[tex]7\sqrt[3]{7}-\sqrt[3]{128}[/tex]

In probability theory, an event is any collection of outcomes or results from a probability experiment. option a) is correct event

It represents a particular occurrence or set of occurrences that we are interested in studying or analyzing. A sample space (option b) is the set of all possible outcomes in a probability experiment. An outcome (option c) is a particular result of a single trial of a probability experiment. An experiment (option d) refers to the process of conducting a trial or series of trials to observe the outcomes and collect data for analysis in probability theory. Therefore, the correct answer is option a) event.

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Complete Question

A(n) _______ is any collection of outcomes from a probability experiment.

a) event

b) sample space

c) outcome

d) experiment

To summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.

An experiment in probability refers to a process of observing or measuring some phenomenon, where the outcomes are uncertain. The collection of all possible outcomes from this experiment is known as the sample space. An outcome is a particular result that occurs as a result of the experiment.

Now, a set of outcomes chosen from the sample space is known as an event. An event can be as simple as a single outcome or as complex as a combination of outcomes. For example, flipping a coin and getting heads is a simple event, while flipping a coin and getting heads or rolling a dice and getting an even number is a compound event.

Finally, a collection of events is simply a group of events that share a common characteristic or property. In probability, we use collections of events to determine the likelihood of certain outcomes occurring. This allows us to make predictions about the experiment based on the available data.

So, to summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.

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Hence, the correct answer are Function  f(x)  is  translated  6  units  to  the left and Function  f(x)  is translated 8 units down.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

The absolute value of a number refers to the distance of a number from the origin of a number line. It is represented as |x|,  which defines the magnitude of any integer ‘x’. The absolute value of any integer, whether positive or negative,  will be the real numbers,  regardless of which sign it has.   It is represented by two vertical lines  |x|,  which is known as the modulus of x.

Function  f(x) = ||x||  is  transformed  to  create function  g(x) =  ||x+6||-8.

To  get  from  f(x)  to  g(x),

we  need  to  perform  the  following  transformations:

Therefore,  the correct  statements  are:

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The probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used in various fields, including mathematics, statistics, and science, to analyze and predict the outcomes of experiments, games of chance, and real-world events.

According to the given information

Using Bayes' theorem, we can write:

P(T|V) = P(V|T) * P(T) / P(V)

We know that two-thirds of the juniors volunteer in their community, so P(V) = 2/3.

We also know that 45% of the juniors who volunteer do so at least twice a week, so P(T) = 0.45.

To find P(V|T), we can use the conditional probability formula:

P(V|T) = P(V and T) / P(T)

We can interpret P(V and T) as the probability of junior volunteering at least twice a week AND volunteering in their community. We don't have that information directly, but we can use the fact that P(T|V) = 0.45 to estimate it:

P(T|V) = P(V and T) / P(V)

0.45 = P(V and T) / (2/3)

P(V and T) = 0.45 * (2/3) = 0.3

Now we can substitute all these values into the original Bayes' theorem formula:

P(T|V) = P(V|T) * P(T) / P(V)

P(T|V) = (P(V and T) / P(T)) * P(T) / P(V)

P(T|V) = 0.3 / (0.45 * (2/3))

P(T|V) = 0.4444...

Therefore, the probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%

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Cash paid for insurance during 2014 was $15,100.The following formula can be used to determine the cash spent on insurance in 2014:

Insurance expense in 2014 minus an increase in prepaid insurance = Cash paid for insurance.

The difference between the prepaid insurance balance at December 31, 2014, and December 31, 2013, can be used to compute the rise in prepaid insurance:

Prepaid insurance at December 31, 2014 minus Prepaid insurance at December 31, 2013 equals $1,500 minus $2,400, or -$900.

The fact that the prepaid insurance balance fell between 2013 and 2014 indicates that the business used more insurance coverage than it had purchased for the year. As a result, the 2014 insurance premiums paid in cash are:

Insurance expense for 2014 minus the increase in prepaid insurance is $14,200 - (-$900) = $15,100 in cash paid for insurance.

The correct response is (C) $15,100.

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B

Step-by-step explanation:

Answer:

Answer is A

Step-by-step explanation:

The average of Fertilizer A is 28 + 23 + 32 + 33 + 35 + 34 + 29 / 7 = 30.57

The average of Fertilizer B is 31+ 17 + 22 + 35 + 37 + 23 + 28 / 7 = 27.57

Because 30.57 > 27.57, then A is the better answer.

