A cubic root function has a domain of x≥−3 and a range of y≥−1. What is the range of its inverse?

Answers

Answer 1

In general, if the range of a function is y≥−1, its inverse has a domain of y≥−1. So, the range of the inverse of the cubic root function is y≥−1.

How do we know this?

The range of a cubic root function becomes the domain of a cube function and vice versa since a cubic root function is an inverse function of a cube function. Therefore, the cube function's range is x3 if the cubic root function's domain is x3.

A function's inverse typically has a domain of y1 if its range is y1. Therefore, y1 is the domain of the inverse of the cubic root function.

Describe a function.

A function is a mathematical relationship between a domain—a set of inputs—and a range—a set of outputs. Each input in the domain is given a distinct output, known as the function value, by a function. An equation or graph can be used to depict the function value.

A function is typically represented symbolically by an equation that describes the relationship between the inputs and outputs and a letter, like f or g, as well as the letter. For instance, the equation of a function that accepts a value of x as input and produces its square is f(x) = x2.

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Related Questions

ABC ∼ DEF. The area of DEF is given. Find the area of ABC.

Answers

Check the picture below.

[tex]\cfrac{12^2}{48^2}=\cfrac{A}{960}\implies \implies \cfrac{144}{2304}=\cfrac{A}{960}\implies \cfrac{1}{16}=\cfrac{A}{960} \\\\\\ 960=16A\implies \cfrac{960}{16}=A\implies \boxed{60=A}[/tex]

Use the point on the unit circle to find the value of the three trigonometric functions below.
sin t=
tan t=
sec t=

Answers

The value of trigonometric equations from the unit circle is

sin t = 1/2

cos t = √3/2

tan t = ( 1 / √3 )

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the point on the unit circle be represented as P ( √3/2 , 1/2 )

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

( √3/2 )² + ( 1/2 )² = 1

4/3 + 1/4 = 4/4 = 1

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Substituting the values in the equation , we get

cos t = √3/2

sin t = 1/2

tan t = sin t / cost

On simplifying the equation , we get

tan t = ( 1 / √3 )

Hence , the equations are solved

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which of the following are problematic tendencies we have in reasoning that, according to the text and lecture, can be diminished by thinking in terms of degrees of confidence rather than binary belief?

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The problematic tendencies that can be diminished by thinking in terms of degrees of confidence rather than binary belief are overconfidence and bias.

Habits, behaviors, or mental patterns that are problematic or undesired and have the potential to produce bad results or issues are known as problematic inclinations. Thinking about degrees of confidence allows one to adopt a more complicated and probabilistic approach to decision-making by considering the information's uncertainty and complexity.

According to the text and lecture, focusing on confidence levels rather than having a strong or weak conviction might assist reduce negative reasoning tendencies like overconfidence in one's beliefs and actions, overgeneralization and oversimplification of complicated situations. Confirmation bias is the practice of selectively seeking out and interpreting data in a way that confirms one's preexisting ideas, and belief persistence is the practice of refusing to change one's beliefs in the face of new evidence.

Answers

A differential equation is an equation that relates a dependent variable y to its derivatives with respect to an independent variable x. The general form of a first-order differential equation is:

dy/dx = f(x,y)

where f(x,y) is some function of x and y. To solve a differential equation, we need to find the function y that satisfies this equation. There are different methods to solve differential equations, including:

Separation of Variables: In this method, we separate the variables x and y on opposite sides of the equation and then integrate both sides to find the solution.
Example:
dy/dx = x^2 + y^2

Separate the variables:
dy/y^2 = dx/x^2

Integrating both sides:
∫(dy/y^2) = ∫(dx/x^2) + C

-1/y = ln|x| + C

y = C/x

Exact Equations: In this method, we try to find a function F(x,y) such that its partial derivative with respect to x is equal to the right-hand side of the differential equation.
Example:
(x + y) dx + x dy = 0

Find F(x,y) such that ∂F/∂x = x + y and ∂F/∂y = x:

F(x,y) = x^2/2 + xy

Integrating both sides with respect to x:
F(x,y) = x^2/2 + xy + g(y)

Taking the partial derivative with respect to y:
∂F/∂y = x + g'(y)

Comparing with the original differential equation:
x + g'(y) = x

g'(y) = 0

g(y) = C

Therefore, F(x,y) = x^2/2 + xy + C.

