A gardener made a scale drawing of a lawn with a scale factor of 18. The dimensions of his drawing are 9 inches long by 5 inches wide His partner plans to make another scale drawing of the lawn, but with a scale factor of 1 16 What are the dimensions of this scale drawing O A The length is 25 inches and the wo 45 inches OB. The length is 10 inches and the chia 18 inches OC. The length is 18 inches and the D. The length is 45 inches and the 25th​

Answer:

(option 1) 1 unit up and 5 units right

Step-by-step explanation:

the x value represents horizontal shifts (left<-->right)
The y value represents vertical shifts (up<---->down)
a positive change in the x or y value is seen as going right or up, respectively. Since a positive value change is seen in both the x and y values, we can eliminate all the options except for option 1.
We can also subtract the initial point from the new point in order to find the exact shift (even though we already narrowed down to our answer).
x(A'-A)=3-(-2)=+5=right 5
y(A'-A)=3-2=+1=up 1

Belgium and Great Britain both experienced industrialization, which led to significant economic and social changes. However, a notable difference between the two is the timing and pace of their industrialization processes.

Both Belgium and Great Britain underwent industrialization during the 19th century, transitioning from predominantly agrarian societies to industrial economies. This transformation involved the mechanization of production, the growth of factories, and the emergence of new industries. Both countries experienced a shift from rural to urban areas, an increase in population, and the rise of a working class. One significant difference between Belgium and Great Britain's industrialization was the timing and pace of their processes. Great Britain is widely regarded as the birthplace of the Industrial Revolution, with industrialization taking off in the late 18th century. The country quickly became a global leader in industrial production and innovation. On the other hand, Belgium's industrialization occurred slightly later, gaining momentum in the mid-19th century. Despite the time lag, Belgium experienced a rapid industrialization process, fueled by factors such as its geographical location, availability of natural resources, and strong transportation network. While both countries saw the development of similar industries like textiles, iron, and coal mining, Great Britain's industrialization had a more profound and widespread impact on a global scale due to its early start and technological advancements. However, Belgium's industrialization played a crucial role in transforming the country into an industrial powerhouse within Europe. In summary, Belgium and Great Britain shared similarities in terms of experiencing industrialization and its associated changes. However, the notable difference lies in the timing and pace of their industrialization processes, with Great Britain leading the way in the Industrial Revolution and Belgium following suit with a slightly delayed but rapid industrialization period.

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In "Dreams from My Father," Obama's embarrassment on his first day of school is caused by his classmates' questions about his father (Option A).

In the book "Dreams from My Father" by Barack Obama, the author recounts his experiences growing up and exploring his identity. On his first day of school, Obama feels embarrassed due to his classmates' questions about his father. As a biracial child with a Kenyan father and American mother, Obama grapples with understanding his roots and fitting in with his peers.

The questions from his classmates about his father highlight his sense of otherness and make him feel self-conscious. This early experience shapes Obama's journey of self-discovery and his exploration of race, identity, and belonging throughout the memoir. It emphasizes the challenges he faced in navigating his multicultural background and the impact it had on his sense of self and personal growth.

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Answer:

There are a lot of advantages of using a chart or graph instead of a table:

- They can present data in a more precise way, and is able to simplify large data in a easier manner.

- They will pretty much show you an overall trend/pattern of the data, it's either be a positive, negative or no trend at all.

To implement the first-best allocation rule in dominant strategies, a second-price auction would need to be modified in this example.

In a second-price auction, the highest bidder wins the auction but pays the price bid by the second-highest bidder. To implement the first-best allocation rule in dominant strategies, several modifications would be necessary. Firstly, the auction mechanism would need to incorporate information about the participants' business needs, preferences, and contract requirements. This could involve collecting detailed profiles and specifications from the members of Money Club and Money Ball. Secondly, the auction would need to consider not only the bid amount but also factors such as the participant's industry, experience, reputation, and potential synergies with other members.

