An Airbus A320 airplane has a length of 123 feet, a wingspan of 117 feet, and a height of 39 feet. (Note that you should not convert units for any part of this problem.) a) If a model of the plane is built to have a scale ratio of 1:40! determine the height. Round your answer to 2 decimal places and include units. b) If a model of the plane is built to have a scale ratio of 1 cm: 5ft, determine the length. Round your answer to 2 decimal places and include units. c) If a model of the plane is built to have a ratio of 3in : 10ft, determine the wingspan. Round your answer to 2 decimal places and include units.

a. The eigenvalues of A are λ\(_1\) = 0.99 and λ\(_2\) = 1 and the associated eigenvectors are \([1 \:\:0]^T\) and \([0\:\: 1]^T\), respectively.

b. Iterations starting with \(q_0 = [1\:\: 1]^T\)is

\(q_1 = [0.99\:\: 1]^T\)

\(q_2 = [0.99 \:\:0.99]^T\)

\(q_3 = [0.9801 \:\:0.99]^T\)

\(q_4= [0.9801 \:\:0.9801]^T\)

a. The matrix A can be written as:

A = \(\left[\begin{array}{ccc}0&1\\1&0\\\end{array}\right]\)

Let \(q_0 = [a \:\:b]^T\) be the starting vector.

Then, the power method generates a sequence of vectors \(q_n\) as follows:

\(q_1 = Aq_0 = [b \:\:a]^T\)

\(q_2 = Aq_1 = [a\:\: b]^T\)

\(q_3 = A\times q_2 = [b\:\: a]^T\)

We can see that the sequence oscillates between \([a \:\:b]^T\) and \([b \:\:a]^T\), and does not converge to a single vector.

This happens because A does not have a dominant eigenvalue (i.e., an eigenvalue with the largest magnitude).

In fact, A has two eigenvalues: λ\(_1\)= 1 and λ\(_2\) = -1, with corresponding eigenvectors \([1 \:\:0]^T\) and  \([0 \:\:1]^T\), respectively.

Since both eigenvalues have the same magnitude, there is no dominant eigenvalue, and the power method fails to converge.

b. The matrix A can be written as:

A = \(\\\left[\begin{array}{ccc}0.99&0\\0&1\\\end{array}\right]\)

The eigenvalues of A are λ\(_1\) = 0.99 and λ\(_2\)  = 1.

The corresponding eigenvectors are \([1\:\: 0]^T\) and \([0 \:\:1]^T\), respectively.

Let \(q_0 = [1 \:\:1]^T\) be the starting vector.

Then, the power method generates a sequence of vectors \(q_n\) as follows:

\(q_1 = Aq_0 = [0.99\:\: 1]^T\)

\(q_2 = Aq_1 = [0.99 \:\:0.99]^T\)

\(q_3 = Aq_2 = [0.9801 \:\:0.99]^T\)

\(q_4 = Aq_3 = [0.9801 \:\:0.9801]^T\)

We can see that the sequence converges to the eigenvector \([1 \:\:0]^T\) corresponding to the eigenvalue λ\(_1\) = 0.99.

In general, if A has a dominant eigenvalue λ\(_1\) with corresponding eigenvector \(v_1,\) and \(q_0\) is a vector not orthogonal to \(v_1\), then the power method will converge to \(v_1\).

The convergence rate is determined by the ratio of the magnitudes of the eigenvalues λ\(_1\) and λ\(_2\) (if there is more than one eigenvalue with the same magnitude, the convergence rate may be slower).

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Answer:

15 days

Step-by-step explanation:

Answer:

27 days

Step-by-step explanation:

Answer:

The skier has a faster rate of speed.

Snowboarder: 15m/s

skier: 18 m/s

Step-by-step explanation:

Answer:

It would be 2242.5

Step-by-step explanation:

1950X0.15=292.5

292.5+1950=2242.5

The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

To determine whether the medication affects performance, we can perform a one-sample t-test with the following hypotheses:

Null hypothesis: The mean score for the population (μ) is 64.

Alternative hypothesis: The mean score for the population (μ) is less than 64.

We will use a significance level of α = 0.1.

First, we need to compute the t-statistic:

t = (M - μ) / (s / sqrt(n))

t = (58 - 64) / (7 / sqrt(16))

t = -2.29

Next, we need to find the corresponding p-value for this t-value with 15 degrees of freedom (n-1=16-1=15). We can use a t-distribution table or calculator to find that the p-value is 0.017.

Since the p-value (0.017) is less than the significance level (0.1), we reject the null hypothesis and conclude that the medication affects performance.

To measure the size of the treatment effect, we can calculate Cohen's d, which is a standardized measure of effect size. Cohen's d is computed as the difference between the sample mean and population mean, divided by the sample standard deviation:

d = (M - μ) / s

d = (58 - 64) / 7

d = -0.86

The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

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The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Hi!

