An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function =Cx+−0.5x2180x25,609. How many engines must be made to minimize the unit cost?
Do not round your answer.

Sea "l" la medida del largo del terreno y "a" la medida del ancho del terreno.

De acuerdo con el problema, el ancho es la mitad del largo, es decir, a = l/2.

El perímetro de un rectángulo se calcula sumando las longitudes de sus cuatro lados, por lo que en este caso:

Perímetro = 2l + 2a = 2l + 2(l/2) = 3l

Sabemos que el perímetro es de 105 metros, entonces:

3l = 105

l = 105/3 = 35

Por lo tanto, el largo del terreno es 35 metros. Y, como el ancho es la mitad del largo, entonces:

a = l/2 = 35/2 = 17.5

Por lo tanto, el ancho del terreno es de 17.5 metros.

En resumen, las medidas del terreno son 35 metros de largo y 17.5 metros de ancho.

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There are 13.5 cubic meters of water in Mr. Johnson's pool.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

To find the volume of water in Mr. Johnson's pool, we need to multiply the length, width, and depth of the pool. The length is 2.5 meters, the width is 4.5 meters, and the depth of water is 1.2 meters.

So, the volume of water in Mr. Johnson's pool is:

2.5 meters x 4.5 meters x 1.2 meters = 13.5 cubic meters

Therefore, there are 13.5 cubic meters of water in Mr. Johnson's pool.

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We can expect  4 giant swallowtails to visit Ellie's garden.

In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).

Now, we can calculate the probability of a giant swallowtail visit:
Probability

= (number of giant swallowtails) / (total butterfly visits)

= 8/96

= 1/12

Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails

= (total butterflies) × (probability of giant swallowtails)

= 48 × (1/12)

= 4

So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.

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The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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The value of the missing side lengths a and b of the right angles triangle are 2 and √2 respectively.

A right-angled triangle's other angle must be 45 degrees because the base angle is that number. The third angle in a triangle must be 90 degrees since the sum of the triangle's three angles is 180 degrees.

Using trigonometric ratios, we know that,

sin(45) = 2√2/a and,

cos(45) = b/a.

Simplifying, we get,

a = 2√2/sin(45)

= 2√2/√2

= 2 and,

b = a cos(45)

= 2 cos(45)

= √2.

Therefore, the value of a is 2 and the value of b is √2.

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The statement that is true is: "The range of the function is all real numbers less than or equal to 9

This quadratic function is indicated by a downward-opening parabola due to the negative coefficient of the squared term.

Found at coordinates (-2, 9), the vertex will be the highest point on this curved graph

Located on the x-axis at points (-5, 0) and (1, 0), each one serves as an intersection. Because of these intersections the following statement can be confidently said: "The range of the function consists of all actual numbers that are lesser or equal to 9."

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The expression that represents the fee for signing up the day of the activity is x + 0.20x. This means that fee for signing up the day of the activity is original fee (x) plus an additional 20% of original fee (0.20x).

For example, if the community center charges $50 for signing up before the day of the activity, then the fee for signing up the day of the activity would be:

$50 + ($50 x 0.20) = $50 + $10 = $60

So, individuals who sign up the day of the activity are charged a higher fee than those who sign up before the day of the activity, because they are charged the original fee plus an extra 20% of the original fee. This is often used as an incentive for individuals to sign up early and to help the community center plan and prepare for the activity accordingly.

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In a regular tiling, if there are six polygons meeting at a vertex, then the angles at the vertex are 120 degrees.

This is because each regular polygon has interior angles that are multiples of 180 degrees divided by the number of sides. For a regular hexagon, which has six sides, each interior angle measures 120 degrees. When six regular hexagons meet at a vertex in a regular tiling, the total angle sum at the vertex is 720 degrees (6 times 120 degrees).

Since the angles must be divided equally among the six hexagons, each angle at the vertex is 120 degrees.

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The coordinate matrix of the linear transformation with respect to the second ordered basis is found by multiplying the change of basis matrix by the coordinate matrix of the linear transformation with respect to the first ordered basis is [tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]

Let V be a vector space with two ordered bases B and B', and let T be a linear transformation from V to V. Suppose that the change of basis matrix from B to B' is P, and the coordinate matrix of T with respect to B is A.

To find the coordinate matrix of T with respect to B', we can use the formula

A' = P⁻¹AP

where A' is the coordinate matrix of T with respect to B'.

To use this formula, we need to find the inverse of P. If P is invertible, then we have

P⁻¹ = 1/det(P) * adj(P)

where det(P) is the determinant of P and adj(P) is the adjugate of P.

