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Answer:

The correct answer is 44°

The P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.

How to calculated the probability density function in standard beta distribution?

Beta distribution is one of the continuous probability distributions set at interval (0, 1) intervals with two positive parameters α and β.

Probability density function can be calculated by this formula

\(\frac{x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta) }\)

B(α,β) is beta function =  Γ(α)Γ(β)/Γ(α+β)

Γ(α) is gamma function of alpha

Γ(β) is gamma function of beta

P(X<0.2) = \(\frac{0.2^{5-1}(1-0.2)^{2-1}}{B(5,2) }\)

= 0.0016

Excel formula for beta distribution is

=BETA.DIST(x;α;β;TRUE)

Thus, the P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.

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Answer:

19. Opposite of a Difference     ↔    E. -(8 - 3·m) = 3·m - 8

20. Opposite of a sum               ↔    A.  -[(-r) + 2p] = -(-r) - 2p

21. Opposite of an Opposite     ↔   F. -1[ -1(9 - 2w)] =  9 - 2w

22. Multiplication by 0               ↔   B.  160 - (3d + 2)(0) = 160 - 0

23. Multiplication by                   ↔   D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t

21. Distributive property             ↔   C.  5(2 - x) = 10 - 5x

Step-by-step explanation:

19. Opposite of a difference is the difference of the opposites

20. Opposite of a sum is the sum if the opposites

21. Opposite of an opposite is the original number

22. Multiplication by 0- The result of multiplication by 0 is 0

23. Multiplication by -1 results in the change in sign of a number

24. Distributive property - Multiplying the sum or difference of two numbers  by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.

a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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The relationship between the variables in terms of direction form and strength.

Given :

the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.

The straight line form with variables is :

y = mx + b is a straight line equation

here x and y are variables

m = slope

b = y - intercept

example :

y = 3x + 3

m = + 3 is a positive slope

y = -2x + 4

here

m = - 2 is a negative slope

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Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

(a) Expected utility is calculated as the weighted average of the utilities of all possible outcomes.

According to the problem, Sam's utility function is u(100) = 1 and u(200) = 2.

The lottery L1 = ( £100, w.p. 0.6; £200, w.p. 0.4 ) has two outcomes with the probabilities of 0.6 and 0.4.

Therefore, the expected utility of the lottery L1 is:

Expected utility of L1 = 0.6 × u(100) + 0.4 × u(200)= 0.6 × 1 + 0.4 × 2= 1.4

Since Sam is willing to pay at most £120 for the lottery L1, this indicates that the expected utility of L1 is worth £120 to Sam. Thus:1.4 = u(£120)

Since we know u(100) = 1 and u(200) = 2, we can linearly interpolate to find u(£120):

u(£120) = u(100) + [(120 - 100)/(200 - 100)] × (u(200) - u(100))= 1 + [(120 - 100)/(200 - 100)] × (2 - 1)= 1.3

Therefore, the expected utility of the lottery L2 = ( £100, w.p. 0.6; £120, w.p. 0.4 ) is:

Expected utility of L2 = 0.6 × u(100) + 0.4 × u(£120)= 0.6 × 1 + 0.4 × 1.3= 0.78

So, Sam's expected utility for the lottery L2 is 0.78

.(b) The risk preferences of Sam can be determined by comparing the utility of the lottery L1 and the sure outcome that gives the same expected value as the lottery L1.

The expected value of the lottery L1 is:Expected value of L1 = 0.6 × £100 + 0.4 × £200= £140

Therefore, Sam needs to be indifferent between the lottery L1 and the sure outcome of receiving £140. Since the expected utility of L1 is 1.4, Sam's utility for receiving £140 must also be 1.4.

This can be represented as:u(£140) = 1.4From part (a), we know that u(£120) = 1.3.

Therefore, the difference between the two utility values is:u(£140) - u(£120) = 1.4 - 1.3= 0.1

The difference in utility is positive but not enough to reflect risk-loving behavior. Therefore, Sam is risk-averse.

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Answer:

\(( {2x}^{2} - 3)(4x + 3) \\ = 8 {x}^{3} + {6x}^{2} - 12x - 9 \\ \)

Step-by-step explanation:

\(h(x).g(x) = (2 {x}^{2} - 3)(4x + 3) \\ \boxed{8 {x}^{3} + 6 {x}^{2} - 12x - 9 }✓\)

These steps in the design process are often iterative, meaning that architects may revisit earlier steps as they refine and develop the design. The overall goal of the design process in architecture is to create a functional, safe, and aesthetically pleasing building that meets the needs and goals of the client.

