The French autoroute network is composed of toll motorways with entrances marked as such. A motorist entering the network obtains a ticket from a toll booth and pays a toll when leaving the motorway. Given the number of vehicles traveling these routes, congestion at both entrances and exits is common. Suppose that four groups, each of 50 motorists, use an autoroute. The price each group is willing to pay, v, differs among groups and falls as the amount of congestion, c, increases in the following way: vij = vi max-cj; i, j = 0, …, 3, where vi max = 0.4 - 0.1 * i euros per kilometer is the maximum group i is willing to pay to use the motorway and cj = 0.06 * j euros per kilometer is the loss in value as more groups use it. The marginal cost of using the autoroute, not including the marginal cost of congestion, is zero.
a. If the toll charged for using the autoroute equals a motorist’s marginal private cost—the price in a competitive market—how many vehicles per minute will use it? Which groups will use it?
b. In the social optimum, which groups of drivers will use the autoroute? That is, which collection of groups using it will maximize the sum of the motorists’ utilities?

Based on the survey results, the student's belief that less than 40% of students at her school fear public speaking is not supported.

To conduct a hypothesis test, we need to set up the null and alternative hypotheses.

Let's denote the proportion of students at the school who fear public speaking as p.

Null Hypothesis (H₀): p ≥ 0.40 (The percentage of students at the school who fear public speaking is greater than or equal to 40%)

Alternative Hypothesis (H1): p < 0.40 (The percentage of students at the school who fear public speaking is less than 40%)

We will use a significance level of 0.05 (5%). If the p-value is less than 0.05, we will reject the null hypothesis.

To conduct the hypothesis test, we will use the normal approximation to the binomial distribution, as the sample size is large (n = 361) and the conditions for using the normal approximation are satisfied.

Let's calculate the test statistic (z-score) and the p-value:

Sample proportion (p') = 139/361 = 0.384

Standard Error (SE) = √(p'(1-p)/n) = √((0.384(1-0.384))/361) = 0.027

Test Statistic (z-score) = (p' - p) / SE = (0.384 - 0.40) / 0.027 = -0.5926

Now, we will calculate the p-value corresponding to the test statistic using a standard normal distribution table or calculator.

The p-value is the probability of observing a z-score less than or equal to the calculated z-score (-0.5926) if the null hypothesis is true.

Using a standard normal distribution table or calculator, the p-value for a z-score of -0.5926 is approximately 0.2772.

Since the p-value (0.2772) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, based on the survey results, the student's belief that less than 40% of students at her school fear public speaking is not supported.

Learn more about hypothesis test click;

https://brainly.com/question/17099835

#SPJ4

The stock declined by 4.25 percentage

The stock of company A lost $2.55

They ended at a value of $57.45

The first step is to add both value together

= 57.45 + 2.55

= 60

The percentage decline can be calculated as follows

= 2.55/60 × 100

=0.0425 × 100

= 4.25

Hence the percentage decline is 4.25%

Read more on percentage here

https://brainly.com/question/14781731

#SPJ1

Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

Answer: 57 R3

‎‎‎‎‎‎‎‎‎‎‎‎‎ ‎‎ ‎

Answer:

57 R 3

Step-by-step explanation:

6 goes into 34 5 times with 4 extra, pull down the 5, and 6 goes into 45 7 times with 3 extra. So the answer is 57 R 3.

In a direct sum of subspaces V = W₁ ⊕ W₂, every vector in V can be expressed as a unique linear combination of u ∈ W₁ and v ∈ W₂, ensuring uniqueness in the decomposition. This property holds for any direct sum of subspaces.

The claim that every vector in V = W₁ ⊕ W₂ can be written as a unique linear combination of u ∈ W₁ and v ∈ W₂ is a fundamental property of a direct sum of subspaces. To prove this claim, we can use the definition of a direct sum.

Let v be a vector in V. Since V = W₁ ⊕ W₂, we can write v as v = w₁ + w₂, where w₁ ∈ W₁ and w₂ ∈ W₂.

To show uniqueness, suppose v = w₁' + w₂', where w₁', w₂' ∈ W₁ and W₂ respectively.

Then, w₁ + w₂ = w₁' + w₂'.

Rearranging the equation, we have w₁ - w₁' = w₂' - w₂.

