DOM Practice Problems

1) An empty boat displaced 2525 cm^3 of water. When you placed an oar on the boat, it displaced 3878 cm^3 of water. What is the weight of the oar in grams?

2) Jane is three times older than her pet and Jane will be 13 next month. How old is Jane’s pet?

Make sure to show work and circle your answer!

*Please add a picture of the work and circle the final answer*

Answer:

1. One solution

2. No solution

3. Infinite solutions

4. Two solutions

5. Three solutions

Step-by-step explanation:

You're welcome  ♡

The closest option to the total distance driven is 270.

We kept an eye on them from afar. Compared to earlier, she perceives a distance between her and her brother. They had been close friends once, but now there was a great distance between them. He desires to disassociate himself from his old boss.

We must combine the distances for each hour in order to calculate the total distance travelled:

Distance total = 62 + 70 + 68 + 72

272 miles roundtrip.

Thus, option 270 comes the closest to the total mileage driven.

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Answerer Latoya got a better deal because she paid less than Herman by 25 cents

Step-by-step explanation:

Latoya 18 divided by 8= $2.25

Herman 15 divided by 6= $2.50

So Latoya saves $0.25 cents

The quadratic equation for the height of the rock, h = -16·t² + 79·t + 50, indicates;

a. The times at which the rock will be 125 feet above the beach are about; 3.66 seconds and 1.28 seconds

b. The maximum height reached is about 147.5 feet and it will take about 2.5 seconds for the rock to reach maximum height

A quadratic equation is an equation of the form, f(x) = a·x² + b·x + c, where; a ≠ 0, and a, b, and c are numbers.

a. The function for the height of the rocket is presented as follows;

h(t) = -16·t² + 79·t + 50

The time at which the height is 125 feet can be found as follows;

h(t) = 125 feet

h(t) = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 125 - 125 = 0

-16·t² + 79·t - 75 = 0

The quadratic formula indicates that we get;

t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32

t = (79 ± √(1441))/32

t = (79 + √(1441))/32 ≈ 3.66

t = (79 - √(1441))/32 ≈ 1.28

b. The time at which the rock is at the maximum height can be obtained by using the formula for finding the input value at the maximum value of a quadratic function, which is; at the maximum height, x = -b/2·a

Therefore, at the maximum height, we get;

The time, t = -79/(2 × (-16)) = 2.46875

The time it takes the rock to reach the maximum height is 2.46875 seconds ≈ 2.5 seconds

The maximum height is therefore;

h(2.46875) = -16×2.46875² + 79×2.46875 + 50 = 147.515625 ≈ 147.5

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The sequence of transformations is:

Let's only follow the coordinates of one of the vertices to identify the transformations, we clearly have a reflection over a vertical line and a reflection over a horizontal line, so first let's apply thes two.

Vertex A starts at (1, -4)

First a reflection over the x-axis will change the sign of the y-component, then we get:

A₁ = (1, 4)

Then a reflection over the y-axis changes the sign of the x-component to:

A₂ = (-1, 4)

Finally we have a translation, we can see that:

A' = (2, 4).

Then we have a translation (a, b) such that:

(-1 + a, 4 + b) = (2, 4)

So we can see that a = 3 and b = 0, then we have a translation of 3 units to the right.

That is the sequence of transformations.

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Step-by-step explanation:

Assuming that the grain required to produce 100 liters of ethanol could feed one person for a year, we can calculate the number of people that could have been fed by the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018.

First, we need to determine the amount of grain required to produce 1 liter of ethanol. This can vary depending on a number of factors, including the type of grain and the production method, but a commonly cited estimate is that it takes around 1.4 kilograms of corn to produce 1 liter of ethanol.

Therefore, to produce 49 billion liters of ethanol, we would need:

49,000,000,000 liters x 1.4 kg of corn per liter = 68,600,000,000 kg of corn

To convert this to the amount of grain required to feed people, we need to divide by the amount of grain needed to feed one person for a year. Again, this can vary depending on the person's age, sex, and level of activity, but a commonly cited estimate is that an adult needs around 700 kilograms of grain per year.

Therefore, the amount of grain required to feed the number of people who could have been fed by the grain used to produce the additional ethanol is:

68,600,000,000 kg of corn / 700 kg of corn per person per year = 98,000,000 people

So the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018 could have fed around 98 million people for a year.