Answer:   The IQR of the peppers produced by the plants treated with fertilizer A is less than the IQR of the peppers produced by the plants treated with fertilizer

Step-by-step explanation:

I took the test!

Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

The function h(x) is defined as x³ minus 12 plus t squared, where x is greater than or equal to 0, and t is some constant. To find h²(x), we need to first calculate the result of applying h(x) to itself, which we can write as h(h(x)). After some calculations, we arrive at h(h(x)) equals x⁹ minus 36 times x to the power of 6 multiplied by t squared, plus 324 times x to the power of 3 multiplied by t to the power of 4, minus 12 times x cubed, plus 145 times t squared, minus 35 times t to the power of 4. Therefore, h²(x) is equal to the same expression we obtained for h(h(x)).

To find h²(x), we need to first find h(h(x)).
h(x) = x^3 - 12 + t^2
h(h(x)) = (h(x))^3 - 12 + t^2
Substituting h(x) into the above equation, we get:
h(h(x)) = (x^3 - 12 + t^2)^3 - 12 + t^2
Therefore, h²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

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Answer:

4/7

Step-by-step explanation:

1-3/7

7/7 -3/7

4/7

The required location on the gird is:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

Consider the provided expression.

We need to place the indicated product in the proper location on the grid.

First open the parenthesis as shown:

(x + y + 3)(x + y - 4) = x(x + y - 4) + y(x + y - 4) + 3(x + y - 4)

[tex](x + y + 3)(x + y - 4) =[/tex] [tex]x^{2} +xy-4x+yx+y^2-4y+3x+3y-12[/tex]

Now add the like terms as shown:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

Hence, the required location on the gird is:

[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]

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As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .

The initial price of the car is set at P = 18300 (units)

The price after lowering drom P becomes A= 16000 (units)

Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.

The formula for calculating percentage change is given as follows,

Change in percentage = [(Change in value)/ ( Initial value) ]*100

⇒Change in percentage = (C/ P)*100

⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)

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The area of the composite figure comprising of a semicircle and a parallelogram is about 110.3 square units.

A composite figure is a figure comprising of two or more simple geometric figures.

The figure consisting of a parallelogram and a semicircle is a composite figure, which indicates  that the area of the figure is the sum of the area of the parallelogram and the area of the semicircle

The dimensions of the semicircle includes;

Diameter length, D = 8 units

The area of the circle = π·D²/4

Therefore; Area of the circle = π × (8 units)²/4 = 16·π square units

The dimensions of the parallelogram are;

The length of the base, b = 10 units

The height of the parallelogram, h = 6 units

The area of the parallelogram = b × h

Therefore; Area of the parallelogram = 10 units × 6 units = 60 square units

The area of the figure = 16·π square units + 60 square units ≈ 110.3 square units

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Answer:

The median is 11.

Step-by-step explanation:

To find the median, you need to put all of the numbers in order.

In this case it would go:

2, 5, 8, 10, 10, 12, 14, 17, 20, 22

Now you find the middle number. Since there is an even amount of numbers, the median will fall between two different numbers. These numbers are 10 and 12. The median will be the number in between these two, which is 11. Therefore, the median is 11.

IM SO SORRY IF THIS DID NOT MAKE SENSE!

Thus, for the given range of data of six integers the value of x is found as: x = 16.

The difference here between maximum and smallest values in a data set is known as the range. Employing the exact same units as the data, it measures variability. More variability is shown by larger values.

Take the highest value and deduct the lowest value from it to determine the range in statistics.

A data set's range

Range is equal to the highest and lowest values.

Since the formula subtracts any smaller value from the larger one, it is impossible for it to be negative.

Given data:

six integers:  5,9,7,12,3,x.

Range = 13

The formula for the range ;

Range  = maximum value - minimum value

x - 3 = 13

x = 13 + 3

x = 16

Thus, for the given range of the data of six integers the value of x is found as: x = 16.

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Answer:

a) The scale factor from A to B is 3/5 since (3/5)(5) = 3.

b) r = (3/5)(11) = 33/5 = 6 3/5

We can simplify the expression by distributing the 2 and combining like terms:

-3.75 + 2(-4x + 6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.75 - 11.25x (combining like terms)

Therefore, any expression that simplifies to -11.75 - 11.25x is equivalent.

Possible equivalent expressions are:

-3(-3.92x + 3.917)

-11.75 - 11.25(x+1)

-11.75 - 9x - 2.25x

-1.5(-15 + 9x)

11.25x - (11.75 + 2(-3.75))

Note that there are many other possible expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x, but the key is that they all simplify to the same value of -11.75 - 11.25x.

