Example Hypothesis Test
A sugar manufacturer sells sugar in bags with a stated weight of 500g. If bags are
consistently underweight, then the manufacturers could be prosecuted by the Trading
Standards Office. If bags which are consistently over-filled, this could lead to loss of
revenue. The manufacturer wishes to establish whether the bags are being over-filled or
under-filled with sugar (You need to decide whether the mean weight is not 500g). A
sample of 20 bags is taken and the sample mean is found to be 497.855g (the population
standard deviation is known to be 5g).

The linear Mapping of the square with vertices

1: x = -1 + (2/2)(x + iy), y = -1 + (2/2)(x - iy)

2: x = -1 + (2/2)(x + y), y = -1 + (2/2)(-x + y)

The first linear mapping can be found by using the following matrix:

M = [a b]

   [c d]

where, a = 2/2, b = -1, c = -2/2, d = 1.

By multiplying the matrix M with the vector [x, y]T, the linear mapping can be obtained.

For example, for the point (0, 1):

M * [0, 1]T = [-1, 1]

Similarly, for the point (1 + i, i):

M * [1 + i, i]T = [-1 + i, -1 + i]

Therefore, we get the linear mapping:

x = -1 + (2/2)(x + iy), y = -1 + (2/2)(x - iy)

The second linear mapping can be found by using the following matrix:

N = [e f]

   [g h]

where, e = 2/2, f = -1, g = 2/2, h = 1.

By multiplying the matrix N with the vector

[x, y]T, the linear mapping can be obtained.

For example, for the point (0, 1):

N * [0, 1]T = [-1, 1]

Similarly, for the point (1 + i, i):

N * [1 + i, i]T = [i, -1 + i]

Therefore, we get the linear mapping:

x = -1 + (2/2)(x + y), y = -1 + (2/2)(-x + y)

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Answer:

Mean: 23

Median: 23.5

Range: 22

Step-by-step explanation:

How to find the mean: Add all the numbers then divide by the amount of numbers.

How to find the median: Find the middle of all the numbers, there are two middle numbers here so you have to add those two middle numbers and then divide by two to get your answer.

How to find range: Take your highest number and subtract by your lowest

The expression of the polynomial is 0.1(x - 1)^2(x - 5)

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

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

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

P(x) = a * (x - 1)^2(x - 5)

The y-intercept is -0.5

So, we have

a * (0 - 1)^2(0 - 5) = -0.5

This gives

a =0.1

So, we have

P(x) = 0.1(x - 1)^2(x - 5)

Henc,e the expression is P(x) = 0.1(x - 1)^2(x - 5)

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The width of this rectangular pool is equal to 71 meters.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

6532 = 92W

Width, W = 6532/92

Width, W = 71 meters.

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Answer:8 16 34

gdgdfgdf

Step-by-step explanation:

dgdfgdfgdfgdfgdfgdf

Answer:by adding 8

Step-by-step explanation:

i just took it

The statement is true. Solving a linear system is the same as finding the solution set of the system. The solution set of a linear system can also expressed using a parametric description.

A linear system can be solved by locating a parametric description of the solution set. The set of all vectors that fulfil a linear system is known as the solution set, and we can parametrically define this set by expressing the solutions in terms of one or more parameters.

We can determine the pivot variables and the free variables once the system is in row-echelon form. The remaining equations determine the values of the pivot variables, which are the leading coefficients in the equations.

In conclusion, since both entail discovering the values of the variables that satisfy the system, finding a parametric description of the solution set of a linear system is comparable to solving the system.

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The area of the triangle will be 1 square foot.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Calculate the value of x of the small right-angle triangle.

4² = ( 3 + x )² + (2 / 3 )²

16 + 9 + 6x + x² + 4 / 9

7 = x² + 6x + 4 / 9

9x² + 54x - 59 = 0

x = 0.9 ft

The area of the triangle will be calculated as:-

Area = ( 1/2 ) x 3.9 x ( 2 / 3 ) - (1/2 ) x 0.9 x ( 2 / 3 )

Area = ( 1 / 2 x 2 / 3 ) ( 3.9 - 0.9 )

Area = ( 1 / 3 ) x 3

Area = 1 square ft

Therefore, the triangle's area will be one square foot.