The following are the steps in the design process, organized in architecture:

Programming: In this first step, architects work with their clients to understand the project requirements, goals, and objectives. They may gather information about the site, zoning and building codes, budget, and other constraints.

Schematic Design: In this step, architects use the information from the programming phase to create rough sketches and drawings that show the basic layout and massing of the building. This phase is an opportunity to explore various design options and to get feedback from the client.

Design Development: In this step, the architects refine the design, incorporating structural and mechanical systems, and developing detailed drawings and specifications. This phase also includes working with consultants such as engineers and contractors.

Construction Documents: In this step, the architects prepare the final construction documents, which include detailed drawings and specifications that will be used by contractors to build the project.

Bidding and Negotiation: In this step, the architects help the client solicit bids from contractors and negotiate the terms of the construction contract.

Construction Administration: In this final step, the architects oversee the construction process, ensuring that the project is built according to the design documents and that any changes or issues are addressed.

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The restriction on x when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

When we divide x³ - 4x² + 5x - 6 by x - 1, we perform polynomial long division or synthetic division to find the quotient and remainder.

In this case, the remainder is zero, indicating that (x - 1) is a factor of the polynomial.

To find the restriction on x, we set the divisor, x - 1, equal to zero and solve for x.

Therefore, x - 1 = 0, which gives us x = 1.

Hence, the value of x that satisfies the restriction when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

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Answer:

18

Step-by-step explanation:

30 + 18 = 48

30 - 18 = 12

Both true, so our solution is correct.

The value of the larger number is 30 and the value of the smaller number is 18.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

Given that the sum of two numbers is 48. if the smaller number is subtracted from the larger the difference is 12. The two numbers will be calculated as,

x + y = 48

x - y = 12

________

2x = 60

x = 30

y = 30 - 12

y = 18

Therefore, the value of the larger number is 30 and the value of the smaller number is 18.

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Given :-

To find:-

Answer:-

As we know that for a quadratic equation in standard form of ax² + bx+ c , discriminant is given by;

\(\implies D = b^2 - 4ac \)

with respect to standard form,

Aslo as we know that, when

So , we have ;

\(\implies D = 4^2 - 4(2)(2) \)

\(\implies D = 16 - 16 =\boxed{0} \)

Hence from the above mentioned points , the graph will cut x axis at single point . So will have only one x intercept .

And we are done!

Answer:

1/5 = 20%

Step-by-step explanation:

Let x be the percentage.

\(\frac{1}{5} * \frac{x}{100}\)

100 = 5x    Cross multiply

x = 20%

Hope this helps!

Answer: 20%

Step-by-step explanation:  1/5=0.2     0.2x100=20    20%

0.2800 is the probability of an american airlines flight arriving late

The foundational ideas of probability theory were established by Blaise Pascal and Pierre de Fermat, who are recognized as the fathers of probability.

Calculating or predicting how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using terms like "certain," "impossible," or "probable." Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

The probability serves as a gauge for how likely an event is to occur. It gauges how likely an occurrence is. The probability equation is stated by the following notation: P(E) = number of favorable outcomes/number of total outcomes.

Let us assume ,

n = 150 be the total number of Airlines flights.

Out of 150 , 108 are on time.

That means 150 - 108 = 42 will be late.

Next, required probability is:

= 42/150

= 0.2800

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Answer:

93000

Step-by-step explanation:

a29 = 93000

Required value of v is (x + w - u) in terms of u, w, and x.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions, often using variables and mathematical operations. In an equation, the expressions on both sides of the equal sign must be equal.

For example, the equation "3x + 5 = 11" asserts that the expression "3x + 5" is equal to the expression "11". To solve for the variable "x" in this equation, one would need to isolate "x" on one side of the equation by performing the same operation on both sides of the equation, such as subtracting 5 from both sides, and then dividing by 3.

Equations are used extensively in many fields of science, engineering, and mathematics to model real-world phenomena and solve problems.

Here given equation is x= v - w + u.

To solve for v, we need to isolate the variable v on one side of the equation.

Subtracting (u-w) from both side and get,

x-(u-w) = v - w + u-(u-w)

So,x + w - u = v

We can do this by adding w and u to both sides of the equation,

x + w - u = v

Therefore, the solution for v in terms of u, w, and x isv = x + w - u

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Answer:

x = 55

Step-by-step explanation:

angles on a straight line add up to 180°.

so we have 60 + (2x + 10)° = 180°.

