FILL THE BLANK. the term statistics refers to a set of mathematical procedures for ______, _______, and ________ information

The integral of 41x^3 - 27 dx is 41/4 x^4 - 27x + c.

Calculating an integral is called integration. To determine the functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

The concept of limit is employed broadly in calculus whenever algebra and geometry are applied. Limits assist us in analyzing how points on a graph behave, such as how they approach one another until their distance approaches zero.

The indefinite integral of 41x^3 - 27 dx is given by:

∫(41x^3 - 27)dx = 41/4 x^4 - 27x + c

where c is the constant of integration.

Correct Question :

evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 41x^3 - 27 dx

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Answer:

s=8

Step-by-step explanation:

The two angles are vertical angles and vertical angles are equal.

110 = 8s-2

Add 2 to each side.

110+2 = 8s-2+2

112 = 8s

Divide each side by 8

112/8=8s/8

14=s

The population mean (μ) is estimated to be: μ = 18 minutes

In this problem, we are given a sample of 81 people who waited in line for a rollercoaster at an amusement park. We are also given the sample mean (18 minutes) and the sample standard deviation (0.5 minutes).

To estimate the population mean (μ), we use the sample mean (18 minutes). Since the sample mean is a good estimate of the population mean, the estimated population mean (μ) is 18 minutes.

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The expected population mean () is: = 18 minutes.

Additionally, the sample mean (18 minutes) and sample standard variation are provided (0.5 minutes).

We use the sample mean to determine the population mean (). (18 minutes). The expected population mean () is 18 minutes because the sample mean is a reliable indicator of the population mean.

The initial cost of the car was $15,000 and the rate of depreciation is 30%.

The equation [tex]15,000(0.7)^t[/tex] models the value of a car after t years. The value of the car after 0 years, or its initial cost, is [tex]15,000(0.7)^0[/tex] = 15,000. The rate of depreciation can be calculated as 1 - 0.7, which equals 0.3 or 30%. This means that each year, the value of the car decreases by 30% of its previous value. This model assumes a constant rate of depreciation, which may not always reflect real-world situations. However, it provides a simple estimate of the decline in value over time for this car.

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Answer: citizen scientists are already providing large amounts of data for monitoring biodiversity, but they could do much more, according to a new study published in the journal Biological Conservation, which suggests that citizen science has the potential to contribute much more to regional and global assessments of biodiversity. Citizen scientists are regular people who provide data or input to science, for example by monitoring species in their community or examining satellite imagery for evidence of deforestation or land use change.

Step-by-step explanation:

The conversion of 150 pounds weight in kilograms 68.039.

What is meant by weight?

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The system has no solution, there is no particular solution x₀, and the general solution does not exist in this case.

The equation Ax = b, where A is a 3x3 matrix and b is a 3x1 column vector, represents a system of linear equations. To find all solutions of this system, we can either use Gaussian elimination or Cramer's rule.

In this case, A = [[2, -5, 3], [-2, 6, -5], [-4, 7, 0]] and b = [[-3], [4], [3]].

Using Gaussian elimination, we can transform the matrix A into its reduced row echelon form and then use back substitution to solve for the variables. The reduced row echelon form of A is:

[[1, 0, 1/2], [0, 1, -5/2], [0, 0, 0]]

Since the last row is all zeros except for the last entry, the system is inconsistent and has no solution.

Alternatively, we can use Cramer's rule to find the solution. The formula for Cramer's rule is:

x_i = det(A_i) / det(A), where A_i is the matrix A with the i th column replaced by the vector b.

In this case, det(A) = 0, so the system has no solution.

The general solution of this system of linear equations is the set of all linear combinations of the columns of A. If the system has a solution, the general solution can be expressed in the parametric vector form as:

x = x₀ + t₁ * v₁ + t₂ * v₂, where x₀ is a particular solution, v₁ and v₂ are the non-trivial solutions, and t₁ and t₂ are scalar parameters.

Since the system has no solution, there is no particular solution x_0, and the general solution does not exist in this case.

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All the given options are paradoxical, and it's not possible to determine their truth value as they depend on their own veracity.