Since w₁ - w₁' ∈ W₁ and w₂' - w₂ ∈ W₂, the left side is in W₁ and the right side is in W₂.

But since W₁ and W₂ are disjoint subspaces, both sides must be zero.

Therefore, w₁ - w₁' = w₂' - w₂ = 0.

This implies that w₁ = w₁' and w₂ = w₂', proving uniqueness.

Thus, every vector in V can be expressed as a unique linear combination of u ∈ W₁ and v ∈ W₂, as claimed.

As for the example of a direct sum of subspaces, let V₁, V₂, ..., Vₙ be a basis for a vector space V. We can construct the direct sum V = V₁ ⊕ V₂ ⊕ ... ⊕ Vₙ.

Suppose we have a vector v in V that can be expressed as v = u₁ + u₂ + ... + uₖ, where uᵢ ∈ Vᵢ for 1 ≤ i ≤ k and 1 ≤ k ≤ n.

Since V₁, V₂, ..., Vₙ are independent, the coefficients of the basis vectors V₁, V₂, ..., Vₙ in the linear combination must be zero. This implies that u₁ = u₂ = ... = uₖ = 0.

Hence, the sum V = V₁ ⊕ V₂ ⊕ ... ⊕ Vₙ is a direct sum, as any vector v in V can be uniquely expressed as a linear combination of vectors from V₁, V₂, ..., Vₙ, and the coefficients of the linear combination are uniquely determined.

To learn more about "vector " refer here:

https://brainly.com/question/28028700

#SPJ11

In caring for A.N., we will perform a number of interventions. The first is to shave all hair within the wound beds, to minimize the risk of infection and reduce the amount of bacteria around the wound.

We will also maintain the room temperature at 85 degrees Fahrenheit (29.4 degrees Celsius) to ensure a warm and comfortable environment for A.N. when she is receiving treatment. We will also use clean technique when changing A.N.'s dressings to reduce the risk of infection. Additionally, we will monitor the CBC and WBC with differential frequently to ensure A.N. is receiving adequate treatment.

Furthermore, we will not allow her to bathe for the initial 72 hours after injury to reduce the chances of infection. Lastly, we will apply a 1/16-inch film of medication, covering the entire burn, to help aid in the healing process and reduce the risk of infection.

know more about interventions here

https://brainly.com/question/29220337#

#SPJ11

Answer:

4/100 is the fraction

Step-by-step explanation:

there are four blue blocks shaded out of the 100

1. The average speed of a car traveling at 50 km/h for 30 minutes, and then at 71 km/h for one hour is 64km/hr.

2. If a racing car has to maintain an average speed of 180 km/h for four laps of a racetrack so that the driver can qualify for a race and the average speed of the first lap is 150 km/h and that of the second lap, 170 km/h, then the average speed of the last two laps is 20km/hr to ensure that the driver qualifies.

1. To calculate the average speed of the car, follow these steps:

Therefore, the average speed of the car is 64 km/h.

2. To calculate the average speed of the last two laps to ensure that the driver qualifies, follow these steps:

Therefore, the average speed for the last two laps must be 20 km/h to ensure the driver qualifies.

Learn more about average speed:

brainly.com/question/4931057

#SPJ11

To find a polynomial f(x) of degree 3 with real coefficients and the zeros -4, 2+i, we can use the conjugate root theorem. Since 2+i is a zero, its conjugate 2-i is also a zero. By multiplying the factors (x+4), (x-2-i), and (x-2+i) together, we can obtain a polynomial f(x) with the desired properties.

Explanation:

The conjugate root theorem states that if a polynomial with real coefficients has a complex root, then its conjugate is also a root. In this case, if 2+i is a zero, then its conjugate 2-i is also a zero.

To construct the polynomial f(x), we can multiply the factors corresponding to each zero. The factor corresponding to -4 is (x+4), and the factors corresponding to 2+i and 2-i are (x-2-i) and (x-2+i) respectively.

Multiplying these factors together, we obtain:

f(x) = (x+4)(x-2-i)(x-2+i)

Expanding this expression will yield a polynomial of degree 3 with real coefficients, as required. The exact form of the polynomial will depend on the specific calculations, but it will have the desired zeros and real coefficients.