2x + 10 = 180 - 60 = 120

2x = 120 - 10 = 110

x = 55

Answer:

Complementary angles,7 & 83

Supplementary angles, 97 & 83

Vertical angles, 83 & 83

Step-by-step explanation:

Complementary angles add up to 90°

Supplementary angles add up to 180°

Vertical angles are equal

There are 8208 different ways that the children can sit.

There are 8 children in total, so we first need to choose one of them to sit in the middle. This can be done in 8 ways.

Once the child in the middle has been chosen, the remaining 7 children can sit in a circle around them. There are (7-1)! = 6! = 720 ways to arrange 7 children in a circle. However, due to the condition that "two seatings are considered identical if the same child is in the middle in both and each child on the outside has the same child on his or her right in both seatings", we need to divide by 7 to account for the fact that there are 7 equivalent circular arrangements.

Therefore, the total number of different ways that the children can sit is:

8 x (6! / 7) = 8 x 720 / 7 = 8208

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Answer:

I Graphed It

Step-by-step explanation:

Answer: im livin in iowa and it sucks

Step-by-step explanation:

The probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}\)

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

Given that, a fertilizer manufacturer produces fertilizer in 10-pound bags with a standard deviation of 0.24 pounds per bag, Normally, the bag weights are distributed.

Given the data in the question;

μ= 10-pound bags

standard deviation s= 0.24 pounds

sample size n = 4

Typically, the bag weights are distributed as follows:

p( x' less than 9.8 ) will be;

p(  (x'-μ_x' / s_x')   <   (9.8-μ_x' / s_x')  )

As we know that;

μ_x' = μ_x = 10

and s_x' = s_x/√n = 0.24/√4

Put the value as

p(  z  <  ( (9.8 - 10) / (0.24/√4)  )

p(  z  <  -0.2 / 0.12   )

p(  z  <  -1.67   )

{ From z-table }

⇒ p(  z  <  -1.67   ) = 0.0475 ≈ 0.05

Thus, the probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.

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The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

               (x – 2)² = 2x – 1

         x² – 4x + 4 = 2x – 1

         x² – 6x + 5 = 0

   x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

       (x – 5)(x – 1) = 0

                         x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

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Answer:

  B.  A pair of intersecting lines

Step-by-step explanation:

The attached image can give you an idea of what you get when a plane perpendicular to the base of a cone intersects the vertex of the cone.

__

In the problem statement here, we assume a double-napped cone with no defined base. That means the lines of intersection with the sides of the cone will meet at the vertex point and extend indefinitely in either direction.

The intersection is a pair of intersecting lines.

Check the picture below.

\(tan(\theta )=\cfrac{11}{10}\implies tan^{-1}[tan(\theta )]=tan^{-1}\left( \cfrac{11}{10} \right) \\\\\\ \theta =tan^{-1}\left( \cfrac{11}{10} \right)\implies \theta \approx 47.73^o\)

Make sure your calculator is in Degree mode.

Answer: $25.38

1.00 - 0.06 = 0.94

27 * 0.94 = 25.38

Here is the expected number of broken machines or tanks and K is the total number of tanks. So (K-L) gives the number of tanks in working condition.

The number of repairmen (R) needed to have an average of at least 180 tanks working is to be determined. Thus as observed from the results obtained for one-way data table, the value of R such that (K-L) is at least 180 is R = 11 repairmen

The Expected number of broken or bad machines (L) is

\(L=\sum j\pi_i\)

The Expected number of machines waiting for service (1) is

\(L=\sum (j-R)\pi_i\)

An expected number of words is often used as a guideline to ensure that the content is neither too long nor too short. In this case, the expected number is 150 words. A 150-word piece of writing can be considered a short composition. It is long enough to convey a basic idea or message, but not so long that it becomes tedious to read. This length is often used in blog posts, news articles, and social media updates.

When writing a 150-word piece, it is important to make every word count. The writing should be clear and concise, with each sentence contributing to the overall message. It may also be helpful to outline the main points before starting to write to ensure that the piece stays focused.

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Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

The semicircle has an arc length of 18.84 units.

In this problem we need to determine the arc length of a semicircle, that is, the length of the arc of the half of a circle. This can be computed by circumference formula:

s = π · r

Where:

Please notice that diameter is twice the radius.

If we know that r = 6, then the arc length of the semicircle is:

s = π · 6

s = 6π

s = 6 · 3.14

s = 18.84

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