I can help you with joy!

How to Find the Reciprocal of a Number?

\(\star\bigstar\) Simply flop the number over.

Example: Suppose we need to find the reciprocal of 2.

We flop it over and get

\(\displaystyle\frac{1}{2}\)

Thus, the reciprocal of -3 is

\(\displaystyle-\frac{1}{3}\)

Hope it helps!

Enjoy your day! :)

\(\bf{-MistySparkles^**^*\)

Answer:

X=90-66

X=24 is the answer

(a) The constant solutions of the given differential equation\(dy/dt = -y^4 - 5y^3 + 6y^2\) are y = -2, y = 0, and y = 3. (b) The function y is increasing for values of y between -2 and 0, and between 3 and positive infinity.

(a) To find the constant solutions, we set dy/dt = 0. Solving -y^4 - 5y^3 + 6y^2 = 0, we factor the equation as y^2(-y^2 - 5y + 6) = 0. This gives us y = -2, y = 0, and y = 3 as the constant solutions.

(b) To determine the intervals where y is increasing, we need to analyze the sign of dy/dt. By factoring the given differential equation, we have dy/dt = y^2(-y^2 - 5y + 6). The factors y^2 and (-y^2 - 5y + 6) correspond to the sign changes in dy/dt.

The factor y^2 is always non-negative, so it does not affect the sign of dy/dt.

For the factor (-y^2 - 5y + 6), we find its roots to be y = -2 and y = 3. By testing the intervals between these roots, we determine that dy/dt is positive for y between -2 and 0, as well as for y greater than 3.

Therefore, y is increasing for values of y between -2 and 0, and between 3 and positive infinity.

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Answer: y=2x-1

Step-by-step explanation:

i think that's correct...

2 is the slope

-1 is the y-intercept

An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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Answer:

C. 1,120 cubic inches

Explanation:

To find the total volume, we will divide the solid as follows:

The edge with a length equal to 10 in was calculated as:

18 in - 8 in = 10 in

Because 18 in is the length of the largest height of the figure and 8 in is the length of the smaller height.

Now, the volume of a rectangular prism can be calculated as:

Volume = Length x Width x Height

So, the volume of solid 1 is equal to:

V₁ = 12 in x 4 in x 10 in

V₁ = 480 in³

In the same way, the volume of solid 2 is equal to:

V₂ = 20 in x 4 in x 8 in

V₂ = 640 in³

Therefore, the total volume of the solid is the sum of both parts. Then:

V₁ + V₂ = 480 in³ + 640 in³

V₁ + V₂ = 1120 in³

So, the answer is C. 1,120 cubic inches

Answer:

3x-4y=-4 as it has the same gradient

The equations which represents the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are,

3x - 4y = -4

y + 2 = 3/4 (x + 4)

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given equation is,

3x - 4y = 7

Rearranging in to slope intercept form,

y = 3/4 x - 7/4

So, slope of the given line = 3/4.

Slopes of two parallel lines are equal.

Any line parallel to the given line will be of the form,

y = 3/4 x + c

Given line passes through (-4, -2).

Substituting to the equation,

-2 = (3/4 × -4) + c

c = 1

Equation is,

y = 3/4 x + 1 [Equation *]

Multiplying whole equation by 4,

4y = 3x + 4

Rearranging,

3x - 4y = -4 [ Equation 1]

Adding whole [Equation *] by 2,

y + 2 = 3/4 x + 1 + 2

y + 2 = 3/4 x + 3

y + 2 = 3/4 (x + 4) [Equation 2]

Hence the two equations are 3x - 4y = -4 and y + 2 = 3/4 (x + 4).

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The lateral surface area pentagonal prism is the perimeter of the base of the prism multiplied by its height. While the total area of a pentagonal prism is the sum of the areas of its two bases and its lateral surface area.

LSA= 5b * h

Where,

LSA = lateral surface area of a pentagonal prism,

b =  base of the prism

h =  height  of the prism

the pentagTSA= 5ab + 5bh

where,

The total surface area of the pentagonal prism, TSA

a=apothem length of the pentagonal prism

b= base length of the pentagonal prism

h= height of the pentagonal prism

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The test statistic is t = 24.135. (option d)

To perform the hypothesis test, we need to calculate a test statistic. In this case, we can use a two-sample t-test since we are comparing the means of two independent samples. The formula for the t-test is:

t = (x₁ - x₂) / (s_p * √(1/n₁ + 1/n₂))

where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, n₁ and n₂ are the sample sizes.

