How Did I Write: X Minus One-half Is One Fourth In Numbers Aka Algebraic Equation (2024)

So, one serving of Kind bars, which is two bars, contributes for roughly 13.8% of a 2,000 calorie diet's daily fat consumption.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.

Here,

The calculation for determining the percentage of daily fat intake in a serving of Kind bars is based on the Recommended Dietary Allowance (RDA) for fat. The RDA is a guideline for the average daily amount of a nutrient that is considered sufficient to meet the needs of most people.

For a 2,000 calorie diet, the RDA for total fat is about 65 grams per day. To calculate the percentage of daily fat intake in a serving of Kind bars, you divide the total amount of fat in the serving by the RDA for daily fat and multiply by 100.

For example, if one serving of Kind bars contains 9 grams of fat, you would perform the following calculation:

9 grams fat ÷ 65 grams RDA for daily fat x 100 = 13.8% daily fat intake

So, one serving of Kind bars, which is two bars, accounts for approximately 13.8% of a person's daily fat intake for a 2,000 calorie diet.

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For any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

Let x be a positive real number and n be a natural number. We want to show that there exists a unique positive real number r such that [tex]x = r^n[/tex]. This can be expressed mathematically as [tex]x^(1/n) = r[/tex], where r is the unique positive real number we are looking for.

To solve for r, we can take the nth root of both sides of the equation. This gives us [tex]r = x^(1/n)[/tex]. Since x is a positive real number and n is a natural number, it follows that r is also a positive real number.

Furthermore, since x is a fixed value and n is a fixed value, we can conclude that the positive real number r is unique. In other words, for any given x and n, there is only one r that satisfies the equation [tex]x = r^n[/tex].

Therefore, for any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

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Answer:

92.3%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Mean μ = 90Standard deviation σ = 7

Therefore, if the speeds that people drive down the Pat Bay Highway are normally distributed:

[tex]\boxed{X \sim\text{N}(90,7^2)}[/tex]

where X is the speed in km/h.

f we want to find what proportion of drivers travel between 80 and 120 km/h, we need to find P(80 ≤ X ≤ 120).

[tex]\implies \sf P(80 \leq X \leq 120)=P(X \leq 120)-P(X \leq 80)[/tex]

Converting to the Z distribution:

[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]

Transform X to Z:

[tex]\sf P(X \leq 120)=P\left(Z \leq \dfrac{120-90}{7}\right)=P\left(Z \leq \dfrac{30}{7}\right)[/tex]

[tex]\sf P(X \leq 80)=P\left(Z \leq \dfrac{80-90}{7}\right)=P\left(Z \leq -\dfrac{10}{7}\right)[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf P(80 \leq X \leq 120)&=\sf P\left( -\dfrac{10}{7} \leq Z \leq \dfrac{30}{7}\right)\\\\&=\sf P\left(Z \leq \dfrac{30}{7}\right)-P\left(Z \leq -\dfrac{10}{7}\right)\\\\&=\sf 0.999990892...-0.0765637255...\\\\&= \sf 0.9234271...\\\\&=\sf 92.34271...\%\end{aligned}[/tex]

Therefore, the proportion of drivers travelling between 80 and 120 km/h is 92.3% (nearest tenth).

The equations can be used to solve for y, the length of the room follows:

B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, we have

length L = y

width W = y - 5

Since the area of a rectangular room is 750 square feet.

So L × W = 750

y(y - 5) = 750

y² – 5y = 750 ....(i)

This can be also written as:

750 – y(y – 5) = 0 ....(ii)

Factorizing the equation (i), we get

(y + 25)(y – 30) = 0

Thus, the correct answer would be options (B), (C), and (E).

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The given expressions are not equivalent. They are numerical expressions.

What are Expressions?

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are -18-(6 * 2) or (18 + 6)*2.

If the expressions are equivalent, then they will have the same values.

If they are not equivalent, then they will have different values.

-18-(6 * 2) = -18 - 12 = -30

(18 + 6)*2 = 24 * 2 = 48

Both the expressions are not equivalent.

Hence the expressions are not equivalent.