These additional criteria would allow for a more comprehensive evaluation of the bidders and help determine the best allocation of contracts. Finally, the auction mechanism would need to account for potential externalities or spillover effects that arise from the interactions between members, as these can affect the overall value generated by the contracts.

By incorporating these modifications, the auction could aim to allocate contracts based on the first-best allocation rule in dominant strategies. This means that the auction would prioritize the most efficient and mutually beneficial matches between businesses, maximizing the overall welfare and value created within the network. Such modifications would require a more sophisticated auction design that considers multiple dimensions beyond just the bid price, taking into account the specific characteristics of the businesses involved and their potential for successful collaboration.

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The distance to the tower from the point on the ground, given the angle of depression would be 21. 94 ft

The angle of depression is the angle between the horizontal line from the observer and the line of sight to the object.

Given that the height of the tower h = 43 feet, and the angle of depression θ = 63°, the tangent trigonometric function, defined as tan(θ) = opposite/adjacent is the best method to use:

d = h / tan ( θ )

d = 43 ft / tan( 63 °)

d = 43 ft / 1.96

d = 21. 94 ft

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Full question is:

The Angle of Depression is measured from the top of a 43 foot tower to a reference point on the ground. Its value is found to be 63°. How far is the base of the tower from the point on the ground

i) The number of cups of coffee sold in a cafeteria during lunch: This variable is discrete since it represents a countable number of cups of coffee sold. It can only take on whole number values (e.g., 0, 1, 2, 3, ...).

ii) The blood pressures of a group of students the day before their final exam: This variable is continuous since blood pressure can take on any value within a certain range (e.g., 120/80 mmHg, 130/90 mmHg, etc.). It can have fractional values and is not restricted to specific points.

To find the probability that exactly 8 out of 14 citizens favor building the police substation (from a survey where 76% of the community favored it), we can use the binomial probability formula.

The probability mass function for a binomial distribution is given by [tex]\[P(X = k) = {n \choose k} \cdot p^k \cdot (1-p)^{n-k}\][/tex], where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the binomial coefficient.

In this case, n = 14, k = 8, and p = 0.76. By substituting these values into the formula, we can calculate the desired probability.

To find the mean and standard deviation of the number of left-handers in a class of 50 students, we can use the properties of a binomial distribution.

In this case, the number of left-handers follows a binomial distribution with n = 50 (number of students) and p = 0.15 (probability of being left-handed).

The mean of a binomial distribution is given by μ = n * p, and the standard deviation is given by σ = sqrt(n * p * (1-p)).

By substituting the values into these formulas, we can calculate the mean and standard deviation.

Therefore, the blood pressures of a group of students the day before their final exam is a continuous variable. It can take on any value within a range, such as 120/80 mmHg or 130/90 mmHg. It is not limited to specific points and can have fractional values.

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3 bags, each holding 1.5 kg of flour, will cost $306.00.

The cost of 3 bags, each holding 1.5 kg of flour, we need to convert the weight from kilograms to grams and then calculate the total cost.

1 kilogram (kg) = 1000 grams (g).

1.5 kg is equal to 1.5 × 1000 = 1500 grams.

Given that 250 grams of flour cost $17.0, we can calculate the cost per gram

Cost per gram = Total cost / Total grams

Cost per gram = $17.0 / 250 grams

Now, we can calculate the total cost for 3 bags of flour

Total cost = Cost per gram × Total grams

Total cost = (Cost per gram × 1500 grams) × 3 bags

Putting in the values, we get

Total cost = ($17.0 / 250 grams) × 1500 grams × 3

Total cost = ($17.0 / 250) × 1500 × 3

Total cost = $0.068 × 1500 × 3

Total cost = $306.00

Therefore, 3 bags, each holding 1.5 kg of flour, will cost $306.00.

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Parkinson Sports puts approximately 0.524 cubic feet of foam in each basketball box to fill the empty space and protect the basketball

To calculate the amount of foam put in each basketball box, we need to determine the volume of the foam required to fill the empty space.

