An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 212.4 3 8.304985 0.001474 3.238867
Within Groups 136.4 8.525
Total 348.8
a) What is the within groups degrees of freedom for this analysis? Explain how you obtain your answer.
b) What is the total degrees of freedom? Explain how you obtain your answer.
c) What is the among-group (between-group) mean squares? Explain how you obtain your answer.
d) At a significance level of 1%, what conclusion can you infer? Explain how you obtain your answer.

For the  given case, in the residual plot, the x range is for the age  and  the y  range must be the  square foot

A residual plot appears the difference between the observed response and the fitted response values. The ideal remaining plot, called the null residual plot, appears as a random scatter of focuses shaping a roughly constant width band around the identity line. It is vital to check the fit of the model and presumptions – steady change, normality, and freedom of the errors, utilizing the residual plot, alongside normal, sequence, and lag plot.We  are given the information  that  there is a relationship between age and square foot range (sqft) of living space, so for  the  residual plot the y range must be for the  square foot and the  x range must the age

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The Function value of f(-2) is -4

What are Function?

Exactly each element of Y is assigned to each element of X in a mathematical function from the a set X to a set Y. Both the set X as well as the set Y are referred to as the function's domain and codomain, respectively. Al-Biruni as well as Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known method for approaching the concept of function. The original conception of functions was the relationship between varying quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically at the conclusion of the 17th century with the development of infinitesimal calculus, and up to until nineteenth century, the functions taken into consideration were differentiable.

Solution:

Given: f(x) = 3x + 2

To find: Value of f(-2)

To solve this problem we will simply replace the value of x in Function with -2

f(-2) = 3*(-2) + 2

f(-2) = -6 + 2

f(-2) = -4

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The expression that shows a way to factor 16 + 72 is 8(2 + 9)

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

16 + 72

Express the terms of the expression as products

So, we have the following representation

16 + 72 = 8 * 2 + 8 * 9

Factor out 8 from the expression

This gives

16 + 72 = 8 * (2 +  9)

Hence, the factored expression of 16 + 72 is 8 * (2 +  9)

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As x approaches 0, the denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity and the numerator approaches 0. Therefore, the expression approaches 0 as x approaches 0.

1. Evaluate the denominator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.

2. The denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity as x approaches 0.

3. Evaluate the numerator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.

4. The numerator of the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.

5. Therefore, the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.

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. A minibus had 23 passengers at the beginning of a journey. The  passengers alighted at the final destination,  passengers were ferried by the minibus through the journey, and money collected during the trip are

Generally, a) The minibus had

23 - 12 + 9 = 20 passengers at the first stop.

After the second stop, it had

20 - 6 + 12 = 26, passengers.

At the final destination, 26 - 6 = 20 passengers alighted.

b) The minibus ferried a total of

23 + 12 + 9 - 6 - 12 = 24 passengers through the journey.

c) The charges for the first stop were

50 * 12 = 600 shillings.

The charges for the second stop were

70 * 6 = 420 shillings.

The charges for the final destination were

85 * 20 = 1700 shillings.

The total amount of money collected during the trip was

600 + 420 + 1700 = 2820 shillings.

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Answer:

the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.

Step-by-step explanation:

To determine the number of mini hotdogs and mozzarella sticks in the combination meal, we can use the following system of equations:

Let x be the number of mini hotdogs in the combination meal.

Let y be the number of mozzarella sticks in the combination meal.

The first equation represents the total number of calories in the combination meal: 60x + 70y = 1080

The second equation represents the difference between the number of mini hotdogs and mozzarella sticks: x - y = 5

Thus, the system of equations is:

60x + 70y = 1080

x - y = 5

To solve this system, we can use a variety of methods, such as substitution or elimination. For example, we can eliminate x by adding the equations together, which yields:

60x + 70y = 1080

x - y = 5

60x - x + 70y - y = 1080 - 5

59x + 69y = 1075

Dividing both sides by 59, we find that x = 18.

Substituting this value into the second equation, we find that y = 18 - 5 = 13.

Therefore, the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.

Answer:

There are 9 pizza rolls and 12 mini hotdogs in the combination meal.