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Answer:

23:15 as a decimal and 23 3/20

Step-by-step explanation:

Just divide by 100 to get decimal. For the fraction divide by 100 and simplify

Answer: [tex]6a-2[/tex]

Step-by-step explanation:

[tex](4a-5)-(-2a-3)\\=4a-5+2a+3\\=6a-2[/tex]

The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

Apply the product rule to 4a^5:

⇒ 4^3(a^5)^3

Raise 4 to the power of 3:

⇒ 64(a^5)^3

Apply the power rule and multiply exponents, (a^m)^n = a^mn:

⇒ 64a^5*3

Multiply 5 by 3:

64a^15

⇒ (4a-5)⇒ = 9a

⇒ (-2a-3)⇒ = 5

Therefore, The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

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The perimeter of the rectangular bedroom is: A. 116 feet.

What is the Perimeter of a Rectangle?

Perimeter of a rectangle = 2(length + width)

To find the perimeter of the rectangular bedroom, we need to calculate the sum of the lengths of its four sides.

Let's start by finding the length of the horizontal sides of the rectangle. The two horizontal sides are defined by the points (21, 18) and (21, −7), which are 25 feet apart in the vertical direction (18 − (−7) = 25). Therefore, the length of each horizontal side is 25 feet.

Next, let's find the length of the vertical sides of the rectangle. The two vertical sides are defined by the points (21, 18) and (−12, 18), which are 33 feet apart in the horizontal direction (21 − (−12) = 33). Therefore, the length of each vertical side is 33 feet.

Now we can add up the four side lengths to get the perimeter:

Perimeter = 2(Length of horizontal sides) + 2(Length of vertical sides)

= 2(25 feet) + 2(33 feet)

= 50 feet + 66 feet

Perimeter = 116 feet

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The solution is:

Biggervolumethe cylinder wich radius is (L/2) and h = WHow much according to the relation L/WLet´s call L and W the dimensions of the piece of paper

Let´s assume that

L > WTheVolume(V) of a cylinder is:V(c) = π×r²×h where r is the radius of the circular base, and h is the height of the cylinderFor the first cylinder (V₁) (the one which h = w then r = (L/2)V₁ = π×(L/2)²×w

For the second cylinder (V₂) ( the one with h = L and r = (W/2)V₂ = π×(W/2)²×LThe relation

V₂/V₁ is:V₂/V₁ = π×(W/2)²×L/π×(L/2)²×wV₂/V₁ = W/LBut L > W then V₂/V₁ < 1 or V₂ < V₁Thevolumeof the first cylinder is bigger than the second one:

n:

Hope this helped :]

The probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.

The probability of exactly one paycheck being in the correct envelope can be calculated by taking the number of possible outcomes where one paycheck is in the correct envelope (1) and dividing it by the total number of possible outcomes (5). This yields a probability of 1 in 5. The probability of at least one paycheck being in the correct envelope is calculated by taking the total number of possible outcomes where at least one paycheck is in the correct envelope (4) and dividing it by the total number of possible outcomes (5). This yields a probability of 4 in 5. Thus, the probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.

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The domain of the function is [0, 3) and the range of the function is [-4, 5).

What is Domain and Range of a Function?

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Here the input values in set A is called the domain and the output values in set B is called the range.

Given is a graph of a function.

The input values or domain includes the value of x which forms the curve in the graph.

The output values or range consists of the values of y formed as a result of the input of x.

Look at the x values corresponding to the end points of curve.

The curve extends from x = 0 to x = 3.

But at x = 3, it is an open circle. So x = 3 is not included.

So the input values are from x = 0 to x = 3, where 3 is not included.

Domain in interval notation = [0, 3).

Similarly the values of y extends from y = -4 to y = 5, where 5 is not included, since there is an open circle there.

Range in interval notation = [-4, 5).

Hence the domain and range are [0, 3) and [-4, 5) respectively.

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Answer:

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

Step-by-step explanation:

I'm sorry, but I cannot see the graph you are referring to. However, I can still answer some of your questions based on the information provided.

When the diameter of the cylinder is 2 cm, the radius is equal to half the diameter, which is 1 cm.

To express the volume of a cube of side length s as an equation, we use the formula for the volume of a cube:

Volume of cube = s^3

Making a table for the volume of the cube at different side lengths, we get:

Side Length (cm)Volume (cm^3)

0 0

1 1

2 8

3 27

To compare the volume of the cube when the side length is 3 cm and the volume of the cylinder when the diameter is 3 cm, we need to find the radius of the cylinder first.

