he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13

Answer:

Step-by-step explanation:

here are step-by-step explanations for each part of the problem:

A. To find the mean, you add up all of the prices and divide by the number of prices. So:

Mean = (350 + 400 + 500 + 650 + 725 + 850 + 1700) / 7

Mean = 517.86

Rounded to the nearest dollar, the mean is $518.

B. To find the median, you need to put the prices in order from smallest to largest and then find the middle value. In this case, there are seven prices, so the middle value is between the 3rd and 4th prices:

350, 400, 500, 650, 725, 850, 1700

The median is the average of the 3rd and 4th prices, so:

Median = (500 + 650) / 2

Median = 575

The median price is $575.

C. Quartiles divide the data set into four equal parts, so you need to find the values that separate the lowest 25%, the next 25%, the next 25%, and the highest 25% of prices.

To find the quartiles, you can use the following steps:

Put the prices in order from smallest to largest:

350, 400, 500, 650, 725, 850, 1700

Find the median (Q2) as calculated in part B:

Median = $575

Divide the data set into two halves, below and above the median. If the median is included in both halves, exclude it from both.

Lower half: 350, 400, 500, 575

Upper half: 650, 725, 850, 1700

Find the median (Q1) of the lower half:

Q1 = (400 + 500) / 2

Q1 = 450

Find the median (Q3) of the upper half:

Q3 = (725 + 850) / 2

Q3 = 787.5

The four quartiles are Q1=$450, Q2=$575 (median), and Q3=$788.

D. The range is the difference between the highest and lowest values in the data set. So:

Range = highest value - lowest value

Range = $1700 - $350

Range = $1350

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). So:

IQR = Q3 - Q1

IQR = $788 - $450

IQR = $338

F. To find the upper boundary for outliers, you add 1.5 times the IQR to Q3. So:

Upper boundary = Q3 + 1.5(IQR)

Upper boundary = $788 + 1.5($338)

Upper boundary = $1282

There are no values above the upper boundary, so there are no upper outliers.

Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

An equation in mathematics is a claim that two expressions are equivalent. Mathematical operations like addition, subtraction, multiplication, division, and exponentiation may be used. It typically includes one or more variables. A connection between two or more variables can be represented by an equation, and it can also be used to determine the value of an unknown variable. Finding the values of the factors that make the equation true is the first step in solving an equation.

given

The projectile is in the air for a maximum of three seconds, so the domain of h(t) is [0, 3], since the equation depicts the projectile's height in feet after t seconds.

Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

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The probability and the likelihood, that the marble drawn is not red is high which is 4/5.

To determine how likely something is gonna occur, use probability. Several things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.

It is stated that there is a 2/10 chance of drawing a red marble at random.

We can deduct the likelihood of drawing a red marble from one to determine the likelihood that the drawn marble is not red (since the probability of an event and its complement add up to 1).

So, the probability of drawing a marble that is not red is -

1 - 2/10 = 8/10 = 4/5

Therefore, the probability that the marble drawn is not red is 4/5.

The likelihood of an event is a measure of how plausible it is, given some evidence or knowledge.

In this case, we can say that the likelihood of drawing a marble that is not red is high, since there are more marbles in the jar that are not red than those that are red.

Therefore, the likelihood of drawing a marble that is not red is high.

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Answer:

look in the comments and have a good day

Answer:

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro cents.

20 + 5 + 2 and two 1 cents will make 29 Euro c

Step-by-step explanation:

Answer: A quarter and 4 pennies

Step-by-step explanation:

25+4=29

The correct option is - D. The degree of F(x) is at most 9, shows the largest number of turning points of polynomial function.

Several kinds of polynomial functions exist. They include linear, quadratic, cubic, among many other types.

A polynomial function with degree n is provided to us.

The largest number of turning points is what we're looking for.

The most turning points a polynomial function can have are:

n - 1

Thus, the degree of F(x) is at most 9.

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The solutions of  x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,

which is the x-coordinate of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9

"It is a polynomial equation with degree two."

"The general form of quadratic equation is  , where a, b, c are real numbers with a ≠ 0."

here, we have,

For given question,

We have been given an quadratic equation  x² - 2x - 4 =  -3x + 9

We simplify above quadratic equation.

=>  x² - 2x - 4 =  -3x + 9

solving we get,

=>  x = -4.14 and x = 3.14

Consider the graphs for y = x² - 2x - 4 and y = -3x + 9 as shown below.

Therefore, the solutions of  x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,

which is the x-coordinates of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9

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For this equation our term is root of -24

What is verbal sentence ?

Verbal sentences consist of a verb + subject + object or adverbial phrase. The subject and object can be either nouns or pronouns.

After solving the equation we get square of n which is equal to three times of eight

If the subject is a pronoun, it is always a suffix; and if the object is pronoun, it is always a dependent pronoun. When the subject is a pronoun, the word order is normal, meaning that the subject follows the verb and precedes the object.

If the subject is a noun and the object is a dependent pronoun, the pronoun object is before the noun subject.