The basketball box has a volume of 1 cubic foot. Assuming the basketball itself perfectly fills the box, we can subtract the volume of the basketball from the box's volume to find the volume of the foam.

The volume of a sphere (basketball) can be calculated using the formula:

Volume of a sphere = (4/3) * π * (radius)^3

Since the basketball perfectly fills the box, the radius of the basketball will be half of the box's side length (since it touches the sides). Therefore, the radius will be 0.5 feet.

Substituting the values into the formula:

Volume of the basketball = (4/3) * π * (0.5)^3

Next, we subtract the volume of the basketball from the volume of the box to find the volume of the foam:

Volume of the foam = Volume of the box - Volume of the basketball

Volume of the foam = 1 cubic foot - [(4/3) * π * (0.5)^3]

Calculating the value:

Volume of the foam ≈ 0.524 cubic feet

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The Basin and Range area of the western United States is a result of normal faulting produced by tectonic forces.

This region is characterized by a series of parallel mountain ranges separated by elongated valleys. The main answer lies in the tectonic activity associated with the extension of the Earth's crust.

The Basin and Range province is situated along the western edge of the North American Plate, where the crust is being stretched apart. This stretching is caused by the interaction of several tectonic forces, including the motion of the Pacific Plate relative to the North American Plate. The crust in this region undergoes extensional stress.

The extensional stress leads to the development of normal faults, where the hanging wall drops down relative to the footwall. These faults create the distinctive fault-block mountains and elongated valleys characteristic of the Basin and Range area. Over time, the continued tectonic activity has produced a series of fault blocks, resulting in the alternating mountain-valley topography that defines the region.

The Basin and Range area of the western United States is a product of normal faulting caused by the extensional stress resulting from the tectonic forces acting along the western edge of the North American Plate.

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The gross requirement for item B in Week 3 is 80 units.

The gross requirement for item B in Week 3, we need to calculate the demand for item B based on the bill of materials and the requirements for item A.

From the MPS (Master Production Schedule) provided, we can see that the gross requirement for item A in Week 3 is 80 units.

According to the bill of materials, item A requires 1 unit of item B. Therefore, the gross requirement for item B can be calculated by multiplying the gross requirement for item A by the quantity needed for item B in the bill of materials.

Gross requirement for item B = Gross requirement for item A × Quantity needed for item B in bill of materials

Gross requirement for item B = 80 units × 1 unit

Gross requirement for item B = 80 units

Therefore, the gross requirement for item B in Week 3 is 80 units.

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In a two-sample hypothesis with a two-tailed test, the aim is to find evidence that the population parameters (1) and (2) are not the same.

A two-sample hypothesis test with a two-tailed test is used to determine if there is a significant difference between two populations. The null hypothesis assumes that the population parameters (1) and (2) are equal, while the alternative hypothesis assumes that they are different. The two-tailed test is called so because it considers deviations in both directions. It seeks evidence that the population parameters (1) and (2) do not belong to the same data.

The test calculates a test statistic, such as the t-statistic or z-score, and compares it to the corresponding critical value from the distribution. If the test statistic falls within the rejection region, which is determined by the significance level, then the null hypothesis is rejected. This rejection indicates evidence of a significant difference between the two populations.

Therefore, a two-tailed test does not specifically seek evidence that one population parameter is smaller or larger than the other. Instead, it aims to find evidence that the population parameters (1) and (2) are different, suggesting that there is a meaningful distinction between the two populations being compared.

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The value of m such that [tex]a_m[/tex] is the 23rd term of the sequence divisible by 9 is 24.

To find the value of m such that [tex]a_m[/tex] is the 23rd term of the sequence divisible by 9, we need to generate the sequence and identify the 23rd term that satisfies this condition.

Let's analyze the pattern in the sequence:

1st term: [tex]a_1[/tex]= 1 (not divisible by 9)

2nd term: [tex]a_2[/tex] = 13 (not divisible by 9)

3rd term: [tex]a_3[/tex] = 135 (divisible by 9)

We see that the 3rd term, [tex]a_3[/tex] = 135, is the first term divisible by 9. From here, we can observe that each subsequent term will have the digits 1, 3, and 5 repeated with additional trailing digits.