When the diameter is 3 cm, the radius is half the diameter, which is 1.5 cm. The height of the cylinder is also equal to the radius, so the volume of the cylinder can be found using the formula:

Volume of cylinder = πr^2h

Substituting r = 1.5 cm and h = 1.5 cm, we get:

Volume of cylinder = π(1.5)^2(1.5) ≈ 10.602 cm^3

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

How to find the mean and standard deviation

XX^2

959025

969216

989604

Sum =28927845

n3

The sample mean96.33333333SUM/n

Population mean96.33333333SUM/n

Sample standard dev[tex]1.527525232\sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population standard dev[tex]1.247219129\sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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Answer:

y= 2x+12

Step-by-step explanation:

y=mx+c

y= 2x+12

(0,y) (-4,4)

2=y-4/4

8=y-4

12=y

The probability of the complement of event E[tex](E^c)[/tex] is 7/12.

a. Outcomes in [tex]E^c[/tex] = {3, 9, 10, 11, 12, 13, 14}

b. The probability of the complement of event E[tex](E^c)[/tex] is the probability of all outcomes in S that are not in E. P[tex](E^c)[/tex] = 1 - P(E).

The probability of E is calculated by counting the number of elements in E and dividing by the total number of elements in the sample space S.

P(E) = 5/12

Therefore, P[tex](E^c)[/tex] = 1 - P(E) = 1 - (5/12) = 7/12

The probability of the complement of event E [tex](E^c)[/tex] is 7/12.

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If f(x), g(x), and h(x) are functions such that f(x) is θ(g(x)) and g(x) is θ(h(x)), it is shown that f(x) is θ(h(x)).

Since f(x) is θ(g(x)), there exist constants A, B > 0 such that

A × g(x) < f(x) < B × g(x) for sufficiently large x.

Similarly, since g(x) is θ(h(x)), there exist constants C, D > 0 such that

C × h(x) < g(x) < D × h(x) for sufficiently large x.

Hence, for a sufficiently large x, we have

f(x) < B g(x) < B × (D × h(x)) = (BD) h(x), and

f(x) > A g(x) > A × (C × h(x)) = (AC) h(x).

Hence, we have constants E, F > 0 (where E = AC and F = BD) such that

E × h(x) < f(x) < F × h(x) for sufficiently large x.

Therefore, f(x) is θ(h(x)).

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The polynomial in standard form after expansion is x² - 7x + 12.

What are Polynomials?

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

The given expression is (x - 3) (x - 4).

We have to expand this as a polynomial in standard form.

Standard form of a polynomial with degree n is,

a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻¹ + aₙ xⁿ

(x - 3) (x - 4) = x (x - 4) - 3 (x - 4)

Applying the distributive property,

= x² - 4x - 3x + 12

= x² - 7x + 12

This is a standard form of a second degree polynomial.

Hence x² - 7x + 12 is the expansion of the given expression.

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The sign that makes the statement true is 792 3/20 ≠ 792 1/2.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

There are two types of fractions: proper fractions in which the numerator is less than the denominator and,

Improper fractions in which the numerator is larger than the denominator.

Given, Are two fractions 792 3/20 and 792 1/2.

The sign that makes the statement true is 792 3/20 ≠ 792 1/2.

Some other signs, for example, Inequalities can also make the statement true.

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Out of a population of 100,000, the number of people who read at least two newspapers is = 33,000.

Let's approach this problem using the inclusion-exclusion principle.

First, we can add up the proportions of people who read each paper to get:

P(I) + P(II) + P(III) = 10% + 30% + 5% = 45%

However, this includes the people who read two or more papers multiple times, so we need to subtract those out. We can calculate these as follows:

P(I&II) + P(I&III) + P(II&III) = 8% + 2% + 4% = 14%

2P(I&II&III) = 2%

Using the inclusion-exclusion principle, we can now find the proportion of people who read at least two papers:

P(at least 2 papers) = P(I) + P(II) + P(III) - (P(I&II) + P(I&III) + P(II&III)) + 2P(I&II&III)

Plugging in the values, we get:

P(at least 2 papers) = 45% - 14% + 2% = 33%

So, the number of people who read at least two newspapers is:

0.33 * 100,000 = 33,000

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Complete question is:

A certain town of population size 100,000 has three newspapers: I , II and III the proportions of townspeople that read these papers are:

I= 10 percent

II= 30% percent

II=5 percent

I&II=8 percent

I&III=2 percent

II&III=4 percent

I&II&III=1 percent

How many people read at least two newspapers?

Answer:

Step-by-step explanation:

Expanding (x + y)^2, we get:

(x + y)^2 = x^2 + 2xy + y^2

We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:

(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42

Therefore, (x + y)^2 = 42.

