -600

Thus, at full employment, Y = 4000 and at the initial equilibrium, Y = 600.

Therefore, the desired increase in government spending (G) can be calculated as follows:

4000 = 250 + 0.75Y + G

Substituting Y = 600, we get:

4000 = 250 + 0.75(600) + G4000 = 250 + 450 + G3300 = G

Therefore, the government needs to raise spending by $3300 to bring the economy to full employment. Rounded to the nearest whole value, this is $3300.

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The constraint (x1 + x2 + x3 + x4 = 3) means that exactly three options should be selected.

The constraint (x1 + x2 + x3 + x4 = 3) represents a binary integer programming model where x1, x2, x3, and x4 are binary decision variables (0 or 1).

To understand the constraint, let's break it down:

The left-hand side of the equation (x1 + x2 + x3 + x4) represents the sum of the binary variables, indicating how many options are selected. Since each variable can take a value of either 0 or 1, the sum can range from 0 to 4.

The right-hand side of the equation (3) specifies that the sum of the variables must be equal to 3.

In the context of the given options, let's consider the variables A and B:

A: Represents the left-hand side of the equation (x1 + x2 + x3 + x4).

B: Represents the right-hand side of the equation (3).

Since the constraint states that exactly three options should be selected, A and B need to be equal. Therefore, the correct relationship between A and B is B - A = 0. This means that the difference between B and A should be zero, indicating that they are equal.

To express this relationship as an inequality, we can rewrite B - A = 0 as B - A ≤ 0. This inequality ensures that B is less than or equal to A, which implies that A and B are equal.

Thus, the correct answer is B - A ≤ 0.

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The cost of materials for the cheapest container is $184.67.

Suppose the width is x and it is given that the length of its base is twice the width, so the length of the base is 2x.

The base area is 2x².

Since the volume is $12m³

The height has to be 12/ 2x² = 6/ x²

The cost of making such a container is.

cost of base = 2x² × 10

= 20x²

The cost of sides =( 2 × 2x 6/x² + 2 × x × 6 / x²) 6

= (24/x + 12/x )6

= 36/x × 6

216/x

The overall cost is hence the sum of the base and the sides = f(x)

= 20x² + 216/x

To get the minimum,

df(x) / dx = 20x² + 216/x = 0

= 40x - 216/x² = 0

x³ = 216/40

= 54/10

= 27/5

x = 3/∛5

= 3/ 1.70

= 1.76

f(x) = 20(1.76)² + 216/ 1.76

= 61.952 + 122.72

= 184.67

Therefore we get the cost of the materials to be $184.67.

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The graph of the proportional relationship is

(c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.

which shows that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

So, The graph is a proportional graph which means that line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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Rounded to two decimal places, the time required for light to travel from the Sun to Earth is approximately 8.33 minutes.

To find the time required for light to travel from the Sun to Earth, we can use the formula:

Time = Distance / Speed

Given:

Distance = 1.5 × 10^11 meters

Speed of light = 3.0 × 10^8 meters per second

Substituting the values into the formula:

Time = (1.5 × 10^11) / (3.0 × 10^8)

Simplifying:

Time = 5 × 10^2 seconds

To convert this to minutes, we divide by 60:

Time = (5 × 10^2) / 60

Simplifying further:

Time ≈ 8.33 minutes

Rounded to two decimal places, the time required for light to travel from the Sun to Earth is approximately 8.33 minutes.

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Domain: The domain of the function \(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4\)  is all real numbers.

Range: The range of the function \(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4\) is all real numbers.

Relative Maximum: There is no relative maximum for the function \(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4.\)

Absolute Minimum: The absolute minimum for the function\(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4\) needs to be determined by finding the critical points and analyzing the behavior of the function.

Relative Minimum: There is no relative minimum for the function\(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4.\)

End Behavior: As x approaches negative or positive infinity, the function \(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4\) approaches positive infinity.

Increasing Intervals: The function f\((x) = x^4 - 4x^3 + 3x^2 + 4x - 4\) is increasing on the entire real number line.

Decreasing Intervals: The function \(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4\) does not have any decreasing intervals.

Let's analyze the characteristics of the function\(f(x) = x^4 - 4x^3 + 3x^2 + 4x - 4.\)

Domain: The function is a polynomial, so its domain is all real numbers, which means there are no restrictions on the possible values of x.

Range: To determine the range, we need to analyze the behavior of the function.

As x approaches negative infinity, the leading term x^4 dominates, so the function becomes increasingly positive.

As x approaches positive infinity, the leading term x^4 also dominates, but in this case, it becomes increasingly positive.

Therefore, the range of the function is all real numbers.

Relative Maximum: To find the relative maximum, we need to find the critical points of the function by taking the derivative and setting it equal to zero:

\(f'(x) = 4x^3 - 12x^2 + 6x + 4 = 0\)

Solving this equation will give us the critical points.

However, since the equation is a cubic, it may not have a simple solution.

We can use numerical methods or graphing technology to estimate the approximate values of the critical points and determine whether they correspond to a relative maximum.

Absolute Minimum: Since the range of the function is all real numbers, there is no absolute minimum.

The function does not have a lower bound.

Relative Minimum: Similarly, since the range is all real numbers, there is no relative minimum.

The function does not have a local minimum.

End Behavior: As mentioned earlier, as x approaches negative infinity, the leading term \(x^4\) dominates, causing the function to approach positive infinity.

As x approaches positive infinity, the leading term \(x^4\) also dominates, and the function approaches positive infinity.

Therefore, the end behavior of the function is that it approaches positive infinity as x approaches negative or positive infinity.

Increasing Intervals: To find the increasing intervals, we can look at the sign of the derivative.

If the derivative is positive, the function is increasing.

If the derivative is negative, the function is decreasing.

Decreasing Intervals: Similarly, to find the decreasing intervals, we can look at the sign of the derivative.

If the derivative is negative, the function is decreasing.

To provide more specific information about the relative maximum, relative minimum, increasing intervals, and decreasing intervals, we need to find the critical points and analyze the behavior of the function between those points.

If you have a specific interval in mind, I can help you analyze the function within that interval.

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Answer:

the correct answer is shown below

Step-by-step explanation:

hope this helps

have an awesome day -TJ

pls mark brainliest if this helps :)

Answer:

3.5

Step-by-step explanation:

28 days = 4 weeks

28 divided by 4 = 1 week

14 gallons divided by 4 = 3.5