The statement "Exactly one of these statements is false" can be referred to as the liar paradox. It is a classic example of self-referential statements, where the truth of the statement depends on its own veracity.

In this paradox, if the statement is true, then it must be false, and if the statement is false, then it must be true. Hence, this statement creates a paradox and it's impossible to determine its truth value.

In the case of options (b), (c), and (d), it's also not possible to determine their truth value as they too depend on the truth value of the other statements, which are paradoxical.

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In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.

An isosceles triangle is one with two equally sized sides. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.

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Sí, considero que para representar la función mediante un gráfico, es necesario primero dibujar el plano cartesiano. Esto es porque el plano cartesiano permite representar gráficamente una relación entre dos variables.

Esto también le permite al usuario visualizar los valores que están relacionados y ver cómo se comportan las variables en relación con el otro. El plano cartesiano también le permite al usuario ver los valores que se encuentran fuera del rango de los datos y ayuda a entender mejor la relación entre los datos.

El hecho de asignar valores al eje de la abscisas de uno en uno y al eje de las ordenadas de 10 en 10 no es necesario para representar la función mediante un gráfico, ya que esto depende de las escalas que se elijan para los ejes. Por ejemplo, si la cantidad de envíos a domicilio es el eje x y el ingreso es el eje y, el usuario puede elegir diferentes escalas para los ejes para representar la relación. Por ejemplo, el usuario puede elegir una escala de 1 en 1 para el eje x y una escala de 10 en 10 para el eje y, o una escala de 2 en 2 para el eje x y una escala de 5 en 5 para el eje y.

Yes, I believe that in order to represent the function using a graph, it is essential to first draw the Cartesian plane. This is because the Cartesian plane allows for graphically representing a relationship between two variables. This also allows the user to visualize the values that are related and see how the variables behave in relation to one another. The Cartesian plane also allows the user to see the values that are outside of the range of the data and helps to better understand the relationship between the data.

Assigning values to the x-axis one by one and to the y-axis 10 by 10 is not necessary to represent the function using a graph, as this depends on the scales chosen for the axes. For example, if the number of deliveries is the x-axis and the income is the y-axis, the user can choose different scales for the axes to represent the relationship. For example, the user can choose a scale of 1 to 1 for the x-axis and a scale of 10 to 10 for the y-axis, or a scale of 2 to 2 for the x-axis and a scale of 5 to 5 for the y-axis.

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The limit of the function [tex]\lim_{x \to9}[/tex]  [( x² - 81 ) / ( x - 9 ) ] is equal to 18.

[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]

Substitute the limit x tends to 9 in the function we have,

= ( 9² - 81 ) / ( 9 - 9 )

= ( 81 - 81 ) / 0

= 0 /0

0 /0 form is not defined term.

Simplify the function before substituting the limit we have,

[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] [ ( x ² - 9² ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] [ ( x - 9 ) ( x + 9 ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] ( x + 9 )

= 9 + 9

= 18

Therefore, the value of the limit for the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) /( x - 9) ] is equal to 18.

The given question is incomplete, I answer the question in general according to my knowledge:

Find the following limit or state that it does not exist.

[tex]\lim_{x \to9} \frac{(x^{2} - 81)}{(x - 9)}[/tex].

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The two computers simultaneously can send the email in 10 minutes.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the company has two large computers. The slower computer can send all the company's emails in 30 minutes. The faster computer can complete the same job in 15 minutes.

The time taken by both the computers together will be:-

1 / t = 1 / 30 + 1 / 15

1 / t = ( 1 + 2) / 30

1 / t = 3 / 30

1 / t = 1 / 10

t = 10 minutes

Hence, the time taken by both computers will be 10 minutes.

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The ship is at a distance of 651 feet away from the lighthouse.

Therefore the answer is 651.

Let's call the distance from the base of the lighthouse to the ship "d". Then, using basic trigonometry:

tan∅ = opposite side/ adjacent side

So here opposite side is the height of the lighthouse and adjacent side is the distance from the base of the lighthouse.

tan(21°) = height of lighthouse/ d

d = height of lighthouse/ tan(21°)

d = 250 / tan(21°)

d = 250 / 0.384 = 651.3 ft

Rounding to the nearest foot, the ship is 651 ft away from the base of the lighthouse.