Assuming that P is invertible, we can compute its inverse as follows

det(P) = 1*(-2) - 2*2 = -5

adj(P) =[tex]\left[\begin{array}{cc}-2&2\\-2&1\end{array}\right][/tex]

So, P⁻¹ = (-1/5)*[tex]\left[\begin{array}{cc}-2&2\\-2&1\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}2/5&-2/5\\2/5&-1/5\end{array}\right][/tex]

Now, we can use the formula to find the coordinate matrix of T with respect to B'

A' = P⁻¹AP =  *[tex]\left[\begin{array}{cc}-2&1\\-1&0\end{array}\right][/tex]*[tex]\left[\begin{array}{cc}-1&2\\2&1\end{array}\right][/tex]= [tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]

Therefore, the coordinate matrix of T with respect to B' is

[tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]

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--The given question is incomplete, the complete question is given

"  Using change of base matrices to find coordinate matrices of linear transformations Let B and C be two ordered bases of R2, and consider a linear transformation T: R2 + R2. Suppose that the change of base matrix Ic, B is given by [0 -2 3 3] and the coordinate matrix Tc,c of T with respect to C is given by [ -1 -1 2 -1] Use this to determine coordinate matrix TB,B of T with respect to B. TB,B ? "--

The area of the outer circle and of the inner circle is :  πr² and,  πx².

Then subtract the area of the inner circle from the outer circle is :

π (r - x) (r+x)

Here, we have,

Given:

Let the radius of outer circle i.e CA be r

Let the radius of inner circle i.e CB be x

The diagram is given below as attachment.

We know that,

area of circle = πR²

Then subtract the area of the inner circle from the outer circle is:

The area of the outer circle - area of the inner circle

= πr² -  πx²

= π (r² - x²)

=π (r - x) (r+x)

So, we get

Then subtract the area of the inner circle from the outer circle is:

π (r - x) (r+x)

Hence, The area of the outer circle and of the inner circle is :  πr² and,  πx².

Then subtract the area of the inner circle from the outer circle is :

π (r - x) (r+x)

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For the function "h(x) = |2x| - 8", the domain is (-∞, ∞) and the range is  [-8, ∞).

The function h(x) = |2x| - 8 is defined for all real numbers x, so the domain of h(x) is the set of all real-numbers, or (-∞, ∞).

To find the range of the function, we determine set of all possible output values of function. Since the function involves the absolute value of 2x, the output can never be less than -8.

When "2x" is positive, |2x| = 2x. When 2x is negative, |2x| = -2x. This means that the function h(x) will have two branches depending on whether 2x is positive or negative.

⇒ When 2x is positive, h(x) = |2x| - 8 = 2x - 8. This branch of the function will have all non-negative values.

⇒ When 2x is negative, h(x) = |2x| - 8 = -2x - 8. This branch of the function will have all non-positive values.

Combining the two , we get the range of the function h(x) as [-8, ∞).

Therefore, the domain of h(x) is (-∞, ∞) and the range of h(x) is [-8, ∞).

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Answer:

36/49.

Step-by-step explanation:

Probability if rains on one day = (6/7)

Probabiilty it rains the next day  also

= 6/7 * 6/7

= 36/49.

The solution to the equation is f = 16. The value of f can be found by multiplying both sides of the equation by 8.

To solve the equation 2 = f/8 for f, we aim to isolate f on one side of the equation.

To do so, we can multiply both sides of the equation by 8, as this will cancel out the denominator of f/8.

By multiplying 2 by 8, we obtain 16 on the left side of the equation.

On the right side, the 8 in the denominator cancels out with the 8 we multiplied, leaving us with just f.

we find that f = 16 is the solution to the equation.

This means that if we substitute f with 16 in the equation, we will have a true statement: 2 = 16/8, which simplifies to 2 = 2.

f = 16 satisfies the original equation and is the solution.

It's important to note that when solving equations, we perform the same operation on both sides to maintain equality.

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None of the bills have an experimental probability of 3, as all probabilities are between 0 and 1.

Based on the table, the experimental probability for each bill being drawn from the bag next can be calculated by dividing the frequency of each bill by the total number of draws (100). Using this formula, we can calculate the experimental probabilities for each bill:

1. For the $1 bill: Experimental probability = [tex]\frac{(Frequency of  $1 bill)}{Total draws} = \frac{8}{100} = 0.28[/tex]
2. For the $10 bill: Experimental probability =[tex]\frac{(Frequency of  $10 bill)}{Total draws} = \frac{56}{100} = 0.56[/tex]
3. For the $20 bill: Experimental probability =[tex]\frac{(Frequency of  $20 bill)}{Total draws} = \frac{2}{100} = 0.02[/tex]

None of the bills have an experimental probability of 3, as all probabilities are between 0 and 1.

