Gabriella needs 120 meters of fence to surround a rectangular garden.
the length of the garden is three times its width, w.
how wide is the fence?
(please solve how the answer is formatted, i already looked at the other posts people made on this question and they did not help)

The matching answers and corresponding colors for the holiday lights are: (Slope: 3) Dark Blue, (Slope: -4) Violet, (Slope: 1/4) Red.

To find the slope of a line passing through two points \((x_1, y_1)\ and\ (x_2, y_2)\), we can use the formula:

Slope = \((y_2 - y_1) / (x_2 - x_1)\)

Let's calculate the slopes for each pair of points:

1. (8, 3) and (10, 9):

Slope = (9 - 3) / (10 - 8) = 6 / 2 = 3

2. (2, -3) and (1, 1):

Slope = (1 - (-3)) / (1 - 2) = 4 / (-1) = -4

3. (-4, -8) and (-8, -9):

Slope = (-9 - (-8)) / (-8 - (-4)) = (-9 + 8) / (-8 + 4) = -1 / (-4) = 1/4

Now let's compare the slopes to identify the matching answers:

1. Slope: 3 (Dark Blue)

2. Slope: -4 (Violet)

3. Slope: 1/4 (Red)

Thus, the corresponding colors for the holiday lights would be:

1. Dark Blue

2. Violet

3. Red

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To determine the ratio of the heights of two similar pentagonal prisms with a volume ratio of 27:125, we need to consider the relationship between the volumes and dimensions of similar prisms. Since the prisms are similar, their corresponding linear dimensions (height, width, and length) have the same ratio.

Let's denote the ratio of their heights as h₁ : h₂. The volume ratio can be expressed as:

(Volume of Prism 1) / (Volume of Prism 2) = 27/125

For a prism, the volume can be calculated as:

Volume = Base Area × Height

Since the prisms are similar, the ratio of their base areas is the square of the ratio of their linear dimensions. Therefore, the ratio of their base areas is (h₁/h₂)².

Now, we can express the volume ratio in terms of their heights:

(h₁ × Base Area 1) / (h₂ × Base Area 2) = 27/125

Since the base areas are proportional, we can substitute the base area ratio with the height ratio squared:

(h₁ × (h₁/h₂)²) / h₂ = 27/125

We can cancel out one h₁ from both the numerator and denominator:

(h₁/h₂)² = 27/125

Now, take the square root of both sides to find the height ratio:

h₁/h₂ = √(27/125) = √(3³/5³) = 3/5

So, the ratio of their heights is 3:5.

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

5/36

Step-by-step explanation:

The chance of drawing a blue marble is 5/12. The chance of drawing a green marble is 4/12. You multiply the fractions to get the probability.

5/12 * 4/12 =20/144 = 5/36 simplified.

Answer:

5/36

Step-by-step explanation:

12 total marbles

5/12 blue, 4/12 green

5/12x4/12=20/144

5/36

Answer:

c. commutative property of addition

Step-by-step explanation:

The probability that is lower than 63 grams is 95%

Given that,

X~ Normal ( 67 grams, 5 grams ) , n = 5

=> E( x ) = 67 grams , Var( X ) =5 grams

* ~ Normal ( 67 grams , 1 grams )

We know that, if X~ Normal ( E ( x) = a . Val (x ) = b)

Then X~ Normal ( E(x) = a, √Var (x)/n = √b/n)

E(x) = a, Var (x)/ = √b/n

Probability that sample mean X , is blw 65 and 70 grams

P ( 65< X<70 ) =

= P(Z<1. 76 ) - P(Z≤-2.65)

Using standard normal table values represent area

left of the Z- score, we get

= 0.96080 - 0.00402

= 0 .95678

=0.9568

So,The probability that is lower than 63 grams is 95%

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Answer:

4

Step-by-step explanation:

The degree of a polynomial is the highest power of its variables. For example, in the polynomial 4x^3 + 2x^2 - 5x + 7, the degree is 3 because x^3 is the term with the highest degree. The degree of a constant polynomial, such as 7, is 0. In general, if a polynomial has n terms, its degree is the degree of its leading term (the term with the highest degree).

The price of the house (y) is directly proportional to the total area of the house (x), you can express the relationship between both variables as follows:

Where "k" is the constant of proportionality.

To determine the price of a house that has 2,000 ft², the first step is to determine the value of the constant of proportionality between both variables. For this, we have to use the known price and size of the house:

-The house has 1,500 ft² → this is the value of x

-The house costs $300,000 → this is the value of y

You can express the relationship as:

To calculate the value of k, you have to divide both sides by 1,500ft²

The constant of proportionality is 200$/ft², this value indicates that the price of the house increases $200 for every additional square foot.

Now that we know the value of the constant of proportionality we can calculate the price of a 2,000ft² house:

For x=2,000ft²

The price of a 2,000ft² is $400,000

Step-by-step explanation:

here ! I used the formula area = length × width

and just some algrbric expressions solving

Special Product are the result of binomials being multiplied, or simplified further, and can be solved with ease using the First Last Inner Outer method. this product is not a special product.