The probability of getting a multiple of 2 or a multiple of 3s:

P = 0.67

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes, which in this case are 12.

The multiples of 2 and the multiples of 3 are

{2, 3, 4, 6, 8, 9, 10, 12}

So 8 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 8/12 = 0.67

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System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. True.

System developers can initiate a formal project as early as the preliminary investigation stage or at any point in the analysis, design, and implementation activities.

The decision to initiate a formal project depends on various factors, including the scope of the project, the availability of resources, the complexity of the system, and the stakeholders' needs and requirements. A formal project may involve a team of developers, analysts, and other experts who work collaboratively to design and implement a system that meets the stakeholders' requirements and objectives.

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True. System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur.

The initiation stage is when the need for a new system is identified, and preliminary investigations are conducted to

determine the feasibility of the project.

If the project is deemed feasible, the formal project can be initiated at this stage.

However, if the project is initiated later on, the analysis, design, and implementation activities will have already begun.

System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur. therefore, the given statement is true.

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The sum of the given polynomial  [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]is [tex]9x^{3} - 8x^{2}[/tex].

Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.

Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.

The following polynomial equation is [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

Polynomial addition is accomplished by combining 'like terms'.

As a result, sorting and adding

= [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

= [tex]7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}[/tex]

= [tex]9x^{3} - 8x^{2}[/tex]

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Complete question:

What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)

Answer:

44 feet

Step-by-step explanation:

To find the perimeter of the garden, we need to add up the lengths of all four sides.

Since the length of the garden is 13 feet and the width is 9 feet, the perimeter can be calculated as:

P = 2L + 2WP = 2(13) + 2(9)

P = 26 + 18P = 44Therefore, the perimeter of the garden is 44 feet.

Answer:

the answer is 44

Step-by-step explanation:

therefore it is perimeter is equals 2l plus 2wp equals 2 (13) plus 2 (9)

26 plus 18

final answer is 44

The mass of the watermelons is 24 kg and the mass of the mangoes is 8 kg.

A physical quantity is mass. The unit of mass measurement is the body's weight. Normal mass units like grammes, kilogrammes, and pounds can be used to measure it.

We are informed of the following:

T + W = 27 (total mass of trolley and watermelons is 27 kg)

T + M = 11 (total mass of trolley and mangoes is 11 kg)

W = 3M (mass of watermelons is three times the mass of mangoes)

Elimination or substitution can be used to solve this set of equations. Substitutions made

We can enter W = 3M into the first equation in place of the third equation to obtain:

T + 3M = 27

From the second equation, we can substitute T = 11 - M into this equation to get:

(11 - M) + 3M = 27

Simplifying this equation, we get:

2M = 16

So, M = 8 kg. This means that the mass of the mangoes is 8 kg.

We can substitute this value of M back into the second equation to get:

T + 8 = 11

So, T = 3 kg. This means that the mass of the trolley is 3 kg.

Finally, we can substitute these values of T and M into the first equation to get:

3 + W = 27

So, W = 24 kg. This means that the mass of the watermelons is 24 kg.

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Answer: We can use the formula for exponential decay to find the mass of substance A in the dish after 12 hours:

A = A0 * e^(-kt)

where:

A0 = initial mass of substance A (500 grams)

A = mass of substance A after time t

k = decay constant

t = time (in hours)

Since the mass of substance A decreases at the rate of 20% every 6 hours, we can find the decay constant as follows:

20% = 0.2 = e^(-k*6)

Taking the natural logarithm of both sides, we get:

ln(0.2) = -k*6

k = -ln(0.2)/6

k ≈ 0.1155

Substituting the values of A0, k, and t into the formula for exponential decay, we get:

A = 500 * e^(-0.1155*12)

A ≈ 169.2 grams

Therefore, the mass of substance A in the dish at the end of 12 hours is approximately 169.2 grams.

Step-by-step explanation:

The mass of substance A in the dish at the end of 12 hours would be 320 grams.

The mass of substance A decreases at a rate of 20% every 6 hours. After 6 hours, the mass of substance A remaining in the dish would be:

500 - (20/100) * 500

500 - 100

400 grams

After another 6 hours (i.e. at 12 hours), the remaining mass of substance A would be:

400 - (20/100) * 400

400 - 80

320 grams

Therefore, the mass of substance A in the dish at the end of 12 hours would be 320 grams.

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The groups that describes 16% of the population of horse jockeys are option (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

To solve this problem, we need to use the standard normal distribution, where we can find the z-score associated with the given percentages using a z-table or calculator. The z-score tells us how many standard deviations a value is from the mean.