Step-by-step explanation:

We are given the following in the question.

Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.

Total number of items in combination meal = 21

Thus, we can write the equation

Calorie in a pizza roll = 60

Calorie in a mini hotdog = 70

Total calories = 1380

Thus, we can write the equation

Solving the two equations, we get,

Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.

When the temperature increased by 19.8 degrees fahrenheit , the temperature in degrees Celsius got increased by 11 degree

The equation C that gives the temperature in degree Celsius is

C = [tex]\frac{5}{9}(x - 32)[/tex]

Where x denotes the degree Fahrenheit

According to the question,

Temperature has increased by 19.8 degree Fahrenheit

So, let the new temperature be " x' "

x' = x + 19.8

Therefore, For calculating temperature in degree Celsius

=> C' = 5/9 (x' - 32)

Substituting the value of x'

=> C' = 5/9 (x + 19.8 - 32)

=> C' = 5/9 ( x - 32) + 5×19.8/9

=> C' = C + 99/9

=> C' = C + 11

Hence , The temperature increased by 11 degree Celsius

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Answer:

178

Step-by-step explanation:

SORRY IF ITS WRONG IM BAD AT MATH :(

Data that are left-skewed would include values that are unusually high.

A data is symmetric when it has a mirror image on both sides of the mean. For a symmetric data the mean = mode = median.

If the data is asymmetric, it can either be left-skewed or right-skewed. A left-skewed data has mots of its values greater than the mean. In this case the mean < median < mode. Left-skewed data mostly contains very less amount of values with smaller magnitudes.

Hence, data that are left-skewed would include values that are unusually high.

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Answer:

8%

Step-by-step explanation:

1. Subtract the larger number from the smaller:

  3780 - 3500 = 280

2. Divide the result from step 1 by the FIRST salary amount:

   280 ÷ 3500 = 0.08  NOTE: Order Matters!!!

3. Change the decimal to a percent

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

The ratio of the actual worth to the total value multiplied by 100 is the formula for calculating the percentage.

The percentage formula is given by

Here we have

A family buys a studio apartment for $ 150,000

The down payment paid by the family is $ 22500

a. Percentage of down payment in the purchase

From the above data,

The percentage of the down payment = [tex][ \frac{22500 }{150,000} \times 100 ][/tex]  

= [tex][ \frac{22500 }{1500} ][/tex] =  15

Therefore,

The percentage of the down payment is 15%  

b. The percentage of the purchase price would be a $67500 down payment?    

Let x  be the percentage of the down payment in the purchase amount  

=>  [tex]\frac{x}{100} \times $ 150,000 = 67500[/tex]  

=>  [tex]x \times 1500 = 67500[/tex]

=>  x = 67500/1500

=>  x = 45%

Therefore,

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

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The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is

x sin⁻¹x + √(1 - x²) + C.

Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as

x sin⁻¹x + √(1 - x²) + C.

where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.

Integral of Sin Reverse proof by integration by parts :

f(x) = sin⁻¹x, g(x) = 1

d(sin⁻¹x)/dx = 1/√(1 - x²)

Using these equations and facts,

∫sin⁻¹x dx = ∫sin⁻¹x.1 dx

= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx

= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx

= x sin⁻¹x - ∫x/√(1 - x²) dx

= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]

= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx

= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}

= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C

= x sin⁻¹x + (1 - x²)1/2 + C

= x sin⁻¹x + √(1 - x²) + C

Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.

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For the following data of group of Scandinavians consisting of Swedes, Finns and Norwegians the probability for the following parts will be:

By using the formula, Circular permutation  = (n-1)

Total permutations = 18 - 1 = 17

(a) all the swedes sit together

Total permutations where all the swedes sit together  

= 13 x 5

all swedes sitting on 5 consecutive seats so they can be arranged  times and everyone including Norwegians as a group can be arranged in

Probability that all the swedes sit together = [tex]\frac{13 X 5}{17}[/tex]

(b) that all the Finns and all the Swedes sit together

Total permutations where all the Finns and all swedes sit together =  8 x 6 x 5

Probability that all the Finns and all swedes sit together = [tex]\frac{8 X 6 X 5}{17}[/tex]

(c) that all the Norwegians, Swedes, and Finns sit together.