4th term: [tex]a_4[/tex] = 1357 (not divisible by 9)

5th term: [tex]a_5[/tex]  = 13579 (divisible by 9)

Now we have the 5th term, [tex]a_5[/tex] = 13579, as the second term divisible by 9. Continuing the pattern:

6th term: [tex]a_6[/tex] = 1357911 (not divisible by 9)

7th term: [tex]a_7[/tex] = 13579113 (not divisible by 9)

8th term: [tex]a_8[/tex] = 135791135 (divisible by 9)

We have found the 8th term, [tex]a_8[/tex] = 135791135, as the third term divisible by 9. The pattern continues as follows:

9th term: [tex]a_9[/tex] = 1357911357 (not divisible by 9)

10th term: [tex]a_{10}[/tex] = 13579113579 (divisible by 9)

From this pattern, we can see that every 3rd term in the sequence is divisible by 9. Therefore, to find the 23rd term divisible by 9, we can determine which group of three terms it falls into.

The 23rd term belongs to the 8th group of three terms (from [tex]a_8[/tex] to [tex]a_{10}[/tex]). So, we need to find the position of the 8th group in the sequence.

Each group has 3 terms, so the number of terms in the groups before the 8th group is (8 - 1) * 3 = 21 terms.

The 8th group starts with the term [tex]a_{22}[/tex], and we need to count forward 2 more terms to reach the 23rd term, which is [tex]a_{24}[/tex].

Therefore, m = 22 + 2 = 24.

Hence, the value of m such that a_m is the 23rd term of the sequence divisible by 9 is 24.

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The dimensions of the rectangular plot can be either 8 meters by 28 meters or 28 meters by 8 meters, depending on the orientation of the rectangle.

Let's solve for the dimensions (length and width) of the rectangular plot of land using the given information:

Let the length of the rectangular plot be L and the width be W.

1. Perimeter:

The border of a square shape is the amount of every one of the four sides. In this case, the perimeter is given as 60 meters:

[tex]2L + 2W = 60[/tex]

2. Area:

The region of a square shape is given by the recipe: [tex]Area = Length * Width[/tex]. In this case, the area is given as 224 square meters:

[tex]L * W = 224[/tex]

To solve for the dimensions, we can use substitution or elimination.

Using substitution:

From equation 2, we have [tex]L = 224 / W[/tex]. Substituting this into equation 1:

[tex]2(224 / W) + 2W = 60[/tex]

Simplifying:

[tex]448 / W + 2W = 60[/tex]

Multiply through by W to eliminate the denominator:

[tex]448 + 2W^2 = 60W[/tex]

Rearranging:

[tex]2W^2 - 60W + 448 = 0[/tex]

Solving this quadratic equation, we find two possible solutions for W: [tex]W[/tex] ≈ [tex]8[/tex] or [tex]W[/tex] ≈ [tex]28[/tex].

Using the values of W, we can find the corresponding lengths:

For [tex]W[/tex] ≈ [tex]8[/tex], [tex]L[/tex] ≈ [tex]224 / 8 = 28[/tex]

For [tex]W[/tex] ≈ [tex]28[/tex],[tex]L[/tex] ≈ [tex]224 / 28 = 8[/tex]

Therefore, the dimensions of the rectangular plot can be either 8 meters by 28 meters or 28 meters by 8 meters, depending on the orientation of the rectangle.