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82.1% of cincinnati household have a computer . If 111,804 households in cincinnati have a computer then 136 households are there altogether in cincinnati.

Given that, 82.1% of Cincinnati households have a computer.

111,804 households in Cincinnati have a computer.

Ratios: It is the realtion between two numbers which shows how much bigger on quantity is than another.

Proportion: It is the an equality of two ratios.

Let total number of houses be x;

According to ratio and proportions we have,

(111,804/x)*100=percentage of Cincinnati households having a computer.

then (111,804/x)*100=82.1

cross multiplying we have

x=(111,804*100)/82.1

x=136 households (Round to the nearest whole number.)

so total households present are 136

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82.1% of Cincinnati households have a computer. If 111,804 households in Cincinnati have a computer then 136 households are there altogether in Cincinnati.

Given that, 82.1% of Cincinnati households have a computer.

111,804 households in Cincinnati have a computer.

Ratios: It is the relation between two numbers that shows how much bigger one quantity is than another.

Proportion: It is the equality of two ratios.

Let the total number of houses be x;

According to the ratio and proportions we have,

(111,804/x)*100=percentage of Cincinnati households having a computer.

then (111,804/x)*100=82.1

cross multiplying we have

x=(111,804*100)/82.1

x=136 households (Round to the nearest whole number.)

so total number of households present are 136

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A piecewise function which is shown on the graph include the following: A. piecewise function A.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

Based on the graph shown above, we can evaluate the piecewise function based on the following domains (input values or independent values);

For the domain x ≤ -2, the value of y (y-value) is equal to 5. Additionally, for the domain -2 < x < 1,we can logically deduce that the function is a polynomial, which implies that it must have this ordered pair (0, -5):

For -2 < x < 1, when x is equal to 0 and y is equal to -5;

y = x² ± 5

For the domain x ≥ 1, we know that, when y is equal to 0, x would lie between 3 and 4;

y = 2^{x - 2} - 3

When y = 0, the value of x is given by:

0 = 2^{x - 2} - 3

2^{x - 2} = 3

x = 3.584.

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Answer:

33x+30

Step-by-step explanation:

If you distribute the x to 14 and 19, you will end up with:

14x+19x+30

Then, if you add the two x values together, you'll end up with:

33x+30

Another way you can do it is adding the numbers in the parentheses first:

x(33)+30

Then distribute the x:

33x+30

The discounted prices are given below.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

a)

Price = $1.20

Off = 25% = 1/4

Discounted amount = 1/4 x 1.20 = $0.3

Discounted price = 1.20 - 0.3 = $0.9

b)

Price = $18

Off = 25% = 1/4

Discounted amount = 1/4 x 18 = $4.5

Discounted price = 18 - 4.5 = $13.5

c)

Price = $150

Off = 30% = 0.3

Discounted amount = 0.3 x 150 = $45

Discounted price = 150 - 45 = $105

d)

Price = $20

Off = 40% = 0.4

Discounted amount = 0.4 x 20 = $8

Discounted price = 20 - 8 = $12

e)

Price = $2.20

Off = 10% = 1/10

Discounted amount = 1/10 x 2.20 = $0.22

Discounted price = 2.20 - 0.22 = $1.98

f)

Price = $1.30

Off = 50% = 1/2

Discounted amount = 1/2 x 1.30 = $0.65

Discounted price = 1.30 - 0.65 = $0.65

Thus,

The discounted prices are given above.

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From the line dot plot of 12 college students wages,

The Mean is $118.25

The Median is $118.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

From the dot plot.

Weekly wages = 112, 113, 116, 116, 116, 118, 118, 119, 119, 124, 124, 124.

Now,

Mean = Sum of all the values / Number of values

= (112 + 113 + 116 + 116 + 116 + 118 + 118 + 119 +119 + 124 +124 +124) / 12

= 118.25

Median = Mid value from the wages.