The dative has a special place in the word-order of verbal sentences. It is expressed by the preposition n in addition to a noun or pronoun referring to a person, if the subject is a pronoun. It assumes a third place following the verb and its subject. However, if the subject is a noun, the dative is allocated a forward position and occurs before the subject.

If the subject is a noun and the object is a pronoun and the sentence consists of a dative, the word order is thus:

Verb + dative + dependent pronoun (object) + subject

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The coordinates of the fourth vertex are (0, -4).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint = [(3 - 6)/2, (6 - 6)/2]

Midpoint = [-3/2, 0/2]

Midpoint = (-1.5, 0).

For the fourth vertex, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(-1.5, 0) = [(-3 + x₂)/2, (4 + y₂)/2]

-3 + x₂ = 2(-1.5)

x₂ = -3 + 3

x₂ = 0.

4 + y₂ = 0

y₂ = -4.

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This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.

An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

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The correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, [tex]\sqrt[3]{24} \sqrt[4]{32}[/tex], we need to simplify it,

Factoring them,

24 = 2 x 2 x 2 x 3

32 = 2 x 2 x 2 x 2 x 2

Therefore,

[tex]\sqrt[3]{24} = 2\sqrt[3]{3}[/tex]

[tex]\sqrt[4]{32} = 2\sqrt[4]{2}[/tex]

[tex]\sqrt[3]{24} \sqrt[4]{32}[/tex] =  [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Hence, the correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

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To show how c and b are related, we can draw a line through these points. A positive sloped straight line should appear on the graph.

Identifying the slope and y-intercept is necessary before putting the equation in y-intercept (y=mx+b) form and figuring out the equation of a graphed line. The slope is the y-to-x change ratio.

Plotting points on the coordinate plane with values for b and calculating the appropriate values for c is necessary to graph the equation c = 2b + 6.

Let's pick some b values and determine the matching c values:

c = 2(0) + 6 = 6 when b = 0.

If b = 1, then c = 2(1) + 6 = 8.

c = 2(2) + 6 = 10 when b = 2

These points can be used to plot the graph:

Set the scene (0, 6)

Set the scene (1, 8)

Set the scene (2, 10)

Now we may illustrate the relationship between c and b by drawing a line across these locations. A positive sloped straight line should appear on the graph.

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Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.

An equation in mathematics is a claim made regarding the equivalence of two expressions. It includes one or more variables (unknown values) and describes how those variables and/or constants relate to one another. For instance, the line on a coordinate plane denoted by the equation y = 3x + 5 has a y-coordinate that is equivalent to three times the x-coordinate plus five. Three and five are constants in this equation, while x and y are factors. Finding the value(s) of the dependent variables) that make the equation true is one way to answer an equation. In the example above, we can enter y = 11 into the equation .

given

We must first determine the revenue function, which is provided by, in order to determine the marginal profit at a production level of 3000:

14x - x/1000x = R(x) = xp(x) = 14x - x2/1000

where the demand function is given by p(x) = 14 - x/1000.

The benefit function is next, and it is provided by:

P(x) = R(x) - C(x) = (10x - x2/1000 - 7000) + (4x) = 14x - x2/1000

where the cost function, C(x), equals 7000 plus 4x.

We must take the derivative of the profit function with regard to x and evaluate it at x = 3000 in order to determine the marginal profit:

P'(3000) = 10 - 3/5 = 9.4

Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.

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Answer:

376.8

Step-by-step explanation:

Area of circle: A = πr^2 = π12^2 = 144π

Area of shade: A = (θ/360º) x πr^2 = (60/360) x 144π = 24π

Area not shaded = 144π - 24π = 120π = 120(3.14) = 376.8

The surface formed by the equation 25x²+4y²+z²=100 is an ellipse.

In mathematics, an ellipse is a planar curve with two focus points, where the total of the two distances from any point on the curve to the focal points is a constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide. The eccentricity of an ellipse is used to calculate its length.

We may set one of the variables at a constant value and then plot the resulting 2D curve in the plane created by the other two variables in order to sketch the surface. This procedure can be repeated for various constant values to get a rough surface drawing.

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Step-by-step explanation:

To find the inverse of the exponential function y = (3/2)^x, we need to interchange the roles of x and y, and then solve for y.

So, starting with y = (3/2)^x, we can write:

x = (3/2)^y

To solve for y, we can take the logarithm of both sides with base 3/2:

log(3/2) x = y

Therefore, the inverse of the exponential function y = (3/2)^x is:

y = log(3/2) x

or in exponential form:

y = (log base 3/2) x

This function is the logarithmic function with base 3/2.

The slope of the linear function is given as follows:

3/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope represents the rate of change of a linear function, meaning that it is calculated as the change in y divided by the change in x.

Considering points (-4,-4) and (-2, -1), we have that when x increases by 2, y increases by 3, hence the slope is given as follows:

m = 3/2.

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By answering the above question, we may infer that The inaccuracy, equation when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The following formula may be used to get the percent error:

percent error is calculated as follows: 100% divided by (actual value - measured value).

Whereas, "|" stands for absolute value.