First, we can standardize the values using the formula

z = (x - μ) / σ

where z is the z-score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

a) To find the jockeys who are shorter than 58 in., we can standardize the value as

z = (58 - 62) / 2 = -2

Using a z-table, we can find that the percentage of values below z = -2 is approximately 0.0228, which is less than 16%. Therefore, a) is not correct.

b) To find the jockeys who are taller than 64 in., we can standardize the value as

z = (64 - 62) / 2 = 1

Using a z-table, we can find that the percentage of values above z = 1 is approximately 0.1587, which is also less than 16%. Therefore, b) is not correct.

c) To find the jockeys who are shorter than 60 in., we can standardize the value as

z = (60 - 62) / 2 = -1

Using a z-table, we can find that the percentage of values below z = -1 is approximately 0.1587, which is less than 16%. Therefore, c) is correct.

d) To find the jockeys who are between 60 in. and 64 in., we can standardize the values as

z1 = (60 - 62) / 2 = -1

z2 = (64 - 62) / 2 = 1

Using a z-table, we can find the percentage between z1 and z2, which is approximately 0.6826. Therefore, d) is also correct.

Therefore, the correct answers are (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

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The given question is incomplete, the complete question is:

Suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in.

Which group describes 16% of the population of horse jockeys?

Select each correct answer.

a) jockeys who are shorter than 58 in.

b) jockeys who are taller than 64 in.

c) jockeys who are shorter than 60 in.

d) jockeys who are between 60 in. and 64 in.

Non-parametric tests are statistical tests that do not require specific assumptions about the population distribution, such as normality or equal variances. They are useful in situations where the data does not meet the assumptions of parametric tests, or when the variables are ordinal or categorical.

There are some additional examples of non-parametric tests.

Hence, non-parametric tests offer a flexible alternative to traditional parametric tests and can be useful in a variety of situations.

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Answer:

Answers down below!

Step-by-step explanation:

Mean: 58.75

Median: 63

Range: 70

Mode: 63

Hope this helps!

Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.

The event A consists of all outcomes in which the number of spots showing on the red die is three or less.

Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:

P(A) = the number of outcomes in A / the total number of possible outcomes.

Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.

Therefore, the number of outcomes in A is three.

Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.

Therefore, we have:

P(A) = 3/36 = 1/12.

The event B consists of all outcomes in which the number of spots showing on the green die is more than three.

There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.

Thus, we have:

P(B) = 3/36 = 1/12.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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Answer:

Step-by-step explanation:

Question 1 :

The statement that best describes the solutions of a two-variable equation is (1) The ordered pairs must lie on the graphed equation. This means that any ordered pair (x,y) that satisfies the equation will corresponds to a point on the graph of the equation. In other words, if we plot all the points (x,y) that make the equation true, we will obtain the graph of the equation. Any points that do not lie on the graph is not a solution to the equation. Therefore, when solving a two-variable equation, we need to find the values of x and y that make the equation true and plot those points on the graph to visualize the solutions.

Question 2 :

To use the arithmetic sequence formula, we need to know the first term (a1), the common difference (d), and the desired term (an). In this case, we are given the first term as 4 and the common difference as 3 (since each term is increasing by 3). To find the 10th term, we would replace the variable "n" with 10 in the formula. Therefore, to determine the 10th term of this sequence, we would use the formula:

a10 = a1 + (n-1)d

a10 = 4 + (10-1)*3

a10 = 4 + 27

a10 = 31

Thus, the 10th term of the given sequence is 31.

Question 3 :

The formula an = al + (n-1)d is used to determine the nth term in an arithmetic sequence, where "a" represents the first term in the sequence, "n" represents the term number being solved for, and "d" is the common difference between terms. The formula essentially states that to find any term in an arithmetic sequence, one must add the common difference between terms multiplied by the number of terms-1 to the value of the first term. This formula can be applied to various situations, such as determining the total cost of goods sold in a business with a constant markup percentage, or calculating the number of days it will take to save a given amount of money with a fixed monthly contribution. By understanding the principles behind the formula, individuals can successfully solve problems involving arithmetic sequences in a variety of contexts.

The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)

Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc

From the information given, we have that;

x -2/x + 3 + 10x/x² - 9

Find the lowest common denominator and simplify

(x-2)(x² - 9) + (x-3)(10x)  /(x²- 9)(x+ 3)

Now, expand the bracket, we get;

x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)

collect the like terms of the denominator and that of the numerator, we get;

11x³ - 39x -2x²/(x²- 9)(x+ 3)

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