= 118

Thus,

The Mean is $118.25

The Median is $118.

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The probability that it is a false negative (test indicates the person does not have the disease when in fact they do) is 0.0348.

This probability indicates that the test's accuracy is 0. 0348; as the likelihood of this inaccuracy is minimal, the test is quite accurate.

The likelihood that a randomly chosen result will be a false negative, meaning that the test will show that the person does not have the condition while in fact they do:

[tex]P(NP|D) = \frac{4}{115} \\\\P(NP|D) = 0.0348[/tex]

We may infer that the occurrence is unlikely to occur and that the test is reasonably accurate because the probability is less than 0.0500.

Probability is simply the possibility that something will happen. When we don't know how something will turn out, we might talk about the possibility of one result or the likelihood of several. The study of occurrences that fit into a probability distribution is known as statistics.

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Answer:93000

—————————————-

The solution of the expression in scientific notation is 1.5 * 10^-2

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

6.0 * 10^4 / 4.0 * 10^8

Divide 6 by 4

So, we have

6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^4/10^8

Evaluate the final quotient

6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^-2

Hence, the solution is 1.5 * 10^-2

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The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.

The correct option is A.

Place value, which is related to a digit's location in a number, is the amount that each digit is worth.

Given:

We have a decimal number 25.381.

From the given choices;

We have number 52.

In the number 52:

The place value of 2 is 2.

The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.

Therefore, the number is 52.

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The complete question:

The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in which of the following numbers:

A) 52.

B) 25534.675

The surface area of the cone with a slant height of 8in and diameter of 10in is 204.1 in².

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The surface area of a cone is expressed as;

A = πrl + πr²

Given that;

Plug the given values into the above formula and simplify

A = πrl + πr²

A = ( 3.14 × 5 × 8 ) + ( 3.14 × 5² )

A = 125.6 + 78.5

A = 204.1 in²

Therefore, the surface area is 204.1 in²

Option B) 204.1 in² is the correct answer.

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The ratio of nonfiction to fiction books is 49 : 2.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The number of fiction books is 2/7 times the number of nonfiction books.

So, If we have 7 nonfiction books then we have 2/7 fiction books.

Therefore, The ratio Nonfiction : Fiction = 7 : 2/7.

Nonfiction : Fiction = 49 : 2.

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If the height of a square pyramid remains fixed while its sides of the base is multiplied by 3, then the volume of the new pyramid is 108 cm³ (option C)

The volume of a square pyramid is given by:

V = A . h = a² . h

Where;

A = the area of the base = a²

h = height of the pyramid

a = sides of the base

In this problem,

V = 12 cm³

a² . h = 12   .... (equation 1)

Now, the sides of the base are multiplied by 3. Hence, the new volume will be:

V = (3a)² . h

  = 9 a² . h

from equation 1 we know that a² . h = 12. Hence,

V = 9 x 12 = 108 cm³

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This type of validity is called concurrent validity.

Concurrent validity refers to the extent to which a new test measures the same construct as an established, well-validated test. In this scenario, the newly developed test is being compared to a traditional intelligence test that has already been shown to be valid, and the hypothesis is that there will be no significant differences between the results obtained from the two tests. By comparing the scores of the two groups, the researchers are attempting to determine whether the new test is measuring the same construct (intelligence) as the established test.

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Adult ticket costs $3 and the student $1.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

1) Gathering the data

1st day

5a +3s =18

2nd day:

7a +1s= 22

2) Let's set a system of Linear equations, given those two equations:

solving we get,

a=3

s=1

3) Hence, the adult ticket costs $ 3 and the student $1.

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Answer:

150

Step-by-step explanation:

80% on time so 20% late, 30 late

30/20% = 150

The parameter used in the probability is the average number of students represented by u.

The confidence interval based on the information will be:

= 3.85 - 2.09(1.348 / ✓20)

= 3.22

Also, 3.85 + 2.09(1.348 / ✓20) = 4.48

The confidence interval simply means that one is 95% confident that the true mean is between 3.22 and 4.48.

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