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Answer:

Step-by-step explanation:

950 times 30 hours = 28,500

28500 + 75= 28,575

75 is 3% of 2500 the total amount of sales he made

He earned 28,500 in his 30 hour week.

The expression which is equivalent to -5(b - 6) as required to be determined in the task content is; -5b + 30.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Since the expression given is; -5(b- 6).

By using the distributive property of numbers

= (-5 × b) + (-5 × -6)

= -5b + 30

Thus, the linear expression which is equivalent to -5(b - 6) as required is; -5b + 30.

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The Question attached seems to be incomplete/ inappropriate. the complete Question is:

Which expression is equivalent to -5(b - 6).

A variable is defined as the alphabetic character that expresses the unknown value or unknown number. It can be changed according to the operations performed.

In this experiment,

Each side of the shower is sprayed with lemonade juice to determine whether it has any changes in the cleanliness of the shower. So each side of the shower with lemon juice is an independent variable.

This dependent variable is a variable that can measure Lemonade a manipulated variable or independent variable has any effect on it, such as whether lemonade juice cleans the slime off of the side or not.

A control is something that remains unchanged to assess the condition or impact which has not changed or may be contrasted to it. In the this scenario, the water spray is under command.

The experiment concludes drinking lemonade seems to not influence the cleaning of slime inside the shower.

Thus, slime is constant.

Hence,

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The correct decision for the test is B.

Value is a concept that has been debated for centuries and is often defined as the worth or importance attributed to an object, person, or idea. It can be quantified, such as by a price, or it can be something intangible, such as respect, trust, or loyalty. Value can also be subjective and differ from one person to the next, depending on their individual needs and desires. Ultimately, the true value of something lies within the eye of the beholder.

The p-value is less than α, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

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Answer: The commutative property of addition states that changing the order of the terms being added does not change the sum. Therefore, we can rearrange the terms in an expression in any order we choose without changing the result.

For example, if we have the expression:

3x + 2y + 4x + 5y

We can use the commutative property of addition to rearrange the terms as:

3x + 4x + 2y + 5y

Then, we can collect the like terms (terms with the same variable and exponent) by combining the coefficients:

7x + 7y

So the simplified expression is 7x + 7y.

Step-by-step explanation:

To keep his blackmailers at bay for 12 months, the Grand Vizier needs to balance the number of gold payoffs and political favors he gives to them. Let's represent the number of gold payoffs by G and the number of political favors by P.

From the given information, we have:

Each gold payoff gives him an average of 1 month of reprieve.

Each political favor gives him an average of 1.5 months of reprieve.

He cannot afford any revelations about his past to come to light within the next year, which means he needs to keep his blackmailers at bay for 12 months.

He wants to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs.

He can do no more than seven political favors per year.

Each gold bar removed from the treasury will cost him four trips.

Each political favor will cost him about two trips.

Let's first calculate the maximum number of political favors he can give in a year:

7 political favors per year

Next, let's find the maximum number of payoffs he can give in a year:

G + P = total number of payoffs

G ≤ 0.25(G+P) (to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs)

Simplifying the second equation, we get:

G ≤ 0.25G + 0.25P

0.75G ≤ 0.25P

3G ≤ P (multiplying both sides by 3)

So the maximum number of payoffs he can give in a year is 7 + G, where G ≤ 3.

Next, we need to find the combination of payoffs that will give him the most reprieve while losing the fewest trips. We can use a table to calculate the reprieve and trip costs for different combinations of payoffs: look at the table

From the table, we see that the best combination is G=3 and P=4, which will give him a total reprieve of 12 months (the required time) while costing him 26 trips (the minimum possible). Therefore, the Grand Vizier will lose 26 trips in the next year.

The number of minutes that the passenger can travel in the taxi would be = 6.67mins.