Special Product (a+b) (a+b) = aa + ab + ab + bb = \(a^{2} + 2ab + b^{2}\).

we can use this formula anytime we are multiplying a binomial of the form a + b.

Factor as a Difference of Squares

factoring:  \(81a^{2} b^{4} - c^{6}\) = \((3^{4}a^{2} . b^{4}) - c^{6}\)

A difference of two perfect squares, \(A^{2} - B^{2}\) can be factored into

\((A+B)(A-B)\\A^{2} - AB + BA - B^{2}\\ A^{2} - AB + AB -B^{2}\\ A^{2} -B^{2}\)

AB = BA is he commutative property of multiplication from the expression.

-AB+BA equal zero and is therefore eliminated from the expression.

81 is the square of 9

\(a^{2}\) is the square of \(a^{1}\)

\(b^{4}\) is the square of \(b^{2}\)

\(c^{6}\) is the square of \(c^{3}\)

Factorization is \((9ab^{2}+c^{3}) . (9ab^{2}-c^{3} )\)

Factoring: \((9ab^{2}+c^{3})\)

A sum of perfect cubes, \(a^{3} + b^{3}\) can be factored into :\((a+b).(a^{2}-ab+b^{2})\\a^{3}-a^{2}b+ab^{2}-b^{2}a+b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)+b^{3}\\ a^{3}+b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Factoring: \((9ab^{2}-c^{3} )\)

A difference of two perfect cubes, \(a^{3} - b^{3}\) can be factored into

\((a-b).(a^{2}+ab+b^{2})\\a^{3}+a^{2}b+ab^{2}-ba^{2}-b^{2}a-b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)-b^{3}\\ a^{3}-b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Hence, 81a2b4 - c6 this solution deals with factoring binomials as the sum or difference of cubes.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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In the context of companies navigating an uncertain future, those who take the existing total industry structure and its future trajectory as given and decide where to compete are known as "strategic planners."

Strategic planners are entities that assess the prevailing industry structure and dynamics, acknowledging the uncertainty of the future but assuming that the industry will largely follow its expected trajectory. They carefully analyze the competitive landscape, including market conditions, customer preferences, technological advancements, and regulatory factors. By doing so, they identify areas where they can leverage their strengths and capabilities to outperform rivals.

Strategic planners understand that the industry structure may evolve over time due to various factors, such as technological disruptions, changing consumer behavior, or new market entrants. However, rather than attempting to reshape the industry or disrupt the status quo, they focus on identifying specific market segments or niches where they can excel within the existing industry framework.

These companies or individuals strategically position themselves by capitalizing on their unique strengths, whether it's cost leadership, differentiation through product innovation, superior customer service, or efficient supply chain management. They align their resources, capabilities, and competitive strategies to effectively compete in the chosen segments, while recognizing the need to adapt and evolve as the industry landscape changes.

By accepting the industry's structure and future trajectory as given, strategic planners mitigate risks associated with attempting to reshape the market or betting on uncertain outcomes. Instead, they concentrate their efforts on optimizing their performance within the existing industry context, thereby maximizing their chances of success in an uncertain future.

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Answer:

-0.009

Step-by-step explanation:

put it on desmos

Answer:

B

Step-by-step explanation:

A function cannot have more than one point on the same x coordinate. So, B is the only option that works.

Answer:

216 red beans

Step-by-step explanation:

Answer:

3 minutes

Step-by-step explanation:

It will take about 9.2 minutes until there are 220 grams of the element remaining.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

We can use the exponential decay formula to solve this problem, which is:

\(N(t) = N_0e^{-rt}\)

where:

N(t) is the amount of substance remaining after time t

N₀ is the initial amount of substance

r is the decay rate (in this case, 19.7% per minute, or 0.197 per minute)

t is the time elapsed

We know the initial mass of the element is 890 grams, and we want to find out how long it will take until there are 220 grams remaining.

So we can set up the equation as follows:

\(220 = 890 e^{-0.197t}\)

Dividing both sides by 890, we get:

\(e^{-0.197t} = 0.247\)

Taking the natural logarithm of both sides, we get:

\(ln e^{-0.197t} = ln(0.247)\)

Simplifying the left side, we get:

-0.197t = ln(0.247)

Dividing both sides by -0.197, we get:

t = ln(0.247) / -0.197

Using a calculator, we can evaluate this to be approximately 9.2 minutes (rounded to the nearest tenth of a minute).

Therefore,

It will take about 9.2 minutes until there are 220 grams of the element remaining.

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Answer:

12.1 cm

Step-by-step explanation:

Answer:

The answer is x = 1800

Step-by-step explanation:

Hope this helps :)

Have a nice day.

To analyze the variables Birth Rate and Death Rate at the same time the scatter plot would be appropriate to use.

A scatter chart, also called as a scatter plot, is a graph that displays the correlation between two variables. They are a very effective type of chart because they enable viewers to see relationships or trends that would be nearly impossible to see in any other form right away.