Numerical Methods: In this method, we approximate the solution by using computational algorithms, such as the Euler method or the Runge-Kutta method.
Example:
dy/dx = x^2 + y^2

Use the Euler method with step size h:
y_n+1 = y_n + h * (x_n^2 + y_n^2)
x_n+1 = x_n + h

Iterate this process until x_n+1 reaches a desired value.

These are some of the most common methods to solve differential equations. The choice of method depends on the form of the equation and the desired level of accuracy

Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest. Do not list the same eigenvalue multiple times.) 0 3 3 ?330 = | 0, _ 3.3 For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x) Need Help?Read It Talk to a Tutor

Answers

The eigenvalues of the matrix 0 3 3 -3 are 3 and -3 with each corresponding eigenspace having a dimension of 1.

An eigenvalue of a matrix is a scalar that satisfies the equation Av = λv, where A is the matrix, v is the eigenvector, and λ is the eigenvalue. The eigenvector v represents a direction in which the matrix transforms the space, and the eigenvalue λ represents the scale factor by which the eigenvector is stretched or shrunk.

In this case, the matrix 0 3 3 330 can be written as:

A = 0 3

3 -3

To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix. In this case, the characteristic equation is:

det(A - λI) = det

0 3 - λ 3 -3 - λ

3 3 -3 -3 - λ

= (0 - λ)(-3 - λ) - 9 = 0

= λ^2 + 3λ - 9 = 0

Solving for λ, we find that the eigenvalues are 3 and -3.

Next, we need to find the dimension of the corresponding eigenspaces, which are the subspaces spanned by the eigenvectors associated with each eigenvalue. In this case, the matrix is 2x2, so the maximum dimension of the eigenspaces is 2. However, since the matrix is symmetric, the eigenvectors are orthogonal, and therefore the sum of the dimensions of the eigenspaces is equal to the dimension of the matrix. So in this case, the dimension of each eigenspace must be 1, since the sum of the dimensions is 2.

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which of the following represents the process that an analyst goes through when performing statistical analysis?

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Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

The process of statistical analysis involves the collection of data, organizing it, and summarizing it in an understandable way. After summarizing the data, the analyst can then use a variety of techniques to analyze the data. For example, the analyst may use descriptive statistics such as the mean, median, and mode to describe the data. The analyst may also use inferential statistics such as chi-square tests or correlation tests to determine the relationships between variables. Finally, the analyst may use regression analysis to predict future outcomes based on the data. All of these techniques involve the use of mathematics, primarily algebra and calculus, to solve equations and generate the desired results. Ultimately, the goal of statistical analysis is to draw meaningful conclusions from the data that can be used to inform decision-making.

Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.

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claim: if x is even then 9x 5 is odd. prove the claim for all x < 0, using the smallest counterexample method.

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The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.

The smallest counterexample method is used to prove that a claim is false by providing an example that does not follow the claim. To prove the claim that if x is even then 9x 5 is odd, for all x < 0, we can use the smallest counterexample method by finding the smallest value of x that would disprove the claim.

Let x = -2, then 9(-2) - 5 = -17. Since -17 is even, it does not follow the claim that if x is even then 9x - 5 is odd, thus disproving the claim for all x < 0.

To explain this with formula and calculation, let x = -2, then 9x - 5 = 9(-2) - 5 = -17. Since -17 is even, the claim that if x is even then 9x - 5 is odd is false. Therefore, the claim is false for all x < 0.

The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.

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Write a system of equations for this word problem. DO NOT SOLVE IT

Tickets to the movie theater are $5.50 for children
and $7.00 for adults. On Saturday, 1,250 people
attended the movie theater (adults and children)
The movie theater received $7,979 in ticket sales.
How many children and how many adults
attended the theater on Saturday?
Put answer here⬇️
Equation
TOPIC—
# of tickets—
$ earned—

PLEASE HELP ASAP

Answers

A system of equations for this word problem is

x + y = 1,2505.5x + 7y = 7,979.

