Jerry writes down all the odd numbers 1, 3, 5, 7, up to 999. How many numbers does he write down?

According to the question,the equation of the parabola is y = (x + 4)² - 6.

An equation is a statement that equates two expressions using mathematical symbols. It is a mathematical statement that two expressions are equal in value. Equations can involve numbers, variables, and constants. Equations are used to solve real-world problems such as determining the speed of a car from the distance traveled and time elapsed.

The equation of a parabola with a focus at (-4, 7) and a directrix of y = 1 is given by:

y = (x + 4)² + 4.

This equation is derived from the standard equation of a parabola:

y = (x - h)² + k,

where (h, k) is the coordinates of the focus.

In this case, the coordinates of the focus are (-4, 7), so the equation becomes:

y = (x + 4)² + 7.

The directrix of the parabola is a line, so its equation is given by:

y = 1.

Substituting this equation into the equation of the parabola, we get:

(x + 4)² + 7 = 1

(x + 4)² = -6

y = (x + 4)² - 6.

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The value of the constant k that makes the function continuous everywhere is [tex]k = \frac{7}{48}$[/tex]

For the function to be continuous everywhere, we need to ensure that the limit of f(x) as x approaches 7 from the left is equal to the limit of f(x) as x approaches 7 from the right.

From the left, we have:

[tex]$$\lim_{x\to7^-}f(x) = \lim_{x\to7^-}kx^2 = k(7)^2 = 49k$$[/tex]

From the right, we have:

[tex]$$\lim_{x\to7^+}f(x) = \lim_{x\to7^+}(x+k) = 7+k$$[/tex]

For the function to be continuous at x=7, we need:

[tex]$$\lim_{x\to7^-}f(x) = \lim_{x\to7^+}f(x)$$[/tex]

Therefore, we need:

[tex]$$49k = 7 + k$$[/tex]

Solving for k:

[tex]$$49k - k = 7$$[/tex]

[tex]$$48k = 7$$[/tex]

[tex]$k = \frac{7}{48}$$[/tex]

Therefore, the value of the constant k that makes the function continuous everywhere is [tex]k = \frac{7}{48}$[/tex]

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The perimeter of the figure is 24 feet.

The perimeter of a shape is the distance between its edges. Learn how to calculate the perimeter of various shapes by adding the side lengths.

To calculate the perimeter of the figure, add the lengths of all the sides. To calculate the perimeter of the figure, add the lengths of all the sides. Label the diagram's points as follows:

Beginning at the top left and working our way clockwise, we have:

A at (0, 4)

B at (6, 4)

C at (6, 0)

D at (4, 0)

E at (4, 2)

F at (2, 2)

G at (2, 0)

H at (0, 0)

Using the distance formula, we can now calculate the length of each side:

[tex]AB = \sqrt{((6-0)^2 + (4-4)^2)}= 6 feet[/tex]

[tex]BC = \sqrt{((6-6)^2 + (0-4)^2)} = 4 feet[/tex]

[tex]CD = \sqrt{((4-6)^2 + (0-0)^2)} = 2 feet[/tex]

[tex]DE = \sqrt{((4-4)^2 + (2-0)^2)} = 2 feet[/tex]

[tex]EF = \sqrt{((2-4)^2 + (2-2)^2)} = 2 feet[/tex]

[tex]FG = \sqrt{((2-2)^2 + (0-2)^2)} = 2 feet[/tex]

[tex]GH = \sqrt{((0-2)^2 + (0-0)^2) }= 2 feet[/tex]

[tex]HA = \sqrt{((0-0)^2 + (4-0)^2)}= 4 feet[/tex]

The perimeter is equal to the sum of these lengths:

Perimeter = 6 + 4 + 2 + 2 + 2 + 2 + 2 + 4

= 24 feet

As a result, the figure's perimeter is 24 feet.

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Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.

A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.

Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).

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The complete question is:

What are all the perfect numbers between 1 and n (where n is a positive integer)?

The total number of cans in the display is 611.

Let's denote the number of cans in the first row as x.

According to the problem statement, each subsequent row has 5 fewer cans than the row beneath it.

Therefore, the number of cans in the second row will be x - 5, the number of cans in the third row will be x - 10, and so on.