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The probability of rolling an even number and then an odd number is 1/4.

The probability of rolling an even number on a fair number cube is 1/2, since there are three even numbers (2, 4, 6) and six possible outcomes (1, 2, 3, 4, 5, 6).

Similarly, the probability of rolling an odd number is also 1/2.

To find the probability of rolling an even number and then an odd number, we need to multiply the probabilities of each event. So:

P(even and odd) = P(even) × P(odd)

P(even and odd) = (1/2) × (1/2)

P(even and odd) = 1/4

So the probability of rolling an even number and then an odd number is 1/4.

The number of desired outcomes for rolling an even number and then an odd number is 9

Since there are three even numbers and three odd numbers, and therefore 3 × 3 = 9 possible outcomes.

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If there are 750 contestants on Monday, Jessica should expect around 75 of them to dunk a teacher.

Based on the table provided, we can see that the percentage of winners at the dunk-a-teacher booth varies from day to day.

On Monday, 10% of contestants were able to dunk a teacher.

Therefore, if there are 750 contestants on Monday, Jessica should expect around 75 of them to dunk a teacher.

This is calculated by multiplying 750 by 0.10, which gives us 75. It's important to note that this is just an estimation, as the actual number of winners may be slightly higher or lower than 75.

However, this gives Jessica a rough idea of what to expect at the booth on Monday.

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The crop sizes for first 4 years without using fertilisers are:

The size of the potato crop for each of the first four years is computed as follows:

For Year 1:

= 15 tonnes * 1

= 15 tonnes

For Year 2:

= 15 tonnes x 0.8

= 12 tonnes

For Year 3:

= 12 tonnes x 0.8

= 9.6 tonnes

For Year 4:

= 9.6 tonnes x 0.8

= 7.68 tonnes

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Coordinates of vertex y are (-12,-1).

To find the coordinates of vertex y in parallelogram WXYZ, we can use the fact that opposite sides of a parallelogram are parallel. We can use this property to find the coordinates of y by first finding the vector between points X and Z, and then adding that vector to the coordinates of point W.

The vector between points X and Z is (-7-2,-3-4)=(-9,-7). Adding this vector to the coordinates of point W gives (-5-9, 2-7)=(-14,-5). Therefore, the coordinates of vertex Y are (-14,-5).

Hence, the coordinates of vertex Y in the parallelogram WXYZ are (-14, -5).

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The total surface area of the prism is 282

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

The net of a triangle prism.

The total surface area of the prism is the sum of the individual shapes

So, we have

Surface area = 2 * 1/2 * 6 * 5 + 3 * 6 * 14

Evaluate

Surface area = 282

Hence. the total surface area of the prism is 282

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Answer:

The total surface area is 282

Answer:

Step-by-step explanation:

The missing numbers are: box 1 = -5x and box 2 = 4sot,  A diamond problem is a type of math puzzle that involves finding two missing values in a diamond-shaped diagram.

The top and bottom numbers of the diamond represent a product, and the left and right sides represent two numbers that add up to a middle value. The goal is to find the two missing values that fit into the diamond.

To solve a diamond problem, we need to factor the product of the top and bottom numbers and look for two factors whose sum is equal to the middle value. This is because the product of two numbers can only be made up of factors that multiply together to form the product. Once we find the two factors, we can insert them into the left and right sides of the diamond.

In the given diamond problem, we have 20x? as the top and sot as the bottom. The product of these two numbers is 20x^2sot. To find the factors, we can list all the possible factor pairs of this product and check which of them adds up to -9x, which is the middle value in the diamond. We found that -5x and 4sot are the factors that add up to -9x.

Solving diamond problems can help improve factoring skills and problem-solving abilities. It requires logical thinking and an understanding of how factors and multiples work. Additionally, diamond problems can be used to introduce algebraic concepts to students in a visual and intuitive way, making them a useful tool for teaching math to learners of all ages.

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The mean of the temperatures shown is -39.4°F.

What is the mean temperature?

The average mean air temperature throughout a specific time period, typically a day, a month, or a year, as measured by a thermometer that has been properly exposed. The mean temperature is often calculated for the year and for each month in climatological tables.

Date:   Low temperature:

January 1   -42°F

January 2 -31°F

January 3  -40°F

January 4  -40°F

January 5  -44°F

Mean = Total sum of all 5 days temperature / total number of days

Mean = -42  - 31 - 40 - 40 - 44 / 5

= -197 / 5

= - 39.4°F

Hence, the mean of the temperatures shown is -39.4°F.