What is a system of equations?

A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.

A system of equations is also called simultaneous equations.

The cost of movie theater tickets per child = $5.50

The cost of movie theater tickets per adult = $7.00

The total attendees on Saturday = 1,250

The total ticket sales = $7,979

Let the number of children who attended = x

Let the number of adults who attended = y

Equations:

x + y = 1,250... Equation 1

5.5x + 7y = 7,979... Equation 2

Multiply Equation 1 by 5.5:

5.5x + 5.5y = 6,875... Equation 3

Subtract Equation 3 from Equation 2:

5.5x + 7y = 7,979

5.5x + 5.5y = 6,875

1.5y = 1,104

y = 736

x = 1,250 - y

x = 1,250 - 736

x = 514

Thus, we can conclude that 514 children and 736 adults attended the movie theater on Saturday.

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which of the following organizations is responsible for validating wlan standards interoperability testing?

Answers

The Wi-Fi Alliance is responsible for validating WLAN standards interoperability testing.

The Wi-Fi Alliance is a global non-profit industry association that is responsible for certifying the interoperability of wireless products based on the IEEE 802.11 family of standards. The Wi-Fi Alliance is responsible for certifying WLAN standards interoperability testing, which ensures that wireless products from different vendors are able to communicate with each other. The organisation also certifies products for compliance with various security standards.

The complete question is :

Which of the following organizations is responsible for validating WLAN standards interoperability testing?

A. The Wi-Fi Alliance

B. The Bluetooth Special Interest Group

C. The Institute of Electrical and Electronics Engineers

D. The World Wide Web Consortium

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Ko Tapu is a vertical limestone rock located off the coast of
Thailand. Peter sets up a camera in a boat to shoot some
footage of the top of Ko Tapu. The horizontal distance from
the camera to a point at the base of the rock is 135 feet, and
the vertical distance from the point at the base of the rock to
a point at the top of the rock is 66 feet, as shown in the
figure.
135 ft
What is the measure of the angle of elevation, to the nearest
degree, that Peter should set the camera so he can video the
top of the rock?

Answers

Answer: The angle of elevation that Peter should set the camera to is 35.3°, rounded to the nearest degree (35°).

Step-by-step explanation: To find the angle of elevation, we can use the tangent function. Let's call the angle of elevation "x". Then:

tan(x) = 66/135

We can find the value of x using the inverse tangent (arctan) function:

x = arctan(66/135)

Finally, we can convert the result from radians to degrees:

x = arctan(66/135) * 180/π

x = 35.3° (rounded to nearest degree)

Determine the domain of each relation, and determine whether each relation describes y as a function of b, x = b

Answers

The Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

Explain about the domain of the function?X is equal to why's absolute value, and we're looking for the domain. Remember that the domain is simply the set of all conceivable X values. As a result, when we look at the this equation, an absolute value sign just on y axis makes all negative numbers positive and all positive numbers, just that one number, positive.

For the stated question:

Relation : x = b

Its absolute value of a negative is equal to the absolute amount of a positive alone.

Since zero's absolute value was only zero, all of the X values has to be positive or zero. Because if an exit value had a negative value, the absolute value sign could be in contravention of its rule.Therefore, the domain includes only positive numbers plus zero, and we can use any value for X to check whether or not it is a function. Let's assume that X is 20. 20 equals are available. the reason in its entirety Since we just observed that absolute value of the a negative number up above, y in this case may either equal only positive 20 and y can equal negative 20. This case's negative 20 is only 20, after all.

Thus, the Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

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A rectangle has an area of 18 meters square and a perimeter of 18 meters. What are its length and width?

Answers

Answer:

6 m or 3 meters

Step-by-step explanation:

Area formula = w * L

Perimeter formula =2 x (l+w)

So, that is how I found the answer.

Hope this helps!