We are given that there are 13 rows in total, and the top row has 1 can. Therefore, we can write the following equation:

x + (x - 5) + (x - 10) + ... + (x - 60) + (x - 65) = 1 + 2 + 3 + ... + 12 + 13

Simplifying the left-hand side, we can combine like terms:

13x - (5 + 10 + 15 + ... + 60 + 65) = 91

Using the formula for the sum of an arithmetic series, we can evaluate the sum of the numbers in parentheses:

5 + 10 + 15 + ... + 60 + 65 = (13/2)(5 + 65) = 455

Substituting this value into the equation, we get:

13x - 455 = 91

Solving for x, we find that:

x = 46

Therefore, the number of cans in each row is:

46, 41, 36, ..., 1

To find the total number of cans, we can use the formula for the sum of an arithmetic series:

n/2(a + l)

where;

In this case, n = 13, a = 46, and l = 1. Plugging in these values, we get:

13/2 x (46 + 1) = 13/2 x 47 = 611.5

Since we can't have a fraction of a can, the total number of cans in the display is 611.

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Answer:

p (even,odd)- more likely

p(2,5) - less likely

p(odd,1)- less likely

The company can produce approximately 425 widgets for $2127.

What is cost function ?

The key concept used here is the concept of cost functions, which is an important concept in economics and business. A cost function is a mathematical function that expresses the total cost of production as a function of the level of output produced. In this case, the cost function is a linear function of the form C = a + bx, where C is the total cost, a is the fixed cost, b is the variable cost per unit, and x is the level of output.

Finding the number of widgets the company can produce given a fixed cost and a variable cost per widget :

To solve this problem, we can set up an equation that relates the total cost to the number of widgets produced.

Let x be the number of widgets produced.

The total cost C is given by:

C = fixed cost + variable cost

C = 1277 + 1.93x

We want to find the number of widgets produced for a total cost of $2127. So we can set up an equation:

2127 = 1277 + 1.93x

Subtracting 1277 from both sides gives:

850 = 1.93x

Dividing both sides by 1.93 gives:

x ≈ 439.9

Since we can't produce a fractional number of widgets, we need to round down to the nearest integer. Therefore, the company can produce approximately 425 widgets for $2127.

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Answer: the distribution to the x and the 3 makes the solution 4

Step-by-step explanation: i got you broski

Alberto's statement is flawed because all squares can be called rectangles, but not vice versa

Alberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.

While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.

A square is a special type of rectangle with all sides equal in length.

Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).

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Answer: (f⋅g)(1) = 10.

Step-by-step explanation:

To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:

(f⋅g)(x) = f(x) * g(x)

= (-7x+3) * (3x^2 - 4x - 1)

= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1

= -21x^3 + 25x^2 + 5x + 1

To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):

(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1

= -21 + 25 + 5 + 1

= 10

Therefore, (f⋅g)(1) = 10.

The 3-dimensional vector space represented in the form subspace dimensions A and B is given by option B. V = A + B.

V be 3-dimensional vector space.

Subspace of dimensions of A and B are 2 and 1 respectively.

And A ∩ B = 0.

It follows that every vector in A is linearly independent of every vector in B.

This implies,

Any vector v in V can be expressed uniquely as a sum of a vector in A and a vector in B.

Let v be an arbitrary vector in V.

A has dimension 2, it has a basis of two linearly independent vectors.

Let {a1, a2} be such a basis.

B has dimension 1, it has a basis consisting of a single nonzero vector b.

Then, any vector v in V can be expressed uniquely as

v = c1a1 + c2a2 + cb,

where c1, c2, and c are scalars.

Thus,

V = A + B.

Therefore, the correct answer to represents 3 dimensional vector space V  as option(B).  V = A + B.

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As the two triangles are congruent to each other, using that we can get the value of x = 13 and y = 9.

Whether two or more triangles are congruent depends on the size of the sides and angles. As a result, a triangle's three sides and three angles determine its size and shape.

Two triangles are said to be congruent if their respective side and angle pairings are both equal.

Now in the given question,

The triangles are congruent so,

ED = QR

5y -7 = 38

⇒ 5y = 38+7

⇒ y = 45/5

⇒ y = 9

Now as the sum of angles in a triangle are 180°,

∠E +∠D +∠F = 180°

⇒ ∠F = 180 - 123 - 29

⇒ ∠F = 28°

As per congruency,

(2x+2) ° = 28°

⇒ 2x = 28-2

⇒ x = 26/2

⇒ x = 13

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The complete question is:

Find the values of x and y. ADEF = AQRS

(5y-7) ft

D

E

123⁰

F

S

S

(2x + 2)° R

= 0, y =

Q

38 ft

P

Answer:

Equation of B represents this graph

The rental cost for each movie and each video game is $3.5 and $5.5 respectively.