The additional ethanol production from corn in 2018 could have potentially fed 49 billion people

To determine how many people could have been fed with the additional 49 billion liters of ethanol produced in the US from corn in 2018 compared to 2001, we need to calculate the amount of grain saved by producing ethanol instead of using it for direct consumption.

According to the information given, the grain required to produce 100 liters of ethanol can feed a person for a year. Therefore, for each liter of ethanol produced, the grain equivalent can sustain one person for a year.

To find the number of people fed, we can multiply the additional 49 billion liters of ethanol produced by the grain equivalent for each liter:

49 billion liters * 1 person/year per liter = 49 billion people

Hence, the additional ethanol production from corn in 2018 could have potentially fed 49 billion people based on the assumption that the grain used to produce ethanol would have been used for direct consumption instead.

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Answer:

9000000 Milligrams

Step-by-step explanation:

We know that,

1 kilogram = 10^6 Miligram

So, 9  Kilpgrams = 9×10^6 = 9000000 Milligrams

17.  Number of hours, h     10 + 2h    Total Cost

         1                             10 + 2 x 1          12

         2                            10 + 2 x 2         14

         3                            10 + 2 x 3         16

         4                             10 + 2 x 4        18

This is true because as shown in the first example, you have to sub in the number of hours into the "h" value, and multiply it times two. After that, you add ten.

Check the picture below.

Answer:

95.522

Step-by-step explanation:

First, we have to find the area of the triangle...

Next, we have to find the area of the sector...

Now we have to add our results together...

Hope this helps, have a lovely day! :)

1) The nth term if the sequences are (a) 9a-7  (b)  13-6a  

A sequence is a list of numbers or objects in a special order.1 It is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequences are

1) (a)  2,11,20,...

the first term a= 2, the common difference d = 11-2 =9

The nth term is given as

Tn = a + (n-1)d

Tn = 2 + (n-1)*9

Opening the brackets to get

2 + 9n -9

Rearrange to have

9n -7

(b)  the sequence is 7,1,-5,...

a = 7 ,

d= 1-7 = -6

Tn = a + (n-1)d

Tn = 7 + (n - 1)-6

Tn = 7 + -6n +6

Tn = 7+6 -6n

Tn = 13 -6n

2) Remember for every Fibonacci sequence

1st+2nd=3rd

2nd+3rd=4th

3rd+4th=5th

4th+5th=6th

Remember for every arithmetic Progression

Tn = a + (n-1)d

For every Geometric Progression,

Tn = arⁿ⁻¹

First five terms        Next three terms      Name of sequence(A,G,F,Q)

  10,6,2,-2,-6                 -10,-14,-18                    arithmetic

  2,8,32,126512        2048, 8192,32768          Geometric

  20,13,33,46,79           125,204,329                 Fibonacci

  200,100,50,25,12.5   6.25, 3.125, 1.5625      Geometric

46,39,32,25,18,              11,4 , -3                         Arithmetic

-2,,2,0,2,2,4                  6,10,16                            Fibonacci

3,6,10,15, 21                 28,35,42                        Arithmetic

25,15,0,-20,-45,           -80,-125,-175                Arithmetic

2,5,7,12,19                    31,50,81                       Fibonacci

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53[/tex]

The smaller acute angle of the right triangle is x-3 = 12.6 degrees.

What is Right Triangle?

A triangle in which one angle is 90 degree is called a Right Angled Triangle.

In a right triangle, if one acute angle is x-3 degrees, then the other acute angle is 90-(x-3) = 93-x degrees.

Using the given equation, we have:

sin(x-3) = cos(6x+9)

Taking the sine of both sides:

sin(x-3) = sin(90 - (6x+9)) = sin(81-6x)

Now we have:

sin(x-3) = sin(81-6x)

Since the two angles have the same sine, they must differ by a multiple of 360 degrees. Thus:

x-3 = 81-6x + 360n or x-3 = 6x-81 + 360n

where n is an integer.

Simplifying each equation:

7x = 84 + 360n or 5x = 78 + 360n

Dividing both sides by 7 or 5, respectively:

x = 12 + 51.43n or x = 15.6 + 72n

The first equation gives us values of x that are too large for an acute angle, so we use the second equation:

x = 15.6 + 72n

The smallest such x that satisfies 0 < x < 90 is when n=0, which gives:

x = 15.6 degrees

Therefore, the smaller acute angle of the right triangle is x-3 = 12.6 degrees.