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Around $441 million worth of food is wasted in the US each day.

According to the United States Department of Agriculture (USDA), about 30-40 percent of the food supply in the United States goes to waste. In terms of dollars, that translates to approximately $161 billion worth of food being wasted each year in the United States.

Dividing that number by 365, we can estimate that around $441 million worth of food is wasted in the US each day.

It's difficult to estimate how many people could be fed with the food that is thrown away, as food waste can take many forms, such as uneaten meals at restaurants, spoiled produce at grocery stores, and expired food in households. However, according to Feeding America, a national food bank network, approximately 42 million Americans, including 13 million children, are food insecure, which means they lack reliable access to affordable, nutritious food.

If we assume that all the food that is currently being wasted in the US could be redistributed to those who are food insecure, it could potentially feed a significant number of people. However, in reality, the logistics of collecting, storing, and distributing food waste can be complex, and some food waste may not be safe or nutritious to eat. Additionally, addressing food waste is just one piece of the puzzle in addressing food insecurity, which is a complex issue with many underlying factors.

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(a) The quadrant in which u/2 lies is either Quadrant I or Quadrant II.

(b) The exact values of sin(u/2), cos(u/2), and tan(u/2) are:
sin(u/2) = √10/5
cos(u/2) = 3√10/10
tan(u/2) = 2/3

(a) To determine the quadrant in which u/2 lies, we need to look at the value of sin u. Since sin u is positive (3/5 is positive and π/2 is in Quadrant I), we know that u is in either Quadrant I or Quadrant II.

To find u/2, we divide u by 2, which means u/2 will be in either Quadrant I or Quadrant II as well. Therefore, the answer is either Quadrant I or Quadrant II.

(b) We can use the half-angle formulas to find the values of sin(u/2), cos(u/2), and tan(u/2):

sin(u/2) = ±√[(1 - cos u)/2]
cos(u/2) = ±√[(1 + cos u)/2]
tan(u/2) = sin(u/2)/cos(u/2)

Since sin u = 3/5, we can find cos u using the identity sin^2 u + cos^2 u = 1:

cos u = ±√[(1 - sin^2 u)] = ±√[(1 - 9/25)] = ±4/5

Since u/2 is in either Quadrant I or Quadrant II, we know that sin(u/2) and cos(u/2) are positive. Therefore, we can choose the positive square roots for sin(u/2) and cos(u/2):

sin(u/2) = √[(1 - cos u)/2] = √[(1 - 4/5)/2] = √[1/10] = √10/10 = √10/5
cos(u/2) = √[(1 + cos u)/2] = √[(1 + 4/5)/2] = √[9/10] = 3/√10 = 3√10/10

Finally, we can use these values to find tan(u/2):

tan(u/2) = sin(u/2)/cos(u/2) = (√10/5)/(3√10/10) = 2/3

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To compute Bu(1.-3) - 88 - (1, -3), we need to substitute the values of u and v into the expression for w.

First, we need to find the values of u and v. Since u = 1.-3 and v = (1, -3), we have:

u = 1.-3 = 1 - 0.3 = 0.7
v = (1, -3)

Next, we can substitute these values into the expression for w:

w = 2xy + y^2 - 4x^2
 = 2(1)(-3) + (-3)^2 - 4(1)^2  (substituting x = 1 and y = -3)
 = -6 + 9 - 4
 = -1

Finally, we can compute Bu(1.-3) - 88 - (1, -3) by multiplying the gradient of w by the vector (1, -3) and subtracting 88:

Bu(1.-3) - 88 - (1, -3) = (-8x + 2y, 2x + 2y)  (1, -3) - 88
                        = (-8(1) + 2(-3), 2(1) + 2(-3))  (1, -3) - 88
                        = (-14, -4)  (1, -3) - 88
                        = (-14)(1) + (-4)(-3) - 88
                        = -14 + 12 - 88
                        = -90

Therefore, Bu(1.-3) - 88 - (1, -3) = -90.

Since the question seems to have some typos or missing information, I'll assume you want to find the partial derivatives of w with respect to x and y, and evaluate them at the point (1, -3).

Given w = 2xy + y² - 4x², let's compute the partial derivatives:

∂w/∂x = 2y - 8x
∂w/∂y = 2x + 2y

Now, let's evaluate these partial derivatives at the point (1, -3):

∂w/∂x(1, -3) = 2(-3) - 8(1) = -6 - 8 = -14
∂w/∂y(1, -3) = 2(1) + 2(-3) = 2 - 6 = -4

Thus, the evaluated partial derivatives are ∂w/∂x(1, -3) = -14 and ∂w/∂y(1, -3) = -4.