Learn more about probability here

brainly.com/question/13604758

#SPJ11

Hi there!

\(\large\boxed{ 14.875}\)

Our interval is from 0 to 3, with 6 intervals. Thus:

3 ÷ 6 = 0.5, which is our width for each rectangle.

Since n = 6 and we are doing a right-riemann sum, the points we will be plugging in are:

0.5, 1, 1.5, 2, 2.5, 3

Evaluate:

(0.5 · f(0.5)) + (0.5 · f(1)) + (0.5 · f(1.5)) + (0.5 · f(2)) + (0.5 · f(2.5)) + (0.5 · f(3)) =

Simplify:

0.5( -2.75 + (-3) + (-.75) + 4 + 11.25 + 21) = 14.875

The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is π/24 units cube.

option D.

The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is calculated as follows;

y = 2x²

x² = y/2

x = √(y/2) ----- (1)

x = y -------- (2)

Solve (1) and (2) to obtain the limit of the integration.

y =  √(y/2)

y² = y/2

y = 1/2 or 0

The volume obtained by the rotation is calculated as follows;

V = 2π∫(R² - r²)

V = 2π ∫[(√(y/2)² - (y)² ] dy

V = 2π ∫ [ y/2  - y² ] dy

V = 2π [ y²/4 - y³/3 ]

Substitute the limit of the integration as follows;

y = 1/2 to 0

V = 2π [ 1/16  -  1/24 ]

V = 2π [1/48]

V = π/24 units cube

Learn more about volume of solid here: https://brainly.com/question/24259805

#SPJ1

Answer:

3x + 11m + c

Step-by-step explanation:

Step 1) Write the Equation: 3x + 5m + 6m + c

Step 2) Add like Terms: 3x + 11m + c

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

for such more questions on percentages

https://brainly.com/question/24877689

#SPJ11

The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

Learn more about wetlands here:

https://brainly.com/question/30010590

#SPJ11

The correlation coefficient is +0.8, it indicates a strong positive relationship between the variables. If it is -0.3, it suggests a weak negative relationship. Keep in mind that correlation does not imply causation; it simply measures the association between variables.

The formula for calculating the correlation coefficient was developed by Karl Pearson, a British mathematician and statistician. Pearson's correlation coefficient, denoted as r, is a measure of the linear relationship between two variables. It quantifies the strength and direction of the relationship, ranging from -1 to +1.

To calculate the correlation coefficient, follow these steps:

1. Standardize the data: Subtract the mean from each data point and divide by the standard deviation for both variables.

2. Multiply the standardized values for each pair of data points and sum them.

3. Divide the sum by the number of data points.

4. This will give you the covariance between the two variables.

5. Next, calculate the standard deviation for each variable and multiply them together.

6. Divide the covariance by the product of the standard deviations.

7. The resulting value is the correlation coefficient, which indicates the strength and direction of the linear relationship.

For example, if the correlation coefficient is +0.8, it indicates a strong positive relationship between the variables. If it is -0.3, it suggests a weak negative relationship. Keep in mind that correlation does not imply causation; it simply measures the association between variables.

Learn more about Standard deviations here,https://brainly.com/question/475676

#SPJ11

Answer: 2/ Points

Step-by-step explanation:

The points can't make up the answer to the equation, so it can't be 3!

I don't think it is the solution, because on a table points are just points of an equation!

Answer:

x=32

Step-by-step explanation:

sum of interior angles of a triangle = 180

add up all angles and equate to 180

(4x-13)+(x+18)+15=180

5x=160

x=160/5=32

x+18  =   32+18    = 50

4x-13  =  4x32-13 = 128-13 = 115

add up all to check whether ans = 180;  15+50+115=180

step 1 solve for x step 2 after getting the value of x ,substitute and get the value of angles

Answer: (A) 16

must be less than 19

and more than 5

Step-by-step explanation:

Answer:

Here, given

g(x) = √x

h(x) = x³-1

For gh(4) , we have to find gh(x), so,

gh(x) = g(x³-1)

        =√x³-1 [Note⇒root is both for x³ and 1]

Now,

gh(4) = √4³-1

        = 3√7 or 7.9

Hope it helps!