Please can someone help me Im stuck

Answers

Solving an exponential equation we will see that the correct option is C.

How to find the interest rate?

We know that if the 1is P ( a percentage) and the initial value is A, then the value after x years is:

A' = A*(1 + P/100%)^x

We want the value $70 to be doubled after 5 years, sowe can write the equation:

$140 = $70*(1 + P/100%)^5

Now we need to solve that for P.

$140/$70 = (1 + P/100%)^5

2 = (1 + P/100%)^5

2^(1/5) = 1 + P/100%

(2^(1/5) - 1)*100% = P

14.8% = P

Then the correct option is C.

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The CPI was 255.7 in 2019 and 258.8 in 2020. Use the CPI to find the rate of inflation from 2019 to 2020.------------------- The CPI was 130.7 in 1990 and 195.3 in 2005. If the cost of household goods in 2005 was $5,400, use the CPI to find the cost of these same household goods in 1990.

Answers

The inflation rate from 2019 to 2020 is 1.21. The goods price in 1990 is $3,614.

From the case, we know that:

CPI 2019 = 255.7

CPI 2020 = 258.8

Inflation 2019 - 2020?

CPI 1990 = 130.7

CPI 2005 = 195.3

Price 2005 = $5,400

Price 1990?

Using the CPI data of 2019 and 2020 we can find the rate of inflation using the formula of:

Inflation = (CPI Y1 - CPI Y0) x 100

CPI Y0

Based on the case, we take:

Y1 = 2020

Y0 = 2019

Then, the rate of inflation from 2019 to 2020 is;

Inflation = (258.8 - 255.7) x 100

255.7

Inflation = 1.21

To find the goods price in 1990, we can use the CPI ratio formula, where:

CPI Y1 = Price Y1

CPI Y0 Price Y0

We take:

Y0 = 1990

Y1 = 2015

The price of goods in 1990 is:

195.3 = $5,400

130.7 Price Y0

Price Y0 = $3,614

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Element X decays radioactively with a half life of 9 minutes. If there are 210 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 20 grams?

Answers

The time it will take for the element to have 20 grams of mass is approximately 30.5 min.

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the initial amount of element present be = 210 grams

The half life of the element = 9 minutes

And , let the time it will take for the element to have 20 grams be T

The radioactive decay of a substance is given by the following formula ,

x ( t ) = x ( 0 ) e ^ ( -λ )t

Substituting the values in the equation , we get

Since the element has a half life of 9 minutes, after this time the mass of the element will be half of it , therefore

x ( t ) / x ( 0 ) = 1/2

1/2 = e ^ ( -λ ) ( 9 )

Taking ln on both sides of the equation , we get

ln ( 1/2 ) = -9λ

λ = - ( ln ( 1/2 ) ) / 9

On simplifying the equation , we get

λ = 0.077016

Now , the mass of the element is

20 = 210 ( e ^ ( -0.077016 ) ( t ) )

On simplifying the equation , we get

e ^ ( -0.077016 ) ( t ) = 0.095238

Taking ln on both sides of the equation , we get

( -0.077016 ) ( t ) = ln ( 0.095238 )

So , the value of t = ln ( 0.095238 ) / ( -0.077016 )

The time t = 30.5 minutes

Hence , the time required is 30.5 minutes

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Someone pls solve this for me and make it organized

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Answer: The inner rectangles area is forty cubic feet, and the outer rectangles area is eighty cubic feet.

PLEASE HELPP it needs to be done by the 3rd!

Answers

Answer:

20 because the breathe is 18 to get it length

1.to study the output of a machine that fills boxes with cereal, a quality control engineer weighed boxes of brand x cereal. the frequency distribution below summarizes his findings. find the mean weight of the boxes of cereal. weight of boxes of cereal x

Answers

The standard deviation is 0.07770.

The above table is given.

First, calculate the class mid-point. This is the average of a class interval.