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Possible number of death rays (D) and claws (C) that Archimedes can build are given by the following system of inequalities: 350D + 200C ≤ 3000. D, C ≥ 0

The first inequality represents the fact that the total amount of gold used to build the machines cannot exceed the 3000 lbs of gold given by the city. The second inequality ensures that the number of death rays and claws cannot be negative.

To explain this system, let us assume that Archimedes builds x death rays and y claws. The amount of gold required to build x death rays and y claws is given by 350x + 200y. The first inequality ensures that this value cannot exceed 3000 lbs of gold. The second inequality ensures that the number of death rays and claws cannot be negative.

Therefore, the solution to this system of inequalities gives us all the possible combinations of death rays and claws that Archimedes can build with the given amount of gold.

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I think it might be C

The minimum number of people that need to be persuaded is two. When there are 0 contributor, 1 contributor, 2 or more contributor this is a the Nash equilibria.

a. Let's first calculate the benefit to each citizen when there are n contributors. According to the problem, the benefit is n^2 dollars. So when there are 0 contributors, the benefit to each citizen is 0 dollars. When there is 1 contributor, the benefit to each citizen is 1 dollar. When there are 2 contributors, the benefit to each citizen is 4 dollars. And so on, up to 10,000 dollars per citizen when all 100 citizens contribute.

Now let's think about the incentives of each citizen to contribute. If no one contributes, everyone gets 0 dollars of benefit. If one person contributes, that person gets 1 dollar of benefit, and everyone else gets 0 dollars. So each person has an incentive to free-ride, hoping that someone else will contribute.

But if two people contribute, each person gets 4 dollars of benefit, which is more than the 1 dollar cost of contributing. So once there are at least two contributors, it becomes rational for everyone else to contribute as well.

Therefore, the minimum number of people that need to be persuaded is two. Once two people contribute, it becomes rational for everyone else to contribute as well.

b. Let's consider the Nash equilibria of the game where each citizen is deciding whether to contribute. A Nash equilibrium is a situation where no one has an incentive to change their strategy, given the strategies of all the other players.

In this case, each citizen has two strategies: contribute or free-ride. Let's consider the case where n citizens are contributing. If everyone else is contributing, then it is rational to contribute as well, since the benefit of contributing is greater than the cost.

If everyone else is free-riding, then it is rational to free-ride as well, since the cost of contributing is greater than the benefit. However, if some people are contributing and some people are free-riding, then it may be rational to contribute, since the benefit of contributing may outweigh the cost, depending on the number of contributors.

Therefore, there are multiple Nash equilibria in this game, depending on the number of contributors. When there are 0 contributors, everyone is free-riding and this is a Nash equilibrium. When there is 1 contributor, that person is contributing and everyone else is free-riding, and this is a Nash equilibrium. When there are 2 or more contributors, everyone is contributing, and this is a Nash equilibrium.

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The choice which best describes the measure of center of these data is (d) Rome data center is "best-described" by median and  data center of "New-York" is "best-described" by mean.

In the table provided below, we see that the "IQR" for Rome is relatively large compared to the IQR for New York, which suggests that that there may be some skewness in the distribution of the Rome data. So, the median would be a better-measure of center than the mean.

On the other hand, the IQR for "New-York" is relatively small, which indicates that the data is more symmetric and the mean would be a better measure of center.

Therefore, the correct answer is (d).

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The given question is incomplete, the complete question is

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:

                    High   Low    Q1     Q3    IQR    Median    Mean    σ

Rome              18       1         3       7        4         6.5          6.4    4.3

New York       14       1        4.5    8.5     4          5.5          6.1     3.2

Which of the choices below best describes how to measure the center of these data?

(a) Both centers are best described by the mean.

(b) Both centers are best described by the median.

(c) The Rome data center is best described by the mean. The New York data center is best described by the median.

(d) The Rome data center is best described by the median. The New York data center is best described by the mean.

It will take the rock 1.5 seconds  to hit the ground

Since the situation is modeled by the equation h = -16t² + 16t + 12

The rock will hit the ground when height is zero i.e. h = 0. Thus, we have:

-16t² + 16t + 12 = 0 and we can then solve for the time (t) .

-16t² + 16t + 12 = 0  (divide through by -16)

t² - t - 3/4 = 0

Using factorization method:

(t + 1/2) (t - 3/2) = 0

t = -1/2 or 3/2

Since t cannot be negative. Thus, t = 3/2 = 1.5.

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