A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

Learn more about Probability:

https://brainly.com/question/26203207

#SPJ4

Answer:

First term=1024

Common ratio = ½

Step-by-step explanation:

Index means its position

Even index means the 2nd, 4th, 6th ....terms

Outliers or extreme skewness in the distribution of pumpkin weights would be clear signs that they are not normally distributed.

There are several signs that can indicate the pumpkin weights are not normally distributed based on the farmer's sample of 20 pumpkins with a mean weight of 26 lb.

Skewed Distribution: If the distribution of pumpkin weights is noticeably skewed, it suggests a departure from normality. Positive skewness occurs when the tail of the distribution is stretched towards higher values, indicating a higher number of lighter pumpkins.

Negative skewness is the opposite, with a tail stretched towards lower values, suggesting a higher number of heavier pumpkins.

Outliers: The presence of extreme values that deviate significantly from the majority of the data can be a clear sign of non-normality. If there are a few pumpkins with exceptionally high or low weights compared to the rest, it indicates the presence of outliers and a potential departure from a normal distribution.

Bimodal or Multimodal Distribution: If the pumpkin weights exhibit multiple peaks or modes instead of a single bell-shaped curve, it suggests a non-normal distribution. This could indicate the presence of distinct subpopulations of pumpkins with different weight ranges.

Non-linear Patterns: If there is a distinct non-linear pattern or trend in the data, it deviates from a normal distribution. For example, if there is a systematic increase or decrease in weights as the pumpkin size increases, it suggests a departure from normality.

Departure from the 68-95-99.7 Rule: In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. If the sample data significantly deviates from these percentages, it indicates a departure from normality.

It is important to note that these signs alone do not definitively prove that the pumpkin weights are not normally distributed. Further statistical tests such as the Shapiro-Wilk test, Anderson-Darling test, or visual inspections of a histogram, Q-Q plot, or kernel density plot can provide more evidence to assess the distributional assumption.

For more question on weights visit:

https://brainly.com/question/30237339

#SPJ8

The correlation that demonstrates the weakest correlation between two variables is option a) +.20.

Among the given options, the correlation that demonstrates the weakest correlation between two variables is option b) -50.

In correlation coefficients, the value ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation or a very weak correlation.

Let's analyze the options provided:

a) +.20:

This indicates a positive correlation, but the value is relatively small (0.20).

It suggests a weak positive relationship between the variables.

b) -50:

This option appears to be a typographical error since the correlation coefficient cannot be negative 50.

Assuming it is meant to be -0.50, this indicates a moderate negative correlation.

c) +.75:

This option represents a strong positive correlation.

With a coefficient of 0.75, it suggests a relatively strong positive relationship between the variables.

d) -76: Similar to option b, this value appears to be a typographical error. A correlation coefficient cannot exceed the range of -1 to +1.

Assuming it is meant to be -0.76, this indicates a strong negative correlation.

Comparing the given options, the weakest correlation is option b) -50, assuming it was intended to be -0.50. A correlation coefficient of -0.50 represents a moderate negative correlation, which is weaker than the other options but still indicates some relationship between the variables.

For similar question on correlation.

https://brainly.com/question/28175782  

#SPJ8

Answer:

Answer: D. Jake paid his loan in 12 months

Step-by-step explanation:

Jake took out an interest-free loan of $2,401.56 from the bank to buy a car.

Since he has to pay no interest for the loan, the monthly payments are totally used to cover the amount of the loan.

He paid the bank $200.13 each month, thus the total months needed to pay the loan is:

\(\frac{\$2,401.56 }{\$200.13}=12\)

Answer: D. Jake paid his loan in 12 months

The given points, only the point (4, -9, -8) lies on line 1.

To determine whether certain points lie on the line 1, which is perpendicular to the plane x - 2y - 4z = 5 and contains the point (2, -5, 0), we can check if the coordinates of those points satisfy the equation of the line.

The direction vector of the line 1 is perpendicular to the plane and can be determined from the coefficients of x, y, and z in the plane equation. In this case, the direction vector of the line is (1, -2, -4).

Now, we can write the parametric equation of the line l as:

x = 2 + t * 1

y = -5 + t * (-2)

z = 0 + t * (-4)

To check if a point (x₀, y₀, z₀) lies on the line 1, we need to find a value of t that satisfies the parametric equations.