The mid-point x is:

[tex]x_{1} =\frac{1}{2} (15.3+15.6) = \frac{1}{2} * 30.9 = 15.45[/tex] ( simplify the equation)

[tex]x_{2} =\frac{1}{2} (15.6+15.9) = \frac{1}{2} * 31.5 = 15.75[/tex]

[tex]x_{3} =\frac{1}{2} (15.9+16.2) = \frac{1}{2} * 32.1 = 16.05[/tex]

[tex]x_{4} =\frac{1}{2} (16.2+16.5) = \frac{1}{2} * 32.7 = 16.35[/tex]

[tex]x_{5} =\frac{1}{2} (16.5+16.8) = \frac{1}{2} * 33.3 = 16.65[/tex]

So, we know that :

x 15.45 15.75 16.05 16.35 16.65

f 14 25 84 18 9

Calculate the mean:

Mean = [tex]\frac{15.45 *14 + 15.75 * 25 + 16.05*84 + 16.35 *18 + 16.65 * 9}{14+25+84+18+9}[/tex]

Mean = [tex]\frac{2402.4}{150}[/tex] (by using division)

Mean = 16.016

The standard deviation is:

σ [tex]=\frac{\sqrt{(15.45-16.016)^{2} + (15.75-16.016)^{2} + (16.05-16.016)^{2} + (16.35-16.016)^{2} + (16.65-16.016)^{2} } }{14 + 25+84+ 18+ 9}[/tex]

σ [tex]=\sqrt{0.00603853333}[/tex]

σ = 0.07770

So, the standard deviation is 0.07770.

Answers

Answer:

Step-by-step explanation:

The volume of a swimming pool can be calculated as follows:

Volume = Length * Width * Depth

In this case, the length is 20 m, the width is 6 m, and the depth is 3 m, so the volume is:

Volume = 20 m * 6 m * 3 m = 360 m^3

To convert this volume to cubic feet, we can use the conversion factor:

1 m^3 = 35.3147 ft^3

So, 360 m^3 = 360 * 35.3147 ft^3 = 12611.32 ft^3

Rounding to 3 significant figures, the volume of the swimming pool in cubic feet is:

12611.32 ft^3 ≈ 12611 ft^3

Therefore, the volume of the swimming pool in cubic feet to 3 significant figures is 12611 ft^3.

Final answer:

The volume of the swimming pool is 12,800 ft^3.

Explanation:

To find the volume of the swimming pool in cubic feet, we need to convert the measurements to feet and then multiply them together. One meter is equal to approximately 3.281 feet. So, the length in feet is 20 m × 3.281 ft/m = 65.62 ft, the width is 6 m × 3.281 ft/m = 19.68 ft, and the depth is 3 m × 3.281 ft/m = 9.84 ft.

Now, multiply the length, width, and depth together: 65.62 ft × 19.68 ft × 9.84 ft = 12,848.156 ft3.

Rounding to 3 significant figures, the volume of the swimming pool is approximately 12,800 ft3.

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a transition probability matrix p is said to be doubly stochastic if the sum over each column equals one; that i

Answers

A doubly stochastic matrix is a matrix whose row and column sums are equal to 1.

A doubly stochastic matrix is a square matrix with nonnegative entries whose rows and columns sum to one. This means that the sum of each row and column must be equal to 1. This is expressed mathematically as:

∑pij = 1

Where pij is the element on row i, column j.

We can calculate the sum of each row and column in a matrix by adding all the elements. For example, for a 3x3 matrix, we have:

Row 1: p11 + p12 + p13 = 1

Row 2: p21 + p22 + p23 = 1

Row 3: p31 + p32 + p33 = 1

Column 1: p11 + p21 + p31 = 1

Column 2: p12 + p22 + p32 = 1

Column 3: p13 + p23 + p33 = 1

Therefore, a doubly stochastic matrix is a matrix whose row and column sums are equal to 1.

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Complete question:

Explain what it means for a transition probability matrix to be doubly stochastic, using a formula and calculation to support your explanation.