In this instance, the measured measurement is 8.5 inches, whereas the real value is 9.1. Hence, by entering these values into the formula, we may obtain:

error = |(9.1 - 8.5) / 9.1| x 100% error = 6.59%

The inaccuracy, when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

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The quantity 8 to the power of x end quantity over 16

In mathematics, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. In other words, equivalent expressions represent the same mathematical object or concept, but they may be expressed in different forms or notations.

Equivalent expressions are expressions that have the same value for all possible values of the variables involved, and they can be used to simplify or manipulate algebraic expressions.

Then we have;

8^x/16

= 2^3(x)/2^4

Then we use the laws of exponents;

2^3x - 4

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The number of students who scored more than 70 but less than 80 is zero.

A stem-and-leaf diagram is a quantitative analysis of a collection of data points that are separated into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

To find the number of students who scored more than 70 but less than 80, we need to look at the stem-and-leaf plot and count the number of leaves that fall within this range.

Stem 7 has a leaf of 6, which represents a score of 76. Therefore, at least one student scored between 70 and 76.

The stem 8 has leaves of 2, 5, and 8, which represent scores of 82, 85, and 88, respectively. Therefore, no students scored between 76 and 80.

Therefore, the number of students who scored more than 70 but less than 80 is zero.

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As a result, 7 is the number of w that solves the problem.

In mathematics, a denominator is the lowest integer in a proportion that indicates how many equal portions are split into a whole. It is a fraction's division. In this case, the fraction is 4, so there are four components overall.

To solve for w in the equation (W+3)/4 = (W-2)/2, we can start by cross-multiplying to eliminate the denominators:

2(W+3) = 4(W-2)

Expanding the brackets:

2W + 6 = 4W - 8

Simplifying:

2W = 14

W = 7

Therefore, the value of w that satisfies the equation is 7.

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Answer:

Step-by-step explanation:

We can simplify the expression using the rules of exponents:

(-27)^(-2/3) = 1/(-27)^(2/3)

Now, we can use the fact that (-a)^(2/3) = (a^(2/3)) to simplify the expression further:

1/(-27)^(2/3) = 1/(3^3)^(2/3) = 1/3^(3*2/3) = 1/3^2 = 1/9

Therefore, x = 1/9.

The organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given:

Two events take place.

Let event A be flipping a coin

Let event B be rolling a 6-sided die.

Now, a coin has two faces; one is the head and the other is the tail.

So, the possible outcomes of event A are: {H, T}

H → Head, T → Tail.

Now, a six-sided die has six faces each marked with a number. The numbers marked ranges from 1 to 6.

So, the possible outcomes of event B are {1, 2, 3, 4, 5, 6}

Now, each element of set A should match all the elements of set B.

Now, the tabular form should have a row of outcomes of B and a column of outcomes of event A. Thus,

Outcomes          1          2       3        4         5          6  

   H                 H1         H2     H3     H4       H5      H6

   T                 T1         T2     T3        T4      T5         T6

Therefore, the organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

Finally, the correct tree diagram is attached below.

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Complete question:

Answer:

f(x)>[tex]\sqrt{1-x}[/tex]

Step-by-step explanation:

because it is above the x axis it is >

Because it is -x is moves to the right

because it is a dotted line and not solid it is >

Step-by-step explanation:

=6+(-4)(2-3)²

=6+(-4)(-1)²

=6-4×1

=2

Answer: A

Step-by-step explanation:

The value of x is -1 and 3 for which x makes the equation.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given: 1 + (x-1)² = 5

We have to solve it for x and find the value of x.

1 + (x-1)² = 5

We solve this equation by factorization and we get

1 + x² - 2x + 1 = 5

x² - 2x + 2 -5 = 0

x² - 2x - 3 = 0

x² + x - 3x - 3 = 0

x(x+1) -3(x+1) = 0

(x+1)(x-3) = 0

x= -1, 3

Hence, the value of x is -1 and 3 for which x makes the equation.

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Answer:

Step-by-step explanation:

Josslyn burns 7 calories per minute while swimming and 5 calories per minute while practicing yoga. Let x be the number of minutes she spends swimming and y be the number of minutes she spends practicing yoga.

The total number of calories burned, C, is given by:

C = 7x + 5y

To burn at least 500 calories each day, we can write the inequality:

7x + 5y ≥ 500

This inequality states that the total number of calories burned from swimming and practicing yoga, 7x + 5y, must be greater than or equal to 500. Josslyn can achieve this goal by spending a combination of x minutes swimming and y minutes practicing yoga.

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

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

Given:- p(x) = 3x^2 + 4x - 3 and g(x) = 3x - 2

p(x) ÷ g(x)

3x^2 + 4x - 3  ÷ ( 3x - 2)  

[tex]\frac{3x^2+4x-3}{3x-2} =(x+2 )+ \frac{1}{3x-2}[/tex]

Quotient =  x + 2

Remainder = 1

Hence, 3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1

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Answer:

30k^2+55k+25

Step-by-step explanation:

30k^2+30k+25k+25

=30k^2+55k+25

[tex]30k { }^{2} + 30k + 25k + 25[/tex]

[tex]30k ^{2} + 55k + 25[/tex]