The amount of money paid for 1 minute = $3.00

The amount of money that a passenger has = $20

The number of minutes that the passenger can travel = ?

That is;

1 minute = $3.00

X minutes = $20

make X the subject of formula:

X mins = 20×1 /3

X mins = 6.67mins

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Assuming the wealthy, generous and whimsical friend chooses the k recipients uniformly at random, there are nCk ways to select the k people from the n who show up at the party.

The number of ways that you and your best friend can both receive iPhones is equal to the number of ways to select k-2 people from the remaining n-2 people, multiplied by 2 (since you can be selected first or second among the k recipients).

Therefore, the probability that you and your best friend both receive iPhones is: 2 * (n-2Ck-2) / nCk

Simplifying this expression using combinatorial identities, we get: 2 * (n-2Ck-2) / nCk = 2 * [(n-2)! / (k-2)! (n-k)!] / [n! / k! (n-k)!] = 2 * k(k-1) / n(n-1)

Thus, the probability that you and your best friend both receive iPhones is k(k-1) / n(n-1).

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The statement of option a "for data sets with different measurement units" and the statement of option b "for data sets with the same measurement units but greatly different magnitudes." is true about comparing standard deviations. So the option a and b is correct.

When comparing standard deviations, it is important to consider the context in which the data was collected. For example, if two datasets have similar means but different standard deviations, the one with the larger standard deviation may indicate more variability or a wider range of values.

On the other hand, if two datasets have different means but similar standard deviations, the one with the larger mean may be more representative of the population as a whole. In either case, it is important to look at the context of the data to make a more informed comparison.

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The complete question is:

Which of the following is true about comparing standard deviations? (Select all that apply)

a. For data sets with different measurement units

b. For data sets with the same measurement units but greatly different magnitudes

c. For data sets with the same measurement units and similar magnitude

d. For data sets with the same measurement units

The pairing that is incorrect is D. Fourth Amendment-freedom of religion.

The Fourth Amendment to the United States Constitution protects citizens from unreasonable searches and seizures and requires that search warrants be issued only with probable cause and based on specific information. It does not address freedom of religion.

The First Amendment protects a number of individual rights, including freedom of speech, freedom of the press, freedom of religion, and the right to assemble and petition the government.

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E(x) for the given data is  6.6 and p(x=0) =0.22 and variance is = 15.26

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within an “x” period of time. In other words, we can define it as the probability distribution that results from the Poisson experiment. A Poisson experiment is a statistical experiment that classifies the experiment into two categories, such as success or failure. Poisson distribution is a limiting process of the binomial distribution.

mean = 9 on a rainy day

mean=3 on a dry day.

Let X denote the number of traffic accidents tomorrow. If it will rain tomorrow with a probability of 0.6,

a)

E[x]= E[X|R]+E[X|D}

E[X]=0.6*9-0.4*3

=5.4-12=6.6

B)

X is equal to zero. Why is it called a small way?

P(Y)=e^(-9*0.6+3*0.4).

P(X=0)=0.22

part C.

He had variance affected also missing. So I will calculate that,

V(x)=x2-E(x) =15.26.

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(i) P(A ∩ B) = 0.32.

(ii) P(A|B) = 0.64.

(iii) P(A ∪ B) = 0.98.

(i) Using the formula P(B|A) = P(A and B) / P(A), we can rearrange to get:

P(A and B) = P(B|A) * P(A) = 0.4 * 0.8 = 0.32

Therefore, P(A ∩ B) = 0.32.

(ii) Using Bayes' theorem, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B)

We are given P(B|A) = 0.4, P(A) = 0.8, and P(B) = 0.5, so:

P(A|B) = 0.4 * 0.8 / 0.5 = 0.64

Therefore, P(A|B) = 0.64.

(iii) Using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we can plug in the values we have already calculated:

P(A ∪ B) = 0.8 + 0.5 - 0.32 = 0.98

Therefore, P(A ∪ B) = 0.98.

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We would expect an ace to be drawn about 32 times out of 200 draws based on Eli's experiment.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A small deck of cards has 4 kings, 3 queens, 2 jacks, and 1 ace.