Select the correct response.
In an election, there are three candidates for governor from parties A, B, and C, three candidates for senator from
parties A, B, and C, and four candidates for representative from parties A, B, C, and D on the ballot. Assume equal
probabilities for selection of all candidates. The approximate probability of all candidates being selected from one party,
A, is
If party D drops from the representative race, then the approximate probability of all candidates being
selected from one party is

Answers

The probability of all candidate being from all party A is [tex]\frac{1}{36}[/tex] and if party D drops then probability of all candidates being selected from one party is [tex]\frac{1}{9}[/tex] .

What is probability?

Probability is the chance which indicate how likely something can happen.

probability of an event to occur from many event is calculated by taking the ratio of the chances of that event to the total number of event.

P(event)=[tex]\frac{Number of that event}{total number of event }[/tex]

Now for the given question:

A) Total number of candidate for governor = 3

Total number of candidate for senator = 3

Total number of candidate for party representative = 4

Total number of candidate= 3×3×4=36

Number of possible way for all candidate to be selected from party A only = 1

Approximate Probability of all candidate being selected from party A= [tex]\frac{1}{36}[/tex]

B) Total number of candidate for governor = 3

Total number of candidate for senator = 3

If party D drops from candidate for party representative race

Total number of candidate for party representative = 3

Total number of candidate= 3×3×3=27

We can get all candidates from party A in only 1 possible way

Similarly for Party B and C. We will consider the case as condition for any party as no party name is mentioned in question.

Number of way of all candidate being selected from one part is= 1+1+1=3.

Approximate Probability of all candidate being selected from one party is = [tex]\frac{3}{27}[/tex]

P= [tex]\frac{1}{9}[/tex]

Hence approximate probability of all candidate be selected from party A and approximate probability of all candidates being selected from one party after party D drops from race is [tex]\frac{1}{36}[/tex] and [tex]\frac{1}{9}[/tex] respectively.

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a bottle of water is supposed to have 12 ounces. the bottling company has determined that 98% of bottles have the correct amount. which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?

Answers

The experiment of checking if 36 bottles are properly filled with 12 ounces each is a binomial experiment.

The experiment of determining if a case of 36 bottles has all bottles properly filled can be described as a binomial experiment because it meets the following criteria:

There are a fixed number of trials: The number of bottles in a case is fixed at 36.Each trial is independent: The outcome of one bottle does not affect the outcome of another bottle.There are only two possible outcomes for each trial: Either the bottle is properly filled with 12 ounces of water, or it is not.The same probability of success is associated with each trial: The probability of a bottle being properly filled is 98%.

Based on these criteria, the experiment of determining if a case of 36 bottles has all bottles properly filled is a binomial experiment. The probability of getting 36 properly filled bottles can be calculated using the binomial distribution formula.

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The mean of the medical test is 72.21 with the standard deviation of 2.5. Find a 95%confidence interval for a random sample of 25 students with the following scores

Answers

The 95% confidence intervals are between 71.05 and 73.37.

95% Confidence Interval Calculation

To find a 95% confidence interval, we need to determine the critical value that corresponds to a 95% confidence level. This critical value is the z-score that separates the top 2.5% of the normal distribution from the rest of the distribution. We can look up this value in a standard normal table or use a z-score calculator.

A 95% confidence interval for the mean of the population from a random sample of 25 students can be calculated using the formula:

mean ± (standard error * critical value)

where standard error = standard deviation / square root of sample size

critical value = z-score corresponding to 95% confidence level

So,

mean = 72.21standard deviation = 2.5sample size = 25

standard error = 2.5 / √(25) = 0.6324555320336759

Using a z-table, the z-score corresponding to 95% confidence level is 1.96.

So, the 95% confidence interval is:

72.21 ± (0.6324555320336759 * 1.96) = (71.05, 73.37)

Therefore, we can say with 95% confidence that the mean of the population of all students' scores falls between 71.05 and 73.37.

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how many different linear arrangements are there of the letters a, b, c, d, e, f for which (a) a and b are next to each other? (b) a is before b? (c) a is before b and b is before c?

Answers

Answer:

the total number of arrangement is six

Step-by-step explanation:

Part (a) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other.

Suppose A and B are together and form a group, then no. of groups are .

These groups can be arranged in

A and B can be arranged in .