Let

cost of each movie = x

Cost of each video game = y

5x + 3y = 34

2x + 12y = 73

Multiply (1) by 4

20x + 12y = 136

2x + 12y = 73

subtract the equations to eliminate y

18x = 63

divide both sides by 18

x = 63/18

x = 3.5

Substitute x = 3.5 into (1)

5x + 3y = 34

5(3.5) + 3y = 34

17.5 + 3y = 34

3y = 34 - 17.5

3y = 16.5

y = 16.5/3

y = 5.5

Therefore, $3.5 and $5.5 is the rental cost of each movie and video game respectively.

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The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.

After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.

To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:

(4/12) * (3/11) = 0.0909

Rounding to the hundredth place, the probability is approximately 0.09.

Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

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The regular expression is (0|1)[0(0|1)1(0|1)] | (0|1)[1(0|1)0(0|1)], which matches any string that is at least 6 symbols long and contains at least one 0 and at least one 1.

One possible regular expression for the language {w | w is at least 6 symbols long and contains at least one 0 and at least one 1} is:

(0|1)[0(0|1)1(0|1)] | (0|1)[1(0|1)0(0|1)]

This regular expression matches any string that satisfies the following conditions:

The string contains at least one 0 and at least one 1.

The string is at least 6 symbols long.

The string can have any number of 0s and 1s before and after the first 0 or 1, but it must contain at least one of each before and after the first 0 or 1.

For example, this regular expression matches strings like "0101010", "1000001", "1110010", but does not match strings like "101", "11111", "0000000".

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Complete question:

Alphabet = {0,1}.

Define a regular expression for the language {w | w is at least 6 symbols long and contains at least one 0 and at least one 1}

The 66th derivative of f(x) is the same as the second derivative of f(x). Thus, we can calculate the 66th derivative as follows f''(x) = -4sin(x).

The derivative of a function is the rate at which the function changes with respect to its input variable. It is a fundamental concept in calculus and is used in many areas of mathematics, science, and engineering.

The derivative of the function f(x) = 4sin(x) with respect to x is:

f'(x) = 4cos(x)

Taking the derivative again, we get:

f''(x) = -4sin(x)

Taking the derivative 3 times, we get:

f'''(x) = -4cos(x)

Taking the derivative 4 times, we get:

f''''(x) = 4sin(x)

We notice that the derivative of f(x) repeats every 4 times, alternating between sin(x) and cos(x) with a sign change. Therefore, to find the 66th derivative of f(x), we can simplify the calculation by considering the remainder when 66 is divided by 4:

66 mod 4 = 2

This means that the 66th derivative of f(x) is the same as the second derivative of f(x). Thus, we can calculate the 66th derivative as follows:

f''(x) = -4sin(x)

Therefore, the 66th derivative of f(x) is:

f^(66)(x) = f''(x) = -4sin(x)

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Step 1: x + 0.5 = 5

Step 2: x = 4.5

Step 3: 2*x^2 - 3x + 6 - 3/x +2/x^2 = 2(4.5)^2 - 3(4.5) + 6 - (3/4.5) + (2/(4.5)^2)

Step 4: 2*4.5^2 - 3*4.5 + 6 - 3/4.5 + 2/(4.5)^2 = 44.25 - 13.5 + 6 - 0.666666667 + 0.044444444 = 36.04444444

[tex]80[/tex] billion dollars' worth of net exports were made by China and Germany. The first claim is accurate.

Export is the process of supplying goods and services to some other nation. Contrarily, importing is the act of acquiring goods from outside and transferring them into one's own nation.

The domestic product (GDP) is a measure of all the products and services generated in the United States; thus, changes in exports change significantly in the demand for goods and services made in the United States abroad.

The total of China's and Germany's net exports would be:

[tex]50[/tex] billion + [tex]30[/tex] billion [tex]= 80[/tex] billion

As a result, Germany & China's consolidated net exports amounted to [tex]80[/tex] billion u.s. dollars, reflecting answer option (a).

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

the probably for the second roll to roll the same number as in the first roll again, is actually pretty high.

it means that we "accept" any result in the first roll. that makes this a 6/6 = 1 probability.

and then for the second roll we have the usual 1/6 probability (to roll the same number again).

so, we have

6/6 × 1/6 = 1/6 = 0.166666666...

P(even, odd) is the probability to roll first an even number (3 out of 6 = 3/6 = 1/2) and then an odd number (again 3 out of 6 = 1/2) :

1/2 × 1/2 = 1/4 = 0.25

so, this is more likely.