Total permutations where all the Norwegians, Swedes, Finns sit together = (3-1)

So Probability that all the Norwegians, Swedes, Finns sit together = [tex]\frac{2 X 6 X 5 X 7}{17}[/tex]

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If the area of the area of the base increases at rate of 2 cm²/sec then the rate at which the height of the box is decreasing is 0.11 cm/sec .

In the question ,

it is given that ,

the volume of the rectangular box having square base is 1100 cm³ ;

the rate of decrease of the area is (dA/dt) is = 2 cm²/sec ;

we know that ; Volume = Area × Height ;

the area of the square base of side 12 cm is = 12 × 12 = 144 ;

So , height = Volume/Area ;

= 1100/144 ;

Now , V = A × h ;

differentiating the above equation w.r.t. "t" ,

we get ;

dV/dt = A×(dh/dt) + h×(dA/dt)

0 = 144×(dh/dt) + (1100/144)×(2)

dh/dt = -2200/(144 × 144)

= -0.106095

≈ -0.11

Therefore , the rate of change of height is = 0.11 cm/sec .

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The length of the ladder is approximately 3 m. The correct option is the first option 3

From the question, we are to calculate the length of the ladder.

From the given information,

The ladder makes an angle 20° with the ground

and

The foot of the ladder is 3 m from the wall

This scenario gives a right triangle where the hypotenuse is the ladder and the adjacent is the distance of the foot of the ladder from the wall.

Let the length of the ladder be x

Thus,

Using SOH CAH TOA

We can write that

cos 20° = 3 / x

x = 3/(cos 20°)

x = 3.19

x ≈ 3 m
Hence, the length is approximately 3 m

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Answer:

The answer is 1.86x10 6

Step-by-step explanation:

10x6 is 100k and the speed light travels is 186k so to get the answer you need to find the one that gets to 100k and then multiply it by 1.86

The mean x=10 and the median=10 are equal, then the data is a normal distribution and the shape will be symmetrical "bell curve".

In the given question, Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch.

He recorded his results in the table.

A 6-column table with 2 rows

The first row contains entries 10, 5, 8, 10, 12, 6.

The second row contains entries 8, 10, 15, 6, 12, 18.

We have to find the relationship between the mean and median reveal about the shape of the data.

The data elements are given as:

10, 5, 8, 10, 12, 6, 8, 10, 15, 6, 12, 18

Start by sorting the above data elements in ascending order.

5, 6, 6, 8, 8, 10, 10, 10, 12, 12, 15, 18

The mean of the dataset is then calculated as:

X = 5+6+6+8+8+10+10+10+12+12+15+18/12

X = 120/12

X = 10

The median of element is then calculated as:

Median = n/2th

Median = 12/2th

Median = 6th

This means that, the median is of the 6th elements.

So, we have:

Median = 10

When the mean and the median are equal, then

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Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.

2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.

3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

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Step-by-step explanation:

Answer:

No solutions, there is nothing that will make the equation true

Step-by-step explanation:

You need to isolate the variable

4(K-8) = -3+4K

First get ride of the parenthesis by distributing

(4 x k) - (4 x 8) =-3+4k

4k-32 = -3+4k

next rearrange the equation to have the variable on only one side

4k-32 = -3+4k   (subtract 4k from one side)

-32 = -3

The variables canceled out, leaving an equation. If the equation is true there are infinite equations while if the equation is false there are no solutions

-32 is NOT equal to -3, meaning there are no solutions

Answer:

8,010,005

Step-by-step explanation:

eight million ten thousand and five

hope this helps

The data shows that United States has less intergenerational mobility than Germany this data means that the success of the children of United States depends more on the parents income status in comparison to Germany.

Intergeneration mobility is the extent to which the outcomes of the doings of an individual are different in comparison to his or her parents. This basically means the extent to which an individual is gaining something by his own potential.

According to the data United States has less intergeneration mobility in comparison to the intergenerational mobility of Germany.

From this data that outcomes of a children born in United States depends highly on the parents economic and financial status than German kids.