Modern scatter charts are based on René Descartes' 17th-century cartesian coordinates system, albeit their exact origins are unknown. The majority of scatter plots used in science journals and publications may be found there.

One of the most adaptable and practical inventions in the history of statistical graphs is the scatter chart. This can seem like a bold statement, but scatter charts help make sense of muddled data. They are a tool for discovery as well as visualisation, which is a much bigger role for them.

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Answer:

The value of x = 513

Step-by-step explanation:

Let x, y, and z be the three numbers

Given

\(x+y+z=855\)

Assuming x be the number which is 50% more than the sum of the other two numbers.

i.e.

(150)% of (y+z) = 1.5(y+z)

                y + z = x/1.5

As we know that

\(x + y + z = 855\)

substituting y + z = x / 1.5 in the equation

\(x+\frac{x}{1.5}=855\)

Multiply both sides by 1.5

\(x\cdot \:1.5+\frac{x}{1.5}\cdot \:1.5=855\cdot \:1.5\)

\(1.5x+x=1282.5\)

\(2.5x=1282.5\)

Divide both sides by 2.5

\(\frac{2.5x}{2.5}=\frac{1282.5}{2.5}\)

\(x = 513\)

Therefore, the value of x = 513

Answer:

x=1

x=-3

Step-by-step explanation:

(x-1)(x^3 + 3x^2 +x +3) = 0

(x-1)( x+3)(x^2 +1)=0

Answer:

C

Step-by-step explanation:

The weight of the container when one quarter filled with water would be = 13.25kg

Weight is defined as the quantity that shows the total amount of matter that can be found in an object and it's measured in grams or Kilograms.

The weight of the empty container = 5kg

The weight of the container and water= 13+25= 38kg

Therefore the weight of water = 38-5= 33kg

If 1 = 33kg

1/4 = X kg

Make X kg the subject of formula;

X kg = 33×1/4

X kg = 8.25 + 5kg( weight of container) = 13.25kg.

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Answer:

1. p^10

2. p^24

Step-by-step explanation:

p^6 x p^4=p^(6+4)=p^10

(p^6)^4=p^(6x4)=p^24

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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If a nonhomogeneous system of linear equations is underdetermined, it can have either infinitely many solutions or no solutions.

A nonhomogeneous system of linear equations is represented by the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. When the system is underdetermined, it means that there are more unknown variables than equations, resulting in an infinite number of possible solutions. In this case, there are infinitely many ways to assign values to the free variables, which leads to different solutions.

To determine if the system has a solution or infinitely many solutions, we can use techniques such as row reduction or matrix methods like the inverse or pseudoinverse. If the coefficient matrix A is full rank (i.e., all its rows are linearly independent), and the augmented matrix [A | b] also has full rank, then the system has a unique solution. However, if the rank of A is less than the rank of [A | b], the system is underdetermined and can have infinitely many solutions. This occurs when there are redundant equations or when the equations are dependent on each other, allowing for multiple valid solutions.

On the other hand, it is also possible for an underdetermined system to have no solutions. This happens when the equations are inconsistent or contradictory, leading to an impossibility of finding a solution that satisfies all the equations simultaneously. Inconsistent equations can arise when there is a contradiction between the constraints imposed by different equations, resulting in an empty solution set.

In summary, when a nonhomogeneous system of linear equations is underdetermined, it can have infinitely many solutions or no solutions at all, depending on the relationship between the equations and the number of unknowns.

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Reading a list of data and answering questions related to comparisons, percentages, and proportions involves analyzing the given information and calculating relevant metrics based on the data.

To determine "how many more" or the difference between two values, you subtract one value from the other. For example, if you are comparing the sales of two products, you can subtract the sales of one product from the other to find the difference in sales.

To calculate "what percentage of" a specific value, you divide the specific value by the total and multiply it by 100. This will give you the percentage. For instance, if you want to find the percentage of customers who rated a product positively out of the total number of customers, you divide the number of positive ratings by the total number of customers and multiply it by 100.

To determine "what proportion of" a group falls into a specific category, you divide the number of individuals in that category by the total number of individuals in the group. This will give you the proportion. For example, if you want to find the proportion of customers who prefer a certain brand out of the total number of customers surveyed, you divide the number of customers preferring that brand by the total number of customers.

By applying these calculations to the given data, you can provide accurate answers to questions regarding comparisons, percentages, and proportions.

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Answer:

y=2x+1

Step-by-step explanation:

Find the slope of the two points (2,5), (5,11). (11-5)/(5-2) = 6/3 = 2, m=2.

Use the point-slope formula to find the equation:

y-5=2(x-2)

y-5=2x-4

y=-2x-4+5

y=2x+1

The given statement is True.

What are parallel lines?

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

True. Two lines either intersect or are parallel.

This means that there are only two possibilities for the relationship between two lines: they either meet at a single point, in which case they are said to intersect, or they never meet, in which case they are said to be parallel.

If two lines are intersecting, then they are not parallel, and if two lines are parallel, then they do not intersect.

Hence, The given statement is True.

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