Using the data provided, we can calculate the sample means and standard deviations for the two samples:

x₁ = 26.3%, s₁ = 0.37%, n₁ = 6

x₂ = 16.9%, s₂ = 0.57%, n₂ = 6

As per the percentage, we can then calculate the pooled standard deviation:

s_p = √(((n₁-1)*s₁² + (n₂-1)*s₂²) / (n₁+n₂-2))

s_p = √(((6-1)*0.37² + (6-1)*0.57²) / (6+6-2)) = 0.471%

Finally, we can calculate the t-statistic:

t = (26.3 - 16.9) / (0.471 * √(1/6 + 1/6)) = 24.135

Therefore, the test statistic is d) t = 24.135.

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Complete Question:

Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

Stick = [26.1, 26.5, 26.5, 25.8, 26.7, 26.2]

Liquid = [16.6, 16.5, 17.1, 17.5, 17.7, 16.3]

We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)

a) t = 34.225

b) z = 34.225

c) z = 34.725

d) t = 24.135

e) t = 34.725

The computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10.

This statement is a false statement.

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample. First, a hazy assumption about the parameter or distribution is made.

The null hypothesis is that 50% is true, while the alternative hypothesis is that 50% is not accurate, for instance, if someone wants to test whether a penny has an exact 50% chance of landing on heads.

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The new length is 35+10=45 and the new width is 18+10=28.

To Find the Area of a rectangle is length times the width.

Given that enclosure at the zoo is 35 feet long by 18 feet wide. It means the length is 35 feet and the width is 18 feet.

Area of Rectangle=Length × Width

=35×18

=630

The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.

(35+x)×(18+x)=1260

630+35x+18x+x2=1260

x2+53x+630-1260=0

x2+53x-630

Now we will apply the quadratic formula we get

x=10.

The new length is 35+10=45

The new width is 18+10=28.

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Answer:

She would make $646.00

The variable X has a binomial distribution in the following distributions:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.

In a binomial distribution, we have a fixed number of independent trials (in this case, the number of patients), and each trial has only two possible outcomes (success or failure). The probability of success remains the same for each trial (in this case, the probability of the medicine working is 30%).

Option B does not represent a binomial distribution since it counts the number of patients for whom the medicine does not work, which is the complement of success. Option D is not a binomial distribution as it counts the number of doses each patient needs to take, which is not a success/failure outcome.

So, the correct answers are:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

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(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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Answer:

t^3

Step-by-step explanation:

(t to the third power)

Based on the information given, we can assume that "x" represents the price of sandwiches, and "demand" refers to the quantity of sandwiches that consumers are willing and able to buy at that particular price. The term "market" refers to the overall demand for sandwiches in the entire market, rather than just one individual consumer.

If x = 1, we can look at the table to see that the quantity demanded is 6 sandwiches. We can use this information to calculate the slope of the market demand curve, which represents the relationship between the price of sandwiches and the quantity demanded by all consumers in the market.

To calculate the slope, we need to find two points on the demand curve. Let's use the points (1,6) and (2,4), since they are the closest to x=1. We can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (4 - 6) / (2 - 1)

slope = -2

So the slope of the market demand curve when the price is on the vertical axis is -2. However, none of the answer choices given match this result.

The closest answer is (b) -1/3, but this is not correct based on the calculations we just did.

Therefore, the correct answer cannot be determined with the information given.

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Equation for a linear line is y=5x-5

What is linear line?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

slope of line passing through two points (-2,-15) and (2,5) is

\(m= (5-(-15))/(2-(-2))\\m=20/4\\m=5\)

Therefore, the slope of the line is 5

Now,finding the y-intercept now by using the slope and one of the two points.

\(y=m*x+b\\5=5*2+b\\b=-5\)

putting this value of b to find equation,

\(y=m*x+b\\y=5x-5\\\)

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Answer:

-1/4

Step-by-step explanation:

2/3+12a=0

3+12a=3×0

3+12a=0

12a=-3

a=-3/12

a=-1/4

Answer:

43

Step-by-step explanation:

firstly, you will make the mixed fraction to an improper fraction

53 3/4= 53.75

53.75/100*80

=43

Answer:

43$

Step-by-step explanation:

53.75%x80$=43

By multiplying 53.75 percent to 80 pounds

Equal to 43 pounds

Suppose A is a 3x3 matrix and B is a vector in the set of real numbers R^3 with the property that Ax = B has a unique solution. The reason why this system has a unique solution is because the matrix A has a full rank, which means its columns are linearly independent.

In this case, the matrix A has an inverse, and the unique solution can be found by multiplying both sides of the equation by the inverse of A: A^(-1)Ax = A^(-1)B.  x = A^(-1)B
Thus, the system Ax = B has a unique solution, which can be obtained using the inverse of the matrix A. (where B is a vector)

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Answer:

it is irrational number

Answer:

C: 7/5

Step-by-step explanation:

In determining the slope of a line, the type of fraction we use is (x-axis/y-axis)

Since the only part of the graph where the x and y are whole numbers (except for the origin but that helps us none lol) is (7, 5), the slope of the line is 7/5