To determine the expected number of times an ace would be drawn out of 200 draws, we need to use the probability of drawing an ace and multiply it by the total number of draws.

The probability of drawing an ace is the number of aces divided by the total number of cards:

Probability of drawing an ace = (12) / (75)

= 4/25

Therefore, the expected number of times an ace would be drawn out of 200 draws is:

Expected number of aces = Probability of drawing an ace x Total number of draws

= (4/25) x 200 = 32

So we would expect an ace to be drawn about 32 times out of 200 draws based on Eli's experiment.

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The cost of the couch when tax has been deducted would be = $646.25

The total cost of the couch used to furnish a new home before tax deduction= $687.50

The percentage of tax deduction = 6% of $687.50

That is,

= 6/100 × 687.50

= 4125/100

= $41.25

Therefore, the cost of the couch after tax deductions would be = 687.50- 41.25

=$646.25

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Answer:

(n - 8)(n + 7)

--------------------

Given trinomial:

Apply Viet's theorem.

The sum of the roots is 1 and the product of the roots is - 56.

This is achieved when the roots are 8 and - 7.

The heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, a cone a volume of 37 units³, we need to find the heights for given radii,

We know that, the volume of a cone = π×radius²×height/3

Therefore,

1) If the cone's radius is 1, then its height =

37 = π×1×h/3

h = 37×3/3.14

h = 35.35 units

2) If the cone's radius is 2, then its height =

37 = π×4×h/3

h = 37×3/3.14×4

h = 8.83 units

3) If the cone's radius is 5, then its height =

37 = π×25×h/3

h = 37×3/3.14×25

h = 1.41 units

4) If the cone's radius is 1/2, then its height =  

37 = π×1×h/3×4

h = 141.40 units

Hence, the heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

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The simplest term is [tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex].

Factorization of a number or an algebraic expression means writing the given number or given expression as a product of its factors. For algebraic expressions these factors can be numbers, variables, or an algebraic expression

Given,[tex]\frac{x-1}{x^{2} -3x+2} +\frac{x-2}{x^{2} -5x+6}[/tex]

By factorizing the denominator we get,

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

By cancelling the common terms we get,

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

Taking LCM we get,

[tex]\frac{(x-2)+(x-3)}{(x-3)(x-2)}[/tex]

By simplifying, we get,

[tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex]

Hence, the simplest term is [tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex]

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Two out of the three given existential quantifications are true, while one is false.

In mathematics, quantifiers are used to describe the properties of a set or a domain. One such quantifier is the existential quantifier, which is used to indicate the existence of at least one element in a set that satisfies a given property. In this case, we are interested in finding out which of the given existential quantifications are true, where the domain of x is restricted to positive integers. Let's explore this in more detail.

The domain of x is the set of positive integers, which means that x can only take on values such as 1, 2, 3, 4, and so on. The given existential quantifications are as follows:

∃x(x²=9)

∃x(x+3=5)

∃x(x²=2)

Let's examine each of these in turn.

∃x(x²=9)

This existential quantification is true. To see why, we need to find an integer value of x such that x² equals 9. We can easily see that x=3 satisfies this property, since 3² = 9. As 3 is an integer and satisfies the condition, the statement is true.

∃x(x+3=5)

This existential quantification is also true. We need to find an integer value of x such that x+3 equals 5. This can be easily done by subtracting 3 from both sides of the equation to get x=2. As 2 is an integer and satisfies the condition, the statement is true.

∃x(x²=2)

This existential quantification is false. We need to find an integer value of x such that x² equals 2. However, there is no such integer value of x. This can be proven using the fact that the square of any integer is always a non-negative integer. Therefore, the statement is false.

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Complete Question:

Which of these existential quantifications are true, where the domain of x is the positive integers?

∃x(x²=9)

∃x(x+3=5)

∃x(x²=2)

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

Perimeter of a rectangle = 2(length + width)

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

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

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

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

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

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

= 50 feet + 66 feet

Perimeter = 116 feet

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