The solution to the statement "add the quotient of 0.4 and 0.7 to the quotient of 1.4 and 0.4" is 4.07

How to determine the solution

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

add the quotient of 0.4 and 0.7 to the quotient of 1.4 and 0.4

Using the above as a guide, we have the following:

0.4/0.7 + 1.4/0.4

Simplify the fractions

4/7 + 7/2

Evaluate the sum

4.07 (approximated)

Hence, the solution is 4.07

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Mancy's monthly earning of $3,000, rent of r, feeding cost of r/2, and utilities cost of (r - 100), indicates that her transportation cost is obtained by the function;

t = $3,100 - 2.5·r

What is a function?

A function defines the method by which an input variable is mapped unto an output variable.

The amount Nancy earns per month = $3,000

The amount she pays as rent = 2 × The cost of her food

Amount spent on utilities and personal items = Her rent - 100

the amount she spends on transportation = The amount remaining from her salary after the other expenditures

The cost of her rent = r

The cost of her transportation = t

Therefore;

Cost of her rent, r = 2 × The food cost

The food cost = r/2

Utilities and personal items cost = r - 100

Transportation cost, t = Monthly earning - Rent - Food - Utilities

t = 3000 - r - r/2 - (r - 100)

t = 3000 - 2.5·r + 100 = 3,100 - 2.5·r

The function that models her transportation cost is therefore;

t = $3,100 - 2.5·r

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Answer:

The only score that falls outside of this range is 35, so that is the outlier.

Step-by-step explanation:

To find the mean of Allins test scores, we add up all the scores and divide by the number of scores:

Mean = (88+90+35+92+82+90)/6 = 77.83 (rounded to two decimal places)

To find the median, we need to arrange the scores in order from least to greatest:

35, 82, 88, 90, 90, 92

The median is the middle value, which in this case is 89.

To find the mode, we look for the value that appears most frequently. In this case, the mode is 90, since it appears twice.

To find the range, we subtract the lowest score from the highest score:

Range = 92 - 35 = 57

To identify the outlier in the data set, we can use the interquartile range (IQR) and the rule that any data point more than 1.5 times the IQR below the first quartile or above the third quartile is considered an outlier.

First, we need to find the quartiles:

Q1 (first quartile) = 80 (the median of the lower half of the data set)

Q3 (third quartile) = 91 (the median of the upper half of the data set)

IQR = Q3 - Q1 = 11

Any data point more than 1.5 times the IQR below Q1 or above Q3 is considered an outlier.

Lower outlier threshold = Q1 - 1.5(IQR) = 63.5

Upper outlier threshold = Q3 + 1.5(IQR) = 107.5

The only score that falls outside of this range is 35, so that is the outlier.

From the given information, the mean is 0.3025, the median is 0.3065, and the mode is 0.277 and 0.321.

To find the mean, we need to add up all the values and divide by the total number of values:

Mean = $\frac{0.302 + 0.278 + 0.321 + 0.283 + 0.311 + 0.312 + 0.320 + 0.276 + 0.275 + 0.281 + 0.305 + 0.277 + 0.308 + 0.303 + 0.322 + 0.317 + 0.305 + 0.291 + 0.321 + 0.277}{20} \approx 0.3025$

To find the median, we need to arrange data in the order from smallest to largest:

0.275, 0.276, 0.277, 0.277, 0.278, 0.281, 0.283, 0.291, 0.305, 0.305, 0.308, 0.311, 0.312, 0.317, 0.320, 0.321, 0.321, 0.322, 0.303, 0.302

There are 20 values, so median is average of the 10th and 11th values:

Median = $\frac{0.305 + 0.308}{2} = 0.3065$

To find the mode, we look for the value that appears most frequently. In this case, there are two modes: 0.277 and 0.321.

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Answer:

Rounding to the nearest cent, the total amount after 9 years is $3182.67.

Step-by-step explanation:

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.

Plugging in these values, we get:

A = 2000(1 + 0.053/2)^(2*9)

= 2000(1.0265)^18

≈ 3182.67

Rounding to the nearest cent, the total amount after 9 years is $3182.67.

The value of f(0) is -2.

Option A is the correct answer.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph, we see that,

f(x) = -1 for -1 ≤ x < 0

Similarly,

f(x) = -2 for 0 ≤ x < 1 _____(1)

Now,

The value of f(x) at x = 0.

