Use the diagram below to answer the questions. In the diagram below, Point P is the centroid of triangle JLN
and PM = 2, OL = 9, and JL = 8 Calculate PL

The PDF of W = X², if X has an exponential distribution with parameter λ, is equal to fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0 and fW(w) = 0 for w < 0.

To find the probability density function (PDF) of the random variable W = X² when X has an exponential distribution with parameter λ,

Apply a transformation to the original PDF.

Let us denote the PDF of X as fX(x) and the PDF of W as fW(w). We want to find fW(w).

To begin, let us express W in terms of X,

W = X²

Now, find the PDF of W, which is the derivative of the cumulative distribution function (CDF) of W.

So, find the CDF of W first.

The CDF of W is ,

FW(w) = P(W ≤ w)

Substituting W = X², we have,

FW(w) = P(X² ≤ w)

To determine the probability of X² being less than or equal to w,

consider that X can take on both positive and negative values.

So,  split the calculation into two cases,

First case,

X ≥ 0

In this case, X² ≤ w implies X ≤ √w, since X is non-negative.

Thus, we have,

FW(w) = P(X² ≤ w) = P(X ≤ √w)

Since X has an exponential distribution, its CDF is given by,

FX(x) = 1 -\(e^{(-\lambda x)}\)  for x ≥ 0

for the case X ≥ 0, we have,

FW(w) = P(X ≤ √w) = FX(√w) = 1 -\(e^{(-\lambda \sqrt{w} )}\)

Second case,

X < 0

X² ≤ w implies X ≤ -√w, since X is negative.

However, for X < 0, X² is always non-negative.

The probability is always 0 in this case.

Combining both cases, we can write the CDF of W as,

FW(w) = 1 - \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

FW(w) = 0 for w < 0

Finally, to find the PDF fW(w), we take the derivative of the CDF with respect to w,

fW(w) = d/dw [FW(w)]

Differentiating, we have,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

Therefore, the PDF of W = X², when X has an exponential distribution with parameter λ, is given by,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

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The above question is incomplete, the complete question is:

If X has an exponential (λ) PDF, what is the PDF of W = X² ?

Answer:

105897 ft²

Step-by-step explanation:

let, r be the radius, so r = 106 ft

Surface area of a hemisphere,

2πr²+πr²

= 2π×106²+π×106²

= 105897 (rounded to the nearest whole number)

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:6+2w=h

The height of the tree will be 32 inches on week 13

Step-by-step explanation:

ok

Answer:

it is b , 1462 dollarrss

Step-by-step explanation:

Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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Merlin and kay are both 69 years old and married. compared with Karin and bill, who are 37 years old and married, merlin and kay probably have a reduced potential for conflict.

Therefore, Merlin and kay are both 69 years old and married. compared with Karin and bill, who are 37 years old and married, merlin and kay probably have a reduced potential for conflict.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

17

Step-by-step explanation:

Answer:

the third one...............

Answer:

the answer to your question is y = two-fifths x minus 1

Step-by-step explanation:

hope it helps

Answer:

d)142º

Step-by-step explanation:

\(\widehat{AB}=2\times71\º=142\º\)

Answer:

40

her age was 36 she added 4nwhich made 40 then doubles makesn80

9514 1404 393

Answer:

  76

Step-by-step explanation:

For age 'a', the special number was supposed to be ...

  2a +4

Tammi's mother actually calculated it as ...

  2(a +4) = 2a +8

a value that is (2a+8) -(2a+4) = 4 more than it was supposed to be.

The special number was supposed to be 80 -4 = 76.

Answer:

$42

Step-by-step explanation:

First calculate how much 20% of $35 is:

$35 * .2 = 7

Now that we have what 20% of $35 is, we can calculate how expensive of a book we can buy including the coupon:

$35 + 7 = $42

Answer:

she can never have an average less than $50 b. ... If demand of gasoline is inelastic, more of the burden of tax can be ...

Step-by-step explanation:

Answer:

\(x= 4\)

Step-by-step explanation:

\(~~~~~~\log_ 6 10 + \log_6 x = \log_6 (40)\\\\\implies \log_6(10x) = \log_ 6 (40)~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\\implies 10x = 40\\\\\implies x = \dfrac{40}{10}\\\\\implies x = 4\)

The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

\(y=-x+11\)

Step-by-step explanation:

We know that the new equation must be parallel to \(y=-x-5\).

Therefore, since they are parallel, the slope of the new equation must be the same as the old.

The slope of the original equation is -1.

Therefore, the slope of our new equation is also -1.

We also know that it has a y-intercept at (0, 11).

And as determined earlier, it has a slope of -1.

So, we can use the slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

We will substitute -1 for m and 11 for b. Thus, our equation is:

\(y=-x+11\)

The required all three situation are explained to the detector.

a. The equation for the distance-time graph of the student's motion is:

distance = rate × time + initial distance

where rate is the speed at which the student is walking (2 feet per second), time is the elapsed time in seconds, and initial distance is the distance between the student and the motion detector at the start (15 feet). This can be written in slope-intercept form as:

distance = 2t + 15

where the slope is 2 (the rate of change of distance with respect to time) and the y-intercept is 15 (the initial distance from the motion detector).

b. In this situation, the slope of the equation (2) represents the speed at which the student is walking towards the motion detector. It tells us that for every one second that passes, the student moves 2 feet closer to the motion detector. In other words, the slope represents the rate of change of distance with respect to time.

c. The y-intercept of the equation (15) represents the initial distance between the student and the motion detector. It tells us that at the start of the motion detector recording, the student was 15 feet away from the detector. When time is 0 (at the start), the distance traveled is just the initial distance, which is the y-intercept.