P(2, 5) is the probability to roll first a 2 (1 out of 6 is 1/6) and then a 5 (again 1 out of 6 is 1/6) :

1/6 × 1/6 = 1/36 = 0.027777777...

so, this is less likely.

P(odd, 1) is the probability to roll first an odd number (3 out of 6 = 1/2) and then a 1 (1 out of 6 = 1/6) :

1/2 × 1/6 = 1/12 = 0.083333333...

so, it is less likely.

As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.

A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.

In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.

Here in the given figure, we can see a quadrilateral is given.

We can see that all the sides of the quadrilateral are given to be equal to each other.

We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.

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a) A function showing the value of the account after t years, where the annual growth rate can be found from a constant, is f(x) = 690 (1+0.0055)^4t.

b) The percentage of growth per year (APY) is 2.2%.

A function is a mathematical expression that shows the relationship between variables.

An example of a mathematical function is an equation that shows the relationship between y and x variables.

Principal = $690

APR = 2.2%

APR per quarter = 0.0055 (2.2%/4)

Compounding = Quarterly

Investment period = t years

Let f(x) = the value of the account after t years.

Future value function, (FV) = PV × (1 + r) ^ n

Where PV = present value or investment

r = compounding rate per period

n = the investment period

Therefore, f(x)  or FV = 690 (1+0.0055)^4t.

APY = 100 [(1 + Interest/Principal)(365/Days in term) - 1]

2.2% = 100 [(1 + $15.18/$690)(365/365) - 1]

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At equilibrium we expect [Reactants} < [Products)  from the the profile that has been shown.

An energy profile diagram, also known as an energy diagram or reaction coordinate diagram, is a graphical representation of the energy changes that occur during a chemical reaction or a physical process. It shows the energy levels of the reactants, products, and any intermediate species that may form during the reaction.

The horizontal axis of an energy profile diagram represents the reaction coordinate, which is a measure of the progress of the reaction from the reactants to the products. The vertical axis represents the energy of the system.

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G(x) is defined instead of F(x) because the property of memoryless is expressed in terms of G(x). Next, professor refers that there is rational numbers in the set of real numbers, so rational number is dense.  G(x) is an exponential distribution with some rate parameter λ because G(x) has the memoryless property.

The reason why the function G(x) is defined as G(x) = P(X > x) = 1 - F(x) instead of just F(x) is because the memoryless property is expressed in terms of G(x).

Specifically, the memoryless property says G(s+t) = G(s)G(t), which means that the probability of X being greater than s+t is equal to the probability of X being greater than s multiplied by the probability of X being greater than t. This property is easier to work with when expressed in terms of G(x) rather than F(x).

When the professor says that taking the limit of rational numbers gives you real numbers, he is referring to the fact that the set of rational numbers is dense in the set of real numbers. This means that between any two real numbers, there exists a rational number.

In the context of the proof, this means that if G(mn) = G(t)^mn holds for all rational numbers mn, then it also holds for all real numbers x = mn, where mn is the limit of a sequence of rational numbers.

To see why G(x) = G(1)x looks like an exponential function, we can rewrite it as G(x) = e^(ln(G(1))x). Now, suppose we define λ = -ln(G(1)). Then we have G(x) = e^(-λx), which is the probability density function of an exponential distribution with rate parameter λ.

Thus, the assumption that G(x) has the memoryless property implies that G(x) is an exponential distribution with some rate parameter λ.

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1/42,1/22,1/10,1/6 are domain of function .

What are a function's domain and range?

The set of all possible inputs and outputs is known as a function's domain, and the same is true for its range. Important features of a function are the domain and range.

                               The range contains all of the function's output values, while the domain contains all of the real numbers that can be used as input values.

g(x) = 1/(x²+6)

Domain: {-6, -4, -2, 0, 2, 4, 6}​

G(-6) = 1/(-6² + 6) = 1/42

G(-4) = 1/(-4² + 6) = 1/22

G(-2) = 1/(-2² + 6) = 1/10

G(0) = 1/(0+6)    = 1/6

 G(2) = 1/(2² + 6) = 1/10

 G(4) = 1/(4² + 6) = 1/22

 G(6) = 1/(6² + 6) = 1/42

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To find Sn for an arithmetic series, you can use the following formula: Sn = (n/2) * (a1 + an).

In this case, Sn = (14/2)*(3 + 42) = 189.

To explain step-by-step:

1. Find the number of terms in the series, n = 14

2. Find the first term in the series, a1 = 3

3. Find the last term in the series, an = 42

4. Plug the values into the formula, Sn = (n/2)*(a1 + an)

5. Simplify the equation and solve, Sn = (14/2)*(3 + 42) = 189

Answer:

Let the four digits be represented by abcd, where a, b, c, and d represent the digits in the thousands, hundreds, tens, and ones places, respectively.