From (1),

f(0) = -2

Thus,

The value of f(0) is -2.

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Your expected winnings from playing this game are 2 pounds.

What is a game?

A game is an activity or a form of play, often with a set of rules and goals, that is undertaken for enjoyment, competition, or skill development.

Let's analyze this game to see what your expected winnings are.

If the first roll is 1, 2, or 3, the game continues and you have a 3 in 6 chance (or 1/2 chance) of continuing to roll the die. Each subsequent roll has the same probabilities and outcomes as the first roll.

Let's start with the case where you win on the first roll with a probability of 1/2. In this case, your winnings are 1 pound.

If you don't win on the first roll, the game continues with a probability of 1/2, and your expected winnings from that point on are the same as your expected winnings from the beginning of the game (since the probabilities and outcomes are the same for all rolls).

Therefore, the expected winnings from the start of the game are:

E = 1/2 * 1 + 1/2 * E

Solving for E, we get:

E = 1 + E/2

E/2 = 1

E = 2

Therefore, your expected winnings from playing this game are 2 pounds.

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Answer:

2.375

Step-by-step explanation:

Another valid range value for this set of scores is 8, which is the interquartile range.

The range is a measure of the spread or variability of a dataset, and it is calculated as the difference between the largest and smallest values in the set. To find the range for the given set of scores, we first need to order the numbers from smallest to largest:

4, 6, 9, 11, 12, 14, 17

The smallest value in the set is 4, and the largest value is 17, so the range is:

17 - 4 = 13

Therefore, the range for the given set of scores is 13.

The range is a useful measure of variability that is simple to calculate and easy to interpret. However, it has a limitation in that it is sensitive to extreme values or outliers in the dataset. As a result, it may not always provide an accurate representation of the spread of the data.

Another measure of range that works particularly well for variables with precisely defined upper and lower bounds is the interquartile range (IQR). The IQR is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the dataset. It is commonly used with measurements of continuous variables and is less sensitive to extreme values than the range.

To calculate the IQR, we first need to find the median of the dataset. The median is the middle value when the numbers are arranged in order:

4, 6, 9, 11, 12, 14, 17

The median is 11.

Next, we need to find the first and third quartiles. The first quartile (Q1) is the median of the lower half of the dataset, and the third quartile (Q3) is the median of the upper half of the dataset. To find Q1 and Q3, we split the dataset into two halves:

Lower half: 4, 6, 9, 11

Upper half: 12, 14, 17

The median of the lower half is:

(6 + 9) / 2 = 7.5

The median of the upper half is:

(14 + 17) / 2 = 15.5

Therefore, the first quartile (Q1) is 7.5 and the third quartile (Q3) is 15.5.

The interquartile range (IQR) is the difference between Q3 and Q1:

IQR = Q3 - Q1 = 15.5 - 7.5 = 8

Therefore, another valid range value for this set of scores is 8, which is the interquartile range.

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The interval of convergence for this power series is (-∞, ∞) and the radius of convergence is infinite.

The power series representation of the function f(x) = 4 - 3x centered at x = 0 is given by the formula:

[tex]f(x) = [infinity]n=0 (4 (-3)^n * x^n)[/tex]

This power series can be used to represent the function for values of x in the interval of convergence. The interval of convergence for this power series is calculated by taking the limit of the absolute value of the coefficient of the highest power of x as n approaches infinity. In this case, the coefficient of the highest power of x is [tex]4(-3)^n[/tex], so the limit of the absolute value of this coefficient is [tex]|4(-3)^∞|[/tex] = 0. Thus, the interval of convergence for this power series is (-∞, ∞).

We can also calculate the radius of convergence for this power series. The radius of convergence is the distance from the center of the series, in this case x = 0, to the point at which the series diverges. To calculate the radius of convergence we can use the ratio test. The ratio test states that if [tex]lim |a(n+1)/a(n)| < 1,[/tex] then the series converges. The ratio of any two consecutive terms in this series is [tex]|4(-3)^(n+1)/4(-3)^n| = |-3|[/tex], which is less than 1. Thus, the radius of convergence for this power series is infinite.

In conclusion, the power series representation of the function f(x) = 4 - 3x centered at x = 0 is given by the formula: [tex]f(x) = [infinity]n=0 (4 (-3)^n * x^n)[/tex]. The interval of convergence for this power series is (-∞, ∞) and the radius of convergence is infinite.

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