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(a) The curl of the vector field F is Curl F = (8x - yz)i + (8xy - yz)j + (y - 8xy)k

(b) The divergence of the vector field F is Div F = 8y + yz + xz

(a) The curl of the vector field F(x, y, z) = 8xyezi + yzexk, we can use the curl operator (∇ × F) which is defined as

∇ × F = (d/dy)(Fz) - (d/dz)(Fy)i + (d/dz)(Fx) - (d/dx)(Fz)j + (d/dx)(Fy) - (d/dy)(Fx)k

In this case, let's calculate the curl

∇ × F = (d/dy)(yzex) - (d/dz)(8xyez)i + (d/dz)(8xyezi) - (d/dx)(yzex)j + (d/dx)(8xyezi) - (d/dy)(8xyez)k

Taking the partial derivatives, we get

∇ × F = (8x - yz)i + (8xy - yz)j + (y - 8xy)k

Therefore, the curl of the vector field F is

Curl F = (8x - yz)i + (8xy - yz)j + (y - 8xy)k

(b) The divergence of the vector field F(x, y, z) = 8xyezi + yzexk, we can use the divergence operator (∇ · F) which is defined as

∇ · F = (d/dx)(Fx) + (d/dy)(Fy) + (d/dz)(Fz)

In this case, let's calculate the divergence

∇ · F = (d/dx)(8xyezi) + (d/dy)(yzexk) + (d/dz)(0)

Taking the partial derivatives, we get

∇ · F = (8y + yz) + (xz) + 0

Simplifying, we have:

∇ · F = 8y + yz + xz

Therefore, the divergence of the vector field F is

Div F = 8y + yz + xz

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The rate of change for the satellite space explorer is 4600 miles per hour.

The rate of change, also known as the slope, measures how one quantity changes in relation to another quantity. It represents the ratio of the change in the dependent variable to the change in the independent variable. In other words, it quantifies the average rate at which one variable changes with respect to another.

The rate of change is a fundamental concept in various fields, including mathematics, physics, economics, and many others. It provides valuable insights into how variables are related and how they behave over a given interval.

To find the rate of change, we need to divide the distance traveled by the time taken. In this case, the satellite space explorer flew 110400 miles in 24 hours.

Rate of Change = Distance / Time

Rate of Change = 110400 miles / 24 hours

Calculating the rate of change:

Rate of Change = 4600 miles per hour

Therefore, the rate of change for the satellite space explorer is 4600 miles per hour.

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The main memory process that accounts for Shayla's ability to retain the vocabulary she learned in her first semester Spanish class is long-term memory.

Long-term memory is a type of memory storage that has a vast capacity and can store information for extended periods of time, ranging from minutes to years. It allows for the encoding, storage, and retrieval of information that can be retained for a long duration.

In Shayla's case, the vocabulary she learned in her Spanish class is stored in her long-term memory, enabling her to access and retain that information even after the class has ended. Long-term memory plays a crucial role in the consolidation and retention of learned knowledge and experiences, contributing to the long-term retention of information.

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Town Y receiving heavy rainfall and having less steep slopes compared to town X, it is more likely to experience mass movement in the near future.

Based on the given information, town Y is more likely to experience mass movement in the near future.

Mass movement refers to the downslope movement of soil, rock, or other materials under the influence of gravity.

Several factors contribute to mass movement, including slope steepness, precipitation, and soil properties.

Town X has steeper slopes than town Y.

Steeper slopes increase the gravitational force acting on the materials, making them more susceptible to mass movement.

Town X remains dry, indicating a lack of precipitation.

On the other hand, town Y experiences heavier-than-normal rain for several days.

Excessive rainfall can saturate the soil, reducing its stability and increasing the likelihood of mass movement.

The soil becomes saturated, it loses its ability to retain its cohesion, which holds the particles together.

This loss of cohesion makes it easier for the soil to slide or flow downslope.

The combination of excessive precipitation and relatively gentler slopes increases the chances of soil instability and mass movement occurrences.

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Answer: 90 degrees (read explanation)

Step-by-step explanation:

The right triangle ABC has a right angle (BCA), and ABD must also equal 90 degrees because lines tangent to circles are tangent at a right angle.