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bc=√{ac²-ab²}

bc=√{16²-11²}

bc=√{256-121}

bc=√{135}

bc=11.62

The shaded area to the right of 4 indicates all values larger than 4 being inequality included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.

A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.

The graph below shows the set of solutions to the inequality where x + 2 is larger than or equal to 6:

From negative 9 to positive 9 is a number line. At positive 4, a closed circle appears. Positive numbers four through nine are shaded on the number line.

This means that the inequality will be satisfied by any value of x larger than or equal to 4. The graph includes the value 4 in the solution set since it has a closed circle there, and because it is shaded to the right of 4, it also includes all values higher than 4.

Here is an illustration of the graph:

  |----|----|----|----|----|----|----|----|----|

     -9   -8   -7   -6   -5   -4   -3   -2   -1    0

                                           o        

                                         ---->      

                                           4        

                                         ----]      

                                           >        

      |----|----|----|----|----|----|----|----|----|

      -9   -8   -7   -6   -5   -4   -3   -2   -1    0

The shaded area to the right of 4 indicates all values larger than 4 being included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.

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The population parameter of interest in this study is the proportion or percentage of all female adults in the entire population who support a ban on public smoking. The Gallup poll was conducted to estimate this proportion or percentage by collecting data from a sample of female adults. By using statistical inference methods, the researchers can use the sample data to make inferences about the population parameter with a certain level of confidence.

Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):

P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)

From the table, we have:

P(male) = 1110/3538 ≈ 0.314

P(nursing major) = 1016/3538 ≈ 0.287

P(male and nursing major) = 94/3538 ≈ 0.027

Therefore:

P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574

Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.

(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:

P(being female or not being a nursing major) = P(female) + P(not nursing major)

From the table, we have:

P(female) = 2428/3538 ≈ 0.686

P(not nursing major) = 1728/3538 ≈ 0.489

Therefore:

P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175

This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):

P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)

From the table, we have:

P(female and nursing major) = 700/3538 ≈ 0.198

Therefore:

P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977

Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.

(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:

P(not being female or being a nursing major) = 1 - P(being female or being nursing major)

From part (a), we have:

P(being male or being nursing major) ≈ 0.574

Therefore:

P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426

Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.

(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.

Step-by-step explanation:

The perimeter of triangle N is 72 inches.

Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.

Here given the triangles M and N are similar, the ratio of sides N:M is 4:3

We can say that M and N with constant term x is, (by ratio proportion rule)

M = 3x and N = 4x and

Given the lengths of triangle M are 12 inches, 18 inches and 24 inches

for triangle M = 3x, (Using above ratio proportion rule)

3x = 12 inches                    3x = 18 inches                    3x = 24 inches

x = 4                                    x = 6                                    x = 8

Similarly, for similar triangle N = 4x, (Using above ratio proportion rule) put all values of x = 4, 6, 8

for x =4                                for x =6                                for x =8

4x = 4×4                               4x = 4×6                              4x = 4×8  

16 inches                             24 inches                            32 inches

Length of triangle N is 16 inches, 24 inches and 32 inches

Perimeter of triangle N = 16+24+32 = 72 inches

Therefore, the Perimeter of triangle N is 72 inches.

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Given statement: Here's the table with the values organized:
X | Y
-----
1 | 5
-3 | 2
7 | 2
6 | 3
7 | -4
5 | 9
8 | 4
1 | 7
1 | 0

This statement is False.

Because, The table provided is not a function because it does not have a clear and unique output value for each input value.

Since the X values 1 and 7 have multiple Y values, the given table is not a function.

In a function, each input value (X) must have a unique output value (y). However, in the given table, there are some input values, such as X = 7 and X = 1, that have multiple output values. For example, when X = 7, the table provides two output values, 2 and -4. Similarly, when X = 1, the table provides two output values, 5 and 0.

A function is a mathematical relationship between the input and output values, where each input value produces only one unique output value. Functions are used to represent many real-world scenarios, including calculating distances, temperatures, and profits. Therefore, it is crucial to ensure that the provided table represents a function by ensuring that each input value has a unique output value.