From the first condition, we have:

a + b = c + d

From the second condition, we have:

a + d = 2(c + b)

Simplifying the second condition, we get:

a - 2b + c - d = 0

From the third condition, we have:

10a + b = 2(10c + d)

Simplifying the third condition, we get:

5a - 2b - 5c + 2d = 0

Now we have four equations with four variables. We can use substitution and elimination to solve for the variables.

From the first equation, we have:

a = c + d - b

Substituting into the second equation, we get:

c + d - b + d = 2(c + b)

Simplifying, we get:

2d - 3b + c = 0

From the third equation, we have:

10c + d = 5a

Substituting a with c + d - b, we get:

10c + d = 5(c + d - b)

Simplifying, we get:

5c - 4d + 5b = 0

Now we have two equations with two variables (2d - 3b + c = 0 and 5c - 4d + 5b = 0). Solving for b in terms of c, we get:

b = (5d - c)/3

Substituting into the first equation, we get:

2d - (5d - c)/3 + c = 0

Simplifying, we get:

7c - 13d = 0

Thus, c = 13/7d. Since c is a digit, d must be a multiple of 7. The only possible values for d are 1, 7, and 9.

If d = 1, then c = 13/7, which is not a digit.

If d = 7, then c = 13, b = 2, and a = 18. This satisfies all the conditions, and the four digits in order are 1872.

If d = 9, then c = 18, which is not a digit.

Therefore, the final four digits are 1872.

(please mark my answer as brainliest)

a) The maximum value for this data set is 31, the minimum value is 11 and the median value is 15.5.

b) Q1 13.5

Q2 15.5

Q3 24

c) 10.5

d) lower than 11 or higher than 31

e) Yes.

f) This data set is slightly positively skewed.

The median is the middle value of a set of data when the values are arranged in numerical order. It is used to find the middle value of a set of numbers or observations.

A. The values can be plotted on the boxplot as follows:

Maximum: 31

Minimum: 11

Median: 15.5

B. To find Q1, Q2 and Q3, the data must first be sorted from lowest to highest: 11; 13; 14; 15; 15; 16; 21; 26; 30; 31. Q1 is the median of the lower half of the data set (11, 13, 14, 15 and 15), which is 13.5. Q2 is the median of the entire data set (15.5). Q3 is the median of the upper half of the data set (16, 21, 26, 30 and 31), which is 24. The values can be plotted on the boxplot as follows:

Q1: 13.5

Q2: 15.5

Q3: 24

C. The Interquartile Range (IQR) is calculated by subtracting Q1 from Q3: IQR = Q3 - Q1 = 24 - 13.5 = 10.5.

D. Outliers are values that are significantly greater or lower than the majority of the data set. In this data set, values that are lower than 11 or higher than 31 would be considered outliers.

E. Yes, this data set has outliers. The value 11 is significantly lower than the majority of the data set, and the value 31 is significantly higher than the majority of the data set.

F. This data set is slightly positively skewed, as the majority of the data points are clustered around the lower end of the range, and there is a longer tail of higher values. This is indicated by the fact that the median (15.5) is lower than the mean (19.4).

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a) The maximum value of the given dataset is 31, while the minimum value is 11 and the median is 15.5.

b) Q1 = 14,

Q2 = 15.5,

Q3 = 21

c) (IQR) = 7

d) Any values below 11 or above 31

e) Yes

f) slightly positively skewed.

Median is a measure of central tendency that is calculated by taking the middle value of a set of numbers when the values are arranged in ascending or descending order.

a) Maximum value: 31,

Minimum value: 11,

Median value: 15.5

b) Q1 = 14,

Q2 = 15.5,

Q3 = 21

c) The Interquartile Range (IQR) is calculated by subtracting Q1 from Q3:

Inter Quartile Range (IQR) = Q3-Q1

=21-14

= 7

d) Any values below 11 or above 31 can be considered as outliers.

As 11 is the lowest value given and 31 is the highest value.

e) Yes, this data set has outliers. The values 31 and 11 are both outliers since they are beyond the range of the Inter Quartile Range (IQR).

The value 11 is significantly lower than the majority of the data set, and the value 31 is significantly higher than the majority of the data set.

f) This data set is slightly positively skewed.

As the majority of the data points are clustered around the lower end of the range, and there is a longer tail of higher values.

This is indicated by the fact that the median (15.5) is lower than the mean.

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