[tex] \text{\sf{That's similarity.}} \\ \sf{So:} [/tex]

[tex] \begin{aligned}\frac{IJ}{LM}&= \frac{JK}{MN} \\ \frac{23}{64.4} &= \frac{17}{x} \\ x & = \frac{64.4 \times 17}{23} \\ x & = \underline{47.6}\end{aligned}[/tex]

[tex] \boxed{\bf{\red{The \: perimeter}}} [/tex]

[tex]\begin{aligned} P &= LM + MN + NL \\ &= 84 + 64.4 + 47.6 \\ &= \bold{\red{196}} \\ \\ \small{\blue{\mathfrak{That's \: it \: :)}}} \end{aligned} [/tex]

For a standard normal distribution, a negative value of z indicates that the observed value is below the mean of the distribution.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a negative value of z indicates that the observed value is located below the mean. The z-score represents the number of standard deviations a data point is away from the mean.

A negative z-score means that the observed value is lower than the mean, indicating that it falls to the left of the center of the distribution. This means that the data point is relatively lower compared to the average and can provide information about its position within the distribution and its deviation from the mean.

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The conditional expectation E(X|Y=y) is equal to 0.

How can we determine the conditional expectation E(X|Y) given the joint distribution of X and Y?

To find the conditional expectation E(X|Y), we need to calculate the expected value of X for a given value of Y in the joint distribution. This involves integrating the product of the conditional probability density function (PDF) of X given Y and X over the range of possible values of X, given a specific value of Y.

To find E(X|Y), the conditional expectation of X given Y, we need to calculate the expected value of X for a given value of Y in the joint distribution.

In this case, the joint distribution of X and Y is the uniform distribution on the circle [tex]x^2 + y^2 < 1[/tex]. Since the distribution is uniform, the probability density function (PDF) is constant over the region of interest.

To find E(X|Y=y), we can integrate the product of the conditional PDF f(x|y) and x over the range of possible values of X, given Y=y. In this case, since the distribution is uniform over the circle, the conditional PDF f(x|y) is also constant.

Since the circle [tex]x^2 + y^2 < 1[/tex], we know that the range of possible values for X given Y=y is from [tex]-\sqrt{(1-y^2)}[/tex] to[tex]\sqrt{(1-y^2)}[/tex] .

The conditional PDF f(x|y) is then 1 divided by the length of the range, which is [tex]2\sqrt{(1-y^2)}[/tex].

Thus, the conditional expectation E(X|Y=y) can be calculated as:

[tex]E(X|Y=y) = \int\limits^{\sqrt{1-y^2}}_{-\sqrt{1-y^2}} {x * f(x|y)}dx\\ =\int\limits^{\sqrt{1-y^2}}_{-\sqrt{1-y^2}} (\frac{x}{(2\sqrt{1-y^2}}) dx[/tex]

= 0 (by symmetry of the uniform distribution)

Therefore, E(X|Y=y) is equal to 0 for any given value of Y=y in the uniform distribution on the circle [tex]x^2 + y^2 < 1.[/tex]

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If you are on the surface of a sphere and cannot leave that surface, you can move in two dimensions. The surface of a sphere is a two-dimensional space.

To understand this, imagine yourself standing on a globe. You can move along the surface by walking in any direction, such as east-west or north-south. These movements are described by two coordinates, typically latitude and longitude, which define your position on the sphere.

However, you cannot move in the third dimension, which would involve going up or down from the surface of the sphere.

The concept of dimensions in this context refers to the number of independent directions in which you can move. In the case of a sphere, the surface is curved and can be represented using two coordinates, giving you the ability to move in two dimensions.

Adding a third dimension would involve moving away from the surface, which is not possible within the constraints of being confined to the sphere's surface.

Therefore, you can move in two dimensions but not in three or four dimensions while on the surface of a sphere.

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Answer:

BOA-30(Given)

BCA-15(See explanation)

BDA- 15(NOT SURE)

Step-by-step explanation:

*Angle at the center is twice the angle at the circumference.

If angle at the center(30) is twice BCA, then BCA is 15.

*I think BDA deals with alternate angles, so might be 15.