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letters :- EMTY

There r only 4 letters in geometry which have one line of symmetry

Since there are a total of 15 shirts,

5 red shirts+4 white shirts= 9 shirts total

3 blue shirts+3 purple shirts= 6 shirts total

The odds that you would pick a red shirt and then a white are 3:2

3 being the 9 red and white shirts combined.

2 being the 6 purple and blue shirts combined.

9:6 simplified=3:2

9/3=3

6/3=2

3:2

Answer: The odds that you would pick a red shirt then a white shirt would be 3:2 or 60%

True, Harvesting at the mathematical maximum sustainable yield (MSY) can be risky for the long-term sustainability of a fishery.

The concept of MSY is based on the idea of maximizing the catch of fish without depleting the population. However, it assumes that fish populations can be managed as single-species entities and that they can be harvested at a constant rate.

In reality, ecosystems are complex and interconnected, and fish populations interact with other species and the environment in various ways. Harvesting at the MSY level may not consider the broader ecological impacts and can lead to unintended consequences.

While maximizing the catch in the short term may seem beneficial, it can result in overfishing and the depletion of fish stocks over time.

This can disrupt the balance of the ecosystem, impact other species that rely on the fish population, and threaten the long-term sustainability of the fishery.

It is important to consider factors such as the reproductive capacity of fish, their life history traits, and the overall health of the ecosystem when setting sustainable fishing limits.

Sustainable fisheries management practices often involve adopting precautionary approaches that prioritize the conservation and responsible use of fishery resources to ensure their long-term viability.

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Answer: 19/20

Step-by-step explanation:

Answer:

19/20

Step-by-step explanation:

3/4 and 1/5 need to have the same denominator. So you turn 3/4 turns into 15/20 because 20 can both be reached by 4 and 5. 1/5 is now 4/20. Add those together you get 19/20.

Answer:

a strong and almost perfect positive linear correlation.

Using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

So, using calibration on the x-axis, the approximate age of the neanderthal fossils came out to be 40,110 years old.

Therefore, using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

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The correct question is given below:
Using the 14c calibration on the x-axis, what is the approximate age of the neanderthal fossil?

a. 5,730 years old

b. 34,380 years old

c. 40,110 years old

d. 45,840 years old

Answer:

A= 75°

Step-by-step explanation:

SinA = opposite÷hypoteneous

A = Sin^-1(32÷33). (inverse sin = sin^-1)

A = 75.85

A= 75°

Note: To calculate we use scientific calculater.

Angle A in triangle ABC is approximately 76 degrees. So, correct option is A.

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. Let's consider triangle ABC, where angle B is the right angle, AC is the hypotenuse, and BC is one of the legs.

We are given that AC = 33 and BC = 32. To find angle A, we can use trigonometric ratios. In this case, we can use the sine function.

The sine of angle A is defined as the ratio of the length of the side opposite angle A (BC) to the length of the hypotenuse (AC):

sin(A) = BC / AC

Substituting the given values, we have:

sin(A) = 32 / 33

Using the inverse sine function (sin⁻¹), we can find the value of angle A:

A = sin⁻¹(32 / 33)

Using a calculator, we find that angle A is approximately 75.85 degrees. Rounding off to the nearest angle we get 76 degrees.

Therefore, angle A in triangle ABC is approximately 76 degrees. So, correct option is A.

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Answer:

I think is 50m.

Step-by-step explanation:

Answer:

The result is a right cone

Step-by-step explanation:

To test the hypothesis H₁: μx = μy versus Hoxy, where μx and μy represent the means of X and Y respectively, we can perform a two-sample t-test. The test compares the means of two independent samples to determine if they are significantly different from each other.

The given information provides the sample means (X = 33.8, Y = 32.5) and the sample standard deviations (Sx = 3.9, Sy = 5.1). The sample sizes for both X and Y are n = m = 25.

Using this information, we can calculate the test statistic, which is given by:

t = (X - Y) / sqrt((Sx^2 / n) + (Sy^2 / m))

Plugging in the values, we get:

t = (33.8 - 32.5) / sqrt((3.9^2 / 25) + (5.1^2 / 25))

Next, we need to determine the degrees of freedom for the t-distribution. Since the sample sizes are equal (n = m = 25), the degrees of freedom for the test is given by (n + m - 2).

Using the t-distribution table or software, we can find the critical value corresponding to a significance level of α = 0.05 and the degrees of freedom.

Finally, we compare the calculated test statistic with the critical value. If the test statistic falls within the rejection region (i.e., the absolute value of the test statistic is greater than the critical value), we reject the null hypothesis. The p-value can also be calculated, which represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

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The approximate probability of rolling between 9 and 16 ones, inclusive, when rolling a die 100 times can be calculated using the binomial probability formula. The answer will be rounded to two decimal places.

To calculate the probability, we need to determine the probability of rolling exactly 9, 10, 11, 12, 13, 14, 15, and 16 ones in 100 rolls of a die, and then sum up these individual probabilities.

The probability of rolling exactly k ones in n rolls of a fair six-sided die is given by the binomial probability formula: P(X = k) = (n choose k) * (1/6)^k * (5/6)^(n-k), where (n choose k) represents the number of ways to choose k successes from n trials.

For each value of k (from 9 to 16), plug in the values into the formula and calculate the probabilities. Then, sum up these probabilities to obtain the approximate probability of rolling between 9 and 16 ones, inclusive.

After performing the calculations, round the final result to two decimal places to obtain the approximate probability.

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