In conclusion, the table provided is not a function as it violates the one-to-one mapping between input and output values.

A function must have a clear and unique output value for each input value.

To determine if the given table represents a function, we need to make sure that each input (X value) corresponds to only one output (Y value).
Now let's check for any repeating X values with different Y values:
1 corresponds to both 5 and 7
7 corresponds to both 2 and -4.

False.

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Answer:

Step-by-step explanation:

The two given points are (8, 0) and (8, -8).

Using the distance formula, the distance between the two points can be calculated as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where x1 = 8, y1 = 0, x2 = 8, and y2 = -8

d = sqrt((8 - 8)^2 + (-8 - 0)^2)

d = sqrt(0 + 64)

d = sqrt(64)

d = 8

Therefore, the distance between the two points is 8 units.

The three accοmpanying questiοns, assuming that the firm is prοfit-maximizing and dοes nοt shut dοwn in the shοrt run

1)Firm's Tοtal Revenue=  $78000

2)Firm's Tοtal Cοst =$128700

3)Firm's Lοss = - $50700

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here in the given graph,

Cοst per unit = $300

Equilibrium quantity = $260 Then,

Firm's Tοtal Revenue = P * Q

=> $300*260 = $78000 (Equilibrium where, MR = MC)

Firm's Tοtal Cοst = Cοst per Unit * equilibrium quantity

=> $495*260 = $128,700

Firm's Lοss = TR - TC

=> $78000 - $128,700 = - $50700

Hence the answers are,

1)Firm's Tοtal Revenue=  $78000

2)Firm's Tοtal Cοst =$128700

3)Firm's Lοss = - $50700

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The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

To solve this problem, we can use the binomial probability formula, which is:

[tex]P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]

where:

n is the sample size (number of workers being interviewed)

k is the number of successes we are interested in (in this case, 2 of the workers being union members)

p is the probability of success (in this case, the probability that a worker is a union member)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))

Plugging in the values, we get:

[tex]P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)[/tex]

[tex]= (6) * (0.96)^2 * (0.04)^2[/tex]

= 0.04403136

Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

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Answer:

Nonexamples of base and exponent in math would be any mathematical expressions that do not involve raising a base to an exponent. For example, 2 + 3 or √4 do not involve base and exponent.

An example of coefficient and exponential form is 5x², where 5 is the coefficient and x² is the exponential form. A nonexample could be x²/5, which does not have a coefficient in front of the exponential form.

An example of expanded form is 5x + 2, where the expression is fully written out. The standard form of the same expression would be 2 + 5x. A nonexample of expanded form is 2(x + 3), where the expression is not fully written out.

Examples of exponent laws include the product rule (a^m * a^n = a^(m+n)), quotient rule (a^m / a^n = a^(m-n)), and power rule ((a^m)^n = a^(mn)). A nonexample of an exponent law could be the sum of powers rule, which does not exist in traditional exponent laws.

The solutions for all the parts are given below.

Exponentiation is one of the mathematics operations.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by 'a' times to itself.

So, a is the exponent of m.

1) Non-examples of a base and exponent in math would be: "2 + 3" or "5 - 7" as these are expressions and not a base raised to an exponent.

2) An example of a coefficient and exponential form would be "2x^3" where 2 is the coefficient and x^3 is the exponential form. A nonexample would be "3x + 2" as it is an expression and not in exponential form.

3) An example of an expanded form would be 235 = 2 x 100 + 3 x 10 + 5 x 1, where each digit is multiplied by its corresponding place value. An example of standard form would be 235 written as is, without being broken down into its place values. A nonexample of expanded form would be 235 written as 2 + 3 + 5, as this is not a multiplication of the digits with their place values.

4). Examples of exponent laws include:

Product law: aᵇ x aⁿ = a⁽ᵇ ⁺ⁿ⁾

Quotient law: [tex]a^m / a^n = a^{(m-n)}\\[/tex]

Power law: [tex](a^m)^n = a^{(m \times n)}[/tex]

Negative exponent law: [tex]a^{(-n)} = 1/a^n[/tex]

Zero exponent law: [tex]a^0 = 1[/tex].