Answer:

Step-by-step explanation:

The expression Marshall used to calculate the perimeter of the rectangular garden is:

Perimeter = 2 * (width + length)

However, there is another equivalent expression that Marshall could use to calculate the perimeter:

Perimeter = 2 * width + 2 * length

Both expressions yield the same result and represent the same concept of adding up all the sides of the rectangular garden to determine its perimeter. The first expression groups the addition of the width and length together before doubling it, while the second expression separately doubles the width and length before adding them together.

If the correlation between two variables is .496, 75.4%. much of the variance has not been accounted for.

What is variable?

In the context of statistics and mathematics, a variable is a characteristic or quantity that can vary or take different values.

The correlation coefficient, which ranges from -1 to 1, measures the strength and direction of the linear relationship between two variables. If the correlation between two variables is 0.496, it indicates a moderate positive correlation.

The coefficient of determination, also known as R-squared, represents the proportion of the variance in one variable that can be explained by the other variable. In this case, if the correlation is 0.496, then the coefficient of determination is [tex](0.496)^2 = 0.246.[/tex]

Therefore, 24.6% of the variance has been accounted for by the correlation, and the remaining 75.4% of the variance has not been accounted for.

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The simplified expression is 4x∛2y + 12x²y∛2y².

We have the Expression

2(∛16x³y)+ 4 (∛54x⁶y⁵)

Now, factorise as

16 = 2 x 2 x 2 x 2

54 = 2 x 3 x 3 x 3

So, we can write

∛16x³y = ∛2× 2 × 2 × 2 × x × x × x × y

∛54x⁶y⁵ = ∛ 2 x 3 x 3 x 3 × x × x × x × x × x × x × y × y × y × y × y

Then, 2(∛16x³y)+ 4 (∛54x⁶y⁵)

= 2(∛2× 2 × 2 × 2 × x × x × x × y) + 4 (∛ 2 x 3 x 3 x 3 × x × x × x × x × x × x × y × y × y × y × y)

= 2 (2x)  (∛2y) + 4 (3x²y) (∛2y²)

= 4x∛2y + 12x²y∛2y²

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The probability that the next call will involve a question about the location of an ATM is 2/15.

We know that the probability of an event is equal to the ratio between the desired outcome and the total number of favorable outcomes.

Hence we can say that probability = desired outcome / total number of outcomes

Now here, to find the probability that the next call will involve a question about the location of an ATM, we need to determine the proportion of ATM-related calls out of the total number of calls.

Out of the last 45 telephone calls, 6 involved questions about ATM location. Therefore, the probability can be calculated as:

Probability = Number of ATM-related calls / Total number of calls

Probability = 6 / 45

Simplifying the fraction, we get:

Probability = 2 / 15

Therefore, the probability that the next call will involve a question about the location of an ATM is 2/15.

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The mass of the unloaded plane is 70500 kg.

Let's denote the mass of the unloaded plane as P.

Given that the fuel and crew are 1/4 of the mass of the unloaded plane, we can express their combined mass as (1/4)P.

Additionally, the passengers and luggage are 1/3 the mass of the fuel and crew, so their combined mass can be represented as (1/3)(1/4)P.

Now, let's calculate the total mass at take-off:

Total mass at take-off = Mass of unloaded plane + Fuel and crew + Passengers and luggage

Since the fuel and crew are 1/4 of the unloaded plane's mass, we have:

Fuel and crew = (1/4)P

Similarly, the passengers and luggage are 1/3 of the fuel and crew's mass, so we have:

Passengers and luggage = (1/3)(1/4)P

= (1/12)P

Now, we can calculate the total mass at take-off:

Total mass at take-off = P + (1/4)P + (1/12)P

Combining like terms:

Total mass at take-off = (12/12)P + (3/12)P + (1/12)P

Total mass at take-off = (16/12)P

Given that the total mass at take-off is 94000 kg, we can set up the equation:

(16/12)P = 94000

To solve for P, we multiply both sides by (12/16):

P = (94000 × 12) / 16

P = 70500 kg

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