Let's consider the following points and determine if they lie on line 1:

Point (3, -6, -4)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (3, -6, -4) into the parametric equations:

x₀ = 2 + t * 1 --> 3 = 2 + t --> t = 1

y₀ = -5 + t * (-2) --> -6 = -5 - 2 --> t = -1

z₀ = 0 + t * (-4) --> -4 = 0 - 4t --> t = 1

The value of t is not consistent across all equations, so the point (3, -6, -4) does not lie on line 1.

Point (2, -5, 0)

This point is given as the point that line 1 contains. Therefore, it lies on line 1.

Point (4, -9, -8)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (4, -9, -8) into the parametric equations:

x₀ = 2 + t * 1 --> 4 = 2 + t --> t = 2

y₀ = -5 + t * (-2) --> -9 = -5 - 2t --> t = 2

z₀ = 0 + t * (-4) --> -8 = 0 - 8t --> t = 1

The value of t is consistent across all equations, so the point (4, -9, -8) lies on line 1.

Therefore, among the given points, only the point (4, -9, -8) lies on line 1.

To know more about parametric equation:

https://brainly.com/question/30748687

#SPJ4

The complete question is:

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

Answer:

78

Step-by-step explanation:

80-2+78 soo,

78+2 +80 with means 102+78 =180

Answer:

102 + 78 = 180

Step-by-step explanation:

The solution of the given inequality is x < –5 or x > 2

Equations are not always balanced on both sides using an "equal to" symbol in mathematics. Sometimes it can be about a "not equal to" relationship, meaning that something is greater than or lower than another.

In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

Here we have

|2x + 3| < 7  

=> 2x + 3 > 7  or 2x + 3 < - 7

Take 2x + 3 > 7

Add  - 3 on both sides    

=> 2x + 3 - 3  > 7 - 3

=> 2x  > 4

Divide by 2 into both sides

=>  2x/2 > 4/2

=> x > 2

Take 2x + 3 < - 7  

Add  - 3 on both sides  

=> 2x + 3 - 3  < - 7 - 3

=> 2x  < -10

Divide by 2 into both sides

=> 2x/2 < -10/2

=> x < -5    

Therefore,

The solution of the given inequality is x < –5 or x > 2

Learn more about Inequality equations

https://brainly.com/question/12490392

#SPJ1

a) The function gof is gof(x) = 3x + 3.

b) The function gof: RR is well-defined.

a. The value of function gof(x) = 3x + 3.

To find the composition gof, we substitute the expression for g into f:

gof(x) = f(g(x))

= f(x + 1)

= 3(x + 1)

= 3x + 3

b. To prove that gof is both one-to-one and onto, we need to show the following:

(i) One-to-one: For any two different inputs x1 and x2, if gof(x1) = gof(x2), then x1 = x2.

(ii) Onto: For every y in the range of gof, there exists an x such that gof(x) = y.

Proof of one-to-one:

Let x1 and x2 be two different inputs. Assume that gof(x1) = gof(x2).

Then, 3x1 + 3 = 3x2 + 3.

Subtracting 3 from both sides, we have 3x1 = 3x2.

Dividing both sides by 3, we obtain x1 = x2.

Therefore, gof is one-to-one.

Proof of onto:

Let y be any real number in the range of gof, which is the set of all real numbers.

We need to find an x such that gof(x) = y.

Consider the equation 3x + 3 = y.

Subtracting 3 from both sides, we have 3x = y - 3.

Dividing both sides by 3, we obtain x = (y - 3)/3.

Thus, for any y in the range of gof, we can find an x such that gof(x) = y.

Therefore, gof is onto.

Since gof is both one-to-one and onto, it is a bijection.

To know more about  function refer here:

https://brainly.com/question/30721594

#SPJ11

Answer:

0.335

Step-by-step explanation:

1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.

2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.

3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)

Delayed of icy weather - 0.3

Delayed of MP when weather is not icy - 0.7·0.05=0.035

Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is

0.3+0.035=0.335

HHHHHHHHHHHHHHHHHHHHHEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPP MMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE NNNNNNNNNNNNNNNNNNNNNNNNOOOOOOOOOOOOOOOOOOOWWWWWWWWWWWWWWWWWWWWWWWW PPPPPPPPPPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEE...............