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The length of the line segment PR from the given parameters is: 8x - 8

The line segment addition postulate is a postulate that states that if we are given two points on a line segment, X and Z, a third point Y lies on the line segment XZ if and only if the distances between the points meet the requirements of the equation XY + YZ = XZ

We are given the parameters:

PQ = 3x - 2

QR = 5x + 6

Thus:

PR = PQ + QR

PR = 3x - 2 + 5x - 6

PR = 8x - 8

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After solving the given problem, we found that the difference between the area of the dilated square and the original square is 32 square centimeters.

The area of the original square with a side length of 2 centimeters can be calculated as:

A = s²

A = 2²

A = 4 square centimeters

When this square is dilated by a scale factor of 3, the new side length will be:

s' = 3s

s' = 3(2)

s' = 6 centimeters

The area of the dilated square can be calculated as:

A' = s'²

A' = 6²

A' = 36 square centimeters

The difference between the area of the dilated square and the original square is:

A' - A = 36 - 4

A' - A = 32 square centimeters

Therefore, the difference between the area of the dilated square and the original square is 32 square centimeters.

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Answer:

[tex]5(4+c)[/tex]

The first derivative of y is: y' = [4tan(πt)sec(πt) - πsec²(πt)]/(π³) and

The second derivative of y is: y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)

The first derivative of a function represents the rate of change or slope of the function. The second derivative represents the rate of change of the first derivative or the curvature of the function.

To find the first derivative of y, we use the quotient rule:

y = [tan(πt)/π²] + [4 sec(πt)/π²]

y' = [π²(sec²(πt)) - 2tan(πt)sec(πt)]/(π⁴) + [4πsec(πt)tan(πt)]/(π⁴)

Simplifying this expression, we get:

y' = [(πsec(πt))(4tan(πt) - πsec(πt))]/(π⁴)

y' = [4πtan(πt)sec(πt) - π²(sec²(πt))]/(π⁴)

To find the second derivative of y, we again use the quotient rule:

y'' = [(π³(sec³(πt)) - 12πtan(πt)sec²(πt)) - 2π(4tan(πt)sec(πt) - πsec²(πt))(πsec(πt))]/(π⁶)

Simplifying this expression, we get:

y'' = [(4πsec(πt))(π²(sec²(πt) - 3tan(πt)))]/(π⁶)

y'' = [4sec(πt)(π²sec²(πt) - 3πtan(πt))]/(π⁴)

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The equations of the other two sides are AD: y = -3x + 3 and DC: y = 1/2x - 1/2.

What is point-slope form?

The point-slope form is a way to write the equation of a straight line in algebra. It is used when you know the coordinates of a point on the line and the slope of the line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.

Since AB and BC are two sides of a parallelogram, they are parallel to each other. Thus, we can use the slope formula to find the slopes of these sides.

Slope of AB:

m = (y₂ - y₁)/(x₂ - x₁)

= (6 - 3)/(6 - 0)

= 3/6

= 1/2

Slope of BC:

m = (y₂ - y₁)/(x₂ - x₁)

= (3 - 6)/(7 - 6)

= -3/1

= -3

Now that we know the slopes of AB and BC, we can use the point-slope form to find the equations of the other two sides.

Equation of AD:

We know that AD is parallel to BC and passes through point A. So, we can use the point-slope form with the slope of BC and point A.

y - y₁ = m(x - x₁)

y - 3 = -3(x - 0)

y - 3 = -3x

y = -3x + 3

Equation of DC:

We know that DC is parallel to AB and passes through point C. So, we can use the point-slope form with the slope of AB and point C.

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 7)

y - 3 = 1/2x - 7/2

y = 1/2x - 1/2

Therefore, the equations of the other two sides are:

AD: y = -3x + 3

DC: y = 1/2x - 1/2

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Based on the information given in the histogram, option B. The distribution of the data is asymmetrical, so the mean and the median are likely outside the "1,000-1,099 photocopies" category is the correct statement.

What is histogram?

The histogram shows that the distribution of the data is asymmetrical, with a longer tail towards the right. This means that there are more schools that made a higher number of photocopies than those that made a lower number of photocopies. Therefore, the mean and median are likely to be higher than the midpoint of the "1,000-1,099 photocopies" category, which has the highest frequency.

In a skewed distribution, the mean is typically affected by the outliers, while the median is a better measure of central tendency. Therefore, the median is more likely to be within the "1,000-1,099 photocopies" category, while the mean is likely to be higher.

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