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The percentage rate of increase or decrease of the function  y=99(1.04)^4 is 4%

This is a type of function that are of 3 main parts

the starting or initial value

base function

the exponents

Considering the given problem, y=99(1.04)^4

the starting = 99

the base = 1.04

the exponents = x

The base is what determines increase or decrease with a base of 1.04 shows a percentage increase is 4%

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From the question the transformations that non-rigid is dilation. The correct answer is B.

Any transformation of a geometric object that alters the size but not the shape is referred to as a nonrigid transformation. Examples of non-rigid types of transformation include stretching and dilation. Any action taken on a shape is referred to as a metamorphosis.

Rigid transformation is When a figure undergoes a stiff transformation, its size and shape are left unaltered. Because the image is unchanged, stiff transformations include translations, rotations, and reflections.

As a result, a dilation is a non-rigid transformation because the size of the image is changing.

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Answer: $10

Step-by-step explanation:

Sue has $10 more than Paul which means she has $20. Who is speaking has $16 more than Sue ($16 more than $20) which means they has $36.

Adding all of their money, $10, $20, and $36, equals $66

An equation is quadratic if the greatest power of the coefficients is 2. Hence, for the given equations, only 6(2x + 4)2 = (2x + 4) + 2 is quadratic in nature.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation with one variable that goes like this: x ax2 + bx + c = 0. with a ≠ 0 .

                              The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be simple or complicated.

Why it is called quadratic equation?

In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring."

                         This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. The Latin word quadratum, which means square, is where the word "quadratic" derives.

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The complete question is -

Select all of the following equation(s) that are quadratic in form.

x4 – 6x2 – 27 = 0

3x4 = 2x

2(x + 5)4 + 2x2 + 5 = 0

6(2x + 4)2 = (2x + 4) + 2

6x4 = -x2 + 5

8x4 + 2x2 – 4x = 0

The amount of calories you consume for the rest of the day is 1800

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

Total amount of calories for a day = 2200 calories

Total amount of calories for one session = 400 calories

The above parameters can be represented as

Total amount of calories for one session + Total amount of calories for the end of the day = Total amount of calories for a day

Substitute the known values in the above equation, so, we have the following representation

400 + Total amount of calories for the end of the day = 2200

Evaluate the like terms

Total amount of calories for the end of the day = 2200 - 400

So, we have

Total amount of calories for the end of the day = 1800

Hence, the amount of calories is 1800

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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

we have dr/dt = 6 in/min and dh/dt = -4 in/min

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

SUbstitute the value we get:

dV/dt = 2π(6)(18)(6) + π(6)²(-4)

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of  3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

We have dr/dt = 6 in/min and dh/dt = -4 in/min

In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

Substitute the value we get:

dV/dt = 2π*6*18*6 + π*6² * -4

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of 3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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There are 66 solutions to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers.

To solve this inequality, we must find all the possible combinations of nonnegative integers x₁, x₂, and x₃ that add up to 11 or less. This can be done by breaking down the problem into a series of nested loops. The outermost loop will iterate through all possible values of x₁, while the two inner loops will iterate through all possible values of x₂ and x₃ that add up to the remaining value of 11 minus x₁. We know that the maximum value of x₁ is 11, so the outermost loop will run from 0 to 11. For each value of x₁, the inner loops will run from 0 to (11 - x₁), incrementing by 1 each time. This will ensure that all possible combinations of x₂ and x₃ that add up to 11 minus x₁ are tested. Once we have all the combinations, we can count them to get the total number of solutions. In this case, there are 66 solutions to the inequality.

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On solving the provided question, by multiplying the give polynomials, we got to know that -  [tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex] = [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex], the coefficient of x3 is 8

An mathematical expression known as a polynomial requires that all of the variables' exponents be integers. Each polynomial variable's exponent must be an integer that is not negative. Although a polynomial is made up of a constant and a variable, it cannot be divided by a variable.

Given polynomials are -

[tex]( 3x^2 - 5x + 7) and (2x^2 + 6x - 4)[/tex]

By multiply the given polynomials, we got -

[tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex]

=  [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex]

So, the coefficient of x3 is 8

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